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+{
+    "title": "Pt nanoshells with a high NIR-II photothermal conversion efficiency mediates multimodal neuromodulation against ventricular arrhythmias",
+    "pre_title": "Pt nanoshell with ultra-high NIR-\u2161 photothermal conversion efficiency mediates multifunctional neuromodulation for cardiac protection",
+    "journal": "Nature Communications",
+    "published": "28 July 2024",
+    "supplementary_0": [
+        {
+            "label": "Supplementary Information",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-024-50557-w/MediaObjects/41467_2024_50557_MOESM1_ESM.pdf"
+        },
+        {
+            "label": "Reporting Summary",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-024-50557-w/MediaObjects/41467_2024_50557_MOESM2_ESM.pdf"
+        },
+        {
+            "label": "Peer Review File",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-024-50557-w/MediaObjects/41467_2024_50557_MOESM3_ESM.pdf"
+        }
+    ],
+    "supplementary_1": [
+        {
+            "label": "Source Data",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-024-50557-w/MediaObjects/41467_2024_50557_MOESM4_ESM.zip"
+        }
+    ],
+    "supplementary_2": NaN,
+    "source_data": [
+        "/articles/s41467-024-50557-w#Sec38"
+    ],
+    "code": [],
+    "subject": [
+        "Biomedical materials",
+        "Inhibition\u2013excitation balance",
+        "Nanoparticles"
+    ],
+    "license": "http://creativecommons.org/licenses/by/4.0/",
+    "preprint_pdf": "https://www.researchsquare.com/article/rs-3985327/v1.pdf?c=1722251221000",
+    "research_square_link": "https://www.researchsquare.com//article/rs-3985327/v1",
+    "nature_pdf": "https://www.nature.com/articles/s41467-024-50557-w.pdf",
+    "preprint_posted": "14 Mar, 2024",
+    "research_square_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "The autonomic nervous system plays a pivotal role in the pathophysiology of cardiovascular diseases. Regulating it is essential for preventing and treating acute ventricular arrhythmias (VAs). Photothermal neuromodulation is a nonimplanted technique, but the response temperature ranges of transient receptor potential vanilloid 1 (TRPV1) and TWIK-elated K+ Channel 1 (TREK1) exhibit differences while being closely aligned, and the acute nature of VAs require that it must be rapid and precise. However, the low photothermal conversion efficiency (PCE) still poses limitations on achieving rapid and precise treatment. Here, we achieved nearly perfect blackbody absorption and one of the highest PCE in the second near infrared (NIR-II) window (73.7% at 1064 nm) via a Pt nanoparticle shell (PtNP-shell). By precisely manipulating the photothermal effect, we successfully achieved rapid and precise multifunctional neuromodulation encompassing neural activation (41.0\u201342.9 oC) and inhibition (45.0\u201346.9 oC). The NIR-II photothermal modulation additionally achieved bi-directional reversible autonomic modulation and conferred protection against acute VAs associated with myocardial ischemia and reperfusion injury in interventional therapy.Physical sciences/Nanoscience and technology/Nanoscale materials/NanoparticlesBiological sciences/Biotechnology/Biomaterials",
+            "section_image": []
+        },
+        {
+            "section_name": "Additional Declarations",
+            "section_text": "There is NO Competing Interest.",
+            "section_image": []
+        },
+        {
+            "section_name": "Supplementary Files",
+            "section_text": "supplementaryinformation.docx",
+            "section_image": []
+        }
+    ],
+    "nature_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Autonomic nervous system disorders play a pivotal role in the pathophysiology of cardiovascular diseases. Regulating it is essential for preventing and treating acute ventricular arrhythmias (VAs). Photothermal neuromodulation is a nonimplanted technique, but the response temperature ranges of transient receptor potential vanilloid 1 (TRPV1) and TWIK-related K+ Channel 1 (TREK1) exhibit differences while being closely aligned, and the acute nature of VAs require that it must be rapid and precise. However, the low photothermal conversion efficiency (PCE) still poses limitations in achieving rapid and precise treatment. Here, we achieve a nearly perfect blackbody absorption and a high PCE in the second near infrared (NIR-II) window (73.7% at 1064\u2009nm) via a Pt nanoparticle shell (PtNP-shell). By precisely manipulating the photothermal effect, we successfully achieve rapid and precise multimodal neuromodulation encompassing neural activation (41.0\u201342.9\u2009\u00b0C) and inhibition (45.0\u201346.9\u2009\u00b0C) in a male canine model. The NIR-II photothermal modulation additionally achieves multimodal reversible autonomic modulation and confers protection against acute VAs associated with myocardial ischemia and reperfusion injury in interventional therapy.",
+            "section_image": []
+        },
+        {
+            "section_name": "Introduction",
+            "section_text": "Cardiovascular disease has emerged as a leading cause of mortality, with acute myocardial infarction being one of the most pernicious ailments1,2. Myocardial ischemia (MI) frequently precipitates acute ventricular arrhythmias (VAs), impeding prompt and efficacious treatment for acute myocardial infarction. Furthermore, conventional interventional procedures for MI are unable to circumvent concomitant myocardial reperfusion injury and associated VAs3. The autonomic nervous system, encompassing sympathetic and parasympathetic nerves, plays a role in cardiovascular modulation; both are naturally antagonistic. Sympathetic inhibition or parasympathetic activation has been shown to stabilize cardiac electrophysiology, safeguard against MI, and reduce the incidence of VAs4. However, cardiac sympathetic denervation (CSD), stellate ganglion block (SGB), and renal denervation (RDN) are associated with certain adverse effects, including Horner\u2019s syndrome5, inadvertent bleeding, and inconsistent ablation outcomes6. Both conventional vagus nerve stimulation (VNS) and optogenetic neuromodulation necessitate the implantation of in vivo electrical stimulation7 or light source8 devices. Furthermore, optogenetic neuromodulation requires viral transfection of photosensitive proteins8, thereby limiting the clinical advancement of these therapeutic approaches.\n\nIn recent years, several studies have demonstrated that light-activated nanotransducers can induce local heating effects, leading to the activation or inhibition of nerves9,10,11. This discovery is attributed to the identification of temperature-sensitive ion channels in neurons, such as transient receptor potential vanilloid 1 (TRPV1)12 and TWIK-related K+ Channel 1 (TREK1)13. The activation of specific temperature-sensitive ion channels necessitates precise temperature ranges12,13,14. Considering the acute nature of neural responses, a therapeutic strategy with rapid and accurate modulation is required. The light in the second near-infrared window (NIR-II, 900\u20131700\u2009nm) has reduced tissue scattering and absorption and increased maximum permissible exposure (MPE) for biological tissues compared to the light in the first near-infrared (NIR-I, 650\u2013900\u2009nm) and visible window15. Consequently, this enables non-invasive and non-implantable neuromodulation using the NIR-II photothermal effect. However, its neural response rate and accuracy are currently limited by low photothermal conversion efficiency (PCE).\n\nIn this work, we report a near blackbody NIR-II Pt nanoparticle shell (PtNP-shell) for protection against MI and myocardial reperfusion injury accompanying intervention. The PtNP-shell, synthesized through a simple electrocoupling substitution reaction using liquid metal nanoparticles as templates (Fig.\u00a01a), possesses surface pores and a hollow structure. It demonstrates a nearly perfect blackbody absorption, enhanced absorption of light, and then a high PCE in the NIR-II window (73.7% at 1064\u2009nm). By leveraging the local heating effect mediated by PtNP-shell, we achieve rapid, efficient, and precise multimodal autonomic neuromodulation. Specifically, parasympathetic activation and sympathetic inhibition are accomplished by activating TRPV1 (41.0\u201342.9\u2009\u00b0C) and TREK1 (45.0\u201346.9\u2009\u00b0C) channels, respectively. Photothermal autonomic neuromodulation mediated by PtNP-shell effectively stabilizes cardiac electrophysiology and reduces VAs incidence in both myocardial ischemia-reperfusion (I/R) injury model and MI model, respectively (Fig.\u00a01b).\n\na The synthesis steps of PtNP-shell and schematic diagram of photothermal effect. b Schematic diagram of multimodal autonomic modulation mediated by photothermal effect of PtNP-shell for the treatment of myocardial ischemia-reperfusion injury and myocardial ischemia-induced ventricular arrhythmias.",
+            "section_image": [
+                "https:////media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41467-024-50557-w/MediaObjects/41467_2024_50557_Fig1_HTML.png"
+            ]
+        },
+        {
+            "section_name": "Results",
+            "section_text": "The PtNP-shell was synthesized through an electrocoupling substitution reaction between chloroplatinate and Ga nanoparticles (GaNPs). Ga nanoparticles were obtained by sonication of pure metal Ga. To achieve a balanced particle size and oxidation degree of GaNPs, pure gallium was sequentially sonicated in ethanol and water for 30\u2009min to obtain gallium nanoparticles with reduced oxidation (Supplementary Fig.\u00a01a). In accordance with the electrochemical redox potential of the redox couple (Ga3+/Ga: \u22120.529\u2009V; PtCl62\u2212/PtCl42\u2212: 0.726\u2009V; PtCl42\u2212/Pt: 0.758\u2009V)16,17, Pt (IV) can be in situ reduced by Ga and deposited on the surface of GaNPs to form a core-shell structure (Supplementary Fig.\u00a01b, c). The hollow PtNP-shell is synthesized after completion of the reaction (Fig.\u00a02a). Simultaneously with the reduction of Pt (IV), Ga oxide is formed, creating the skeleton of the PtNP-shell (right in Fig.\u00a02a). The surface of the PtNP-shell exhibits a rough texture (Supplementary Fig.\u00a02). The scanning transmission electron microscopy (STEM) images reveal numerous irregular and uneven pores on its surface (Supplementary Fig.\u00a03a) and PtNP-shell is composed of Pt nanoparticles (PtNPs) with 2\u20135\u2009nm (Fig.\u00a02b). High-resolution TEM (HRTEM) image is acquired to character the structure of PtNPs. As shown in Supplementary Fig.\u00a03b, PtNPs exhibit a single crystal structure with a lattice stripe spacing of 0.23\u2009nm corresponding to the (111) crystal plane. Meanwhile, the corresponding Fast Fourier Transform (FFT) pattern (inset in Supplementary Fig.\u00a03b) shows the typical diffraction patterns of face-centered cubic structure along [111] zone axis.\n\na TEM image of PtNP-shell, n\u2009=\u200910 independent replicates (inset: schematic diagram of PtNP-shell; right: element mapping). b STEM images of PtNP-shell surface, n\u2009=\u20096 independent replicates. c XRD spectrum of PtNP-shell (inset: SAED pattern). d UV\u2013vis\u2013NIR absorption spectrum of GaNPs, Ga@Pt NPs, and PtNP-shell (75\u2009\u03bcg\u2009mL\u22121). e Temperature elevation curves of PBS, GaNPs, Ga@Pt NPs and PtNP-shell (50\u2009\u03bcg\u2009mL\u22121) under NIR-II laser irradiation (1\u2009W\u2009cm\u22122). f Calculation of the PCE at 1064\u2009nm (PtNP-shell: 50\u2009\u03bcg\u2009mL\u22121). Source data are provided as a Source Data file.\n\nIn the X-ray powder diffraction (XRD) spectrogram result (Fig.\u00a02c), all peaks can be attributed to the crystal phase of Pt (JCPDS: 87-0640), consistent with the selected area electron diffraction (SAED) pattern findings (inset in Fig.\u00a02c). However, no peaks corresponding to gallium oxide were observed in the XRD spectrogram, possibly due to its low content. The XRD spectrogram (Supplementary Fig.\u00a04) of PtNP-shell prior to reacting with KOH showed that the gallium oxide contained in PtNP-shell was GaOOH (JCPDS: 06-0180). X-ray photoelectron spectroscopy (XPS) analysis reveals the presence of Ga and O in GaNPs, while Ga@Pt NPs and PtNP-shell exhibit the coexistence of Ga, O, and Pt (Supplementary Fig.\u00a05). As depicted in the Supplementary Fig.\u00a06, despite treatment with KOH, no presence of K element was detected in the PtNP-shell. The strong signals of Pt 4f5/2 and Pt 4f7/2 indicate that the Pt in Ga@Pt NPs and PtNP-shell exists in a metallic state18. In GaNPs, the peak centered at 1118.11\u2009eV is attributed to Ga3+ 2p3/2, while the peak centered at 1115.89\u2009eV corresponds to Ga 2p3/2. In Ga@Pt NPs, the peak centered at 1118.80\u2009eV is assigned to Ga3+ 2p3/2, and the peak centered at 1116.52\u2009eV corresponds to Ga 2p3/2. As for PtNP-shell, the presence of a peak around 1118.56\u2009eV indicates complete oxidation of Ga in PtNP-shell into Ga3+\u200916. The O 1s spectrum was fitted using two peak functions, which were assigned to Ga\u2013O at 530.44\u2009eV (GaNPs), 530.98\u2009eV (Ga@Pt NPs), 531.74\u2009eV (PtNP-shell) and Ga\u2013OH at 531.71\u2009eV (GaNPs), 532.08\u2009eV (Ga@Pt NPs), 532.74\u2009eV (PtNP-shell)19. Compared to GaNPs and Ga@Pt NPs, the binding energy of the Ga\u2013O and Ga\u2013OH peaks in the PtNP-shell is shifted toward higher values, indicating a lower oxidation degree of the PtNP-shell. PtNP-shell was treated with KOH (0.67\u2009M) to reduce the gallium oxide content and the surface potential was reduced from 45.8 to \u221225.7\u2009mV, and then encapsulated with methoxypoly(ethylene glycol) thiol (mPEG-SH5000) to enhance its biocompatibility and the surface potential was changed to \u221219.9\u2009mV (Supplementary Table.\u00a01). The statistically averaged hydrated nanoparticle size of PtNP-shell based on the dynamic light scattering diagram was 200.1\u2009nm with a uniform size distribution, indicating the nanoparticle was well dispersed in water (Supplementary Fig.\u00a07). After standing for different days, the statistically averaged hydrodynamic size of PtNP-shell was determined using dynamic light scattering (Supplementary Fig.\u00a08). It is worth noting that the change of the average hydrated nanoparticle size of PtNP-shell remains negligible after 14 days, indicating its excellent stability.\n\nDue to the presence of pores and a hollow structure in the PtNP-shell, light propagating in the space bounces at the rough surface of PtNP-shell until it encounters one of the pores, where it continues to bounce within the PtNP-shell. The random distribution of these pores results in completely random light reflection, akin to Brownian motion20. Consequently, the probability of light escaping from other pores is extremely low, rendering PtNP-shell behave like a blackbody and produce an efficient infrared heater21,22,23. This enhanced absorption of light by PtNP-shell exhibits nearly perfect blackbody absorption characteristics (Supplementary Fig.\u00a09a). In the range of 250\u20131300\u2009nm, the PtNP-shell exhibits an absorbance close to 1 at 75\u2009\u03bcg\u2009mL\u22121, which is significantly enhanced in the range of 400\u20131300\u2009nm compared to GaNPs and Pt-coated Ga nanoparticles (Ga@Pt NPs) (Fig.\u00a02d). According to the Lambert\u2013Beer law (A/L\u2009=\u2009\u03b5C, where \u03b5 is the extinction coefficient), a linear relationship between absorption intensity (at 1064\u2009nm) and concentration was established, with an extinction coefficient measured as 13.3\u2009Lg\u22121\u2009cm\u22121 at 1064\u2009nm (Supplementary Fig.\u00a09b). Varying concentrations of PtNP-shell resulted in different shades of gray being generated, with significantly darker grayness observed under identical conditions compared to GaNPs and Ga@Pt NPs (Supplementary Fig.\u00a010a). These distinctive features were characterized by their respective positions within an RGB cube representation, wherein on the diagonal connecting darkest and brightest points, PtNP-shell was found closer to the darkest point than both other materials (Supplementary Fig.\u00a010b).\n\nThe photothermal properties of PtNP-shell were verified by irradiating the dispersion of PtNP-shell in water with NIR-II light at 1064\u2009nm (1\u2009W\u2009cm\u22122). Even in vitro, PtNP-shell (50\u2009\u03bcg\u2009mL\u22121) exhibited rapid temperature elevation, achieving a rise from room temperature to 41.0 and 45.0\u2009\u00b0C within only 96 and 133\u2009s, respectively. However, for GaNPs (409\u2009s and over 600\u2009s) and Ga@Pt NPs (317\u2009s and over 600\u2009s), it took significantly longer time to reach the same temperatures (Fig.\u00a02e). The corresponding thermal images of the PtNP-shell with different concentrations under different irradiation times are shown in Supplementary Fig.\u00a011. The heating effect of the PtNP-shell (50\u2009\u03bcg\u2009mL\u22121) gradually increased the \u2206T from 7.72 to 52.17\u2009\u00b0C when exposed to NIR-II laser for a duration of 600\u2009s while varying the optical power density at 1064\u2009nm between 0.25 and 1.5\u2009W\u2009cm\u22122 (Supplementary Fig.\u00a012). The heating rate of the SH-PEG modified PtNP-shell is significantly higher compared to that of the unmodified PtNP-shell (Supplementary Fig.\u00a013a), potentially attributed to the agglomeration tendency of unmodified PtNP-shell at elevated temperatures, leading to a reduction in photothermal performance. Following 600\u2009s of laser irradiation at 1064\u2009nm, the statistically averaged hydrodynamic size for SH-PEG-modified PtNP-shell was measured as 206.5\u2009nm (Supplementary Fig.\u00a013b), whereas unmodified PtNP-shell exhibited a size of 1517\u2009nm (Supplementary Fig.\u00a013c). TEM analysis further confirmed the observed agglomeration behavior in unmodified PtNP-shell subsequent to laser irradiation (Supplementary Fig.\u00a013). The PCE of PtNP-shell was quantified as 73.7% when balancing the energy input from photons with heat dissipation within the system (Fig.\u00a02f), representing a high PCE at 1064\u2009nm (Supplementary Table\u00a02). These results indicate that PtNP-shell exhibits excellent photothermal performance in the NIR-II window. Additionally, no significant changes in temperature or morphology were observed even after five cycles of irradiation (Supplementary Fig.\u00a014), suggesting exceptional photothermal stability.\n\nTo investigate the photothermal effects of PtNP-shell on neuronal activity at multiple levels, we conducted calcium imaging experiments in hippocampal neuron (HT-22) cells (Fig.\u00a03a, b). The immunoblotting results revealed abundant expression of both TRPV1 and TREK1 ion channels in HT-22 cells (Fig.\u00a03c). The direct effect of PtNP-shell on the excitability of these two different ion channels was assessed under NIR-II irradiation using a calcium ion indicator (Fluo-4 AM). Upon NIR-II laser irradiation, the temperature of the PtNP-shell (+) group increased compared to that of the PtNP-shell (\u2212) group, resulting in a significantly higher percentage of responding cells (Fig.\u00a03d) (p\u2009<\u20090.001). The micrographs fluorescence intensity curve of HT-22 neurons cultured with PtNP-shell showed significant Ca2+ influx upon NIR-II laser irradiation for 35\u2009\u00b1\u20095\u2009s and after the temperature reached 42.0\u2009\u00b0C (Fig.\u00a03e). In contrast, application of NIR-II laser irradiation with phosphate-buffered saline (PBS) did not induce significant Ca2+ influx.\n\na Flowchart of calcium imaging assay performed on HT-22 cells. b calcium imaging of HT-22 cells under different experimental conditions, n\u2009=\u20096 biologically independent replicates. c Western blotting for TRPV1 and TREK1 from HT-22 and HEK-293T cells, n\u2009=\u20094 biologically independent replicates. Percentage of d TRPV1 and f TREK1 groups of HT-22 cells within the field of view of the fluorescence microscope that responded to laser stimulation, n\u2009=\u20096 biologically independent replicates. Temporal dynamics of Ca2+ signals in e TRPV1 and g TREK1 groups of cells. The solid lines indicate the mean, and the shade represents the standard error of the mean (SEM). h Cell viability of HT-22 treated with different concentrations of PtNP-shell for 24\u2009h. Effect of NIR-II laser irradiation with varying durations on the viability of HT-22 cells treated with PtNP-shell (50\u2009\u03bcg\u2009mL\u22121) (Power densities: i 0.75\u2009W\u2009cm\u22122 and j 1\u2009W\u2009cm\u22122), n\u2009=\u20096 biologically independent replicates. The error bar indicates S.E.M. Two-way ANOVA with Tukey\u2019s honestly significant difference (HSD) test was applied for statistical analysis of (d) and (f). One-way ANOVA with Dunnett\u2019s multiple comparisons test was applied for statistical analysis of (i) and (j). Source data are provided as a Source Data file.\n\nSubsequently, neuronal excitation was induced and calcium signals were increased by perfusion of 15\u2009mM KCl in the PtNP-shell (\u2212) group and PtNP-shell (+) group (50\u2009\u03bcg\u2009mL\u22121), respectively. This phenomenon can be attributed to the elevation of extracellular potassium ion concentration, which triggers neuronal depolarization and subsequently leads to a substantial increase in intracellular calcium ion concentration24. Under NIR-II laser irradiation, the proportion of HT-22 cells responding to high-concentration KCl stimulation was significantly lower in the PtNP-shell (+) group compared to that in the PtNP-shell (\u2212) group at ~46.0\u2009\u00b0C (Fig.\u00a03f). The difference may be due to the activation of the TERK1 ion channel in the PtNP-shell (+) group, which can induce neuronal hyperpolarization and make intracellular and extracellular calcium ion concentrations tend to recover25. Interestingly, the PtNP-shell influenced the fluorescence intensity of HT-22 cells not with a sustained decrease but with an initial rise followed by a subsequent decrease (Fig.\u00a03g). This observation may be associated with the activation of TRPV1 channel at around 42.0\u2009\u00b0C9. With increasing temperature, TRPV1 and TREK1 channels were sequentially activated. These findings suggest that PtNP-shell can achieve precise temperature control within a short duration through its own high PCE for both neuronal excitation and inhibition.\n\nCytotoxicity assays were then conducted to investigate the potential neurotoxicity of PtNP-shell application. As shown in Fig.\u00a03h, concentrations of PtNP-shell below 100\u2009\u03bcg\u2009mL\u22121 exhibited no significant toxic effects on HT-22 cells. Even when the concentration of PtNP-shell was increased to 200\u2009\u03bcg\u2009mL\u22121, the survival rate of neuronal cells remained approximately at 52.11%. After neurons were co-cultured with PtNP-shell (50\u2009\u03bcg\u2009mL\u22121) for 24\u2009h, cross-sectional TEM and SEM images showed that PtNP-shell was randomly distributed inside or on the surface of the cells (Supplementary Fig.\u00a015). This is attributed to the fact that the PtNP-shell exhibits a particle size of ~200\u2009nm, enabling smaller particles to traverse the cell membrane. Furthermore, the impact of PtNP-shell photothermal stimulation parameters on cell viability was assessed through analysis of HT-22 cell survival under NIR-II laser irradiation. Notably, when a concentration of 50\u2009\u03bcg\u2009mL\u22121 PtNP-shell and an NIR-II laser with a power density of 0.75\u2009W\u2009cm\u22122 was applied for a brief duration, the survival rate exceeded 91.87% for HT-22 cells (Fig.\u00a03i). Even with an increase in power density to 1\u2009W\u2009cm\u22122, the survival rate for HT-22 cells remained around 82.71% after 90\u2009s of irradiation (Fig.\u00a03j). These results indicate that PtNP-shell does not induce significant damage to neurons under controlled NIR-II laser irradiation.\n\nWestern blotting analysis of peripheral ganglia from the canine autonomic nervous system revealed the expression of TRPV1 and TREK1 heat-sensitive ion channels in both the nodose ganglion (NG) and the left stellate ganglion (LSG). Notably, TRPV1 was abundantly expressed in the NG of the parasympathetic nervous system, while TREK1 exhibited higher levels in the LSG of the sympathetic nervous system (Supplementary Fig.\u00a016). To investigate whether the photothermal effect induced by PtNP-shell under NIR-II irradiation can precisely regulate the parasympathetic nerve, 100\u2009\u03bcL PtNP-shell (50\u2009\u03bcg\u2009mL\u22121) and PBS were injected into NG of PtNP-shell group and control group (six beagle dogs in each group), respectively (Fig.\u00a04a, b). It can be observed that upon irradiation with NIR-II laser (0.8\u2009W\u2009cm\u22122), the temperature of NG injected with PtNP-shell increased to 41.0\u2009\u00b0C within a very short period of time (12\u2009\u00b1\u20093\u2009s). Subsequently, the temperature of NG could be kept in the range of 41.0\u201342.9\u2009\u00b0C for 5\u2009min by adjusting the power density to 0.45\u2009W\u2009cm\u22122 (Fig.\u00a04c, d). As a crucial node within the parasympathetic neural network, activation of NG significantly reduces heart rate (HR) (Fig.\u00a04e)26. Therefore, NG function was assessed by the maximum decrease in heart rate under direct electrical stimulation. As shown in Fig.\u00a04f\u2013h, NG function and activity were significantly elevated in the PtNP-shell group than in the control group after stimulation. The function and activity of NG recovered close to baseline within 3\u2009h after turning off the NIR-II laser, indicating that the photothermal modulation induced by PtNP-shell was reversible within NGs (Fig.\u00a04h, Supplementary Figs.\u00a017, 18). After NIR irradiation with the same parameters, the local temperature increase of the NG was <2\u2009\u00b0C, while there was no significant change in parasympathetic nerve function (Supplementary Fig.\u00a019).\n\na Location of the canine NG. b Schematic illustration of the process of photothermal modulation of NG. c Temperature curves of NG under NIR-II laser irradiation. d Typical thermal imaging diagram of photothermally modulated activation of NG. e Representative images of HR reduction induced after stimulation of NG with different voltages. Maximal HR changes of beagle treatment with PtNP-shell or control f before and g after NIR-II exposure, n\u2009=\u20096 biologically independent replicates. h Quantification of the NG neural activity recordings, n\u2009=\u20096 biologically independent replicates. i Representative immunofluorescent images of VAChT, c-Fos, and TRPV1 in the NG of beagles following different treatments. Data are shown as the mean\u2009\u00b1\u2009S.E.M. Unpaired two-tailed Student\u2019s t-test was applied for statistical analysis of (g). Two-way ANOVA with Tukey\u2019s HSD test was applied for statistical analysis of (h). NG nodose ganglion, HR heart rhythm. Source data are provided as a Source Data file.\n\nIn addition, the stability of the electrophysiology of the heart is reflected by measuring the effective refractory period (ERP) in various regions, including left ventricular apex (LVA), median left ventricular area (LVM), and left ventricular base (LVB). In the PtNP-shell group, the ERP was significantly elevated compared to the control group and remained elevated for 1\u2009h after photothermal intervention in NG (Supplementary Fig.\u00a020). Furthermore, immunofluorescence staining for vesicular acetylcholine transporter protein (VAChT), c-Fos, and TRPV1 on histopathological sections of photothermally modulated NGs served to localize parasympathetic neurons and reflect neuronal activity as well as TRPV1 protein expression, respectively (Fig.\u00a04i). Quantitative analysis (Supplementary Fig.\u00a021) revealed a substantial increase in the proportion of TRPV1+ (86.63\u2009\u00b1\u20092.65 vs. 45.45\u2009\u00b1\u20092.98) and c-Fos+ (77.81\u2009\u00b1\u20093.91 vs. 17.27\u2009\u00b1\u20093.08) neurons among VAChT+ parasympathetic neurons in the PtNP-shell group compared to the control group (all P\u2009<\u20090.001). These findings suggest that PtNP-shell can precisely regulate temperature and subsequently activate TRPV1 ion channels on NG to enhance parasympathetic activity.\n\nAnimal modeling and intervention manipulations were conducted to further elucidate the protective effects of precise modulation of NG by PtNP-shell against myocardial ischemia-reperfusion (I/R) injury and associated VAs, following the experimental protocols depicted in Fig.\u00a05a, b. PtNP-shell and PBS were microinjected into the NG of the PtNP-shell group and control group, respectively, each consisting of six beagle dogs. The left anterior descending (LAD) coronary artery was occluded for 1\u2009h to induce myocardial ischemia. Subsequently, NIR-II laser irradiation was applied to NG for 5\u2009min, followed by reperfusion treatment achieved by opening the ligated knot.\n\na Schematic diagram and b flowchart of regulating NG to protect against myocardial I/R injury and associated VAs. c Representative visual depictions of VAs, including VPB, VT, and VF. d Quantitative analysis of the ratio of sVT and VF incidence between different groups, n\u2009=\u20096 biologically independent replicates. Quantitative analysis of the number of e VPBs, f VTs, and g the duration of sVT of beagles. Effects on ventricular ERP at different sites in beagles treatment with PtNP-shell or control h before and i after myocardial I/R injury modeling. Levels of markers of myocardial injury, including j MYO and k c-TnI, after different treatments in beagles n\u2009=\u20096 biologically independent replicates. Data are shown as the mean\u2009\u00b1\u2009S.E.M. Unpaired two-tailed Student\u2019s t-test was applied for statistical analysis of (e\u2013k). NG nodose ganglion, LADO left anterior descending coronary occlusion, VPB ventricular premature beat, VT ventricular tachycardia, sVT sustained VT, VF ventricular fibrillation, ERP effective refractory period, LVA left ventricular apex, LVM median left ventricular area, LVB left ventricular base. Source data are provided as a Source Data file.\n\nFollowing I/R injury, electrocardiography (ECG) was recorded to monitor the occurrence of VAs events within 1\u2009h, including ventricular premature beats (VPBs), ventricular tachycardia (VT), and ventricular fibrillation (VF) (Fig.\u00a05c)27. Under NIR-II laser irradiation, the PtNP-shell group exhibited a lower incidence of sustained VT (sVT, duration >30\u2009s) or VF compared to the control group (50% vs. 83%) (Fig.\u00a05d). Moreover, the number of recorded VPBs (70.83\u2009\u00b1\u20095.38 vs. 116.00\u2009\u00b1\u20096.36, P\u2009<\u20090.05), VTs (3.17\u2009\u00b1\u20090.87 vs. 8.83\u2009\u00b1\u20092.15, P\u2009<\u20090.05) and duration of the VTs (7.00\u2009\u00b1\u20093.173\u2009s vs. 26.83\u2009\u00b1\u20097.89\u2009s, P\u2009<\u20090.05) in the PtNP-shell group were significantly reduced compared to that in the control group (Fig.\u00a05e\u2013g).\n\nThere were no statistically significant differences between the two groups in terms of preoperative ERP for LVB, LVM, and LVA. In the postoperative period, all three positions showed shortened ERPs in the control group. The PtNP-shell group exhibited significantly higher ERPs compared to the control group, indicating that photothermal modulation of nerves by PtNP-shell has a protective effect on cardiac electrophysiology (Fig.\u00a05h, i). Serum ELISA assay revealed significantly lower levels of markers of myocardial injury (MYO and c-TnI) at 4\u20135\u2009h post-infarction in the PtNP-shell group compared to the control group (all p\u2009<\u20090.05, Fig.\u00a05j, k), indicating an improvement in myocardial injury28. This may be attributed to the activation of \u03b1-7 nicotinic acetylcholine receptor by stimulating parasympathetic nerves, thereby alleviating inflammatory reactions and oxidative stress29,30. Postoperatively, heart rate variability analysis demonstrated lower low frequency (LF) and higher high frequency (HF) and the lower ratio of LF to HF (LF/HF) values in the PtNP-shell group compared to the control group (all p\u2009<\u20090.05, Supplementary Fig.\u00a022). These results suggest that PtNP-shell reduces VAs by activating the parasympathetic nerve.\n\nThe sympathetic nervous system was modulated by performing microinjections of PtNP-shell or PBS into the LSG, followed by irradiation with a NIR-II laser (Fig.\u00a06a, b). The temperature curve demonstrates that upon exposure to a NIR-II laser (0.8\u2009W\u2009cm\u22121) for 25\u2009\u00b1\u20095\u2009s, the temperature rapidly escalated to 45.0\u2009\u00b0C, crossing the range of 41.0\u201342.9\u2009\u00b0C within a mere duration of 6\u2009\u00b1\u20091\u2009s. Subsequently, the power density was immediately decreased to 0.6\u2009W\u2009cm\u22122, effectively maintaining LSG at a steady temperature between 45.0 and 46.9\u2009\u00b0C (Fig.\u00a06c, d). Due to the substantial increase in systolic blood pressure (SBP) induced by LSG activation (Fig.\u00a06e), the function of LSG was evaluated by quantifying the maximum SBP change corresponding to five consecutive incremental voltages of high-frequency electrical stimulation. After 5\u2009min of NIR-II laser irradiation, the activity and function of LSG in the PtNP-shell group were significantly suppressed compared to the control group (p\u2009<\u20090.05) and they returned close to baseline after 3\u2009h (Fig.\u00a06f\u2013h and Supplementary Figs.\u00a023, 24). Similarly, after NIR irradiation with the same parameters, the local temperature increase in the LSG did not exceed 2\u2009\u00b0C, while there was no significant change in sympathetic nerve function (Supplementary Fig.\u00a025).\n\na Location of the canine LSG. b Schematic illustration of the process of photothermal modulation of LSG. c Temperature curves of LSG under NIR-II laser irradiation. d Typical thermal imaging diagram of photothermally modulated activation of LSG. e Representative images of BP elevation induced after stimulation of LSG with different voltages. Maximal SBP changes of beagle treatment with PtNP-shell or control f before and g after NIR-II exposure, n\u2009=\u20096 biologically independent replicates. h Quantification of the LSG neural activity recordings, n\u2009=\u20096 biologically independent replicates. i Representative immunofluorescent images of TH, c-Fos, and TREK1 in the LSG of beagles following different treatments. Data are shown as the mean\u2009\u00b1\u2009S.E.M. Unpaired two-tailed Student\u2019s t-test was applied for statistical analysis of (g). Two-way ANOVA with Tukey\u2019s HSD test was applied for statistical analysis of (h). LSG left stellate ganglion, BP blood pressure, SBP systolic BP. Source data are provided as a Source Data file.\n\nProlonged ERP effects were observed in all left ventricles, while the protective effect exhibited a duration of only 2\u2009h (Supplementary Fig.\u00a026). Furthermore, immunofluorescence staining was conducted on LSG tissues to examine the expression of tyrosine hydroxylase (TH), c-Fos, and TREK1 (Fig.\u00a06i). These markers indicate the localization of sympathetic neurons, neuronal activity, and TREK1 protein expression, respectively. The quantitative analysis (Supplementary Fig.\u00a027) revealed a significant decrease in the proportion of c-Fos+ expression in TH+ neurons within the PtNP-shell group (8.80\u2009\u00b1\u20091.80 vs. 44.78\u2009\u00b1\u20095.55, P\u2009<\u20090.001) indicating that PtNP-shell exerted a photothermal inhibitory effect on LSG neurons under NIR-II irradiation. However, the proportion of TREK+ expression was significantly increased within TH+ neurons in the PtNP-shell group (83.51\u2009\u00b1\u20093.72 vs. 57.20\u2009\u00b1\u20095.89, P\u2009<\u20090.01). This increase could lead to hyperpolarization of the cell membrane potential, reduction in neuronal excitability and inhibition of sympathetic nerve activity.\n\nIn order to investigate the impact of PtNP-shell photothermal effect on reducing VAs occurrence induced by MI, NIR-II light was applied to make LSG reach the target temperature of about 46.0\u2009\u00b0C before ligating LAD coronary artery (Fig.\u00a07a, b). Under NIR-II laser irradiation, the PtNP-shell group exhibited a significantly reduced incidence of sVTs or VF compared to the control group (16% vs. 50%) (Fig.\u00a07c). In the PtNP-shell group, ECG recordings within infarction 1 exhibited a reduced incidence of VAs events compared to the control group, with fewer VPBs recorded in the PtNP-shell group than in the control group (51.50\u2009\u00b1\u20095.53 vs. 70.83\u2009\u00b1\u20095.375, P\u2009<\u20090.05, Fig.\u00a07d). However, there were no significant differences between the two groups in terms of VT numbers and duration (Supplementary Fig.\u00a028). Additionally, VA inducibility measurements demonstrated that after photothermal neuromodulation with PtNP-shell, there was a decrease in VA score (1.50\u2009\u00b1\u20090.76 vs. 4.83\u2009\u00b1\u20091.14, P\u2009<\u20090.05) effective heart protection (Fig.\u00a07e, f). Furthermore, PtNP-shell photothermal inhibition of LSG produced similar protective effects on ventricular electrophysiological index ERP as activation of NG (Fig.\u00a07g, h), and had a higher VF threshold than the control group (24.33\u2009\u00b1\u20094.24 vs. 12.33\u2009\u00b1\u20093.16, P\u2009<\u20090.05, Fig.\u00a07i). In addition, the light inhibition of LSG followed the same trend as heart rate variability after activation of NG (Supplementary Fig.\u00a029). These results suggest that PtNP-shell protects against cardiac damage and reduces VAs by modulating the autonomic nervous system, specifically by decreasing sympathetic activity and enhancing parasympathetic tone.\n\nModulation of LSG to protect against MI and associated VAs a schematic diagram and b flowchart. c Quantitative analysis of the ratio of sVT and VF incidence between different groups, n\u2009=\u20096 biologically independent replicates. d Quantitative analysis of the number of VPBs of beagles. e Typical images of VA induced by programmed electrical stimulation. f Quantitative analysis of VAs score in different groups. Effects on ventricular ERP at different sites in Beagles treatment with PtNP-shell or control g before and h after MI modeling. i Quantitative analysis of VF threshold in different groups, n\u2009=\u20096 biologically independent replicates. Data are shown as the mean\u2009\u00b1\u2009S.E.M. Unpaired two-tailed Student\u2019s t-test was applied for statistical analysis of (d, f\u2013i). LSG left stellate ganglion, SBP systolic blood pressure, MI myocardial infarction, VPB ventricular premature beat, VT ventricular tachycardia, VF ventricular fibrillation, VA ventricular arrhythmia, ERP effective refractory period, LVA left ventricular apex, LVM median left ventricular area, LVB left ventricular base. Source data are provided as a Source Data file.\n\nTo validate the biocompatibility of PtNP-shell photothermal modulation on the autonomic nervous system, we conducted rapid excision of LSG and NG tissues followed by hematoxylin and eosin (H&E) staining and Terminal deoxynucleotidyl transferase (TdT) dUTP Nick-End Labeling (TUNEL) assay. As shown in Supplementary Fig.\u00a030, H&E and TUNEL staining did not reveal any indications of neuronal damage in both the PtNP-shell and control groups for both NG and LSG, indicating that the neuromodulation of PtNP-shell is repeatable. Meanwhile, to further investigate the long-term biosafety of PtNP-shell, a microinjection of 200\u2009\u03bcl PtNP-shell (50\u2009\u03bcg\u2009mL\u22121) or PBS was administered into the ganglion of dogs and the tail vein of rats, respectively. After a follow-up period of 30 days, no significant damage was detected in the ganglia or major organs, including the heart, liver, spleen, lungs, and kidneys (Supplementary Figs.\u00a030, 31a, i). Furthermore, blood biochemical analyses indicated no hepatotoxicity, nephrotoxicity, and induction of inflammatory responses (Supplementary Fig.\u00a031b\u2013h, j\u2013p). These results unequivocally demonstrate that PtNP-shell exhibits exceptional biocompatibility and long-term biological safety.",
+            "section_image": [
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+            ]
+        },
+        {
+            "section_name": "Discussion",
+            "section_text": "The PtNP-shell reported in this study exhibits nearly perfect blackbody absorption properties, making it an efficient absorber with a high PCE in the NIR-II window (73.7% at 1064\u2009nm). Furthermore, local heating induced by PtNP-shell activation effectively triggers temperature-sensitive ion channels TRPV1 and TREK1, enabling precise and efficient modulation of autonomic nerves. This innovative approach holds great potential for non-invasive treatment of MI and associated VAs, as well as protection against reperfusion injury during interventional therapy.\n\nCardiac sympathetic denervation is a clinical procedure aimed at targeting the autonomic ganglia for refractory ventricular arrhythmias. However, ganglion removal can be traumatic for patients and may lead to complications due to the loss of original physiological function31. Currently, \u03b2-blockers are the primary pharmacological drugs employed in clinical practice for arrhythmia treatment32,33. However, their administration during acute myocardial ischemia remains unclear and is contraindicated in patients with heart failure. Additionally, previous research investigated the local ganglion blockade using botulinum toxin A to protect the heart34. Nevertheless, its prolonged blocking effect renders it unsuitable for acute myocardial ischemia management. Conversely, PtNP-shell-based photothermal neuromodulation offers reversible modulation within a short timeframe, exhibiting superior efficacy and controllability. In this study, we validated the protective efficacy of PtNP-shell photothermal neuromodulation strategy in models of acute myocardial infarction and acute reperfusion injury to mitigate ventricular arrhythmia incidence. However, further evaluation through experiments such as assessment of cardiac function and infarct area is required to determine the cardioprotective potential of this strategy in chronic myocardial injury models.\n\nMoreover, the minimal tissue damage caused by light can be disregarded within the maximum permissible exposure (MPE) range, rendering it one of the safest interventions for organisms. The interaction between light and tissue is intricate, and further research could aid in selecting more suitable wavelengths to achieve deeper penetration within the MPE range. Leveraging the nearly impeccable blackbody absorption of PtNP-shell and ultrasound-guided microinjection technology, remote and precise neuromodulation strategies can be developed, holding promise for non-invasive protection against MI and reperfusion injury-associated VAs. Simultaneously, exploiting the presence of blood vessels surrounding the ganglion presents an opportunity to minimize photon propagation within tissues. Consequently, photothermal modulation via NIR-II fibers in proximity to the ganglion through vascular routes during interventional therapy emerges as a promising avenue for direct clinical translation. The significance of this approach extends beyond VAs as it exhibits broad therapeutic prospects for chronic diseases like refractory hypertension35 and stable atherosclerosis36 due to the wide distribution of autonomic nerves and the universality of nerve regulation.",
+            "section_image": []
+        },
+        {
+            "section_name": "Methods",
+            "section_text": "The gallium was purchased from Shanghai Minor Metals Co., Ltd. Anhydrous ethanol (\u226599.7%) and KOH (AR) were purchased from Sinopharm Chemical Reagent Co., Ltd. Na2PtCl6 (98%) was purchased from Shanghai Aladdin Biochemical Technology Co., Ltd. mPEG-SH5000 was purchased from Shanghai Macklin Biochemical Co., Ltd. STR-identified correct HT-22 cells or human embryonic kidney 293T (HEK-293T) cells were purchased with the corresponding specialized cell culture media (Procell, Wuhan, China). Rabbit monoclonal anti-TRPV1 antibody (Cat. No. A23386, Clone No. ARC57842) used for protein blotting was purchased from ABclonal (Wuhan, China). Mouse monoclonal anti-TREK1 antibody (Cat. No. sc-398449, Clone No. F-6) used in western blot and immunofluorescence staining was purchased from Santa Cruz Biotechnology (TX, USA). Rabbit monoclonal Anti-c-Fos (Cat. No. A24620, Clone No. ARC63309), rabbit polyclonal anti-VAChT (Cat. No. A16068), rabbit polyclonal anti-TH (Cat. No. A12756) and rabbit polyclonal Anti-TRPV1 (Cat. No. A8564) antibodies used in immunofluorescence staining were purchased from ABclonal. Glyceraldehyde 3-phosphate dehydrogenase (GAPDH) was purchased from Servicebio (Wuhan, China). Serum troponin I (c-TnI) and myoglobin (MYO) ELISA kits were purchased from MIbio (Shanghai, China). Tumor necrosis factor alpha (TNF-\u03b1) and Interleukin 6 (IL-6) ELISA kits were purchased from Jianglaibio (Shanghai, China). 4,6-diamidino-2-phenylindole (DAPI) was purchased from Servicebio (Wuhan, China).\n\nThe morphology of PtNP-shell was characterized by an F200 transmission electron microscope (TEM) (JEOL, Japan) operated at 200\u2009kV. STEM and HRTEM images were obtained by a JEM-ARM200CF (JEOL, Japan) at 200\u2009kV. The EDX elemental mapping was carried out using the JEOL SDD-detector with two 100\u2009mm2 X-ray sensors. X-ray diffraction (XRD) patterns were performed on a SmartLab 9\u2009kW X-ray powder diffractometer (Cu-target, 0.154\u2009nm) (Rigaku, Japan). XPS measurements were carried out with an ESCALAB 250Xi spectrometer (Thermo Fisher Scientific, USA) under vacuum. Ultraviolet\u2013visible\u2013near-infrared light (UV\u2013vis\u2013NIR) absorption spectra were collected using a UV-3600 spectrophotometer (Shimadzu, Japan). Zeta potential (Z) and dynamic light scattering (DLS) were recorded using a Zetasizer Nano ZSP (Malvern Panalytical, UK). The fluorescence microscopy images of HT-22 cells were acquired by FV3000 Microscope (Olympus, Japan), excited with a 488\u2009nm laser. TEM of HT-22 cells was characterized by HT7800 TEM (HITACHI, Japan). SEM of HT-22 cells was characterized by SU8100 SEM (HITACHI, Japan). Beagle\u2019s respiration is maintained by a WATO EX-20VET ventilator (Mindray, Shenzhen, China). ECG and blood pressure data were recorded by a Lead 7000 Computerized Laboratory System (Jinjiang, Chengdu, China). NIR-II light at 1064\u2009nm is generated by LWIRPD-1064-5F laser (Laserwave, Beijing, China). Thermal imaging was obtained by FLIR C2 thermal imager (FLIR, USA). High-frequency electrical stimulation was performed by a Grass stimulator (Astro-Med; West Warwick, RI, USA). The electrical signals of autonomic nerves are recorded by the Power Lab data acquisition system (AD Instruments, NSW, Australia) and visualized and analyzed by Labchart software (version 8.0, AD Instruments). Serum biochemical indices were determined by a fully automatic biochemical analyzer BK-1200 (BIOBASE, Jinan, China).\n\nThe GaNPs were obtained by sonication of liquid Ga. The liquid Ga (300\u2009mg) was transferred to anhydrous ethanol (8\u2009mL), and the solution was sonicated by nanoprobe sonication for 1\u2009h (3\u2009s on and 3\u2009s off) at the power of 290\u2009W. Then the ethanol was replaced with Milli-Q water to continue sonication for 1\u2009h. The solution at the end of sonication was collected and centrifuged at 102\u2009\u00d7\u2009g for 5\u2009min, and the upper liquid layer was aspirated for later use.\n\nFirst, the GaNPs and 3\u2009mL Na2PtCl6 (0.1\u2009M) were evacuated for 30\u2009min and Ar was introduced for 15\u2009min. Then, 3\u2009mL Na2PtCl6 (0.1\u2009M) was added dropwise to GaNPs and the solution was stirred for 4\u2009h (droplet volume: 0.02\u2009mL, dropwise rate: 1 droplet/s). After the reaction, the solution was collected and centrifuged at 8326\u2009\u00d7\u2009g for 10\u2009min. The solids at the bottom were washed with Milli-Q water three times and finally dispersed in 6\u2009mL Milli-Q for later use.\n\nThe PtNP-shell was first covered with a small amount of mPEG-SH to protect the structure from KOH. 30\u2009mg mPEG-SH5000 was added to 6\u2009mL PtNP-shell and the solution was stirred for 12\u2009h. After the reaction, the solution was collected and centrifuged at 8326\u2009\u00d7\u2009g for 10\u2009min. The solids at the bottom were washed with Milli-Q water three times and dispersed in 6\u2009mL Milli-Q water. The above solution was stirred with 12\u2009mL of KOH (1\u2009M) for 4\u2009h. The reaction-completed solution was collected and centrifuged at 8326\u2009\u00d7\u2009g for 10\u2009min, and the solids at the bottom were washed three times with Milli-Q water and finally dispersed in 6\u2009mL Milli-Q water. The above solution was stirred with 60\u2009mg mPEG-SH5000 for 12\u2009h. After the reaction, the solution was collected and centrifuged. The solids at the bottom were washed with Milli-Q water three times and finally dispersed in 6\u2009mL PBS.\n\nFirst, the GaNPs and 1\u2009mL Na2PtCl6 (0.04\u2009M) were evacuated for 30\u2009min and Ar was introduced for 15\u2009min. Then, 1\u2009mL Na2PtCl6 (0.04\u2009M) was added dropwise to GaNPs and the solution was stirred for 10\u2009min (droplet volume: 0.02\u2009mL, dropwise rate: 1 droplet/s). After the reaction, the solution was collected and centrifuged at 8326\u2009\u00d7\u2009g for 10\u2009min, washed three times with Milli-Q water, and dispersed in 6\u2009mL Milli-Q water. The above solution was stirred with 60\u2009mg mPEG-SH5000 for 12\u2009h. After the reaction, the solution was collected and centrifuged (8326\u2009\u00d7\u2009g, 10\u2009min). The solids at the bottom were washed with Milli-Q water three times and finally dispersed in 6\u2009mL PBS.\n\nThe relationship between temperature rise and energy transfer in the system can be described by Eq.\u00a01,\n\nwhere \\({Q}_{{{\\rm{abs}}}}\\) is the total energy absorbed by the system, \\({Q}_{{{\\rm{NPs}}}}\\) is the energy absorbed by the nanoparticles, \\({Q}_{{{\\rm{solvent}}}}\\) is the energy absorbed by the solvent, \\({Q}_{{{\\rm{ext}}}}\\) is the energy loss from the system to the environment. mi and ci are the mass and specific heat capacity of the solution, respectively. T is the solution temperature and t is the irradiation time. The conversion of the light energy into heat energy can be expressed in terms of Eq.\u00a02,\n\nwhere I is the laser power, A is the absorbance value of PtNP-shell at 1064\u2009nm, \u03b7 is the photothermal conversion efficiency. \\({Q}_{{{\\rm{solvent}}}}\\) can be calculated by the following Eq.\u00a03,\n\nwhere h is the convective heat transfer coefficient and s is the surface area of the sample cell. \\({T}_{{{\\rm{solvent}}}}\\) is the maximum temperature that the solvent can reach under laser irradiation. \\({T}_{{{\\rm{surr}}}}\\) is the ambient temperature. \\({Q}_{{{\\rm{ext}}}}\\) can also be written as,\n\nThe heat output will increase with the increase in temperature when the NIR-II laser power is determined according to Eq.\u00a04. The temperature of the system will reach the maximum when the heat input is equal to the heat output, so the following equation can be obtained,\n\nwhere \\({Q}_{{{\\rm{ext}}}-\\max }\\) is the heat transferred from the system surface through the air when the sample cell reaches equilibrium temperature, and \\({T}_{\\max }\\) is the equilibrium temperature. Combining Eqs.\u00a02, 3, and 5, \u03b7 can be expressed as,\n\nwhere A is the PtNP-shell absorption at 1064\u2009nm. To obtain hs, the dimensionless temperature \u03b8 is introduced,\n\nand a time constant of sample system, \\({\\tau }_{{{\\rm{s}}}}\\)\n\nCombining Eqs.\u00a01, 4, 7, and 8, the following equation can be obtained,\n\nAfter the laser is turned off, in the cooling stage, there is no external input energy, \\({Q}_{{{\\rm{NPs}}}}+{Q}_{{{\\rm{solvent}}}}=0\\), and Eq.\u00a09 can be written as,\n\nBy integrating Eq.\u00a010, the following equation can be obtained,\n\nTherefore, the system heat transfer time constant (\\({\\tau }_{{{\\rm{s}}}}\\)) at 1064\u2009nm is 242.25\u2009s (Fig.\u00a03f). In addition, m is 1\u2009g and c is 4.2\u2009J\u2009g\u22121. Therefore, hs can be determined from Eq.\u00a08. The laser power (I) used here can be determined as 1\u2009W. Then the photothermal conversion efficiency (\u03b7) of the PtNP-shell at 1064\u2009nm can be calculated to be 73.7% by substituting hs into Eq.\u00a06.\n\nAll animal experiments were approved by the Animal Care and Use Committee of Renmin Hospital of Wuhan University (WDRM20230805A). All experimental procedures were in accordance with the Declaration of Helsinki for animals and were conducted according to the guidelines established by the National Institutes of Health. All adult male beagle dogs (8\u201312\u2009kg) were anesthetized intravenously with 3% sodium pentobarbital (30\u2009mg\u2009kg\u22121 induction dose, 2\u2009mg\u2009kg\u22121 maintenance dose/h) and respiration was maintained by endotracheal intubation using a ventilator. Arterial blood pressure was continuously monitored through femoral artery catheterization with a pressure transducer attached. ECG and blood pressure data were recorded throughout the procedure. A heating pad was used to maintain the core body temperature at 36.5\u2009\u00b1\u20090.5\u2009\u00b0C.\n\nThe cells were cultured in a humid incubator containing 5% CO2 at a temperature of 37.0\u2009\u00b0C. The cell-specific medium was prepared by mixing Dulbecco\u2019s modified Eagle\u2019s medium (DMEM), fetal bovine serum, and penicillin\u2013streptomycin mixture at 89%, 10%, and 1%, respectively.\n\nWe performed separate experiments for each biological sample in our in vitro and in vivo experiments, performing duplicate experiments with different subjects to ensure the reproducibility and accuracy of our studies.\n\nWestern blotting was used to assess the expression of TRPV1 and TREK1 in neuronal cells and ganglion tissues. HT-22 cells or HEK-293T cells were cultured in six-well plates for 24\u201348\u2009h, then lysed and centrifuged (12000\u2009\u00d7\u2009g, 10\u2009min) to collect cells. Ganglion tissues were obtained from deceased animals and frozen in liquid nitrogen or stored at \u221280.0\u2009\u00b0C. Total protein was determined using BCA protein assay reagent after tissue grinded and cells lysed. Afterward, the procedure was followed according to the manufacturer\u2019s instructions. Primary antibodies were anti-TRPV1 (dilution ratio 1:1000) and anti-TREK1 (dilution ratio 1:1000). Expression levels of specific proteins were normalized to GAPDH (dilution ratio 1:20000).\n\nThe effect of PtNP-shell photothermal modulation on ion channels in HT-22 cells was explored through calcium imaging experiments. HT-22 cells were incubated in 35\u2009mm confocal dishes for 24\u2009h. Cells were washed three times with PBS and then stained with 5\u2009\u03bcM Fluo-4 AM (dilution ratio 1:500) for 30\u2009min in a cell incubator at 37.0\u2009\u00b0C, protected from light. To induce activation of TRPV1 and TREK1 ion channels, the culture dish was exposed to a 1064\u2009nm laser (0.75\u2009W\u2009cm\u22122, TRPV1: 50\u2009s, TREK1: 80\u2009s), resulting in an elevation of temperature. TRPV1, being a calcium channel, exhibited observable changes in the flow of calcium ions upon activation, while TREK1 as a potassium channel did not display such behavior. Therefore, the effect of PtNP-shell photothermal modulation on neuronal cells via TREK1 was observed by introducing a 15\u2009mM KCl solution prior to NIR-II irradiation. Fluorescence signals at 525\u2009nm were recorded using a confocal microscope with 488\u2009nm as the excitation wavelength. XYT images in the region of 1064\u2009nm illumination were acquired and collected under a 20\u00d7 objective lens. The average fluorescence intensity of the cells was analyzed using ImageJ software (Fiji). The normalized fluorescence change was calculated as follows: \u0394F/F = (F\u2009\u2212\u2009F0)/F0, where F is the original fluorescence signal; F0 is the average baseline intensity before irradiation with NIR-II laser.\n\nThe cytotoxicity of PtNP-shell on neuronal cells was evaluated by Cell Counting Kit-8 (CCK-8) assay. HT-22 cells were seeded in 96-well plates at a density of 1\u2009\u00d7\u2009104\u2009well\u22121 and cultured for 24\u2009h. HT-22 cells were then treated with different concentrations (10, 25, 50, 100, 150, 200\u2009\u03bcg\u2009mL\u22121) of PtNP-shell for another 24\u2009h. Cell viability was determined by CCK-8 assay after incubating with the CCK-8 reagent for 1\u2009h. To investigate the impact of PtNP-shell\u2019s photothermal effect on neuron cell viability, HT-22 cells were co-cultured with PtNP-shell (50\u2009\u03bcg\u2009mL\u22121) for 12\u2009h followed by irradiation with a 1064\u2009nm laser (0.75 and 1\u2009W\u2009cm\u22122) for various durations (0, 30, 60, and 90\u2009s). After incubation again for 12\u2009h, the absorbance at 450\u2009nm was recorded using a microplate reader. Cell survival (%)\u2009=\u2009(ODsamples\u2009\u2212\u2009ODblank)/(ODcontrol\u2009\u2212\u2009ODblank)\u2009\u00d7\u2009100%.\n\nPart 1: exploring the in vivo effects of precise photothermal stimulation of the parasympathetic nervous system by PtNP-shell under NIR-II irradiation. Twelve beagles were randomly assigned to the control group (100\u2009\u03bcL phosphate-buffered saline (PBS) was microinjected into the NG, n\u2009=\u20096) and the PtNP-shell group (100\u2009\u03bcL PtNP-shell (50\u2009g\u2009mL\u22121) was microinjected into the NG, n\u2009=\u20096). NG nerve activity, heart rate (HR), and ventricular electrophysiological parameters were recorded at baseline and at multiple consecutive time points after NIR-II irradiation (Fig.\u00a04b).\n\nPart 2: the protective effect of PtNP-shell activation of the parasympathetic nervous system against myocardial I/R injury was investigated. The same grouping pattern as in Part 1 was used, with NIR-II irradiation (heating stage: 0.8\u2009W\u2009cm\u22122, 12\u2009\u00b1\u20093\u2009s; equilibrium stage: 0.45\u2009W\u2009cm\u22122, 5\u2009min) of the NG before opening the occluded LAD coronary vessel. Afterward, ventricular electrophysiological parameters, heart rate variability (HRV), and ECG data were recorded and analyzed (Fig.\u00a05b).\n\nPart 1: the in vivo effects of precise photothermal stimulation of the sympathetic nervous system by PtNP-shell under NIR-II irradiation (heating stage: 0.8\u2009W\u2009cm\u22122, 25\u2009\u00b1\u20095\u2009s; equilibrium stage: 0.6\u2009W\u2009cm\u22122, 5\u2009min) were explored. Twelve beagles were randomly assigned to the control group (100\u2009\u03bcL PBS microinjected into the LSG, n\u2009=\u20096) and the PtNP-shell group (100\u2009\u03bcL PtNP-shell (50\u2009g\u2009mL\u22121) microinjected into the LSG, n\u2009=\u20096). LSG nerve activity, SBP, and ventricular electrophysiological parameters were recorded at baseline and at multiple consecutive time points after NIR-II irradiation (Fig.\u00a06b).\n\nPart 2: to investigate the protective effect of PtNP-shell inhibition on the sympathetic nervous system in improving MI, we used the same grouping pattern as in Part 1, with 5-min NIR-II irradiation of the LSG before ligation of LAD vessels. Finally, ventricular electrophysiological parameters, HRV, and ECG data were also recorded and analyzed (Fig.\u00a07b).\n\nWe selected NG and LSG as targets for modulation in the autonomic nervous system to explore the multimodality of the PtNP-shell photothermal strategy. A \u201cC\u201d incision is made behind the left ear, and the angle between the occlusal and trapezius muscles serves as the access approach37. The tissue is bluntly separated to expose the carotid sheath and identify the parasympathetic nerve. Moving upstream along the nerve, a distal expansion is observed as NG (Fig.\u00a04a). LSG can be visualized and localized by left-sided thoracotomy (Fig.\u00a06a)34. PtNP-shell (50\u2009\u03bcg\u2009mL\u22121) or PBS was slowly injected into two sites within the NG and LSG tissues to achieve homogeneous photothermal conversion. Initial vertical irradiation of NIR-II laser (1064\u2009nm) at 0.80\u2009W\u2009cm\u22122 was performed on NG and LSG surfaces. The power density of the NIR-II laser was reduced to 0.45\u2009W\u2009cm\u22122 for continuous irradiation when the temperature of the NG reached 42.0\u2009\u00b0C, and was reduced to 0.6\u2009W\u2009cm\u22122 for continuous irradiation when the temperature of the LSG reached 46.0\u2009\u00b0C. The NIR-II laser irradiation remains stable with a spot size maintained at 1.0\u2009cm\u22122. Dual temperature monitoring using a thermal imager and T-type thermocouple was performed to plot the temperature-time curve.\n\nThe NG is a ganglion located upstream of the cervical parasympathetic nerve and can significantly inhibit HR after receiving direct electrical stimulation26. The LSG, as an important peripheral sympathetic ganglion, can rapidly elevate blood pressure when activated by electrical stimulation. Based on the functional properties of different autonomic ganglia, we assessed the function of NG and LSG. A pair of special electrodes made with silver wires were directly connected to the surfaces of NG and LSG for stimulation. High-frequency electrical stimulation (HFS: 20\u2009Hz, 0.1\u2009ms) was applied to the ganglion. The voltage was set to five levels in continuous increments (level 1: 0\u20132\u2009V; level 2: 2\u20134\u2009V; level 3: 4\u20136\u2009V; level 4: 6\u20138\u2009V; level 5: 8\u201310\u2009V), while keeping the stimulation voltage values consistent with the baseline at different time points during the experiment. The percentage of sinus rate or AV conduction (measured by the A\u2013H interval) slowing down constructed voltage level/degree of HR decrease curves reflecting NG function. On the other hand, the percentage increase in SBP built the voltage level/degree of SBP increase to reflect LSG function.\n\nTwo specially designed microelectrodes were inserted into the NG and LSG, respectively, while a grounding wire was connected to obtain signals from the autonomic nerves. These electrical signals were recorded by a Power Lab data acquisition system, filtered through a band-pass filter (300\u20131000\u2009Hz) and amplified 30\u201350 times by an amplifier. Finally, the signals were digitized and analyzed in LabChart software (version 8.0, AD Instruments).\n\nThe left anterior descending coronary occlusion (LADO) method was used to establish the MI model27. The ligation site was located beneath the first diagonal of the LAD, and the successful MI model was confirmed by observing ST-segment elevation on the ECG. After ensuring cardiac electrophysiological stabilization, the junction was released to reperfuse the occluded coronary arteries, completing the construction of the myocardial I/R injury model38.\n\nThe ERP was measured at three locations: LVA, LVB, and LVM (located between the LVA and LVB). Malignant arrhythmic events occurring within 1\u2009h of MI and I/R injury were assessed by electrocardiographic recordings in a canine model using a Lead 7000 Computerized Laboratory System. VAs were classified according to Lambeth Conventions as VPBs, VT (three or more consecutive VPBs), and VF39. The sVT is defined as continuous VT for more than 30\u2009s. In addition, arrhythmia inducibility was further assessed by programmed ventricular stimulation at the right ventricular apex (RVA). Eight consecutive stimuli (S1S1) were performed at intervals of 330\u2009ms, followed by additional stimuli until VT/VF occurred. Arrhythmia inducibility was assessed based on a modified arrhythmia scoring system40. If VF occurs during the evaluation, a defibrillator is required to restore sinus rhythm, followed by a waiting period of 30\u2009min to restore cardiac electrophysiological stability. The VF threshold was assessed in the perimyocardial infarction region. Pacing was initiated using a Grass stimulator with a voltage of 2\u2009V (20\u2009Hz, 0.1\u2009ms duration, 10\u2009s). The stimulation voltage was increased in 2\u2009V increments until VF was induced. The lowest voltage that induced VF was regarded as the VF threshold41.\n\nThe ECG data were recorded using the Power Lab data acquisition system. And the ECG segments recorded more than 5\u2009min before modulation and after MI or I/R injury were analyzed by LabChart software with the Lomb\u2013Scargle periodogram algorithm42. Frequency domain metrics of HRV were calculated, including LF (0.04\u20130.15\u2009Hz, reflecting sympathetic tone), HF (0.15\u20130.4\u2009Hz, reflecting parasympathetic tone), and LF/HF (reflecting autonomic balance). The results were expressed in standardized units.\n\nThe ganglions were rapidly dissected for histopathological staining after the experimental animals died. Tissues were fixed with 4% paraformaldehyde, embedded in paraffin, and cut into 5\u2009\u03bcm-thick sections. NG was stained with multiple immunofluorescence staining using anti-VAChT (dilution ratio 1:100), anti-c-Fos (dilution ratio 1:100), and anti-TRPV1 (dilution ratio 1:100) antibodies. VAChT is an essential protein for the transport of acetylcholine and can therefore localize parasympathetic neurons belonging to cholinergic neurons. Expression of c-Fos serves as a marker for neural cell activation. And LSG was stained by multiple immunofluorescences using anti-TH (dilution ratio 1:100), anti-c-fos (dilution ratio 1:200), and anti-TREK1 (dilution ratio 1:100) antibodies. Sympathetic neurons can be localized by TH protein expression. Cell nuclei were stained with DAPI. Images were taken at 100\u00d7 magnification and analyzed using ImageJ software (Fiji).\n\nIn myocardial I/R injury model experiments, 5\u2009mL of venous blood was obtained from the jugular vein of each beagle 4\u20135\u2009h after ligation of the coronary vessels (3\u20134\u2009h after reperfusion treatment). After standing for 1\u2009h, the blood was centrifuged at 1237\u2009\u00d7\u2009g for 15\u2009min. The upper serum layer was collected and stored at \u221280.0\u2009\u00b0C. Myocardial injury levels were detected by c-TnI and MYO. Standard process analyses were performed according to the instructions of each ELISA kit. To evaluate the long-term biosafety and biocompatibility of PtNP-shell in vivo, beagle dogs and rats were randomly divided into PtNP-shell and PBS groups.\n\nTo evaluate the long-term biosafety and biocompatibility of PtNP-shell in vivo, beagle dogs and rats were randomly divided into two groups: a PtNP-shell group (n\u2009=\u20096) and a PBS group (n\u2009=\u20096). In the PtNP-shell group, 200\u2009\u03bcL PtNP-shell (50\u2009\u03bcg\u2009mL\u22121) was microinjected into canine ganglion tissue and tail vein of rats to explore long-term biosafety. Blood and tissue samples were collected from each dog and rat 1 month after injection. One month after injection, blood samples were collected from the jugular vein of dogs as well as from the inferior vena cava of rats for analysis of serum biochemical indices, including alanine transaminase (ALT), aspartate aminotransferase (AST), urea, creatinine (Crea) and lactate dehydrogenase-1 (LDH1). Tissue H&E staining was also performed on major organs, including the heart, liver, spleen, lung, and kidney.\n\nAll graphical data are presented as mean\u2009\u00b1\u2009standard error of the mean (S.E.M.), and the distribution of data was assessed by the Shapiro\u2013Wilk test. Differences between groups were determined using the Student\u2019s t-test or Mann\u2013Whitney U test. Data distribution was assessed by the Shapiro\u2013Wilk test for normality. Differences between the two means were tested using unpaired Student\u2019s t-test for Gaussian distributed data. Analysis of variance followed by one-way ANOVA with Dunnett test (one independent variable) or two-way ANOVA with Tukey test (two independent variables) were used as appropriate and indicated in the figure legend. The P values of <0.05 were considered statistically significant. Data were analyzed and plotted using GraphPad Prism 9.0 software (GraphPad Software, Inc., La Jolla, CA, USA) and Oringinpro 2018 (OriginLab, USA).\n\nFurther information on research design is available in the\u00a0Nature Portfolio Reporting Summary linked to this article.",
+            "section_image": []
+        },
+        {
+            "section_name": "Data availability",
+            "section_text": "All data underlying this study are available from the corresponding author upon request.\u00a0Source data are provided with this paper.",
+            "section_image": []
+        },
+        {
+            "section_name": "References",
+            "section_text": "Virani, S. S. et al. Heart disease and stroke statistics\u20142020 update: a report from the American Heart Association. Circulation 141, E139\u2013E596 (2020).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nTrayanova, N. A. Learning for prevention of sudden cardiac death. Circ. Res. 128, 185\u2013187 (2021).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nYu, L. L. et al. Low-level tragus stimulation for the treatment of ischemia and reperfusion injury in patients with ST-segment elevation myocardial infarction a proof-of-concept study. JACC Cardiovasc. Interv. 10, 1511\u20131520 (2017).\n\nArticle\u00a0\n    MathSciNet\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nHerring, N., Kalla, M. & Paterson, D. J. The autonomic nervous system and cardiac arrhythmias: current concepts and emerging therapies. Nat. Rev. Cardiol. 16, 707\u2013726 (2019).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWebster, G. & Monge, M. C. Left cardiac sympathetic denervation. Circ. Arrhythm. Electrophysiol. 8, 1007\u20131009 (2015).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBhatt, D. L. et al. A controlled trial of renal denervation for resistant hypertension. N. Engl. J. Med. 370, 1393\u20131401 (2014).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nStavrakis, S. et al. Low-level vagus nerve stimulation suppresses post-operative strial fibrillation and inflammation: a randomized study. JACC Clin. Electrophysiol. 3, 929\u2013938 (2017).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nYu, L. et al. Optogenetic modulation of cardiac sympathetic nerve activity to prevent ventricular arrhythmias. J. Am. Coll. Cardiol. 70, 2778\u20132790 (2017).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLiu, J. S. et al. Antibody-conjugated gold nanoparticles as nanotransducers for second near-infrared photo-stimulation of neurons in rats. Nano Converg. 9, 13 (2022).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nYe, T. et al. Precise modulation of gold nanorods for protecting against malignant ventricular arrhythmias via near-infrared neuromodulation. Adv. Funct. Mater. 29, 1902128 (2019).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nZhang, L. et al. AIEgen-based covalent organic frameworks for preventing malignant ventricular arrhythmias via local hyperthermia therapy. Adv. Mater. 35, 2304620 (2023).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nPrescott, E. D. & Julius, D. A modular PIP2 binding site as a determinant of capsaicin receptor sensitivity. Science 300, 1284\u20131288 (2003).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMaingret, F. et al. TREK\u20101 is a heat\u2010activated background K+ channel. EMBO J. 19, 2483\u20132491 (2000).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nGrandl, J. et al. Temperature-induced opening of TRPV1 ion channel is stabilized by the pore domain. Nat. Neurosci. 13, 708\u2013714 (2010).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nJiang, Y. Y. & Pu, K. Y. Multimodal biophotonics of semiconducting polymer nanoparticles. Acc. Chem. Res. 51, 1840\u20131849 (2018).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nZhao, B. et al. Liquid-metal-assisted programmed galvanic engineering of core-shell nanohybrids for microwave absorption. Adv. Funct. Mater. 33, 2302172 (2023).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nYang, N. L. et al. A general in-situ reduction method to prepare core-shell liquid-metal/metal nanoparticles for photothermally enhanced catalytic cancer therapy. Biomaterials 277, 121125 (2021).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nJackson, C. et al. Electronic metal-support interaction enhanced oxygen reduction activity and stability of boron carbide supported platinum. Nat. Commun. 8, 15802 (2017).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDuan, L. et al. Liquid-metal molecular scissors. ACS Appl. Mater. Interfaces 16, 4212\u20134221 (2024).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLiu, C. et al. Enhanced energy storage in chaotic optical resonators. Nat. Photonics 7, 474\u2013479 (2013).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nGreffet, J. J. et al. Coherent emission of light by thermal sources. Nature 416, 61\u201364 (2002).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMann, D. et al. Electrically driven thermal light emission from individual single-walled carbon nanotubes. Nat. Nanotechnol. 2, 33\u201338 (2007).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nGranqvist, C. G. Radiative heating and cooling with spectrally selective surfaces. Appl. Opt. 20, 2606\u20132615 (1981).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMa, J. X. et al. In vitro model to investigate communication between dorsal root ganglion and spinal cord glia. Int. J. Mol. Sci. 22, 9725 (2021).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nZyrianova, T. et al. K2P2.1 (TREK-1) potassium channel activation protects against hyperoxia-induced lung injury. Sci. Rep. 10, 22011 (2020).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nJayaprakash, N. et al. Organ- and function-specific anatomical organization of vagal fibers supports fascicular vagus nerve stimulation. Brain Stimul. 16, 484\u2013506 (2023).\n\nArticle\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nZhou, Z. et al. Metabolism regulator adiponectin prevents cardiac remodeling and ventricular arrhythmias via sympathetic modulation in a myocardial infarction model. Basic Res. Cardiol. 117, 34 (2022).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nde Lemos, J. A. Increasingly sensitive assays for cardiac troponins: a review. JAMA 309, 2262\u20132269 (2013).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBazoukis, G., Stavrakis, S. & Armoundas, A. A. Vagus nerve stimulation and inflammation in cardiovascular disease: a state-of-the-art review. J. Am. Heart Assoc. 12, e030539 (2023).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKiss, A. et al. Vagal nerve stimulation reduces infarct size via a mechanism involving the alpha-7 nicotinic acetylcholine receptor and downregulation of cardiac and vascular arginase. Acta Physiol. 221, 174\u2013181 (2017).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nSchwartz, P. J. & Ackerman, M. J. Cardiac sympathetic denervation in the prevention of genetically mediated life-threatening ventricular arrhythmias. Eur. Heart J. 43, 2096\u20132102 (2022).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nPark, J. J. et al. Effect of \u03b2\u2010blockers beyond 3 years after acute myocardial infarction. J. Am. Heart Assoc. 7, e007567 (2018).\n\nArticle\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nByrne, R. A. et al. 2023 ESC guidelines for the management of acute coronary syndromes. Eur. Heart J. 44, 3720\u20133826 (2023).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nZhang, S. et al. Ultrasound-guided injection of botulinum toxin type A blocks cardiac sympathetic ganglion to improve cardiac remodeling in a large animal model of chronic myocardial infarction. Heart Rhythm 19, 2095\u20132104 (2022).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMancia, G. & Grassi, G. The autonomic nervous system and hypertension. Circ. Res. 114, 1804\u20131814 (2014).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nJiang, Y. Q. et al. The role of age-associated autonomic dysfunction in inflammation and endothelial dysfunction. GeroScience 44, 2655\u20132670 (2022).\n\nArticle\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBruneau, M. & George, B. The juxtacondylar approach to the jugular foramen. Oper. Neurosurg. 63, 75\u201380 (2008).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nChen, M. X. et al. Low-level vagus nerve stimulation attenuates myocardial ischemic reperfusion injury by antioxidative stress and antiapoptosis reactions in canines. J. Cardiovasc. Electrophysiol. 27, 224\u2013231 (2016).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWalker, M. J. A. et al. The Lambeth conventions: guidelines for the study of arrhythmias in ischaemia, infarction, and reperfusion. Cardiovasc. Res. 22, 447\u2013455 (1988).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nYu, L. et al. Chronic intermittent low-level stimulation of tragus reduces cardiac autonomic remodeling and ventricular arrhythmia inducibility in a post-infarction canine model. JACC Clin. Electrophysiol. 2, 330\u2013339 (2016).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDalonzo, A. J. et al. Effects of cromakalim or pinacidil on pacing- and ischemia-induced ventricular fibrillation in the anesthetized pig. Basic Res. Cardiol. 89, 163\u2013176 (1994).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLai, Y. et al. Non-invasive transcutaneous vagal nerve stimulation improves myocardial performance in doxorubicin-induced cardiotoxicity. Cardiovasc. Res. 118, 1821\u20131834 (2022).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDownload references",
+            "section_image": []
+        },
+        {
+            "section_name": "Acknowledgements",
+            "section_text": "The research was supported by the National Natural Science Foundation of China (Grants 22025303: L.F., 82241057: L.L.Y., 82270532: L.L.Y., and 82200556: L.P.Z.); and the National Key Research and Development Program of China (Grant 2023YFC2705705: L.F.); and Foundation for Innovative Research Groups of Natural Science Foundation of Hubei Province, China (Grant 2021CFA010: L.L.Y.); and the Interdisciplinary\u00a0Innovative Talents Foundation from Renmin Hospital of Wuhan University (Grant JCRCFZ-2022-005: H.J.). We thank the Core Facility of Wuhan University for their substantial support in sample characterization, including SEM, XPS, DLS, and XRD. We thank the Center for Electron Microscopy at Wuhan University for their support of STEM, HRTEM, and EDX characterization. We also thank Meimei Zhang in the Institute for Advanced Studies of Wuhan University for their assistance in TEM characterization.",
+            "section_image": []
+        },
+        {
+            "section_name": "Author information",
+            "section_text": "These authors contributed equally: Chenlu Wang, Liping Zhou, Chengzhe Liu.\n\nCollege of Chemistry and Molecular Sciences, Wuhan University, Wuhan, China\n\nChenlu Wang,\u00a0Luyang Wang,\u00a0Yaxi Liu,\u00a0Bi Xu,\u00a0Mengqi Zeng\u00a0&\u00a0Lei Fu\n\nDepartment of Cardiology, Renmin Hospital of Wuhan University, Wuhan, China\n\nLiping Zhou,\u00a0Chengzhe Liu,\u00a0Jiaming Qiao,\u00a0Xinrui Han,\u00a0Qinfang Qiu,\u00a0Zizhuo Zhang,\u00a0Jiale Wang,\u00a0Xiaoya Zhou\u00a0&\u00a0Lilei Yu\n\nHubei Key Laboratory of Autonomic Nervous System Modulation, Wuhan, China\n\nLiping Zhou,\u00a0Chengzhe Liu,\u00a0Jiaming Qiao,\u00a0Xinrui Han,\u00a0Qinfang Qiu,\u00a0Zizhuo Zhang,\u00a0Jiale Wang,\u00a0Xiaoya Zhou\u00a0&\u00a0Lilei Yu\n\nCardiac Autonomic Nervous System Research Center of Wuhan University, Wuhan, China\n\nLiping Zhou,\u00a0Chengzhe Liu,\u00a0Jiaming Qiao,\u00a0Xinrui Han,\u00a0Qinfang Qiu,\u00a0Zizhuo Zhang,\u00a0Jiale Wang,\u00a0Xiaoya Zhou\u00a0&\u00a0Lilei Yu\n\nHubei Key Laboratory of Cardiology, Wuhan, China\n\nLiping Zhou,\u00a0Chengzhe Liu,\u00a0Jiaming Qiao,\u00a0Xinrui Han,\u00a0Qinfang Qiu,\u00a0Zizhuo Zhang,\u00a0Jiale Wang,\u00a0Xiaoya Zhou\u00a0&\u00a0Lilei Yu\n\nCardiovascular Research Institute, Wuhan University, Wuhan, China\n\nLiping Zhou,\u00a0Chengzhe Liu,\u00a0Jiaming Qiao,\u00a0Xinrui Han,\u00a0Qinfang Qiu,\u00a0Zizhuo Zhang,\u00a0Jiale Wang,\u00a0Xiaoya Zhou\u00a0&\u00a0Lilei Yu\n\nTaikang Center for Life and Medical Sciences, Wuhan University, Wuhan, China\n\nLiping Zhou,\u00a0Chengzhe Liu,\u00a0Jiaming Qiao,\u00a0Xinrui Han,\u00a0Qinfang Qiu,\u00a0Zizhuo Zhang,\u00a0Jiale Wang,\u00a0Xiaoya Zhou,\u00a0Lilei Yu\u00a0&\u00a0Lei Fu\n\nInstitute of Molecular Medicine, Renmin Hospital of Wuhan University, Wuhan, China\n\nLiping Zhou,\u00a0Chengzhe Liu,\u00a0Jiaming Qiao,\u00a0Xinrui Han,\u00a0Qinfang Qiu,\u00a0Zizhuo Zhang,\u00a0Jiale Wang,\u00a0Xiaoya Zhou,\u00a0Lilei Yu\u00a0&\u00a0Lei Fu\n\nThe Institute for Advanced Studies, Wuhan University, Wuhan, China\n\nLei Fu\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nL.F., L.L.Y., and M.Q.Z. conceived the research concept. L.F., L.L.Y., M.Q.Z., and X.Y.Z. supervised the research; C.L.W., L.P.Z., C.Z.L., J.M.Q., X.R.H., B.X., Q.F.Q., Z.Z.Z., and J.L.W. performed the experiments; C.L.W., L.P.Z., C.Z.L., L.Y.W., and Y.X.L. discussed the results; C.L.W., L.P.Z., and C.Z.L. analyzed the data and co-wrote the manuscript. All authors commented on the manuscript.\n\nCorrespondence to\n                Xiaoya Zhou, Lilei Yu or Lei Fu.",
+            "section_image": []
+        },
+        {
+            "section_name": "Ethics declarations",
+            "section_text": "The authors declare no competing interests.",
+            "section_image": []
+        },
+        {
+            "section_name": "Peer review",
+            "section_text": "Nature Communications thanks David J. Lundy, and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. A peer review file is available.",
+            "section_image": []
+        },
+        {
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+            "section_text": "Open Access  This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article\u2019s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article\u2019s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.\n\nReprints and permissions",
+            "section_image": []
+        },
+        {
+            "section_name": "About this article",
+            "section_text": "Wang, C., Zhou, L., Liu, C. et al. Pt nanoshells with a high NIR-II photothermal conversion efficiency mediates multimodal neuromodulation against ventricular arrhythmias.\n                    Nat Commun 15, 6362 (2024). https://doi.org/10.1038/s41467-024-50557-w\n\nDownload citation\n\nReceived: 01 March 2024\n\nAccepted: 16 July 2024\n\nPublished: 28 July 2024\n\nVersion of record: 28 July 2024\n\nDOI: https://doi.org/10.1038/s41467-024-50557-w\n\nAnyone you share the following link with will be able to read this content:\n\nSorry, a shareable link is not currently available for this article.\n\n\n\n\n                            Provided by the Springer Nature SharedIt content-sharing initiative\n                        ",
+            "section_image": [
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+            ]
+        },
+        {
+            "section_name": "This article is cited by",
+            "section_text": "Communications Chemistry (2025)",
+            "section_image": []
+        }
+    ]
+}

07d4a546b84977cbe671fd9636cce724b9118c33a913f81362f52341cbf8a751/metadata.json

@@ -0,0 +1,127 @@
+{
+    "title": "Spin Seebeck in the weakly exchange-coupled Van der Waals antiferromagnet across the spin-flip transition",
+    "pre_title": "Spin Seebeck in the weak exchange coupled van der Waals antiferromagnet",
+    "journal": "Nature Communications",
+    "published": "28 March 2025",
+    "supplementary_0": [
+        {
+            "label": "Supplementary Information",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-58306-3/MediaObjects/41467_2025_58306_MOESM1_ESM.pdf"
+        },
+        {
+            "label": "Transparent Peer Review file",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-58306-3/MediaObjects/41467_2025_58306_MOESM2_ESM.pdf"
+        }
+    ],
+    "supplementary_1": NaN,
+    "supplementary_2": NaN,
+    "source_data": [
+        "https://doi.org/10.6084/m9.figshare.28557785"
+    ],
+    "code": [],
+    "subject": [
+        "Spintronics"
+    ],
+    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
+    "preprint_pdf": "https://www.researchsquare.com/article/rs-5308219/v1.pdf?c=1743246332000",
+    "research_square_link": "https://www.researchsquare.com//article/rs-5308219/v1",
+    "nature_pdf": "https://www.nature.com/articles/s41467-025-58306-3.pdf",
+    "preprint_posted": "27 Oct, 2024",
+    "research_square_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Spin Seebeck effect (SSE) refers to the creation of spin currents due to a temperature gradient in the magnetic materials or across magnet-normal metal interfaces, which can be electrically detected through the inverse spin Hall effect (ISHE) when in contact with heavy metals. It offers fundamental insights into the magnetic properties of materials, including the magnetic phase transition, static magnetic order, and magnon excitations. However, the SSE in van der Waals antiferromagnet is still elusive, especially across the spin-flip transition. Here, we demonstrate the SSE in the weak exchange coupled van der Waals antiferromagnet CrPS4. The SSE increases as the magnetic field increases before the spin-flip transition due to the enhancement of the thermal spin current as a function of the applied field. A peak of SSE is observed at the spin-flip field, which is related to the magnon mode edges across the spin-flip field. Our results extend SSE research to van der Waals antiferromagnets and demonstrate an enhancement of SSE at the spin-flip transition.Physical sciences/Physics/Condensed-matter physics/SpintronicsPhysical sciences/Materials science/Condensed-matter physics/Spintronics",
+            "section_image": []
+        },
+        {
+            "section_name": "Additional Declarations",
+            "section_text": "There is NO Competing Interest.",
+            "section_image": []
+        },
+        {
+            "section_name": "Supplementary Files",
+            "section_text": "SupportingInformation.pdf",
+            "section_image": []
+        }
+    ],
+    "nature_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Spin Seebeck effect refers to the creation of spin currents due to a temperature gradient in the magnetic materials or across magnet-normal metal interfaces, which can be electrically detected through the inverse spin Hall effect when in contact with heavy metals. It offers fundamental insights into the magnetic properties of materials, including the magnetic phase transition, static magnetic order, and magnon excitations. The behavior of the spin Seebeck effect across the spin-flop transition has been extensively studied, whereas the spin Seebeck effect across the spin-flip transition remains poorly understood. Here, we demonstrate the spin Seebeck effect in a weakly exchange-coupled van der Waals antiferromagnet CrPS4. The spin Seebeck effect increases as the magnetic field increases before the spin-flip transition due to the enhancement of the thermal spin current as a function of the applied field. A peak of spin Seebeck effect is observed at the spin-flip field, which is related to the magnon mode edges across the spin-flip field. Our results extend spin Seebeck effect research to van der Waals antiferromagnets and demonstrate an enhancement of spin Seebeck effect at the spin-flip transition.",
+            "section_image": []
+        },
+        {
+            "section_name": "Introduction",
+            "section_text": "Thermoelectricity combines heat transfer and electric voltage in solid materials, presenting a promising option for green energy production by harnessing waste heat with a simple device design1. In particular, the thermal spintronics effect utilizes nonequilibrium magnon transport phenomena in the presence of a heat gradient, enabling magnetic insulators to serve as effective thermoelectric devices2. The spin Seebeck effect (SSE) has therefore drawn significant interest, where a temperature gradient (\u2207T) in magnetic materials leads to the generation of spin currents (Js). SSE can be subsequently detected via the inverse spin Hall effect (ISHE) in a heavy metal contact with strong spin-orbit coupling3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24.\n\nIn ferromagnet/heavy metal bilayers, the SSE observed below the Curie temperature is associated with the spin current generated by thermally excited magnons that exhibit only right-handed chirality19. The SSE mechanism in antiferromagnetic heterostructures is more complex due to two magnetic sublattices, which result in different magnon modes20,21,22,23. In a uniaxial antiferromagnet, there are two magnon branches with opposite chirality carrying opposite angular momentum. These modes degenerate at zero magnetic fields, meaning there is no net magnon current until a field is applied to lift this degeneracy. A change in the sign of the SSE was observed during the spin-flop transition14,15, which is attributed to the change in the chirality of the thermally excited magnon mode, which dominates. Additionally, the interfacial N\u00e9el coupling and spin conductance can influence the sign and magnitude of the SSE21,23. Recent studies have explored magnon transport and interfacial spin transport in MnPS325, as well as spin caloritronics in CrBr326, CrI3/NiCl227. More recent work has also investigated magnon transport in CrPS428,29,30. Especially, in Ref. 29, in addition to discovering nonlocal magnon transport of CrPS4/Pt with in-plane magnetic field across the spin-flip transition, a distinct peak of SSE signal around the spin-flip transition and a sign change of non-local SSE signal below 15\u2009K were observed but the mechanism remains to be understood29. Although the SSE is not the main focus of Ref. 29, it is nonetheless a pioneering study on the magnetic field dependence (especially spin flip) of this effect in CrPS4. These latest results indicate that the spin Seebeck effect in van der Waals antiferromagnets, especially across the spin-flip transition, remains an area requiring further investigation31,32. This is particularly relevant for van der Waals systems with interlayer antiferromagnetic coupling, where the weak exchange coupling and low spin-flip fields are typically observed.\n\nCrPS4 is an antiferromagnetic van der Waals material constituted of chains of chromium octahedra interconnected through phosphorus33,34,35,36,37,38,39 as shown in Fig.\u00a01a. Due to the chemical composition and multi-bonded crystal structures, CrPS4 is a comparably air-stable material that makes the device fabrication easier compared with other van der Waals materials40. It shows a sizeable N\u00e9el temperature (TN=36 K) and A-type antiferromagnetic ordering33. Unlike the conventional bulk antiferromagnetic materials, CrPS4 with a layered structure exhibits extremely weak interlayer interactions between sublattice spins, where spins within each monolayer are aligned ferromagnetically out of the plane, subsequently leading to the weak spin-flop field (0.8\u2009T at 15\u2009K) and spin-flip field (7\u2009T at 15\u2009K) as shown in Fig.\u00a01b. This characteristic also significantly lowers the frequency of antiferromagnetic magnons to the GHz range41. As a result, it provides easier access to antiferromagnetic dynamics. Notably, it improves the efficiency of the thermal magnon population compared to traditional antiferromagnets with a large magnon gap, making CrPS4 an excellent candidate for investigating the mechanism of SSE in antiferromagnets.\n\na Crystal structure of CrPS4. The red and blue arrows indicate the direction of the magnetic moment. b The magnetic measurements at 15\u2009K are taken both along and perpendicular to the c-axis. The spin-flop and spin-flip transitions appear when the magnetic field is aligned with the c-axis. In contrast, only the spin-flip transition occurs when the field is applied perpendicularly to the c-axis, c Schematic of the Hall bar devices for the longitudinal spin Seebeck effect. The alternating current heats the sample, creating a vertical heat gradient and generating a spin current perpendicular to the sample plane. d Angular dependence (in the xz plane) of Rxy2\u03c9 at different fields at a temperature of 15\u2009K and an applied current of 1\u2009mA (peak value). e Applied current dependence of Rxy2\u03c9 (at 9\u2009T) at 15\u2009K. The dashed-dot line is the linear fit.\n\nHere, we investigate the SSE in CrPS4 in contact with a heavy metal. A vertical temperature gradient in CrPS4 drives the magnon current in the longitudinal SSE configuration. The SSE increases as a function of the applied field before the spin-flip transition. The enhancement of the canted magnetization leads to a pronounced magnon pumping. At the spin-flip field, a peak of SSE is observed that further disappears above the N\u00e9el temperature. A theoretical model indicates that the linear increase of SSE with increasing magnetic field below the spin-flip transition is dominated by the spin canting angle, while the decrease of SSE with further increasing magnetic field above the spin-flip transition is dominated by increased energy of magnon modes.",
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+        {
+            "section_name": "Results",
+            "section_text": "High-quality CrPS4 single crystals are used to fabricate the devices, with magnetic properties shown in Supplementary Fig.\u00a0S1. To obtain CrPS4/Pt heterostructures for the SSE measurements, we deposited 5\u2009nm Pt on top of exfoliated CrPS4 flakes and subsequently fabricated Hall bar devices (see methods for details and schematic in Fig.\u00a01c). The structure and phase of the CrPS4 are characterized with X-ray Diffractometer and Raman spectroscopy (details see Supplementary Fig.\u00a0S2). The microscopic picture of the CrPS4/Pt Hall bar device can be found in Supplementary Fig.\u00a0S3, where one could obtain the thickness of the CrPS4 flake to be 75\u2009nm. The high-quality interface of the CrPS4/Pt heterostructure has been clearly demonstrated through cross-sectional transmission electron microscopy, as shown in Supplementary Fig.\u00a0S4. An alternating current (I~) is applied to the Hall bar to generate vertical temperature gradient \u2207T, leading to the population of spin current Js=\u2212S\u2207T. S is the SSE coefficient. By further applying a magnetic field, it is possible to observe the SSE detected via the inverse spin Hall effect. The resultant electric field EISHE is given by3\n\nWhere \u03b8SH is the spin Hall angle.\u03c3 is the spin polarization direction, which is parallel to the equilibrium magnetization M. Since the temperature gradient results from the heating power of Pt, which is proportional to I~2=I0sin2(\u03c9t), it is expected that the thermal signal can be detected through the second harmonic response Rxy2\u03c9=Vxy2\u03c9/I0.\n\nIn the magnetic material/Pt bilayer system, Rxy2\u03c9 typically involves different factors, including current-induced torque and thermal effects, which encompass the Nernst and spin Seebeck effects42. The electric field induced by the Nernst effect can be expressed as ENE\u221d\u2207T\u00d7M43, which shares the same symmetry as SSE in the longitudinal configuration. When a strong magnetic field is applied, the current-induced torque is suppressed42, leaving only thermal effects in the second harmonic response Rxy2\u03c9. Figure\u00a01d illustrates the angular dependence of Rxy2\u03c9 in the xz plane under different applied fields with the applied current of 1\u2009mA (peak value) and the ambient temperature (chamber temperature) of 15\u2009K. Rxy2\u03c9 reaches the maximum when the magnetic field is aligned with the x-axis and disappears when aligned with the z-axis (or c-axis), and the angular dependence data can be fitted well using the sine function following the Eq. (1). By applying an in-plane magnetic field, the Zeeman splitting lifts the degeneracy of the two magnon eigenmodes, resulting in the spin current that induces the SSE signal. In the canted phase, the SEE increases with the strength of the applied magnetic field, similar to the local SSE signal in Ref. 29. This increase is generally attributed to the larger canted magnetization resulting from a strong magnetic field23,44 or the increased SSE coefficient in response to the magnetic field45. This fundamentally differs from the SSE in ferromagnets, where an increased applied field would open the magnon gap, causing a decrease in SSE due to the reduction of the thermal magnon population4. Additionally, the magnitude of Rxy2\u03c9 is proportional to the applied current as shown in Fig.\u00a01e, demonstrating a thermoelectric nature similar to previous findings46. It is important to note that CrPS4 has a semiconducting characteristic with an energy gap of Ea=1.4eV33, which yields a very high resistivity and prevents the electrical conduction through CrPS4 at low temperature28, allowing us to safely rule out the Nernst effect from conducting electrons in CrPS4.\n\nTo better distinguish the SSE from other spurious effects, we utilize Pt and Ta in the two Hall bar devices (Fig.\u00a02a and b). Due to the opposite spin Hall angles47, the thermally generated spin current should yield SSE signals with opposite polarities in Pt and Ta samples. In contrast, other magnetic thermoelectric effects, such as the Nernst effect arising from the proximity effect48, retain the same polarity in both Pt and Ta. As illustrated in Fig.\u00a02c and d, the Rxy2\u03c9 shows the opposite polarities in Pt and Ta samples, suggesting that the phenomenon originates from the SSE. As the temperature increases, the strength of the SSE decreases, and the SSE remains present even at temperatures exceeding the TN of CrPS4. A more apparent trend is illustrated in Fig.\u00a02e. Although the propagation of spin waves without magnetic interactions is not permitted in the paramagnetic phase, short-range magnetic interactions still facilitate short-wavelength magnetic excitations, resulting in the paramagnetic SSE16. In addition to the increase in Rxy2\u03c9 with the applied field, peaks of Rxy2\u03c9 are observed in both samples at varying temperatures. Similar effects are observed in the sample with a different Pt thickness (see Supplementary Fig.\u00a0S5 for details) and also seen in local and non-local SSE signals in Ref. 29, which confirm the robustness of this effect. The magnetic field at which the Rxy2\u03c9 peak occurs aligns with the spin-flip field of CrPS4, as illustrated in Fig.\u00a02f, suggesting a strong connection between the Rxy2\u03c9 peak and the magnetic phase transition induced by the magnetic field. We note that the proximity effect could potentially lead to magnetization of the Pt layer, which might contribute to the Nernst effect. However, since the peak in Rxy2\u03c9 disappears above TN, while the proximity effect would still be present, we conclude that the proximity effect does not contribute to the observed peak in Rxy2\u03c9. The longitudinal resistances for CrPS4/Pt and CrPS4/Ta are ~ 600 \u03a9 and 1560\u03a9 respectively, with applied currents of 1\u2009mA and 0.6\u2009mA for the two samples. This results in a higher heating power in CrPS4/Pt, causing a larger temperature difference between the sample and the variable temperature insert (VTI) chamber. There is expected to be a shift in the spin-flip field for the samples with and without heating at the same VTI chamber temperatures, and this discrepancy will become more pronounced at lower temperatures (see Fig.\u00a02f and also Supplementary Fig.\u00a0S5 for the current dependence of SSE). A numerical simulation of the temperature distribution in the device can be seen in Supplementary Fig.\u00a0S6. The simulation shows that a temperature change of about 4\u2009K is induced in CrPS4 via Joule heating under the experimental conditions, in good agreement with the observed change in the spin-flip field. The simulation also shows a prominent temperature gradient in the CrPS4 layer (~4.2\u2009\u00d7\u2009106\u2009K/m), which is the basis for the observed SSE.\n\na, b The schematics of spin Seebeck effect in CrPS4 in contact with Pt and Ta, the differing signs of the spin Hall angle result in a change in the sign of the SSE. c, d Field dependence (\u03bc0Hx) of Rxy2\u03c9 at various temperatures for both CrPS4/Pt (5\u2009nm) (applied current of 1\u2009mA) and CrPS4/Ta (11\u2009nm) (applied current of 0.6\u2009mA). e Temperature dependence of the SSE effective resistance in CrPS4/Pt at 9\u2009T, along with the magnetization as a function of temperature under a 50 mT applied field. The N\u00e9el temperature (TN) is identified as 36\u2009K, however, the SSE signal continues to be present even above TN. f The field of the Rxy2\u03c9 peak decreases with increasing temperature (blue star and red square), which is similar to the temperature dependence of the spin-flip transition field (black circle).\n\nThe peak of Rxy2\u03c9 observed at the spin-flip field is intriguing, as it is not associated with the static magnetic moment, which would not exhibit an increased canted magnetization during the spin-flip transition, as illustrated in Fig.\u00a03a. In Fig.\u00a03b, the angular dependence (in the xz plane) of Rxy2\u03c9 is shown as the applied field approaches the spin-flip transition at a temperature of 15\u2009K and an applied current of 1\u2009mA in the CrPS4/Pt. The curves can be well-fitted with the sine function according to Eq.(1), with a maximum observed at 6.8\u2009T, indicating that the peak originates from the SSE. Additionally, the SSE continues to be present above TN, while the peak of Rxy2\u03c9 disappears beyond TN (see Fig.\u00a02c, d). Although the paramagnetic phase could exhibit a SSE, the loss of long-range ordering above the TN causes the spin-flip transition to disappear. This highlights the significant connection between the peak of SSE and the spin-flip transition.\n\na Comparison of the field dependence of Rxy2\u03c9 in CrPS4/Pt (obtained at 15\u2009K) and magnetic moment CrPS4 flake (measured at 20\u2009K). b Angular dependence (in the xz plane) of Rxy2\u03c9 when the applied field approaches the spin-flip field at a temperature of 15\u2009K and an applied current of 1\u2009mA. c Magnon mode edges (k\u2009=\u20090) as a function of the applied field perpendicular to the c axis. The inset shows the simulated magnetic moment as a function of the magnetic field. d The canted magnetization of \u03c9\u03b1 mode processes around the applied field, while that of \u03c9\u03b2 mode oscillates in the direction of the applied field.\n\nThe SSE signal involves the following three physical processes: first, the temperature gradient excites the magnetization dynamics, leading to a non-equilibrium magnon current; second, the magnon current is transformed into a conduction-electron spin current through the s-d interaction, which travels across the interface connected to the metal; finally, the spin current is converted into a charge current via the ISHE. We highlight the efficient spin transport at the interface of CrPS4 and sputtered Pt, as recent studies on CrPS4/Pt have demonstrated effective magnon transport28,29,30,49. Notably, detecting the spin current is not crucial for the SSE peak, as both the CrPS4/Pt and CrPS4/Ta samples exhibit peaks (see Fig.\u00a02c, d). The only remaining likely mechanism for the SSE peak is related to the pumped spin current Js from the antiferromagnet into heavy metals which includes the effect of both thermal magnon excitation and interfacial spin mixing conductance49.\n\nConsidering the canted magnetic phase, the magnetic field dependence of magnon frequency can be obtained by diagonalizing the spin Hamiltonian50 with eigenfrequencies51. Before the spin-flip field, \u03bc0H\u22642\u03bc0HE+\u03bc0HA,\n\nAfter the spin-flip field, \u03bc0H>2\u03bc0HE+\u03bc0HA,\n\nwhere \u03bc0H, \u03bc0HE, and \u03bc0HA represent the applied in-plane field, interlayer exchange field, and anisotropic field along the c-axis, respectively. The simplified model only considers the anisotropic field along the c-axis. \u03c9\u03b1 and \u03c9\u03b2 are the two magnon modes. \u03b3 is the gyromagnetic ratio and \u03c6 is the canted angle along the c-axis applied in the plane field, \u03c6=arcsin\u2061\u03bc0H2\u03bc0HE+\u03bc0HA.\n\nThe field dependence of the magnon mode frequency is plotted in Fig.\u00a03c with parameters \u03bc0HE=3.5T and \u03bc0HA=0.12 T41. The \u03c9\u03b1 mode has the potential to transport angular momentum due to the canted magnetization of the mode rotating around the applied magnetic field. This mode is similar to the quasi-ferromagnetic mode that emerges following a spin-flop transition when a magnetic field is applied along the c-axis14. Moreover, the SSE in CrPS4/Pt has the same sign as that in YIG/Pt (see Supplementary Fig.\u00a0S7 for details), suggesting that right-handed magnons (\u03c9\u03b1 mode) are responsible for the SSE signal. In contrast, the \u03c9\u03b2 mode oscillates in the direction of the applied field (see Fig.\u00a03d).\n\nWe further calculate the spin current in the heavy metal following Ref. 23 using a minimal model where the CrPS4 sample is modeled as a one-dimensional antiferromagnetic chain with periodic boundary conditions. The model has an interfacial s-d coupling that couples the localized spins in the antiferromagnet with the itinerant electrons in the heavy metal. Using Fermi\u2019s Golden rule to calculate the transition probability for the spins to be pumped from the antiferromagnet into the heavy metal, the thermal spin current density polarized along the x-axis in the heavy metal is given by Tang & Bauer23\n\nwhere \u039b is a constant depending on the interface and the density of states for the electrons in the heavy metal, \u0394T is the temperature difference across the interface, k is the wave vector of the one-dimensional chain, and \u0394 parametrizes the degree of compensation at the interface; \u0394=0 corresponds to a compensated interface and \u0394=\u00b11 corresponds to a fully uncompensated interface where only one of the two sublattices couple to the heavy metal. The \u03c9\u03b2 mode only contributes to the spin current for an uncompensated interface, reflecting the linearly polarized nature of the mode (see Supplementary Fig.\u00a0S8 for the calculation of the spin current as a function of the applied field).\n\nThe effect of the in-plane magnetic field on the pumped spin current in the heavy metal is twofold: first, the magnetic field increases the canting angle \u03c6, causing a linear increase of the factor sin\u2061\u03c6 in Eq. (6). Physically, this can be interpreted by noting that each of the two sublattices pumps a spin current that on average is polarized along the sublattice equilibrium direction, thus, the measured spin current is given as the projection on the x-axis, which is proportional to sin\u2061\u03c6. Second, the magnetic field changes the magnon frequencies of both magnon modes. Above the spin-flip critical field, the energy of the \u03c9\u03b1 mode and the \u03c9\u03b2 mode increases with the in-plane field. This causes a decrease in the terms inside the sum in the above equation. Importantly, the increase due to the change in canting angle is proportional to sin\u2061\u03c6\u223cH below the critical field and constant above the critical field since the canting angle has reached its maximum at this point. In total, these two effects explain the observed peaks and saturation in SSE of CrPS4/Pt at the spin-flip field.\n\nThe gap closure of the \u03c9\u03b2 mode frequencies at the critical field could further increase the peak observed in the spin Seebeck effect at the critical field for systems with an uncompensated interface. However, to probe the low-frequency excitations, the temperature needs to be smaller than or comparable to the gap energy, which for CrPS4 is 0.4K in units of temperature. Therefore, a sharper peak is expected for temperatures approaching this value (see Supplementary Fig.\u00a0S8 for details).\n\nThe nonlocal configuration is further introduced to explore the SSE in CrPS4/Pt as shown in Fig.\u00a04a (see method and Supplementary Fig.\u00a0S3 for details). An in-plane heat gradient is created by passing current through one of the Pt strips, resulting in a nonequilibrium distribution of magnons. At the detection part, the magnon spin current is injected into Pt, which leads to the SSE. It is worth noting, in this configuration, that the temperature gradient \u2207T is oriented along the x-axis, while the spin current Js flows along the z-axis, differing from the longitudinal SSE previously discussed. Figure\u00a04b shows the field dependence of SSE at different angles (\u03b8) at 5\u2009K with the applied current of 1\u2009mA. By applying the in-plane field (\u03b8=0\u2218), the SSE as a function of the applied field is similar to the longitudinal configuration, and a peak of SSE is also observed at the spin-flip field.\n\na Schematics of nonlocal SSE measurement. b Field dependence of SSE at different angles at 5\u2009K with the applied current of 1\u2009mA. Inset shows the field dependence SSE when the applied field is slightly off the c-axis (z-axis).\n\nA weak SSE response occurs when the applied field is close to the z-axis, with nominal angles of \u03b8\u2009=\u200992\u00b0 and 87\u00b0. Typically, the SSE should not be present when the field is directed along the z-axis, as the parallel alignment of spin polarization \u03c3 and spin currents Js does not generate a SSE voltage. However, a slight deviation from the z-axis in the direction of the applied field results in a finite value of Js\u00d7\u03c3, since the spin polarization aligns with the canted magnetization. This accounts for the observed positive and negative SSE at strong positive fields when \u03b8\u2009=\u200987\u00b0 and 92\u00b0, respectively. The plateau in the SSE is observed before the spin-flop transition, as there is no x-component of the canted magnetization. In particular, one could also find a peak of SSE at the spin-flop field, which is attributed to the divergence of spin conductance as the magnon gap closes approaching the spin-flop transition49. Similar effects are also observed in the longitudinal SSE configuration (see Supplementary Fig.\u00a0S5 for details).",
+            "section_image": [
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+            ]
+        },
+        {
+            "section_name": "Discussion",
+            "section_text": "We report evidence of the SSE in a weakly interlayer exchange-coupled van der Waals antiferromagnet CrPS4 in contact with the heavy metal. We showed how the SSE is substantially enhanced by tuning the magnetic field. In particular, we observe a peak of SSE which shares the same temperature dependence as the spin-flip transition of CrPS4 when applying magnetic field perpendicular to the c-axis. By considering the thermal spin current density into the heavy metal, we conclude that the SSE peak is related to the magnon mode edges as a function of the applied field across the spin-flip field.\n\nField-induced peaks in SSE were also observed in Y3Fe5O12/Pt52, Lu2BiFe4GaO12/Pt53, Fe3O4/Pt54, and Cr2O3/Pt55 bilayers. These peaks in SSE arise when the magnetic field adjusts the magnon energy to the point of anticrossing between the magnon and phonon dispersion curves, creating magnon-polarons52. The combined magnetoelastic excitation couples the long-lasting acoustic phonons in single crystals with the short-lived magnons, increasing the magnon lifetime and the associated SSE53. The SSE peak in CrPS4/Pt (Ta) exhibits similar field-like behaviors, but it arises from a mechanism involving the magnon mode and spin conductance. Given that the SSE peak in CrPS4/Pt (Ta) is observed at low temperatures where the phonon population is frozen, we do not expect the magnon-polarons to dominate the signal our samples.\n\nThe SSE is a sensitive tool for investigating the interfacial spin conductance and magnon population across various materials. Our findings indicate that the magnon spin transport in CrSP4/Pt(Ta) can be effectively modulated through adjustments in temperature and applied magnetic field, particularly at the spin-flip field. This approach paves the way for innovative magnonic devices that utilize weakly exchange-coupled van der Waals antiferromagnetic materials.",
+            "section_image": []
+        },
+        {
+            "section_name": "Methods",
+            "section_text": "CrPS4\u00a0single crystals are synthesized\u00a0using\u00a0chemical vapor transport technique. Chromium (Aladdin,99.99%), red phosphorus (Aladdin,99.999%), and sulfur (Aladdin,99.999%) powders were measured in a stoichiometric ratio of 1:1:4 and combined with 5% more sulfur as transport agents. The mixed powders were sealed in a quartz tube and placed in a two-zone furnace, where the temperatures at the source and sink ends were maintained at 923\u2009K and 823\u2009K for a duration of 7 days. The atomic structure was analyzed using X-ray diffraction (XRD) with Cu K\u03b1 radiation (\u03bb\u2009=\u20091.54056\u2009\u00c5). The magnetic properties were measured using a Superconducting Quantum Interference Device (SQUID). The CrPS4 flakes were mechanically exfoliated from the single crystals using adhesive tape and transferred onto a SiO2/Si substrate. CrPS4/Pt(Ta) samples were prepared with the magnetron sputtering in a vacuum of approximately 6\u2009\u00d7\u200910\u22128 torr. The thickness of the Pt layer is 5\u2009nm, while the Ta layer is 15\u2009nm; 5\u2009nm of Ta will oxidize in air, leaving 10\u2009nm of Ta to facilitate the inverse spin Hall effect for detecting spin current generation. The Hall bar with 10\u2009\u03bcm in width and 25\u2009\u03bcm in length was fabricated using photolithography followed by ion beam etching. The width of the heater and the detection Pt strips are designed to be 1.4\u2009\u03bcm and 2.3\u2009\u03bcm, the distance of the two stipes is 1.6\u2009\u03bcm in the nonlocal device. An atomic force microscopy image of the samples is provided in Supplementary Information Fig. S3, showing the thickness of the CrPS4 flake in the Hall bar device\u00a0to be 75\u2009nm.\n\nThe SSE is measured at different temperatures by varying the magnetic field in the Physical Properties Measurement System (PPMS-9T). An alternating current ranging from 0.4 to 1\u2009mA at a frequency of 13\u2009Hz was supplied to the Hall bar or nonlocal device using a Keithley 6221 instrument, while the transverse voltage was measured with a lock-in amplifier (SR830).",
+            "section_image": []
+        },
+        {
+            "section_name": "Data availability",
+            "section_text": "The data that support the findings of this study are available in figshare with the identifier https://doi.org/10.6084/m9.figshare.28557785.",
+            "section_image": []
+        },
+        {
+            "section_name": "References",
+            "section_text": "Zoui, M. A., Bentouba, S., Stocholm, J. G. & Bourouis, M. A review on thermoelectric generators: progress and applications. Energies 13, 3606 (2020).\n\nHirohata, A. et al. Review on spintronics: principles and device applications. J. Magn. Magn. Mater. 509, 166711 (2020).\n\nArticle\u00a0\n    CAS\u00a0\n    MATH\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nAdachi, H., Uchida, K.-i, Saitoh, E. & Maekawa, S. Theory of the spin Seebeck effect. Rep. Prog. Phys. 76, 036501 (2013).\n\nArticle\u00a0\n    ADS\u00a0\n    PubMed\u00a0\n    MATH\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKikkawa, T. & Saitoh, E. Spin Seebeck effect: sensitive probe for elementary excitation, spin correlation, transport, magnetic order, and domains in solids. Annu. Rev. Condens. Matter Phys. 14, 129\u2013151 (2023).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    MATH\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nUchida, K. et al. Observation of the spin Seebeck effect. Nature 455, 778\u2013781 (2008).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    MATH\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nUchida, K. et al. Spin Seebeck insulator. Nat. Mater. 9, 894\u2013897 (2010).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    MATH\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nUchida, K.-i et al. Observation of longitudinal spin-Seebeck effect in magnetic insulators. Appl. Phys. Lett. 97, 172505 (2010).\n\nArticle\u00a0\n    ADS\u00a0\n    MATH\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nCornelissen, L. J., Liu, J., Duine, R. A., Youssef, J. B. & van Wees, B. J. Long-distance transport of magnon spin information in a magnetic insulator at room temperature. Nat. Phys. 11, 1022\u20131026 (2015).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMallick, K., Wagh, A. A., Ionescu, A., Barnes, C. H. W. & Anil Kumar, P. S. Role of spin mixing conductance in determining thermal spin pumping near the ferromagnetic phase transition in EuO1-x and La2NiMnO6. Phys. Rev. B 100, 224403 (2019).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nGepr\u00e4gs, S. et al. Origin of the spin Seebeck effect in compensated ferrimagnets. Nat. Commun. 7, 10452 (2016).\n\nArticle\u00a0\n    ADS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    MATH\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWu, S. M. et al. Antiferromagnetic spin Seebeck effect. Phys. Rev. Lett. 116, 097204 (2016).\n\nArticle\u00a0\n    ADS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLi, J. et al. Spin Seebeck effect from antiferromagnetic magnons and critical spin fluctuations in epitaxial FeF2 films. Phys. Rev. Lett. 122, 217204 (2019).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nGray, I. et al. Spin Seebeck Imaging of Spin-Torque Switching in Antiferromagnetic Pt/NiO Heterostructures. Phys. Rev. X 9, 41016 (2019).\n\nCAS\u00a0\n    MATH\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLi, J. et al. Spin current from sub-terahertz-generated antiferromagnetic magnons. Nature 578, 70\u201374 (2020).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    MATH\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nRoss, A. et al. Exceptional sign changes of the nonlocal spin Seebeck effect in antiferromagnetic hematite. Phys. Rev. B 103, 224433 (2021).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWu, S. M., Pearson, J. E. & Bhattacharya, A. Paramagnetic spin Seebeck effect. Phys. Rev. Lett. 114, 186602 (2015).\n\nArticle\u00a0\n    ADS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nAkopyan, A. et al. Spin Seebeck effect in Cu2OSeO3: test of bulk magnon spin current theory. Phys. Rev. B 101, 100407 (2020).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    MATH\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nChen, Y. et al. Triplon current generation in solids. Nat. Commun. 12, 5199 (2021).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    MATH\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nJenni, K. et al. Chirality of magnetic excitations in ferromagnetic SrRuO3. Phys. Rev. B 105, L180408 (2022).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    MATH\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nRezende, S. M., Rodr\u00edguez-Su\u00e1rez, R. L. & Azevedo, A. Theory of the spin Seebeck effect in antiferromagnets. Phys. Rev. B 93, 014425 (2016).\n\nArticle\u00a0\n    ADS\u00a0\n    MATH\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nYamamoto, Y., Ichioka, M. & Adachi, H. Antiferromagnetic spin Seebeck effect across the spin-flop transition: a stochastic Ginzburg-Landau simulation. Phys. Rev. B 105, 104417 (2022).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    MATH\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMasuda, K. & Sato, M. Microscopic theory of spin Seebeck effect in antiferromagnets. J. Phys. Soc. Jpn. 93, 034702 (2024).\n\nArticle\u00a0\n    ADS\u00a0\n    MATH\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nTang, P. & Bauer, G. E. W. Thermal and coherent spin pumping by noncollinear antiferromagnets. Phys. Rev. Lett. 133, 036701 (2024).\n\nArticle\u00a0\n    MathSciNet\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nPei, Q. L. et al. Spin dynamics, electronic, and thermal transport properties of two-dimensional CrPS4 single crystal. J. Appl. Phys. 119, 043902 (2016).\n\nArticle\u00a0\n    ADS\u00a0\n    MATH\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nFeringa, F., Vink, J. M. & van Wees, B. J. Spin-flop transition in the quasi-two-dimensional antiferromagnet MnPS3 detected via thermally generated magnon transport. Phys. Rev. B 106, 224409 (2022).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLiu, T. et al. Spin caloritronics in a CrBr3-based magnetic van der Waals heterostructure. Phys. Rev. B 101, 205407 (2020).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nTan, X., Ding, L., Du, G.-F. & Fu, H.-H. Spin caloritronics in two-dimensional CrI3/NiCl2 van der Waals heterostructures. Phys. Rev. B 103, 115415 (2021).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nQi, S. et al. Giant electrically tunable magnon transport anisotropy in a van der Waals antiferromagnetic insulator. Nat. Commun. 14, 2526 (2023).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    MATH\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nde Wal, D. K., Zohaib, M. & van Wees, B. J. Magnon spin transport in the van der Waals antiferromagnet CrPS4 for noncollinear and collinear magnetization. Phys. Rev. B 110, 174440 (2024).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nde Wal, D. K., Mena, R. L., Zohaib, M. & van Wees, B. J. Gate control of magnon spin transport in unconventional magnon transistors based on the van der Waals antiferromagnet CrPS4. Phys. Rev. B 110, 224434 (2024).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nXing, W. et al. Magnon transport in quasi-two-dimensional van der Waals antiferromagnets. Phys. Rev. X 9, 011026 (2019).\n\nCAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMa\u00f1as-Valero, S., van der Sar, T., Duine, R. A. & van Wees, B. J. Fundamentals and applications of van der Waals magnets in magnon spintronics. Newton 1, 100018 (2025).\n\nLee, J. et al. Structural and optical properties of single- and few-layer magnetic semiconductor CrPS4. ACS Nano 11, 10935\u201310944 (2017).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    MATH\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nPeng, Y. et al. Magnetic structure and metamagnetic transitions in the Van der Waals antiferromagnet CrPS4. Adv. Mater. 32, 2001200 (2020).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDing, S. et al. Magnetic phase diagram of CrPS4 and its exchange interaction in contact with NiFe. J. Phys. Condens. Matter 32, 405804 (2020).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nCalder, S. et al. Magnetic structure and exchange interactions in the layered semiconductor CrPS4. Phys. Rev. B 102, 024408 (2020).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    MATH\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nYang, J. et al. Layer-dependent giant magnetoresistance in two-dimensional CrPS4 magnetic tunnel junctions. Phys. Rev. Appl. 16, 024011 (2021).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    MATH\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWu, R. et al. Magnetotransport study of Van der Waals CrPS4/(Pt,Pd) heterostructures: spin-flop transition and room-temperature anomalous hall effect. Phys. Rev. Appl. 17, 064038 (2022).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nGu, K. et al. Exchange bias modulated by antiferromagnetic spin-flop transition in 2D Van der Waals heterostructures. Adv. Sci. 11, 2307034 (2024).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nSon, J. et al. Air-stable and layer-dependent ferromagnetism in atomically thin Van der Waals CrPS4. ACS Nano 15, 16904\u201316912 (2021).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLi, W. et al. Ultrastrong magnon\u2013magnon coupling and chirality switching in antiferromagnet CrPS4. Adv. Funct. Mater. 33, 2303781 (2023).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nAvci, C. O. et al. Interplay of spin-orbit torque and thermoelectric effects in ferromagnet/normal-metal bilayers. Phys. Rev. B 90, 224427 (2014).\n\nArticle\u00a0\n    ADS\u00a0\n    MATH\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBehnia, K. & Aubin, H. Nernst effect in metals and superconductors: a review of concepts and experiments. Rep. Prog. Phys. 79, 046502 (2016).\n\nArticle\u00a0\n    ADS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLebrun, R. et al. Tunable long-distance spin transport in a crystalline antiferromagnetic iron oxide. Nature 561, 222\u2013225 (2018).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    MATH\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nReitz, D., Li, J., Yuan, W., Shi, J. & Tserkovnyak, Y. Spin Seebeck effect near the antiferromagnetic spin-flop transition. Phys. Rev. B 102, 020408 (2020).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLuo, R. et al. Spin Seebeck effect at low temperatures in the nominally paramagnetic insulating state of vanadium dioxide. Appl. Phys. Lett. 121, 102404 (2022).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    MATH\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLau, Y.-C. & Hayashi, M. Spin torque efficiency of Ta, W, and Pt in metallic bilayers evaluated by harmonic Hall and spin Hall magnetoresistance measurements. Jpn. J. Appl. Phys. 56, 0802B0805 (2017).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKikkawa, T. et al. Longitudinal spin Seebeck effect free from the proximity Nernst effect. Phys. Rev. Lett. 110, 067207 (2013).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    MATH\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBender, S. A., Skarsv\u00e5g, H., Brataas, A. & Duine, R. A. Enhanced spin conductance of a thin-film insulating antiferromagnet. Phys. Rev. Lett. 119, 056804 (2017).\n\nArticle\u00a0\n    ADS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nRezende, S. M., Azevedo, A. & Rodr\u00edguez-Su\u00e1rez, R. L. Introduction to antiferromagnetic magnons. J. Appl. Phys. 126, 151101 (2019).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nde Wal, D. K. et al. Long-distance magnon transport in the van der Waals antiferromagnet CrPS4. Phys. Rev. B 107, L180403 (2023).\n\nArticle\u00a0\n    MATH\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKikkawa, T. et al. Magnon polarons in the spin Seebeck effect. Phys. Rev. Lett. 117, 207203 (2016).\n\nArticle\u00a0\n    ADS\u00a0\n    PubMed\u00a0\n    MATH\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nRamos, R. et al. Room temperature and low-field resonant enhancement of spin Seebeck effect in partially compensated magnets. Nat. Commun. 10, 5162 (2019).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    MATH\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nXing, W. et al. Facet-dependent magnon-polarons in epitaxial ferrimagnetic Fe3O4 thin films. Phys. Rev. B 102, 184416 (2020).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLi, J. et al. Observation of magnon polarons in a uniaxial antiferromagnetic insulator. Phys. Rev. Lett. 125, 217201 (2020).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDownload references",
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+            "section_name": "Acknowledgements",
+            "section_text": "This work is supported by the National Key R&D Program of China (grant no. 2022YFA1203902 (Y.H., R.W.)), the National Natural Science Foundation of China (NSFC) (grant nos. 12241401 (J.Y.), 12374108 (R.W.) and 12104052 (R.W.), 52027801(Y.H.), 92263203(Y.H.)), and the China-Germany Collaboration Project (M-0199 (Y.H., M.K.)), the Guangdong Provincial Quantum Science Strategic Initiative (Grant No. GDZX2401002 (R.W.)), the GJYC program of Guangzhou (Grant No. 2024D01J0087 (R.W.)), the Fundamental Research Funds for the Central Universities, the State Key Lab of Luminescent Materials and Devices, South China University of Technology, and GBRCE for Functional Molecular Engineering (R.W.). M.K. acknowledges support by the German Research Foundation (CRC TRR 288\u2014422213477 Project A12 and CRC TRR 173\u2014268565370 Projects A01 and B02). A.B. acknowledges the Research Council of Norway through its Center of Excellence 262633 \u201cQuSpin\u201d.",
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+        },
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+            "section_name": "Author information",
+            "section_text": "Spin-X Institute, School of Physics and Optoelectronics, State Key Laboratory of Luminescent Materials and Devices, and Guangdong-Hong Kong-Macao Joint Laboratory of Optoelectronic and Magnetic Functional Materials, South China University of Technology, Guangzhou, China\n\nXue He,\u00a0Jicheng Wang\u00a0&\u00a0Rui Wu\n\nDepartment of Materials, ETH Z\u00fcrich, Z\u00fcrich, Switzerland\n\nShilei Ding\u00a0&\u00a0Mingxing Wu\n\nCenter for Quantum Spintronics, Norwegian University of Science and Technology, Trondheim, Norway\n\nHans Gl\u00f8ckner Giil,\u00a0Mathias Kl\u00e4ui\u00a0&\u00a0Arne Brataas\n\nInstitute of Physics, Johannes Gutenberg-University Mainz, Mainz, Germany\n\nMona Bhukta\u00a0&\u00a0Mathias Kl\u00e4ui\n\nCenter for Electron Microscopy, South China University of Technology, Guangzhou, China\n\nWen Shi\n\nState Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing, China\n\nZhongchong Lin,\u00a0Zhongyu Liang\u00a0&\u00a0Jinbo Yang\n\nSchool of Materials, Shenzhen Campus of Sun Yat-Sen University, Shenzhen, China\n\nYanglong Hou\n\nSchool of Materials Science and Engineering, Beijing Key Laboratory for Magnetoelectric Materials and Devices, Peking University, Beijing, China\n\nYanglong Hou\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nS.D. and R.W. conceived the experiments. X.H. fabricated the devices. X.H., S.D., J.W. and R.W. carried out the transport and magnetic measurements. Z.C.L., Z.Y.L. and J.Y. made the single crystal samples and carried out basic characterizations. H.G.G. and A.B. contributed to the theoretical calculation. X.H., S.D., R.W., and M.K. contributed to data analysis. W.S. contributes to the Transmission Electron Microscopy characterization. M.B. and M.W. contribute to the temperature distribution simulation. S.D. drafted the manuscript and all authors contributed to the reviewing and revising of the manuscript. Y.H. and R.W. supervised the research and contributed to the acquisition of the financial support for the project leading to this work.\n\nCorrespondence to\n                Shilei Ding, Jinbo Yang, Yanglong Hou or Rui Wu.",
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+            "section_text": "He, X., Ding, S., Giil, H.G. et al. Spin Seebeck in the weakly exchange-coupled Van der Waals antiferromagnet across the spin-flip transition.\n                    Nat Commun 16, 3037 (2025). https://doi.org/10.1038/s41467-025-58306-3\n\nDownload citation\n\nReceived: 22 October 2024\n\nAccepted: 18 March 2025\n\nPublished: 28 March 2025\n\nVersion of record: 28 March 2025\n\nDOI: https://doi.org/10.1038/s41467-025-58306-3\n\nAnyone you share the following link with will be able to read this content:\n\nSorry, a shareable link is not currently available for this article.\n\n\n\n\n                            Provided by the Springer Nature SharedIt content-sharing initiative\n                        ",
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07ed9c6d9e6ca0cab5b9b0180c58f6b6054610c90c12780b9cc4a7e3a9a2f0e1/metadata.json

@@ -0,0 +1,165 @@
+{
+    "title": "Molecular manipulation of polyamide nanostructures reconciles the permeance-selectivity threshold for precise ion separation",
+    "pre_title": "Molecular Manipulation of Polyamide Nanostructures Reconciles the Permeance\u2013Selectivity Threshold for Precise Ion Separation",
+    "journal": "Nature Communications",
+    "published": "04 August 2025",
+    "supplementary_0": [
+        {
+            "label": "Supplementary information",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-62376-8/MediaObjects/41467_2025_62376_MOESM1_ESM.pdf"
+        },
+        {
+            "label": "Transparent Peer Review file",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-62376-8/MediaObjects/41467_2025_62376_MOESM2_ESM.pdf"
+        },
+        {
+            "label": "Description of Additional Supplementary Files",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-62376-8/MediaObjects/41467_2025_62376_MOESM3_ESM.docx"
+        },
+        {
+            "label": "Supplementary Data 1",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-62376-8/MediaObjects/41467_2025_62376_MOESM4_ESM.xlsx"
+        },
+        {
+            "label": "Supplementary Data 2",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-62376-8/MediaObjects/41467_2025_62376_MOESM5_ESM.xlsx"
+        },
+        {
+            "label": "Supplementary Data 3",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-62376-8/MediaObjects/41467_2025_62376_MOESM6_ESM.txt"
+        },
+        {
+            "label": "Supplementary Data 4",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-62376-8/MediaObjects/41467_2025_62376_MOESM7_ESM.txt"
+        }
+    ],
+    "supplementary_1": [
+        {
+            "label": "Source Data",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-62376-8/MediaObjects/41467_2025_62376_MOESM8_ESM.xlsx"
+        }
+    ],
+    "supplementary_2": NaN,
+    "source_data": [
+        "/articles/s41467-025-62376-8#Sec16"
+    ],
+    "code": [],
+    "subject": [
+        "Chemical engineering",
+        "Polymer synthesis",
+        "Polymers"
+    ],
+    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
+    "preprint_pdf": "https://www.researchsquare.com/article/rs-5431568/v1.pdf?c=1754391994000",
+    "research_square_link": "https://www.researchsquare.com//article/rs-5431568/v1",
+    "nature_pdf": "https://www.nature.com/articles/s41467-025-62376-8.pdf",
+    "preprint_posted": "16 Dec, 2024",
+    "research_square_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Membrane nanofiltration (NF) has emerged as a prominent energy-efficient separation technology for widespread applications related to the water\u2012energy nexus. However, state-of-the-art polyamide (PA) NF membranes are markedly constrained by a ubiquitous, pernicious tradeoff between water permeance and selectivity. Leveraging the prestigious structure-determining performance rationale, this work conceives a facile and robust molecular engineering approach that enables simultaneous improvements in water permeance and co-cation selectivity through synthetic molecular construction of a PA nanofilm with unique cationic triazolyl heterocyclic polyamide (CTHP) structures during scalable interfacial polymerization. Experimental data in conjunction with molecular simulations reveal that the CTHP structures instigate exquisite regulation of the PA subnanometer pore architecture and the specific binding affinity with water and ions, which not only affords precise ion sieving ability and advanced Donnan exclusion selectivity but also energetically facilitates the partitioning and transport of water molecules. The exemplified PA membrane exhibits unparalleled divalent cation rejections of over 99%, accompanied by a 9-fold increase in monovalent/divalent cation sieving selectivity, which is substantially greater than that of the pristine benchmark, a superior water permeation rate, and excellent chemical and operational stability, circumventing the permeance/selectivity threshold. We believe that the molecular engineering strategy implemented in this work holds broad prospects for the rational design and fabrication of semipermeable polymeric NF membranes for sustainable and precision separations.Physical sciences/Engineering/Chemical engineeringPhysical sciences/Chemistry/Polymer chemistry/NanocompositesNanofiltrationPolyamide membraneInterfacial polymerizationIon separationPermselectivity",
+            "section_image": []
+        },
+        {
+            "section_name": "Additional Declarations",
+            "section_text": "There is NO Competing Interest.",
+            "section_image": []
+        },
+        {
+            "section_name": "Supplementary Files",
+            "section_text": "SupportinginformationNov112024.pdf",
+            "section_image": []
+        }
+    ],
+    "nature_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Membrane nanofiltration (NF) has emerged as a prominent technology for efficient separations of ions, but state-of-the-art polyamide (PA) NF membranes are constrained by a pernicious tradeoff between water permeance and selectivity. This work conceives a versatile molecular engineering strategy to simultaneously improve water permeance and co-cation selectivity through molecular construction of cationic triazolyl heterocyclic polyamide (CTHP) nanofilms via scalable interfacial polymerization. Experimental data and molecular simulations reveal that the CTHP structures precisely regulate the subnanometer pore architecture and binding affinity with water and ions, affording advanced size-sieving and Donnan exclusion while facilitating water partitioning and transport. The exemplified PA membrane exhibits ultrahigh divalent cation rejections of over 99% with a 9-fold increase in monovalent/divalent cation sieving selectivity relative to the pristine benchmark, exceptional water permeance, and good fouling resistance. The implemented molecular engineering strategy holds broad prospects for the rational design of high-performance polymeric membranes for sustainable and precision separations.",
+            "section_image": []
+        },
+        {
+            "section_name": "Introduction",
+            "section_text": "Precision discrimination of target ions and molecules from complex aqueous mixtures of similar species remains a considerable challenge in widespread applications such as water, clean energy, and resource reclamation1,2,3. Membrane nanofiltration (NF), featuring phase-free conversion separation, has evolved into a premier tool for sustainable water separation because of its high energy efficiency, low carbon footprint, compact design, and manufacturing scalability4,5. The rapid dissemination of NF technology relies on high-performance membranes that ideally have high values of both water permeance and selectivity to fully exploit the prominent process advantages, but such a combination is exceedingly difficult to achieve particularly for polymeric membranes, as the material properties that affect solute transport would, in turn, exert influence on water permeation6,7,8.\n\nPolyamide (PA) thin-film composite membranes are state-of-the-art NF membranes that are particularly attractive for water filtration in practical modules across all scales9,10,11,12. However, the deleterious tradeoff between water permeance and membrane selectivity consistently poses a stumbling block for further performance advancement, where increasing water permeance is inevitably accompanied by a diminished ability to selectively reject solutes13,14. According to the prevailing membrane separation mechanisms, effective strategies for rationally regulating mass transport across the PA membranes hinge on well-defined pore sizes with a narrow size distribution, finely tuned interactions with the permeants of interest, and a thin PA selective layer15,16,17. Innovative materials and fabrication methods that can precisely regulate PA chemistry and nanostructures have therefore become essential pursuits of academic research.\n\nA prevalent approach that has been widely adopted to increase the permselectivity of PA membranes toward charged species involves surface charge optimization to strengthen electrostatic exclusion via in situ and/or post-synthetic modifications18,19. However, most of the approaches reported thus far have primarily focused on promoting solute rejection or selectivity rather than overcoming the permeance/selectivity tradeoff threshold20,21. Recently, exceptional size sieving ability and co-cation selectivity have been achieved by trailblazing studies that use interfacial modulators to narrow the pore size distribution of the PA layer22,23,24,25. Unfortunately, a significant decrease in water permeance is usually accompanied by a concomitant increase in water transport resistance23,24. Many studies have also focused on exploring advanced membrane materials, ranging from biological ion channels and aquaporins to two-dimensional nanomaterials such as vermiculite and graphene, as well as emerging microporous materials including zeolites, metal-organic frameworks (MOFs), covalent organic frameworks (COFs), polymers of intrinsic microporosity (PIM), conjugated microporous polymers (CMPs), macrocycles, and porous organic cages, some of which achieved remarkable permselectivity with unprecedented combinations of high permeance and selectivity26,27,28. Although the practicality of these intriguing materials is markedly restricted by many daunting limitations that vary from inherent low structural stability to inferior material availability and the feasibility of membrane fabrication on a large scale, their distinct structural features underscore the importance of well-defined pore sizes and finely regulated mutual interactions in achieving exceptional molecular sieving capabilities and water transport rates29,30,31. Hereupon, we speculate that multifunctional monomers with synthetically engineered chemistry that enable the formation of a PA structure that not only imparts subnanometer pores with a narrow size distribution but also provides low resistance for water transport are likely to achieve disruptive improvements in both water permeance and solute selectivity. Unfortunately, there is currently a lack of rational material design and feasible membrane fabrication strategies to accomplish this arduous undertaking.\n\nHerein, we demonstrate a facile and effective molecular engineering approach for precise regulation of the mass transfer behavior of PA membranes to circumvent the formidable permeance/selectivity tradeoff in nanofiltration for ion discrimination. Our strategy is contingent on molecular-level control over the nanoporous structure of the PA nanofilm and its interactions with water and ions through in situ construction of cationic triazolyl heterocyclic polyamide (CTHP) structures via scalable interfacial polymerization (IP) using rationally designed quaternary triazole ammonium monomers. Experimental data and molecular simulations revealed that the CTHP structures endow the PA nanofilm with well-defined subnanometer pores with a narrow size distribution and abundant positive charge but low intrinsic water transport resistance, which not only synergistically enhances steric hindrance sieving and Donnan exclusion but also facilitates the permeation of water. The advantages of this molecularly engineered PA structure were demonstrated by its exceptional performance within precise co-cation sieving (Fig.\u00a01a), achieving a 9-fold increase in monovalent/divalent cation selectivity with a tripled water flux relative to the benchmark, successfully reconciling the tradeoff threshold. Considering the diverse array of monomer chemistries, the implemented design strategy provides a promising gateway to advance the development of effective PA membranes with exceptional permselectivity for precise ion separations toward clean water and renewable energy.\n\na Working principle of precision co-ion separation via nanofiltration. b Schematic diagram of the interconnected subnanometer-sized pores in a desired PA nanofilm with high selectivity and low water transport resistance, and three-dimensional view of an amorphous cell of the PA polymer (cell size: 65\u2009\u00d7\u200965\u2009\u00d7\u200965\u2009\u00c53). c Synthetic reaction formula of DAT-NH2 isomers and the visualized conformation of their atomic electrostatic potential. d 1H NMR spectra and liquid chromatography (upper left inset) of DAT-NH2 isomers. e Schematic illustration of interfacial polymerization between DAT-NH2/PEI and TMC at the water/hexane interface to form a PA nanofilm. f Molecular structure of the DP-M PA nanofilm (left) and its corresponding polymer chain structure derived from an amorphous cell generated by molecular dynamic (MD) simulations. g FT-IR spectra of the DP-M and P-M PA nanofilms. h N 1\u2009s XPS spectra of the DP-M PA nanofilm. The N1s core level spectrum was deconvoluted into three components located at 399.7, 400.4, and 401.7\u2009eV corresponding to N\u2009\u2212\u2009(C\u2009=\u2009O)\u2009\u2212\u2009, N(H)\u2009\u2212\u2009C\u2009\u2212\u2009, and N+\u2009\u2212\u2009C\u2009\u2212\u2009, respectively.",
+            "section_image": [
+                "https:////media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41467-025-62376-8/MediaObjects/41467_2025_62376_Fig1_HTML.png"
+            ]
+        },
+        {
+            "section_name": "Results",
+            "section_text": "Figure\u00a01b shows the conceptual illustration of the ideal PA structure that we intend to construct to circumvent the permeance/selectivity tradeoff in precision nanofiltration (NF). Specifically, the PA layer is synthetically designed with well-defined permeate-PA binding affinity and steric sieving selectivity to simultaneously manipulate the enthalpy and entropy barriers for water and solute transport32,33. To realize this design strategy, we molecularly constructed a multifunctional monomer with primary amine dangling and a highly polarized triazolyl heterocyclic ring bearing quaternary ammonium such as 3,5-diamino-4/1-(2-aminoethyl)\u22121,2,4-triazole (DAT-NH2, Fig.\u00a01c). Our pursuit of such a molecular architecture was inspired by seminal studies revealing that nitrogen-containing heterocycles, like imidazole derivatives, could induce energetically preferential interactions with water molecules to facilitate their permeation during membrane filtration, while the primary amine pendants with concentrated electron density concurrently provide highly reactive sites to crosslink with trimesoyl chloride (TMC) to form tightly crosslinked PA network with enhanced hydrophilicity and interconnected subnanometer pores. We speculate that these effects are likely to be maximized in triazole-derived compounds, given its five-membered aromatic ring that contains three sp2-hybridized nitrogen atoms and two carbon atoms. Electrostatic potential mapping and quantitative analysis of the key molecular and electronic descriptors of a series of five-membered rings with various numbers of nitrogen heteroatoms by density functional theory (DFT) revealed that the triazole unit possesses the most asymmetric charge distribution and the largest dipole moment (3.974 Debye) (Supplementary Fig.\u00a01). These features suggest that the triazole moiety may introduce localized hydrophilic domains within the PA polymer matrix due to its high polarity and electron delocalization, which could enhance water affinity and thus facilitate transport. DFT-based electronic structure analyses of the DAT-NH2 isomers and PEI fragments further demonstrated that the former exhibits significantly higher molecular polarity, enhanced nucleophilicity, and denser positive electrostatic potentials than the latter (Supplementary Fig.\u00a02, Supplementary Table\u00a01 and 2), further substantiating our hypothesis that the DAT-NH2 isomers can enable the formation of highly ionizable cationic PA structures with preferential water transport pathways.\n\nThe molecularly designed DAT-NH2 monomer was synthesized via a one-pot quaternization reaction between 3,5-diamino-1,2,4-triazole and 2-bromoethylamine in dimethylformamide (DMF) and then purified by nonsolvent-induced precipitation (Fig.\u00a01c and Supplementary Fig.\u00a03 and 4). Intriguingly, liquid chromatography\u2013mass spectrometry (LC\u2013MS) measurements reveal that a mixture of 3,5-diamino-4/1-(2-aminoethyl)\u22121,2,4-triazole isomers was obtained from the synthesis. As shown in Fig.\u00a01d, two distinct peaks with almost the same intensity and area ratio were observed in the LC chromatogram pattern. Subsequent MS analysis of these two peaks showed one coincident peak at m/z 143 (Supplementary Fig.\u00a05), which is in good agreement with the molecular weight of the DAT-NH2 isomers (C4N6H11+, MW\u2009=\u2009143\u2009Da). Proton nuclear magnetic resonance (1H NMR) spectra corroborate these results, where four 1H NMR peaks corresponding to the two types of protons in each isomer are spotted at 3.11 (labeled H I), 3.30 (labeled H I), 3.35 (labeled H II), and 3.99 (labeled H II) ppm. The area ratios of the two peaks (H I/H II) in the 1H NMR spectrum were measured to be 0.88 and 1.04 for the isomers, which are close to the theoretically expected values based on the DAT-NH2 chemical structure. The visualized atomic electrostatic potential image of DAT-NH2 intuitively proclaims the positive charge characteristics of the triazole ring, and quantitative analysis of the molecular van der Waals surface electrostatic potential (ESP) shows that the distribution area and intensity of the positive ESP of the DAT-NH2 isomers are greater than the negative values (Fig.\u00a01c and Supplementary Fig.\u00a06).\n\nA self-sustaining PA thin film with good stability immediately formed when DAT-NH2 was brought in contact with TMC at the water/hexane interface (Supplementary Fig.\u00a07), indicating a high polymerization rate between DAT-NH2 and TMC. DFT calculations further confirmed the high nucleophilic substitution reactivity of the amino groups on DAT-NH2 toward acyl chloride (Supplementary Figs.\u00a08 and 9). Comprehensive ESP and average local ionization energy (ALIE) analyses reveal that the backbone and chemical functional moieties of the PA structures formed by the two isomers with TMC are almost identical (Supplementary Fig.\u00a010). Therefore, the DAT-NH2 isomers were directly used for PA membrane preparation without further purification. A continuous PA nanofilm can also be in situ synthesized via a similar interfacial polymerization (IP) procedure on top of a polyethersulfone (PES) substrate to prepare robust PA thin-film composite membranes for NF tests (Supplementary Fig.\u00a011). Unfortunately, we observed that the obtained DAT-NH2/TMC PA membrane experienced severe water swelling and thus relatively low permselectivity were obtained in nanofiltration (Supplementary Fig.\u00a012), likely owing to the enhanced hydrophilic nature of the cationic triazolyl heterocyclic structures. We thereby further modified the PA chemical structure by using polyethyleneimine (PEI) as the comonomer during IP to increase the membrane stability and separation performance (Fig.\u00a01e, f). PEI is a benchmark monomer that is widely used for the synthesis of positively charged PA NF membranes (Supplementary Fig.\u00a013). Synthesis condition optimization experiments confirmed that the DP-M membrane fabricated with a 0.06\u2009wt% DAT-NH2 shows an optimum combination of water permeance and ion selectivity in addition to the exceptional robustness (Supplementary Figs.\u00a014 and 15), substantially exceeding those of the PA membrane formed solely by PEI (denoted as the P-M benchmark). The Fourier transform infrared spectroscopy (FT-IR) peaks observed at 1621\u2009cm\u22121, 1806 cm\u22121, and 1705\u2009cm\u22121 are associated with the amide I band, which arises from the stretching vibration of C\u2009=\u2009O and the coupling with the bending of N\u2013H in subtly different chemical environments (Fig.\u00a01g and Supplementary Fig.\u00a016), validating the formation of PA structure. The quaternary ammonium peak at 401.8\u2009eV in the X-ray photoelectron spectroscopy (XPS) spectrum of DP-M (Fig.\u00a01h and Supplementary Figs.\u00a017 and 18) confirms the presence of DAT-NH2 moieties in the PA layer. It is noteworthy that a significant decline in the O/N ratio was observed by DP-M compared with that of the P-M benchmark, where the O/N ratio decreases from ~1.50 to 0.96 (Supplementary Table\u00a03), suggesting a substantial increase in the PA crosslinking degree of DP-M. The elevated crosslinking degree constricts the space between the stacked polymer chains, thus diminishing the pore sizes and augmenting the mechanical strength of the PA nanofilm (Supplementary Fig.\u00a015). According to the chemical characterization and molecular simulations, the DAT-NH2 modulated PA layer of DP-M has a semirigid 3D polyamide network with a large amount of intrinsic positive charges and smaller chain space compared to the P-M benchmark (Fig.\u00a01f and Supplementary Figs.\u00a019 and 20).\n\nField emission scanning electron microscopy (FESEM) images corroborate the uniformity and integrity of the formed PA thin layer at the macroscopic scale (Fig.\u00a02a, b and Supplementary Fig.\u00a021). At a finer scale, the PA layer of DP-M appears a smooth and compact surface, whereas the counterpart of the P-M benchmark shows a crumpled surface with numerous ridged wrinkles unequivocally seen on top. This surface morphological discrepancy was further manifested by the atomic force microscopy (AFM) data, where the surface roughness of DP-M (Rq = 3.44\u2009nm) is distinctly lower than that of P-M (Rq = 9.09\u2009nm) (Fig.\u00a02c, d and Supplementary Fig.\u00a022). A smooth surface is conducive to alleviating the fouling tendency. Cross-sectional transmission electron microscopy (TEM) images showcase that DP-M has an low PA thickness of 59\u2009\u00b1\u20092\u2009nm (Fig.\u00a02e, f and Supplementary Fig.\u00a023), which is much thinner than that of the P-M benchmark (i.e., 88\u2009\u00b1\u20092\u2009nm). The significantly reduced PA thickness might be attributed to the rapid formation of a relatively dense nascent PA film mediated by DAT-NH2 at an initial stage of IP (Supplementary Fig.\u00a024), which subsequently stymies the diffusion of aqueous monomers at the interface and thus suppresses the subsequent growth of the PA nanofilm34,35. On the other hand, the positively charged structure of DAT-NH2 may slow down the diffusion of PEI towards the interface via H-bonding interactions, further retarding the growth of the PA film36,37,38,39,40. In the context of membrane filtration, a thinner PA selective layer spontaneously confers shorter transport pathways and lower water penetration resistance, which is favorable for achieving high water permeance.\n\na, b Surface FESEM images. c, d 2D and 3D AFM images. e, f Cross-sectional TEM images. Top: P-M. Bottom: DP-M. g Pore radius distribution of PA membranes obtained by PEG rejection tests (the inset illustrates the geometric standard deviation). h Molecular dynamics (MD) simulations of the fractional free volume (FFV) of PA layers (left). The dark blue and gray colors represent the voids between the polymer chains and the space occupied by the polymer skeleton, respectively. Representative porous molecular structures of the DP-M and P-M PA networks (right). i MD simulations of the pore radius distribution of the PA nanofilms. j Zeta potential as a function of pH. k Summary of the MWCO, water contact angle (CA), root mean square roughness (Rq), FFV, polyamide layer thickness, and zeta potential (ZP) at pH = 6 for DP-M and P-M.\n\nThe rejection tests with neutral solutes of polyethylene glycol (PEG) indicate that DP-M has a molecular weight cutoff (MWCO) of 245\u2009Da, almost two times smaller than that of the P-M benchmark (MWCO\u2009=\u2009479\u2009Da, Supplementary Fig.\u00a025). Correspondingly, a small effective mean pore radius of 2.8\u2009\u00c5 accompanied by a narrow size distribution was achieved by DP-M (Fig.\u00a02g), whereas P-M shows a relatively larger mean pore radius of 3.1\u2009\u00c5 and broader pore size distribution, in accordance with our design strategy and the XPS-derived crosslinking degree (Fig.\u00a01b, h). Molecular dynamics (MD) simulations were further performed to construct realistic structural models to glean molecular-level insights into the microporous structure of the PA layer. As shown in Fig.\u00a02h, the fractional free volume (FFV) of DP-M and P-M PA layers are ~10.3% and 21.6%, respectively. The pore size survey conducted by MD molecular simulations substantiates that the majority of pores within the DP-M PA layer are ~2.75\u2009\u00c5 in radius, which is significantly smaller than that of the P-M benchmark (i.e., 3.38\u2009\u00c5). Further analyses of the interior cavity radius disclose a narrower distribution of pore sizes within DP-M (Fig.\u00a02i and Supplementary Fig.\u00a026), signifying the compact structure of the PA layer mediated by DAT-NH2 (Fig.\u00a01c). Notably, the microscopic pore features derived from molecular simulations coincide well with those experimentally obtained from neutral solute rejection tests (Fig.\u00a02g, i). The tight nanostructure of DP-M constricts membrane pores to dimensions more favorable for size sieving, with precise ionic and molecular sieving capabilities and a threshold of 5.6\u2009\u00c5 in pore diameter. Furthermore, aligning with the chemical features of the CTHP structures in DP-M (Fig.\u00a01g), the cationic DAT-NH2 moieties elevate the membrane hydrophilicity and positive charge density, as manifested by its smaller surface water contact angle (CA) and higher zeta potential (ZP) than that of the P-M benchmark (Supplementary Fig.\u00a025 and Fig.\u00a02j). In the realm of NF applications, the enhanced hydrophilicity facilitates surface partitioning and interior diffusion of water molecules, whereas the ameliorated positive charge density reinforces the electrostatic repulsion selectivity. Collectively, the advanced characteristics gained by the DP-M membrane resonate with our intended design strategy illustrated in Fig.\u00a01b, which underpins the significance of synthetic molecular engineering in precisely regulating the nanoporous structure and chemical features of the PA selective layer (Fig.\u00a02k).\n\nThe well-defined subnanometer pores with a sharped size distribution and the inherent positive charges of the DP-M membrane would afford prominent molecular sieving and electrostatic repulsion selectivity in NF applications. We subsequently examined the mass transport behavior of a wide spectrum of inorganic salts through DP-M using a crossflow filtration system. In contrast to the acquiescent expectation that a decrease in membrane pore size along with a downscaled FFVs generally accompanied by a concomitant decline in the water permeation rate, a substantial increase in the water permeance was achieved by DP-M, where the water permeation flux of DP-M is almost tripled at the same pressure compared to the P-M benchmark (Fig.\u00a03a), corresponding to an approximately 3-fold increase in pure water permeance (PWP). The incongruence between the enhanced water permeance and the reduced pore sizes and FFVs likely stems from the molecularly constructed CTHP structures and the low thickness of the PA layer, which provide facilitated water transport pathways with low resistance.\n\na Pure water flux (PWF) of DP-M and P-M at different operation pressures. b Water flux and ion rejections of DP-M for filtrating different cation solutions. (Feed salt concentration: 1000 ppm; test pressure: 6.0\u2009bar). c MgSO4 and MgCl2 rejections of P-M and DP-M (feed salt concentration: 1000 ppm, test pressure: 6.0\u2009bar). d Effect of operation pressure on the water permeance and MgCl2 rejection of DP-M (feed: 1000 ppm MgCl2). e Effect of pH on the water flux and LiCl rejection of DP-M (feed: 1000 ppm LiCl, test pressure: 6.0\u2009bar). f Effect of operation time on the water flux and MgCl2 rejection of DP-M (feed: 1000 ppm MgCl2, test pressure: 6.0\u2009bar). g Effect of operation pressure on the water permeance and SLi+/Mg2+ of DP-M (feed: 2000 ppm binary mixture of MgCl2 and LiCl with a MgCl2/LiCl mass ratio of 20). h Effects of the Mg2+/Li+ ratio on the water flux and SLi+/Mg2+ ratio of DP-M (feed: 2000 ppm binary mixture of MgCl2 and LiCl with various MgCl2/LiCl mass ratios; test pressure: 6.0\u2009bar). i Performance comparison of DP-M with state-of-the-art PA NF membranes operated under cross-flow nanofiltration. The corresponding references for the data points in (i) are specified in Supplementary Table\u00a04.\n\nAt the same time, DP-M shows a sharp size-exclusion cutoff of ~2.5\u2009\u00c5 in the Stokes radius of cations (Fig.\u00a03b), adhering to its densified catatonic PA molecular structure, which thereby facilitates the transport of smaller monovalent cations (i.e., Rb+, K+, Na+, and Li+) while sufficiently blocks larger divalent cations (i.e., Ni2+, Ca2+, Mg2+, and Zn2+), with rejection rates greater than 98.0% and high water flux of 50\u2009L\u2009m\u22122 h\u22121 (LMH). It is noteworthy that ultrahigh rejections of up to 99.1% towards MgCl2 and MgSO4 were specifically achieved by DP-M (Fig.\u00a03c), exceeding most state-of-the-art NF membranes, and similar rejections and water permeance were maintained over a wide pressure range of 2\u201316\u2009bar (Fig.\u00a03d). In contrast, LiCl rejection monolithically increased from 45.7% to 81.2% when the pressure was raised from 2 to 16\u2009bar (Supplementary Fig.\u00a027). As a result, an ideal Li+/Mg2+ selectivity of 35.8\u201342.9 was obtained based on single salt rejections (Supplementary Fig.\u00a028), demonstrating its promising capability for precise cation sieving. In the same vein, the P-M benchmark is inferior in terms of both salt rejection and cation differentiation selectivity (Fig.\u00a03b and Supplementary Fig.\u00a029).\n\nThe separation performances of conventional NF membranes are generally susceptible to the feed salt concentration and pH due to the electrostatic screening effects. Interestingly, DP-M consistently retains its water flux, salt rejection, and co-cation selectivity across a wide range of feed salt contents and pH values. As demonstrated by the cycling performance tests, the Mg2+ rejection of the DP-M membrane decreased slightly from 99.1% to 95.7% while the Li+ rejection dropped from 59.8% to 23.3% as the feed salt content spanned from 1000 to 7000\u2009mg/L, while the rejections were almost fully recovered to the initial values when the feed content was switched back to 1000\u2009mg/L (Supplementary Fig.\u00a030), substantiating good electrostatic shielding resistance toward high ionic strength. There were also no obvious deteriorations in salt rejections and water flux as the feed pH escalated from 1 to 13 (Fig.\u00a03e), underscoring the ability of DP-M to maintain high separation performance in both acidic and alkaline environments. The exceptional pH and salinity stabilities of DP-M are consistent with the inherent structural features of CTHP and the enhanced size-sieving ability endowed by the narrow pore size distribution (Fig.\u00a02g, i). The exceptional hydrophilicity and positive surface charge imparted by the catatonic CTHP structures also affords DP-M with exceptional fouling resistance to positively charged foulants (i.e., DTAB, dodecyltrimethylammonium bromide) (Supplementary Fig.\u00a031). Moreover, DP-M shows exceptional structural durability and performance stability throughout long-term filtration for 120\u2009h (Fig.\u00a03f), where MgCl2 rejection consistently surpassed 99%, with a stable water flux of ~51 LMH being retained. Notably, the DP-M membrane maintained a high MgCl2 rejection of above 99% and a water flux of greater than 50 LMH even after being stored in water for one month (Supplementary Fig.\u00a032). In addition, the DP-M membrane exhibits exceptional chlorine resistance. As shown in Supplementary Fig.\u00a033, relatively stable MgCl2 rejections and water flux were observed throughout the 175\u2009h exposure to 200 ppm sodium hypochlorite (NaClO), while the MgCl2 rejection of the P-M benchmark decreased dramatically from 92.4% to 29.5% with a concomitant rapid increase in water flux from 20.4 to 149.3 LMH. FT-IR analysis (Supplementary Fig.\u00a033c, d) further reveals that the characteristic peak of the amide bond (~1660\u2009cm\u22121) in P-M substantially decreased with the extension of exposure time, whereas the counterpart peak in the DP-M membrane remained nearly unchanged, demonstrating the exceptional structural durability of the DP-M membrane under oxidative conditions.\n\nThe co-cation sieving ability of DP-M was further illuminated by binary salt filtration tests using a mixture of LiCl and MgCl2 as the probe solutes. Similar to the single-salt tests (Supplementary Fig.\u00a028), DP-M shows high Li+/Mg2+ selectivity with a separation factor of greater than 39.0 (SLi+/Mg2+) for the binary mixtures at different operation pressures (Fig.\u00a03g), which signifies a 9-fold greater magnitude than that achieved by the P-M benchmark (SLi+/Mg2+ = 4.3), accompanied by an approximately 2.5-fold increase in water permeance. The persistently high rejections toward divalent cations and co-cation selectivity are presumably ascribed to the advanced molecular sieving and electrostatic repulsion effects afforded by the regulated subnanometer pores and inherent positive charges of DP-M. Furthermore, slight fluctuations in the co-cation selectivity were observed when the feed Mg2+/Li+ mass ratio altered from 1 to 120, where the SLi+/Mg2+ oscillated between 33.5 and 44.3 and the water flux was consistently higher than 51.4 LMH (Fig.\u00a03h). Compared with other reported PA NF membranes with similar chemical and structural properties, DM-P exhibits upper-level water permeance and co-cation sieving selectivity (i.e., Li+/Mg2+) (Fig.\u00a03i), which potentially contributes to a more streamlined separation process with diminished energy consumption (Supplementary Fig.\u00a034), underscoring its remarkable potential for energy-efficient and cost-effective NF separations. To validate the uniformity and scalability of the developed PA membranes, a large-sized DP-M membrane (1\u00d70.3\u2009m) was fabricated via the same interfacial polymerization (Supplementary Fig.\u00a035). Membrane coupons randomly selected from different regions exhibited consistent performance, with the MgCl2 rejection rate stably maintained at 98% while the water flux remained around 50 LMH, indicating the exceptional scalability and stability. Furthermore, the generality of NF performance enhancement by triazole derivatives was demonstrated by extending to other quaternary ammonium triazole analogs (i.e., 3,5-diamino-4/1-(3-aminopropyl)\u20131,2,4-triazole, DAAT-NH2) and benchmarking against non-triazole monomers (Supplementary Fig.\u00a036 and Fig.\u00a037). The successful breakthrough of the permeance/selectivity tradeoff underpins our membrane design strategy and exemplifies the feasibility of synthetic molecular engineering in rational membrane design.\n\nGiven that the DP-M membrane possesses strong intrinsic positive charges and an average micropore diameter of 5.6\u2009\u00c5 with narrow size distribution (i.e., from 1.1 to 5.9\u2009\u00c5) (Fig.\u00a02g), we hypothesize that its high rejections toward divalent cations and enhanced co-cation sieving ability lean upon the on-demand tuning of the PA chemistry and nanoporous structure according to the size and valence differences between cations, which instigates unusual differences in energy barriers that cations need to overcome for dissolution and migration. As illustrated in Fig.\u00a04a, the average pore size of DP-M (5.6\u2009\u00c5) falls between the Stokes diameter (4.8\u2009\u00c5) and hydrated diameter (7.6\u2009\u00c5) of Li+. Given the substantial difference in hydration energy between Mg2+ and Li+ (1828 vs. 474\u2009kJ/mol), Li+ ions are more susceptible to undergo partial dehydration and subsequent selective permeation through the well-defined micropores of DP-M, enabling effective discrimination between Li+ and Mg2+ cations. This energy discrepancy is further corroborated by DFT calculations (Supplementary Fig.\u00a038), which estimate the hydration energies of Mg2+ and Li+ to be \u22121922.45 and \u2212563.52\u2009kJ/mol, respectively, indicating that the hydrated Mg2+ encounters a significantly higher energy barrier than Li+ to dehydrate at identical transmembrane pressure.\n\na Pore size distributions of P-M and DP-M membranes and the sizes of Li+ and Mg2+ cations. Schematic illustration of transmembrane transport of hydrated Li+ and Mg2+ through the subnanometer pores in DP-M. b Analysis of the binding configurations between P-M/DP-M molecular fragments and hydrated Li+ and Mg2+ using the independent gradient model based on Hirshfeld partition (IGMH). c, d Differential scanning calorimetry (DSC) thermogram derived crystallization and melting behavior of the DP-M membrane after being equilibrated with 1000 ppm c MgCl2 and (d) LiCl aqueous solutions. The lower right inset shows the melting enthalpy (\u0394Hm), crystallization enthalpy (\u0394Hc), and their difference (\u0394Hm\u2212c). e The binding energies between the hydrated Li+/Mg2+ and the PA molecular fragments of P-M/DP-M. The numbers represent the calculated energy gaps between Li+ and Mg2+ in P-M and DP-M. f Interaction region indicator analysis of the PA fragments interacting with Mg2+. The effects of the hydration layer and TMC were shielded (the arb. units here represents energy, and 1 arb. units is approximately 27.21\u2009eV). g Interaction region indicator analysis of the PA fragments derived from DAT-NH2 and the visualized structure diagram. h van der Waals surface area ratio corresponding to various electrostatic potential intervals of the PA molecular fragments.\n\nTo gain fundamental insights into the influences of the pore environment on cation dehydration behavior, dynamic molecular simulations were performed to examine the interactions between PA fragments and hydrated Li+ and Mg2+ ions (Fig.\u00a04b and Supplementary Fig.\u00a039). Compared with P-M, the independent gradient model based on Hirshfeld partitioning (IGMH) analysis shows that DP-M has weaker hydrogen bonding and van der Waals interactions with water molecules in the hydration shell of Mg2+ ions, which is unfavorable for stabilizing the configuration. In addition, the lower intrinsic charge number of Li+ relative to Mg2+ leads to the weaker binding energy of its hydration layer (Supplementary Fig.\u00a040), while the positively charged CTHP structures in DP-M further promote the escape of polar water molecules from the Li+ hydration shell by exerting extensive van der Waals and hydrogen bonding interactions, as demonstrated in the DP-M/hydrated Li+ configuration (Fig.\u00a04b), thereby aggrandizing the dehydration of Li+ during transmembrane permeation. These effects of promoting Li+ dehydration expedite its transport through DP-M, which plays an important role in enhancing Li+/Mg2+ selectivity, especially when the membrane pore sizes are diminished and the size distribution is constricted. Differential scanning calorimetry (DSC) measurements were also performed to experimentally explore the hydration/dehydration behavior of Li+ and Mg2+ within the polyamide polymer matrix. As shown in Fig.\u00a04c, d, the obtained crystallization enthalpy reveals that Mg2+ (\u0394Hc = \u2212303.0\u2009J/g) tends to form a more structured and strongly bound hydration shell within the polyamide matrix of DP-M compared to Li+ (\u0394Hc = \u2212188.2\u2009J/g). Furthermore, the melting enthalpy (\u0394Hm, 314.8 vs. 237.8\u2009J/g) indicates that Mg2+ is more likely to establish stable coordination interactions with the functional groups and chemical bonds of the polyamide network, thereby requiring greater energy to disrupt the hydration structure. These thermodynamic distinctions disclose the underlying rationale for the enhanced Li+/Mg2+ selectivity of the DP-M membrane, which is in good agreement with the modeling results. Contrarily, for the P-M benchmark (Supplementary Fig.\u00a041), the melting (\u0394Hm = 338.9 vs. 357.4\u2009J/g) and crystallization (\u0394Hc = \u2212303.0 vs. \u2212320.3\u2009J/g) enthalpies associated with hydrated Mg2+ and Li+ are comparable, indicating that the P-M benchmark lacks the thermodynamic ability to discriminate between hydrated Mg2+ and Li+, which sheds light on its low Li+/Mg2+ selectivity.\n\nDFT calculations were further performed to illuminate the mutual interactions between PA and cations by performing configuration optimization and cation\u2013PA binding energy calculations (Supplementary Table\u00a05). As displayed in Supplementary Fig.\u00a042, the negative binding energies of hexahydrated Mg2+ with the DP-M PA fragments are consistently lower than those with the P-M fragments, suggesting that the binding interactions between Mg2+ and P-M are relatively more stable. On the contrary, the similar binding energies of hydrated Li+ to DP-M and P-M PA fragments (\u201328.83 vs. \u201329.65\u2009kcal/mol) acknowledge that the transport of hydrated Li+ through the two membranes is subjected to similar energetic penalties despite the diminished and narrowed pore sizes of the former (Fig.\u00a04e). However, the binding energy gaps between Li+ and Mg2+ in the DP-M fragments are 16.80 and 9.90\u2009kcal/mol, respectively, which are markedly larger than those in the P-M fragments (i.e., 2.82 and 6.66\u2009kcal/mol) (Fig.\u00a04e), implying that DP-M has an overwhelming advantage over P-M to differentiate Li+ and Mg2+ from the energy perspective. The interaction region indicator (IRI) was subsequently applied to conduct an in-depth analysis of the specific types of interactions between the PA fragments and hexahydrated Mg2+41 (Supplementary Fig.\u00a043). The corresponding scatter plots reveal that the interaction forces involved are intricate and hard to distinguish (Supplementary Fig.\u00a044). Therefore, the hydration layer of Mg2+ and the influence of TMC were shielded to better disclose the contributions of DAT-NH2 moieties in the PA (Fig.\u00a04f). Examining their respective IRI scatter plots, eminent peaks appear near sign(l2)r values of \u22120.05 and 0.06 arb. units in the DP-M PA molecular fragments. From the electron density point of view, the peak at \u22120.05 arb. units corresponds to a weak interaction of higher strength, whereas the peak at 0.06 arb. units stems from a stronger spatial repulsion. Notably, the scatter plot of the weak interaction portion ascertains an anomalous peak at approximately 0.013 arb. units in DP-M (Supplementary Fig.\u00a045), which indicates that the CTHP structures derived from DAT-NH2 may generate proprietary steric hindrance at the molecular level. The two distinct peaks in the scatter plot obtained from interaction decomposition confirm that CTHP instigates both attractive and repulsive interactions (Fig.\u00a04g). Further analysis of the IRI visualized isosurface shows that the peak near \u22120.05 arb. units is attributed to intramolecular H-bonding interactions. These H-bonds account for the in situ formation of the cyclic conformations in the CTHP structures (Fig.\u00a04g), which dictate additional steric hindrance at approximately 0.013 arb. units (the peak near 0.013 is retained in Supplementary Fig.\u00a046). Moreover, the peak at approximately 0.06 arb. units is associated with the strong repulsion induced by the overlapping of the triazole rings in CTHP driven by van der Waals surfaces. Other than the narrowed subnanometer pore sizes, these anomalous intramolecular H-bonding structures provide additional steric hindrance at the molecular level, further amplifying the permeation energy barrier acting on divalent cations.\n\nIn addition to the non-Coulombic interactions, long-range Coulombic electrostatic forces (i.e., Donnan exclusion) also play an imperative role in the cation\u2013PA interactions, particularly considering the strongly charged PA structure of DP-M. Qualitative and quantitative analyses of the electrostatic potential (ESP) were conducted to acquire the van der Waals surface ESP distributions of the PA molecular fragments of DP-M and P-M. As illustrated in Fig.\u00a04h and Supplementary Fig.\u00a047\u201348, DP-M exhibits a exceptional positive potential and this observation was reaffirmed by the quantitative calculation of the ESP region proportions, where DP-M shows a large positive potential region proportion of 97% and an average ESP value of 55.55\u2009kcal/mol, far exceeding the respective value of P-M. The pronounced electrostatic repulsion between DP-M and the positively charged hexahydrated cations is unequivocally conferred by the CTHP structures of the PA layer. The ESP of hydrated Mg2+ is nearly twice as high as that of hydrated Li+ (193.29 vs. 98.53\u2009kcal/mol, Supplementary Fig.\u00a040), which inevitably invokes formidable Donnan exclusion selectivity towards the positively charged DP-M (55.55\u2009kcal/mol). Overall, the intriguing co-cation sieving ability of DP-M proceeds through a cooperative mechanism of steric hindrance and electrostatic exclusion, as corroborated by comprehensive modeling and experimental characterization.\n\nWater molecules need to overcome certain energy barriers when dissolving and diffusing through the PA membrane, which is primarily governed by the chemical features and nanoporous structure of the PA selective layer (Fig.\u00a05a). The mutual interactions of water molecules with the binding sites on the PA network thereby have substantial impacts on water permeation rate. To gain a fundamental understanding of the mechanisms governing the facilitated permeation of water through the DP-M membrane, DFT atomistic calculations and MD simulations were performed. DFT was employed to specifically evaluate the molecular interactions between water and the cationic DP-M PA fragments by calculating the surface free energy (SFE, Supplementary Table\u00a06) and the molecular polarity index (MPI), which reflect membrane hydrophilicity from the perspectives of interfacial thermodynamics and quantum chemistry. As displayed in Fig.\u00a05b, DP-M shows a higher MPI value than that of P-M (i.e., 56.0 vs. 19.7), which is consistent with the lower surface water contact angle of the former. Meanwhile, the SFE value of DP-M is greater than that of P-M (i.e., 50.5 vs. 41.4\u2009kJ/m2), indicating a clear preference of polar water molecules for wetting and partitioning into the PA fragments of DP-M (Fig.\u00a05c and Supplementary Table\u00a06). To further elucidate the diffusion behavior of water molecules within the PA layer, MD simulations were subsequently conducted to acquire the molecular-level binding affinities of water cluster to the PA fragments (Fig.\u00a05d). The radial distribution functions (RDFs) plots with respect to the PA fragments labeled in green (I), blue (II), and orange (III) reveal that the peak of I-H2O in the first coordination layer is significantly higher than those of II-H2O and III-H2O (Fig.\u00a05e), closely aligned with the DFT calculations and experimental data. Furthermore, the water bonding (WB) capacity calculated by RDFs follows an order of WBI\u2009>\u2009WBII\u2009>\u2009WBIII, while the computed binding energies (BE) of fragments I, II, and III with water are in the order of |BEI\u2009|\u2009> |BEII\u2009|\u2009> |BEIII\u2009|\u2009(Fig.\u00a05f). Hereupon, the cationic triazolyl heterocyclic PA structures derived from DAT-NH2 in DP-M have a relatively lower affinity to water clusters. Such energy metrics accentuate a thermodynamic inclination of DP-M to facilitate the transport of water by providing favorable water binding sites with moderate resistance, aligned with our design strategy and the ideal PA nanostructure we intend to construct (Fig.\u00a05g).\n\na Schematic representation of the advanced structure of an ultrapermeable PA membrane with precise co-cation sieving capability. b DFT atomistic calculations of polarity differences between DP-M and P-M molecular fragments. c ESP distributions of van der Waals surfaces of the water molecules obtained by DFT calculations. d Three representative PA molecular fragments of DP-M and P-M (left) and the schematic illustration of water cluster distribution in each fragment (right). e The radial distribution functions (RDFs) between water and the three PA fragments. f Binding energy (BE) and the number of water molecules (NW) around the three PA fragments. All the information and data described in (d\u2013f) were obtained from MD simulations. g Schematic illustration of the working principle of the semipermeable DP-M for ultrafast co-cation nanofiltration (yellow and blue spheres represent monovalent and divalent cations, respectively).",
+            "section_image": [
+                "https:////media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41467-025-62376-8/MediaObjects/41467_2025_62376_Fig2_HTML.png",
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+                "https:////media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41467-025-62376-8/MediaObjects/41467_2025_62376_Fig5_HTML.png"
+            ]
+        },
+        {
+            "section_name": "Discussion",
+            "section_text": "Advanced nanofiltration membranes with exceptional permselectivity offer promising solutions to address pressing challenges associated with water scarcity and renewable energy. This study demonstrates a feasible molecular engineering strategy to reconcile the tradeoff between water permeance and selectivity in state-of-the-art PA nanofiltration membranes for ultrafast co-cation sieving. Our approach is contingent on the fine-tuned regulation of the porous nanostructure and the mutual interactions of the PA layer with water molecules and ions by molecular construction of cationic triazolyl heterocyclic polyamide (CTHP) structures via in situ interfacial polymerization using synthetic DTA-NH2 isomers. The obtained PA membranes exhibited simultaneously enhanced water permeance and selectivity for cation separation, achieving high divalent cation rejections of over 99%, accompanied by a 9-fold increase in monovalent/divalent cation sieving selectivity and tripled water permeance in comparison with the pristine benchmark, as well as outstanding chemical stability and fouling resistance. Experimental data in conjunction with molecular simulations confirm that the intriguing permselectivity springs from the advanced molecular structures of the CTHP-modulated PA layer, which not only investigates a substantial decrease in the membrane pore size and narrows the size distribution but also affords high positive charge density and polarity. Coincidentally, the CTHP structures also provide preferential water binding sites with low energy barriers, energetically facilitating the accommodation and diffusion of water molecules within the PA layer, which eliminates the increased water transport resistance caused by pore size shrinkage. The developed synthetic engineering strategy sheds light on the rational design and fabrication of high-performance polymer membranes for precision NF separations affiliated with water\u2012energy nexuses.",
+            "section_image": []
+        },
+        {
+            "section_name": "Methods",
+            "section_text": "Polyethyleneimine (PEI, MW\u2009=\u200970000\u2009Da, 50\u2009wt% aqueous solutions), trimesoyl chloride (TMC, 98.0%), 1,2,4-triaminobenzene (95%), 3-bromopropylamine (97%), and sodium dodecyl sulfate (SDS, 99.0%) ordered from Macklin (Shanghai, China) were used to synthesize the polyamide benchmark membrane via interfacial polymerization. Hexane (99.0%) purchased from Macklin was used as the solvent for the TMC monomer. 3,5-Diamino-1,2,4-triazole (DAT, 98%), 2-bromoethylamine (98%), acetonitrile (99%), and N,N-dimethylformamide (DMF, 98%) were obtained from Macklin for the synthesis and purification of DAT-NH2 isomers. Ethylene glycol (62\u2009Da), diethylene glycol (106\u2009Da), glucose (180\u2009Da), and polyethylene glycols of different molecular weights (i.e., PEG200, PEG400, PEG600, and PEG1000) were provided by Aladdin (Tianjin, China) for membrane pore size characterization. Sodium sulfate (Na2SO4), lithium sulfate (Li2SO4), magnesium sulfate (MgSO4), magnesium chloride (MgCl2), lithium chloride (LiCl), sodium chloride (NaCl), rubidium chloride (RbCl), potassium chloride (KCl), nickel chloride (NiCl2), calcium chloride (CaCl2), and zinc chloride (ZnCl2) were obtained from Macklin for salt rejection tests. Dodecyltrimethylammonium bromide (DTAB) used in the fouling study was purchased from Macklin (Shanghai, China). Sodium hydroxide (NaOH, 99.9%) was supplied by Shanghai Aladdin Biochemical Technology Co., Ltd. Hydrochloric acid (HCl, AR) was purchased from Fuchen (Tianjin) Chemical Reagent Co., Ltd. Unless otherwise indicated, all chemicals and reagents were used as received without further purification. Polyether sulfone (PES) ultrafiltration membrane with a molecular weight cutoff of 20\u201330\u2009kDa from Weihua Technology Co., Ltd., China was used as the substrate for preparing the polyamide membranes for nanofiltration tests. Deionized water was supplied by a Millipore-D 24 UV ultrapure water integrated system (Millipore Instruments, 18.2 M\u03a9 cm).\n\n3,5-Diamino-4/1-(2-aminoethyl)\u22121,2,4-triazole (DAT-NH2) isomers were synthesized via a one-step quaternization reaction following the reaction path shown in Supplementary Fig.\u00a03. In a typical synthesis, 4.24\u2009g of 3,5-diamino-1,2,4-triazole (DAT, 42.8\u2009mmol) and 8.77\u2009g of 2-bromoethylamine (42.8\u2009mmol) were dissolved in 90\u2009mL of N,N-dimethylformamide (DMF) in a 150\u2009mL round-bottom flask. The flask with the reaction mixture was then heated to 45\u2009\u00b0C in a water bath and reacted at this temperature for 24\u2009h under vigorous stirring. A pale green solution rapidly formed with increasing reaction time. When the reaction was complete, the resulting mixture was immediately transferred into a 500\u2009mL beaker, and 180\u2009mL of acetonitrile was then added to obtain a milky white suspension. The obtained flocculent precipitates were subsequently redissolved in 10\u2009mL of DMF and then precipitated with 180\u2009mL of acetonitrile. The white solids were collected via high-speed centrifugation. The above dissolution and precipitation treatment was repeated three times. Finally, the as-synthesized DAT-NH2 was vacuum dried at 40\u2009\u00b0C overnight and then stored in a sealed container for subsequent characterization and membrane fabrication.\n\nFor the fabrication of the PA thin-film composite NF membrane, the polyether sulfone (PES) substrate was first immersed in an amine monomer aqueous solution with 0.1\u2009wt% sodium dodecyl sulfate (SDS) and 0.1\u2009wt% Na2CO3 for 5\u2009min. After the excess water on the top surface was removed via filter paper, the amine-monomer saturated PES substrate was sandwiched into a homemade frame with the top surface facing upward. Interfacial polymerization was initiated by carefully adding excessive 0.3\u2009wt% trimesoyl chloride (TMC) solution into the frame to cover the surface, which was allowed to react for 1\u2009min. When the reaction was complete, the excess hexane solution was drained, and the resulting membrane was dried at 60\u2009\u00b0C for 30\u2009min. Specifically, DP-M represents a PA membrane that was prepared following the above synthesis procedure using a mixture of DAT-NH2 (0.06\u2009wt%) and polyethyleneimine (PEI) (0.44\u2009wt%) as the amine monomer. The P-M benchmark membrane was fabricated solely by using PEI as the amine monomer. All the as-synthesized PA membranes were stored in deionized water at 5\u2009\u00b0C for further characterization and performance tests. The detailed preparation process of the PA nanofilm is included in the\u00a0Supplementary Information (Supplementary Note\u00a01). Two model membranes were prepared by replacing DAT-NH2 with 3,5-diamino-4/1-(3-aminopropyl)\u22121,2,4-triazole (DAAT-NH2) and 1,2,4-triaminobenzene, respectively, under identical interfacial polymerization conditions. Large-sized DP-M membranes (1\u00d70.3\u2009m) were fabricated using a custom-made interfacial polymerization apparatus under the same reaction conditions as the laboratory-scale preparation.\n\nThe successful synthesis of DAT-NH2 isomers was confirmed by mass spectrometry (MS, MSQ Plus, USA) and high-performance liquid chromatography (HPLC, Ultimate 3000 RS, USA). The chemical structure of DAT-NH2 was characterized by proton nuclear magnetic resonance (1H NMR) spectroscopy (Bruker AVANCE AV400, USA). The chemical features of the PA membranes were also analyzed via Fourier transform infrared spectroscopy (FT-IR, Nicolet IN10, Thermo Fisher, USA) and X-ray photoelectron spectroscopy (XPS, Escalab 250Xi, Thermo Fisher, USA). The membrane surface morphology and roughness were examined via field emission scanning electron microscopy (FESEM, Quanta 250 FEG, FEI, USA) and atomic force microscopy (AFM, Nano Wizard 4, Bruker, Germany). The membrane cross-sectional morphology was identified via high-resolution transmission electron microscopy (TEM, FEI Tecnai G2 F30, FEI, USA). Surface hydrophilicity was assessed via water contact angle measurements on a contact angle goniometer (HARKE-SPCA, HARKE, China). The surface zeta potential was measured via a SurPASS electrokinetic analyzer (Anton Paar, GmbH, Austria). The molecular weight cutoff (MWCO) and pore size distribution of the membrane were obtained via solute retention tests using polyethylene glycol (PEG) probes with different molecular weights. The thermal behavior related to the hydration state of the ions within the membrane matrix was characterized using a TA Q2000 differential scanning calorimeter (TA Instruments, USA). The detailed procedures for each measurement are included in the\u00a0Supplementary Information (Supplementary Notes\u00a02\u20133).\n\nThe separation performance of the PA membranes was characterized in nanofiltration mode at 23\u2009\u00b0C via a cross-flow filtration apparatus with an effective membrane filtration area of 6.0\u2009cm2. Before data collection, the membrane sample was conditioned at a pressure of 2\u2009bar greater than the intended test pressure until the water flux stabilized. The pure water flux (Jw, L m\u22122 h\u22121, abbreviated as LMH) was measured using deionized water as the feed, and the water permeance (A, LMH/bar) was calculated via Eq. (1).\n\nwhere \u2206P (bar) is the trans-membrane hydraulic pressure, \u2206V (L) is the volume of permeate water collected during a time interval of \u2206t (h), and S (m2) is the effective membrane filtration area.\n\nThe membrane ion sieving ability was examined via rejection tests that were conducted under various conditions using a wide spectrum of inorganic salts as solutes. Specifically, Na2SO4, Li2SO4, MgSO4, MgCl2, LiCl, NaCl, RbCl, KCl, NiCl2, CaCl2, and ZnCl2 solutions with different concentrations and compositions were used as the feed. The single salt rejection (R, %) was calculated via Eq. (2).\n\nwhere Cp and Cf are the salt contents of the permeate and feed, respectively. The salt concentration was determined via conductivity measurement via a SevenCompact\u2122 S230 (Mettler Toledo) conductivity meter. Binary mixtures of MgCl2 and LiCl with different mass ratios were used to evaluate the membrane selectivity for co-cation fractionation. The Li+/Mg2+ separation factor (SLi+/Mg2+) was calculated via Eq. (3).\n\nwhere Cf Mg2+ and Cf Li+ and where Cp Mg2+ and Cp Li+ represent the concentrations of Mg2+ and Li+ in the feed and permeate, respectively. An inductively coupled plasma optical emission spectrometer (ICP\u2012OES, iCAP 7000, Germany) was used to quantify the ion contents of the solution. Each data point was tested three times under the same conditions using randomly selected membrane samples, and the average value was reported.\n\nThe long-term stability of the membrane was evaluated by monitoring the water flux and salt rejection for up to 120\u2009h at 6\u2009bar using 1000 ppm MgCl2 solution as the feed. The pH stability of the membrane was assessed by measuring the water flux and salt rejection in a feed pH range of 1\u2009\u2212\u200913 using 1000 ppm LiCl solution as the probe feed, during which the solution pH was adjusted via HCl and NaOH. The concentrations of the single salt solution and binary mixed solution (MgCl2/LiCl mass ratio of 20) involved in the experiment were 1000 and 2000 ppm, respectively. All nanofiltration tests were performed at room temperature (25\u2009\u00b0C), and no additional pH adjustment was made to the feed except for the pH influence tests. The chlorine resistance of the membrane was evaluated by immersing the membrane samples in aqueous sodium hypochlorite solution (NaClO, 200 ppm, pH = 6) under continuous stirring. To ensure that the chlorine concentration remained consistent throughout the exposure period, the NaClO solution was replaced every 24\u2009h. After a specified exposure duration, the membranes were thoroughly rinsed with deionized water to eliminate residual chemicals and then subjected to nanofiltration performance tests. The chlorine tolerance was assessed by measuring the MgCl2 rejection and water flux using a 1000 ppm MgCl2 solution as the probe feed under a transmembrane pressure of 6\u2009bar. Antifouling performance was evaluated using a cross-flow filtration system at 6\u2009bar. A baseline water flux was recorded over 2\u2009h using a 1000 ppm MgCl2 solution as feed. The membrane was then exposed to 200 ppm DTAB in a 1000 ppm MgCl2 solution for 8\u2009h to monitor flux degradation. After three 10-minute deionized water rinse cycles, the recovered flux was evaluated using a 1000 ppm MgCl2 solution for 2\u2009h.\n\nDensity functional theory (DFT) atomistic calculations were conducted via ORCA quantum chemistry software (version 5.0.4)42,43,44. The binding energy and ion hydration energy were obtained via single-point energy calculations. Electrostatic potential (ESP)45,46, average local ionization energy (ALIE)47, interaction region indicator (IRI)41, independent gradient model based on Hirshfeld partition (IGMH)48, and molecular polarity index (MPI)49 analyses were performed with the Multiwfn software package to gain insights into molecular electronic properties and interaction patterns50. LAMMPS and GROMACS were employed for molecular dynamics (MD) simulations51,52, where LAMMPS was used to calculate the free volume fraction of the PA nanofilm, whereas GROMACS was applied to analyze the distribution and binding energy of water molecules around specific PA molecular segments. These simulations enabled a detailed exploration of water\u2012PA interactions, which is crucial for understanding the hydration behavior and separation performance of the membrane. Comprehensive details of the computational methods and protocols are provided in Supplementary Note\u00a04 and Note\u00a05.",
+            "section_image": []
+        },
+        {
+            "section_name": "Data availability",
+            "section_text": "All relevant data in the main text or the supplementary materials are available from the corresponding authors upon request.\u00a0Source data are provided with this paper.",
+            "section_image": []
+        },
+        {
+            "section_name": "References",
+            "section_text": "Zhang, F., Fan, J.-b & Wang, S. Interfacial Polymerization: From Chemistry to Functional Materials. Angew. Chem. Int. Ed. 59, 21840\u201321856 (2020).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLu, X. & Elimelech, M. Fabrication of desalination membranes by interfacial polymerization: history, current efforts, and future directions. Chem. Soc. Rev. 50, 6290\u20136307 (2021).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nEpsztein, R., DuChanois, R. M., Ritt, C. L., Noy, A. & Elimelech, M. Towards single-species selectivity of membranes with subnanometre pores. Nat. Nanotechnol. 15, 426\u2013436 (2020).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWang, K. et al. Tailored design of nanofiltration membranes for water treatment based on synthesis\u2013property\u2013performance relationships. Chem. Soc. Rev. 51, 672\u2013719 (2022).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nSengupta, B. et al. Carbon-doped metal oxide interfacial nanofilms for ultrafast and precise separation of molecules. Science 381, 1098\u20131104 (2023).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLu, C. et al. Dehydration-enhanced ion-pore interactions dominate anion transport and selectivity in nanochannels. Sci. Adv. 9, eadf8412 (2023).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nJi, Y. et al. Electric field-assisted nanofiltration for PFOA removal with exceptional flux, selectivity, and destruction. Environ. Sci. Technol. 47, 18519\u201318528 (2023).\n\nZhang, Y. et al. Ice-confined synthesis of highly ionized 3D-quasilayered polyamide nanofiltration membranes. Science 382, 202\u2013206 (2023).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nFreger, V. & Ramon, G. Z. Polyamide desalination membranes: formation, structure, and properties. Prog. Polym. Sci. 122, 101451 (2021).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nTan, Z., Chen, S., Peng, X., Zhang, L. & Gao, C. Polyamide membranes with nanoscale Turing structures for water purification. Science 360, 518\u2013521 (2018).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nZhao, G.-J. et al. Polyamide nanofilms through a non-isothermal-controlled interfacial polymerization. Adv. Funct. Mater. n/a, 2313026 (2024).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nGeise, G. M. Why polyamide reverse-osmosis membranes work so well. Science 371, 31\u201332 (2021).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLopez, K. P., Wang, R., Hjelvik, E. A., Lin, S. & Straub, A. P. Toward a universal framework for evaluating transport resistances and driving forces in membrane-based desalination processes. Sci. Adv. 9, eade0413 (2023).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nCulp, T. E. et al. Nanoscale control of internal inhomogeneity enhances water transport in desalination membranes. Science 371, 72\u201375 (2021).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWang, Z. et al. Manipulating interfacial polymerization for polymeric nanofilms of composite separation membranes. Prog. Polym. Sci. 122, 101450 (2021).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nZhou, X. et al. Intrapore energy barriers govern ion transport and selectivity of desalination membranes. Sci. Adv. 6, eabd9045 (2020).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLiu, C. et al. Interfacial polymerization at the alkane/ionic liquid interface. Angew. Chem. Int. Ed. 133, 14757\u201314764 (2021).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nRaaijmakers, M. J. T. & Benes, N. E. Current trends in interfacial polymerization chemistry. Prog. Polym. Sci. 63, 86\u2013142 (2016).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nShen, L. et al. Polyamide-based membranes with structural homogeneity for ultrafast molecular sieving. Nat. Commun. 13, 500 (2022).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLi, X. et al. Polycage membranes for precise molecular separation and catalysis. Nat. Commun. 14, 3112 (2023).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nYuan, B. et al. Self-assembled dendrimer polyamide nanofilms with enhanced effective pore area for ion separation. Nat. Commun. 15, 471 (2024).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nZhao, G., Gao, H., Qu, Z., Fan, H. & Meng, H. Anhydrous interfacial polymerization of sub-1 \u00c5 sieving polyamide membrane. Nat. Commun. 14, 7624 (2023).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nChen, W., Liu, M., Ding, M., Zhang, L. & Dai, S. Advanced thin-film composite polyamide membrane for precise trace short-chain PFAS sieving: Solution, environment and fouling effects. Process Saf. Environ. Prot. 169, 493\u2013503 (2023).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDai, R. et al. Nanovehicle-assisted monomer shuttling enables highly permeable and selective nanofiltration membranes for water purification. Nat. Water 1, 281\u2013290 (2023).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nPeng, H. & Zhao, Q. A nano-heterogeneous membrane for efficient separation of lithium from high magnesium/lithium ratio brine. Adv. Funct. Mater. 31, 2009430 (2021).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nHong, S. et al. Precision ion separation via self-assembled channels. Nat. Commun. 15, 3160 (2024).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nZhang, S. et al. Solar-driven membrane separation for direct lithium extraction from artificial salt-lake brine. Nat. Commun. 15, 238 (2024).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nZhou, Z. et al. Electrochemical-repaired porous graphene membranes for precise ion-ion separation. Nat. Commun. 15, 4006 (2024).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nPeng, H., Liu, X., Su, Y., Li, J. & Zhao, Q. Advanced lithium extraction membranes derived from tagged-modification of polyamide networks. Angew. Chem. Int. Ed. 62, e202312795 (2023).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nPeng, H., Su, Y., Liu, X., Li, J. & Zhao, Q. Designing gemini-electrolytes for scalable Mg2+/Li+ separation membranes and modules. Adv. Funct. Mater. 33, 2305815 (2023).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nGuo, B.-B. et al. Double charge flips of polyamide membrane by ionic liquid-decoupled bulk and interfacial diffusion for on-demand nanofiltration. Nat. Commun. 15, 2282 (2024).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nShefer, I., Peer-Haim, O. & Epsztein, R. Limited ion-ion selectivity of salt-rejecting membranes due to enthalpy-entropy compensation. Desalination 541, 116041 (2022).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWang, W. et al. Simultaneous manipulation of membrane enthalpy and entropy barriers towards superior ion separations. Angew. Chem. Int. Ed. 63, e202408963 (2024).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nFreger, V. Nanoscale heterogeneity of polyamide membranes formed by interfacial polymerization. Langmuir 19, 4791\u20134797 (2003).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMuscatello, J., M\u00fcller, E. A., Mostofi, A. A. & Sutton, A. P. Multiscale molecular simulations of the formation and structure of polyamide membranes created by interfacial polymerization. J. Membr. Sci. 527, 180\u2013190 (2017).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nZhu, Q.-Y. et al. Can the mix-charged NF membrane directly obtained by the interfacial polymerization of PIP and TMC? Desalination 558, 116623 (2023).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nZhang, M. et al. Modulating interfacial polymerization with phytate as aqueous-phase additive for highly-permselective nanofiltration membranes. J. Membr. Sci. 657, 120673 (2022).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKaran, S., Jiang, Z. & Livingston, A. G. Sub\u201310 nm polyamide nanofilms with ultrafast solvent transport for molecular separation. Science 348, 1347\u20131351 (2015).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKo\u0161uti\u0107, K., Dolar, D., A\u0161perger, D. & Kunst, B. Removal of antibiotics from a model wastewater by RO/NF membranes. Sep. Purif. Technol. 53, 244\u2013249 (2007).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nSarkar, P., Ray, S., Sutariya, B., Chaudhari, J. C. & Karan, S. Precise separation of small neutral solutes with mixed-diamine-based nanofiltration membranes and the impact of solvent activation. Sep. Purif. Technol. 279, 119692 (2021).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLu, T. & Chen, Q. Interaction region indicator: a simple real space function clearly revealing both chemical bonds and weak interactions**. Chem. Methods 1, 231\u2013239 (2021).\n\nNeese, F., Wennmohs, F., Becker, U. & Riplinger, C. The ORCA quantum chemistry program package. J. Chem. Phys. 152, 224108 (2020).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nStoychev, G. L., Auer, A. A. & Neese, F. Automatic generation of auxiliary basis sets. J. Chem. Theory Comput. 13, 554\u2013562 (2017).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nNeese, F. Software update: The ORCA program system\u2014Version 5.0. WIREs Computational Mol. Sci. 12, e1606 (2022).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nManzetti, S. & Lu, T. The geometry and electronic structure of aristolochic acid: possible implications for a frozen resonance. J. Phys. Org. Chem. 26, 473\u2013483 (2013).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLu, T. & Manzetti, S. Wavefunction and reactivity study of benzo[a]pyrene diol epoxide and its enantiomeric forms. Struct. Chem. 25, 1521\u20131533 (2014).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nZhang, J. & Lu, T. Efficient evaluation of electrostatic potential with computerized optimized code. Phys. Chem. Chem. Phys. 23, 20323\u201320328 (2021).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLu, T. & Chen, Q. Independent gradient model based on Hirshfeld partition: a new method for visual study of interactions in chemical systems. J. Comput. Chem. 43, 539\u2013555 (2022).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLiu, Z., Lu, T. & Chen, Q. Intermolecular interaction characteristics of the all-carboatomic ring, cyclo[18]carbon: focusing on molecular adsorption and stacking. Carbon 171, 514\u2013523 (2021).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLu, T. & Chen, F. Multiwfn: a multifunctional wavefunction analyzer. J. Comput. Chem. 33, 580\u2013592 (2012).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nHess, B., Kutzner, C., van der Spoel, D. & Lindahl, E. GROMACS 4:\u2009 algorithms for highly efficient, load-balanced, and scalable molecular simulation. J. Chem. Theory Comput. 4, 435\u2013447 (2008).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nThompson, A. P. et al. LAMMPS - a flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales. Comput. Phys. Commun. 271, 108171 (2022).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDownload references",
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+        },
+        {
+            "section_name": "Acknowledgements",
+            "section_text": "The authors gratefully acknowledge the financial support from the National Natural Science Foundation of China (22125603 & 92475205 to G.H.), the Tianjin Applied Basic Research Diversified Investment\u2013Urban Fire Protection Project (Grant No. 24JCQNJC00010 to G.H.), the General Program of Tianjin Natural Science Foundation (Grant No. 24JCYBJC01550 to G.H.), and the Fundamental Research Funds for the Central Universities (040-63253198 & 040-63243125 to G.H.). Special thanks are also made to the Han Gang Research Lab members for their helpful suggestions related to the characterization of materials.",
+            "section_image": []
+        },
+        {
+            "section_name": "Author information",
+            "section_text": "College of Environmental Science and Engineering, Tianjin Key Laboratory of Environmental Remediation and Pollution Control, Nankai University, 38 Tongyan Road, Tianjin, China\n\nZhenxiang Pan,\u00a0Yalong Lei,\u00a0Tiange Yan,\u00a0Fuxin Zheng,\u00a0Yu Liao,\u00a0Jiang Zhan,\u00a0Tong Zhang\u00a0&\u00a0Gang Han\n\nState Key Laboratory of Urban Water Resource and Environment, School of Chemistry and Chemical Engineering, Harbin Institute of Technology, Harbin, China\n\nLu Shao\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nZ.X.P., Y.L.L., and G.H. designed research; Z.X.P. and Y.L.L. performed research; Z.X.P., Y.L.L., T.G.Y., F.X.Z., Y.L., J.Z., and T.Z. analyzed data; Z.X.P., Y.L.L., L.S. and G.H. wrote the paper.\n\nCorrespondence to\n                Lu Shao or Gang Han.",
+            "section_image": []
+        },
+        {
+            "section_name": "Ethics declarations",
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+            "section_image": []
+        },
+        {
+            "section_name": "Peer review",
+            "section_text": "Nature Communications thanks Niveen Khashab and the other, anonymous, reviewers for their contribution to the peer review of this work. A peer review file is available.",
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+            "section_image": []
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+        },
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+            "section_text": "Open Access  This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article\u2019s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article\u2019s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.\n\nReprints and permissions",
+            "section_image": []
+        },
+        {
+            "section_name": "About this article",
+            "section_text": "Pan, Z., Lei, Y., Yan, T. et al. Molecular manipulation of polyamide nanostructures reconciles the permeance-selectivity threshold for precise ion separation.\n                    Nat Commun 16, 7171 (2025). https://doi.org/10.1038/s41467-025-62376-8\n\nDownload citation\n\nReceived: 02 December 2024\n\nAccepted: 17 July 2025\n\nPublished: 04 August 2025\n\nVersion of record: 04 August 2025\n\nDOI: https://doi.org/10.1038/s41467-025-62376-8\n\nAnyone you share the following link with will be able to read this content:\n\nSorry, a shareable link is not currently available for this article.\n\n\n\n\n                            Provided by the Springer Nature SharedIt content-sharing initiative\n                        ",
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+        {
+            "section_name": "Abstract",
+            "section_text": "Solitary foraging ants excel in following long visual routes in complex environments with limited sensory and neural resources\u2014an ability that remains challenging for robots with minimal computational power. Here, we introduce a self-supervised, insect-inspired neural network that enables robust route-following on the compact, low-cost Antcar robot. The robot leverages key aspects of ant brain and behavior: (i) continuous, one-shot visual route learning using panoramic encoding in a mushroom body-inspired network, (ii) categorization of low-resolution egocentric panoramas via oscillatory movements, (iii) opponent-process control of angular and forward velocities based on visual familiarity, (iv) recognition of places of interest along routes, and (v) motivation-based memory modulation. Antcar autonomously followed routes between indoor or outdoor destinations, forward or backward, while remaining stable in both theoretical analysis and real-world testing despite occlusions and visual changes. Across 1.3 km of autonomous travel, Antcar achieved challenging route-following with sub-20 cm lateral error at speeds up to 150 cm/s, requiring only 148 kilobits of memory and processing panoramas every 62 ms. This efficient, brain-inspired architecture stands out from more sensor-intensive and computationally demanding methods, presenting a neuromorphic approach with valuable insights into insect navigation and practical robotic applications.Biological sciences/Computational biology and bioinformatics/Computational modelsPhysical sciences/Engineering/Mechanical engineering",
+            "section_image": []
+        },
+        {
+            "section_name": "Additional Declarations",
+            "section_text": "There is NO Competing Interest.",
+            "section_image": []
+        },
+        {
+            "section_name": "Supplementary Files",
+            "section_text": "ContinuousvisualnavigationSupplementaryInformation.pdfSupplementary NotesContinuousvisualroutefollowingVF.mp4Continuous Visual Navigation with Ant Inspired Memories",
+            "section_image": []
+        }
+    ],
+    "nature_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Solitary foraging ants excel at route following using minimal neural resources, Robots don\u2019t. Recent biological studies proposed lateralized, nest-centric memories to explain ants\u2019 direct visual homing but did not address how ants follow curved visual routes away from their nest. We present a biologically inspired neuromorphic model for one-shot panoramic route learning and continuous route following, implemented on a compact car-like robot, Antcar. We demonstrate that route-centric lateralized memories, inspired by the insect mushroom body, enable Antcar to achieve bi-directional route-following, with motivation-driven recognition of route extremities and familiarity-based velocity control. With rigorous Lyapunov-based stability analysis and an empirical memory scalability evaluation, the model was tested over 1.6 km across 113 challenging real-world trials. The system achieves less than 25 cm median lateral error using minimal resources (800-pixel input, 300 MB RAM, 500 mW power, and 18.75 kB memory per 50 m route), offering insights into insect cognition and advancing autonomous robotics under strict resource constraints.",
+            "section_image": []
+        },
+        {
+            "section_name": "Introduction",
+            "section_text": "Insect navigation has long intrigued researchers across various fields, from biology to robotics, driving the development of cutting-edge technologies for autonomous mobile robots1,2,3. Autonomous navigation remains a demanding and interdisciplinary challenge with applications ranging from space exploration to last miles delivery4,5, especially in scenarios where robots cannot rely on satellite systems6. Simultaneously, robots serve as valuable tools for studying insects navigation and brain structure, advancing neuromorphic engineering7,8,9,10,11.\n\nIn Robotics, visual teach-and-repeat methods combined with dead-reckoning techniques have gained in popularity12,13,14,15. However, experienced solitary foraging ants navigate along familiar routes using only visual memories, without relying on dead reckoning (called path integration in insect literature)16,17,18. This behavior has inspired various robotic models, although current implementations are generally limited to short-range experiments of about ten meters, with modest computational efficiency, precision, and accuracy19,20,21,22,23,24. While ant-inspired models achieve results comparable to conventional computer vision approaches13,25, they struggle in dynamic environments where computational efficiency must be balanced with resource use.\n\nThese challenges are partly due to early navigation models that emphasized hymenopteran behavior rather than underlying brain processes. Early models, referred to as perfect memory models, stored periodic snapshots at specific waypoints26,27. Then, during autonomous route following (or exploitation), forced scanning movements compared acquired views to an image bank, using rotational image differences to establish the most familiar image and desired heading, a process known as the insect-based visual compass28,29,30,31,32,33. However, these approaches has revealed two main limitations when applied in robotics.\n\nThe first limitation involves the cumulative storage of snapshots, which significantly increases memory and computational demands as the route lengthens, making it unsuitable for long-distance navigation. This issue was partially addressed by the Infomax neural network34, which enables efficient encoding of increasing numbers of images without a corresponding rise in memory load20,32,35. However, Infomax requires substantial adjustments to synaptic weights for each input through a non-local learning mechanism, limiting its biological plausibility.\n\nIn parallel, research on the Mushroom Body (MB), a key part of the insect brain, has highlighted its essential role in olfactory and visual learning36,37. In the MB, learning occurs through synaptic depression between thousands of Kenyon Cells (KCs) \u2013 intrinsic neurons that sparsely encode sensory input \u2013 and a few Mushroom Body Output Neurons (MBONs), which modulate behavioral responses based on learned associations. These processed signals are then transmitted to downstream neural circuits, influencing decision-making38. The first MB model simulating visual route following used a Spiking Neural Network with 20,000 KCs and one MBON to compute familiarity39. Despite this advancement, a second limitation remains: navigation requires forced, systematic scanning, which slows robotic movement due to non-continuous command updates21. Also, this limitation does not reflect natural ant behavior, where scanning occurs only occasionally40,41,42.\n\nTo address the second limitation, an early robotic implementation combined a klinokinesis model with perfect memory, enhancing short-distance route-following by replacing cumbersome scanning with alternating, ballistic left and right turns where familiarity adjusted turn amplitude19 (later also observed in ants43).\n\nTo move beyond random, undirected kinesis, an early visual homing strategy was proposed that simulates directed movement toward a goal (e.g., a nest). In this model, tested in a particle-based simulation, the firing activity of KCs\u2014which encode visual input\u2014is categorized based on the path integration vector into two pairs of lateralized MBONs. Specifically, views acquired when the nest lies to the left are assigned to the left MBON, and vice versa44,45. This approach mirrors how insects, through continuous lateral body oscillations, sample multiple directions around their nest position43,46.\n\nIn this paper, we focus on route following, which is considered distinct from visual homing in the ant navigation framework,\u00a0and aligns\u00a0with\u00a0Visual Teach & Repeat\u00a0paradigms in robotics47. While visual homing is goal-directed and attractor-based, route following relies on on-route visual memories48. Some recent robotic models have attempted to extend lateralization to route following by splitting the field of view into left and right memories. However, these methods have shown limited success in real-world conditions23,49, and they diverge from biological evidence: in ants, the entire panoramic field is processed binocularly by the MB50. Our approach, therefore, uses the full panoramic view and categorizes visual input with right and left MBON in a route-centric manner, i.e., with respect to a local route orientation, without splitting the field-of-view.\n\nBuilding on our earlier one-MBON model for route learning in an indoor robot21,22, and the lateralization principle for nest-centric homing in simulation45, we present a fully-embodied, biologically realistic, and route-centric lateralized MB architecture implemented and tested on a real-world robot. This work introduces several contributions that significantly advance the field:\n\n(i) Route-centric lateralized learning: We replace the nest-centered categorization with a local, route-aligned reference frame, enabling two lateralized MBONs (right and left) to memorize panoramas as seen on the right or left of the route. This supports curved and goal-directed navigation without requiring a global home vector. (ii) Bi-directional navigation with start/end recognition: Two additional MBONs allow the robot to recognize route extremities, enabling stop and back-and-forth route following, a behavior observed in ants51,52,53,54. (iii) Familiarity-based velocity control: The robot adapts its speed based on visual familiarity, accelerating on known routes and decelerating in novel environments, mirroring ant behavior40. (iv) Analytical stability via oscillatory learning: We show that oscillatory heading movements during learning lead to stable route following, supported by a Lyapunov-based proof of convergence in the local route frame. (v) Empirical memory scalability analysis: We propose a metric to quantify memory capacity in relation to network hyperparameters, providing insights into the scalability of Mushroom Body-based architectures for longer and more complex routes. (vi) Extensive real-world validation: Embedded in the compact Antcar robot (Fig.\u00a01, 2a), our model was tested across 113 autonomous trajectories covering 1.6 km in both indoor and outdoor settings with different environmental conditions and challenges. The system achieved median lateral and angular errors of 24\u2009cm and 4\u00b0, with processing rates of 16\u2009Hz during exploitation and 38\u2009Hz during learning \u2014 all using a single 32\u2009\u00d7\u200932-pixel panoramic camera and minimal computational resources: 300 megabytes of RAM, 500\u2009mW power consumption, and just 18.75 kilobytes of memory. Overall, this paper delivers a biologically grounded and resource-efficient implementation of the proposed panoramic, route-centric and lateralized visual route-following on a physical robot. It integrates neural plausibility, theoretical robustness, and practical feasibility, bridging the gap between insect-inspired models and real-world autonomous robotics.\n\nAn ant in the foreground symbolizes nature\u2019s efficient navigational strategies, while the Antcar robot in the background integrates these principles into a neuromorphic system. The blurred image captures only the large masses of the environment, similar to the low-pass spatial filter in the ant\u2019s visual system, which retains these large features even when objects obstruct the view between the robot and the building. \u24d2Tifenn Ripoll - VOST Collectif / Institut Carnot STAR.",
+            "section_image": [
+                "https:////media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41467-025-62327-3/MediaObjects/41467_2025_62327_Fig1_HTML.jpg"
+            ]
+        },
+        {
+            "section_name": "Results",
+            "section_text": "Our proposed MB model emulates ant visual processing by encoding panoramic images as low resolution neural representations (800-pixel input), enabling efficient learning and route recognition with minimal computational demands (see Methods for details, Fig.\u00a02b). The model operates in two main phases: learning (Fig.\u00a02c) and exploitation (Fig.\u00a02d). During the learning phase, our self-supervised model encodes the route using two route-centric MBONs, with a in silico scanning, and stores place-specific memories for the nest and feeder as route extremities (see \u201cMethods\u201d, Fig.\u00a02c). In the exploitation phase, the robot processes each view through all memory pathways, yielding four familiarity values (left, right, nest and feeder MBON activities). The lateralized difference of route familiarities (\u03bbdiff) directs steering, while the maximum familiarity value modulates forward speed. In addition, a motivational control modulates motor gain, allowing the robot to stop or reverse based on a familiarity threshold set by place-specific MBONs (see \u201cMethods\u201d, Fig.\u00a02d).\n\nThis figure illustrates the processing pipeline from image encoding to navigation control, spanning both the learning and exploitation phases. a The Antcar robot: a compact car-like platform equipped with a panoramic camera and a GPS-RTK (Global Positioning System - Real-Time Kinematic) system for ground truth data. b Image encoding: this process mimics the ant\u2019s visual system. Panoramic images (I) are captured, blurred, sub-sampled, and edge-filtered to produce a low-resolution 32\u2009\u00d7\u200932 pixel panorama (IS). The resulting image is then transformed into Projection Neurons (PN), expanded into Excitatory Post-Synaptic Projections (EP), and reduced into Action Potentials (AP) via a \u03ba-WTA function, forming the sparse Kenyon Cell (KC) representation. c Learning phase: the robot follows a route (C) from a start point (N). An in silico scan (simulated image rotation) generates images with a defined angular error (\\(\\hat{{\\theta }_{{{\\rm{e}}}}}\\)), used to continuously categorize views at 38\u2009Hz in a route-centric manner---i.e., as facing to the right or left of the local route orientation. These continuous categorizations drive the update of synaptic weights in the corresponding Mushroom Body Output Neurons (MBONs), allowing visual inputs to be associated with specific route memories in a self-supervised fashion. Joystick inputs are used to define learning boundaries at the start and end of the route, modulating plasticity. d Exploitation phase: the robot seeks to minimize lateral (d) and angular (\u03b8e) errors with respect to the learned route. The encoded image continuously activates MBONs at 16Hz based on previously learned synaptic weights, enabling the robot to infer route orientation and adjust its steering and speed accordingly. MBON familiarity indices (\u03bb) operate in an opponent process: differences in familiarity between left and right MBONs guide steering, while the overall familiarity magnitude modulates speed. Special MBONs associated with route extremities affect motivational states, enabling route polarity correction or halting movement.\n\nThis study begins with an offline analysis of the proposed self-supervised, route-centric MB model using two route MBONs to assess stability (Fig.\u00a03), followed by experimental route-following tasks in challenging indoor and outdoor environments (Figs.\u00a04, 5 and 6). Next, a homing task is described, in which the robot follows a long outdoor route in reverse toward the starting area, designated as the nest (N), and stops nearby, utilizing three MBONs (Fig.\u00a07). Finally, a shuttling task is introduced, where the robot, after a single learning trial with two route MBONs and two extremities MBONs for the nest and feeder, autonomously shuttles to and fro between these two locations, driving both forward and backward (Fig.\u00a07).\n\nThis figure illustrates the familiarities differentiation and maximum value of route Mushroom Body Output Neurons (MBONs) during offline analysis of panoramic images and positional data from indoor (Mediterranean Flight Arena) and outdoor (Luminy Campus, Marseille, France) environments. The mapping was performed using an oscillation amplitude (A) of 45\u00b0. a, b Raw familiarities from the left and right MBONs. c, f Familiarity difference index (\u03bbdiff) mapped in the route\u2019s frame of reference, showing variations with both lateral (d) and angular (\u03b8e) errors. The defined operating area is highlighted in pink. d, g familiarity maximum index (\\({\\lambda }_{\\max }\\)) mapped similarly. e Overview of the indoor environment with the learned route highlighted in red. h Overview of the outdoor environment i, j Cross-sectional view of \u03bbdiff and \\({\\lambda }_{\\max }\\), respectively, plotted against \u03b8e when d is zero. Indoor conditions are represented by a solid line, and outdoor conditions by a dotted line. k Pearson correlation coefficient illustrating the linear relationship between \u03bbdiff and \u03b8e as a function of oscillation amplitude A. This plot also indicates the learning time required for a single oscillation cycle per image captured by the robot.\n\nEffects of steering direction and lighting variation with artificial visual cues. Detailed environmental configurations and familiarity data are shown in Supplementary Fig.\u00a0S4 and the accompanying video. a Autonomous route following experiments for two distinct learned routes (route 1: solid black line, route 2: dashed black line), each approximately 8 m long and represented independently by separate pairs of route MBONs. Learned trajectories are indicated in red. b Kidnapped robot tests performed independently for each learned route, assessing robustness to positional uncertainty. c, d Route following tests performed under bright (c) and dim (d) lighting conditions, while routes were learned under standard office lighting. e\u2013g Overview images of the indoor experimental environment.\n\nAntcar robot navigating indoor and outdoor routes under challenging conditions after a single learning phase. a, b Indoor experiments along an 8\u2009m route marked with artificial visual cues, featuring walking pedestrians (a) and large dynamical occlusions (b). c, d Outdoor experiments along a narrow (1.5\u2009m) forest-like footpath of 21\u2009m length, without (c) and with (d) static occlusions. e, g Third-person views of indoor and outdoor experimental environments. f, h Robot\u2019s first-person views illustrating dynamic and static occlusions in the frontal field of view.\n\na First-day experiments: learning and autonomous route following with several cars along the 55\u2009m road. b, f Overviews of the outdoor environment on the first and second days, respectively. c, d, g, h Familiarities difference (\u03bbdiff) and maximum (\\({\\lambda }_{\\max }\\)) values plotted against distance traveled on the first and second days, respectively. e Second-day experiments conducted at the same hour demonstrate autonomous route following using day-one memories in an altered, car-free environment.\n\na Outdoor homing experiments along a 50\u2009m L-shaped route in a cloudy environment. Two route MBONs and one motivation MBON guided an autonomous return route in the opposite direction. b Indoor shuttling experiments with artificial visual cues, using two route MBONs and two place MBONs. Autonomous routes swing back (blue) and forth (black). In both figures, the inset shows the robot\u2019s point of view. c Familiarity nest index (\u03bbN) plotted against distance traveled under a fixed stopping condition (p\u2009=\u20090.2). d Familiarity nest (\u03bbN) and feeder (\u03bbF) indices plotted against the traveled distance, with an inset zooming in on the values to highlight the backward and forward movements.\n\nThe continuous in-silico rotation of the panoramic image, along with the route-centric hypothesis and the robot\u2019s assumption that each captured image corresponds to the route direction, drives a self-supervised route-learning mechanism. We first evaluated the self-supervised model for route learning (using only two MBONs) with a dataset of indoor and outdoor parallel routes (Fig.\u00a03e, h). Results demonstrated that, with a controlled oscillation amplitude during learning, the model accurately estimated its heading error based on the differential familiarity \u03bbdiff, handling angular deviations up to 135\u00b0 indoors and 90\u00b0 outdoors (Fig.\u00a03c, f, i). Furthermore, the maximum familiarity index \\({\\lambda }_{\\max }\\), used as feedback for speed control, increased proportionally with heading error, enabling the robot to slow down when misaligned with the route. This behavior was consistent even when the robot was moved laterally off-route. Outdoors, these gradients were steeper (Fig.\u00a03c, d, f and g), indicating a higher visual contrast with larger landmarks.\n\nThe model\u2019s ability to identify heading error accurately across training oscillation amplitudes up to 135\u00b0 (Fig.\u00a03k, see also Supplementary Note\u00a01 and Supplementary Fig.\u00a0S1) suggests that this parameter may not require further tuning below this threshold. However, larger oscillation amplitudes increased computation time, especially on the Raspberry Pi platform (0.4s for \u00a0\u00b1\u200945\u00b0, Fig.\u00a03k). Notably, the familiarity difference index (Fig.\u00a03i) closely matched the spatial derivative of the maximum familiarity index, corresponding to the catchment area and turn rate amplitude observed in ants (Fig.\u00a03j, Supplementary Note\u00a01, 2, Supplementary Figs.\u00a0S1 and S244).\n\nThis analysis helped establish the operational limits of our MB model, maintaining stable behavior within a lateral error (d) of 2 meters and an angular error (\u03b8e) within the learning oscillation amplitude, set here at 45\u00b0. For asymptotic stability (i.e., the system\u2019s ability to return to equilibrium), we assumed a proportional relationship between \u03bbdiff and \u03b8e, supported by the Pearson correlation coefficient being close to 1 (Fig.\u00a03k) and expressed as Kdiff \u22c5 \u03bbdiff\u2009=\u2009\u2212\u2009\u03b8e, where Kdiff is a tuned negative gain. Integrating this relationship into the robot\u2019s motion equations, we applied a Lyapunov function for stability analysis. Results confirmed that the system converged to equilibrium points at de\u2009=\u20090 and \\({\\theta }_{{{\\rm{e}}}}^{e}=0\\), effectively correcting small deviations and enabling the robot to remain aligned with the learned route. The full derivation of these equations and Lyapunov stability proof are provided in the Methods (section 6) and Supplementary Note\u00a03, 4 and Supplementary Fig.\u00a0S3.\n\nThe proposed self-supervised approach for route learning was validated through a series of indoor and outdoor route-following tasks in fully autonomous mode, with only two MBONs. After a first outbound route with online learning, where images were captured continuously to update synaptic weights in real-time, the robot demonstrated robust route-following in various configurations (Figs.\u00a04, 5 and 6). First, the Antcar robot successfully navigated two routes in a cluttered indoor environment of approximately 8 meters (median lateral error \u2009\u00b1\u2009median absolute deviation (MAD)\u2009=\u20090.21\u2009\u00b1\u20090.09 m, angular error \u2009\u00b1\u2009MAD\u2009=\u20093.4\u2009\u00b1\u20096.2\u00b0, Fig.\u00a04a, e and Fig.\u00a08a). Moreover, the robot showed resilience in a kidnapped robot scenario, realigning with the learned route after being displaced from 1 to 2\u2009m away and oriented from 0 to 50 degree, (lateral error\u2009\u00a0\u00b1\u2009MAD\u2009= 0.26 \u2009\u00b1\u20090.14\u2009m, angular error\u2009\u00b1\u2009MAD\u2009=\u20096.45\u2009\u00b1\u20094.19\u00b0, Fig.\u00a04b, and Fig.\u00a08a). Only one predictable crash occurred when the robot exceeded theoretical angular limits (see Supplementary Fig.\u00a0S5).\n\na Detailed error analysis for each experiment. b Weighted bi-variate distribution for lateral (d) and angular errors (\u03b8e) across 13 experimental configurations.\n\nFurther tests assessed the robot\u2019s adaptability to bright and dim light conditions (Fig.\u00a04c, f, d, g). Despite a single learning trial under standard lighting (815 Lux), the robot accurately followed its route in bright (1340 Lux) and dim (81 Lux) lighting, with similar lateral and angular errors across tests (Fig.\u00a08). This indicates that the route-centric MB-based control system is robust to significant changes in illumination.\n\nIn indoor dynamic conditions with pedestrians and camera occlusions (Figs.\u00a05a, b), the robot maintained reliable route-following performance. When encountering pedestrians, the lateral error was \u00a0\u00b1\u2009MAD\u2009=\u20090.27 \u2009\u00b1\u20090.15 m and the angular error was \u00a0\u00b1\u2009MAD\u2009=\u20094\u2009\u00b1\u20092.8\u00b0 (Figs.\u00a05a, e and \u00a08a). Similarly, in the presence of dynamic occlusions, the robot achieved a lateral error of \u00a0\u00b1\u2009MAD\u2009=\u20090.22\u2009\u00b1\u20090.13\u2009m and an angular error of \u00a0\u00b1\u2009MAD\u2009=\u20094.7\u2009\u00b1\u20093.3\u00b0 (Figs.\u00a05b, f and 8a). The presence of pedestrians and occlusions resulted in a reduction of maximum familiarity, leading to slower speeds and increased oscillatory motion\u2014approximately 15% slower than in experiments without these disturbances (Fig.\u00a05a, b, Supplementary Figs.\u00a0S5 and Supplementary Movie\u00a01). Across all seven autonomous routes with dynamic occlusions, occlusions occupied on average 11% of the image area, with peaks up to 56% (see Methods and Supplementary Fig.\u00a0S4 for occlusion detection using YOLOv1155).\n\nOutdoor experiments demonstrated the model\u2019s robustness in diverse settings\u2014from a narrow 1.5\u2009m pathway in a tree-like environment to a wider 5 m semi-urban route\u2014while maintaining stable performance under static occlusions and altered conditions. On a semi-cloudy day, a 20 m route was learned and accurately recapitulated with low errors (lateral error \u00a0\u00b1\u2009MAD\u2009=\u20090.3 \u2009\u00b1\u20090.12\u2009m; angular error \u00a0\u00b1\u2009MAD\u2009=\u20094\u2009\u00b1\u20092.3\u00b0; Figs.\u00a05c and 8a). Then, a static occlusion was introduced, consisting in a fixed black spot in the frontal field of view, covering 4 to 15% of the entire visual field (and 8 to 30% of the front view), the performance remained robust (lateral error \u00a0\u00b1\u00a0MAD\u2009=\u20090.38\u2009\u00b1\u20090.10\u2009m; angular error\u2009\u00b1\u2009MAD\u2009=\u20095.6 \u2009\u00b1\u20093\u00b0; Figs.\u00a05d and 8a).\n\nOver a 55 m route under altered conditions, the robot first navigated a sunny day with low errors (lateral error \u2009\u00b1\u2009MAD\u2009=\u20090.39 \u2009\u00b1\u20090.13\u2009m; angular error \u00a0\u00b1\u2009MAD\u2009=\u20095.8 \u2009\u00b1\u20092.8\u00b0; Figs. 6a and 8a). The following day, at the same hour, with parked cars removed and a higher speed gain (cruising at 1.5\u2009m/s versus 1\u2009m/s), errors increased slightly (lateral error \u00a0\u00b1\u2009MAD\u2009=\u20091.3\u2009\u00b1\u20090.5\u2009m; angular error \u00a0\u00b1\u2009MAD\u2009=\u20096. \u2009\u00b1\u20093.2\u00b0; Figs.\u00a06e and 8a) yet remained within acceptable limits. During exploitation, the difference and maximum index values were marginally higher on the second day (Fig.\u00a06g, h) than during the first day (Fig.\u00a06c, d), likely due to the increased lateral error. These results underscore the system\u2019s resilience and adaptability under challenging conditions (See environment\u2019s picture taken at similar place from day one Fig.6b to day two Fig.\u00a06f).\n\nBuilding on the validated route-following strategy, further tests refined the robot\u2019s behavior, focusing on ant-like homing. Homing, by definition, include graphicsis the ability to return to a specific location after displacement. To test this, we evaluated the robot\u2019s ability to follow a 50 m outdoor route in reverse, stopping at a designated nest area (point N in Fig.\u00a07a). During learning, a 180\u00b0 shift in the visual oscillation pattern simulated the \u201cturn back and look\u201d behavior observed in ants and led to homeward route following.\n\nThe robot successfully followed the 50\u2009m route in reverse under cloudy outdoor conditions (lateral error \u00a0\u00b1 MAD = 0.9 \u00a0\u00b1 0.5 m, angular error \u2009\u00b1\u2009MAD\u2009=\u20096.3\u2009\u00b1\u20094.2\u00b0, Figs,\u00a06a, 8a). Although maximum familiarity was higher than in previous outdoor experiments (see Supplementary Note\u00a06, Supplementary Fig.\u00a0S5 and Supplementary Table\u00a0S1), overall accuracy remained stable and emerging oscillatory movements was demonstrated (see Supplementary Movie\u00a01).\n\nTo enable autonomous stopping at the nest, a place-specific MBON was used to learn \u2018nest-views\u2019 at the starting point of the route. Subsequent \u2018recognition\u2019 in this MBON, based on a familiarity threshold, acted as a motivational cue to halt route-following behavior and reduce the robot\u2019s linear velocity. This mechanism was sufficient for the robot to successfully reach and stop at the nest area in 4 out of 5 trials, with a median stopping distance of 1.4 m (Fig.\u00a07c, see also Supplementary Fig.\u00a0S7b for detailed familiarities values over distance).\n\nReverse route-following is also commonly observed in ants and was successfully replicated on board Antcar. Homing ants can pull food items backward when it is too large to carry forward, maintaining body alignment with the outbound route learned forward, and using outbound memories with an opposite valance53. Shuttling tests show the robot\u2019s ability to switch movement direction and drive backward while maintaining alignment with the outbound route (Fig.\u00a06b).\n\nThis foraging behavior was made possible by incorporating two additional place MBONs, which learned a series of panoramic views defining each endpoint of the route (feeder and nest). During shuttling, the model triggered a switch in motor gain polarity upon recognizing these panoramic views corresponding to the feeder or nest areas. In a cluttered indoor environment along a 6-meter learned route, the robot autonomously shuttled to and fro between the feeder and the nest, covering a total distance of 160 meters without interruption. Using a similar familiarity threshold on the two route-extremity MBONs, the robot detected the endpoints 22 times, achieving a median stopping distance of 0.31 m (Fig.\u00a07d) (See Supplementary Fig.\u00a0S7a for detailed familiarities values over distance).\n\nThis continuous shuttling revealed distinct differences in error profiles between forward and backward movement (Fig.\u00a07b). During forward motion, the robot maintained stable control with minimal deviations (lateral error\u2009\u00b1\u2009MAD\u2009=\u20090.1\u2009\u00b1\u20090.03\u2009m, angular error\u2009\u00b1\u2009MAD\u2009=\u20091.26\u2009\u00b1\u20090.83\u00b0, Fig.\u00a07b). However, during backward motion, the traction-driven setup amplified steering effects, resulting in slightly larger deviations from both accuracy and precision, though overall performance remained acceptable (lateral error\u2009\u00b1\u2009MAD\u2009=\u20090.19\u2009\u00a0\u00b1\u20090.08\u2009m, angular error\u2009\u00b1\u2009MAD\u2009=\u20092.7\u2009\u00b1\u20092.1\u00b0, Figs.\u00a07b and 8a). The increased \u2018motor\u2019 variability led to a lower visual recognition signal and thus usefully affected speed, which decreased by 14% compared to forward motion (see Supplementary Note\u00a06, Supplementary Fig.\u00a0S5 and Supplementary Table\u00a0S1). Nonetheless, the robot consistently realigned with the correct path after such minor deviations. These results highlight the model\u2019s versatility across different driving dynamics, capability to implement inverted steering, and adaptability to variations in motor kinematics and propulsion.\n\nAcross all experiments, including both indoor and outdoor route-following, homing and shuttling tasks, the model demonstrated robust and stable navigation performance, completing 113 autonomous trajectories with a total of 1.6 km traveled. The theoretical limits of the system were validated, with convergence toward equilibrium points consistently achieved under various environmental conditions, even in the presence of noise (lateral error\u2009\u00b1\u2009MAD\u2009=\u20090.24\u2009\u00b1\u20090.13\u2009m, angular error\u2009\u00b1\u2009MAD\u2009=\u20094\u2009\u00b1\u20092.7\u00b0, Fig.\u00a08b). Lateral errors were within acceptable margins for both indoor and outdoor contexts, aligning within the standard widths of roads in France (5\u2009m) and typical indoor corridor (1.5\u2009m).\n\nIn addition, statistical analysis showed no significant differences in the lateral or angular errors across the eleven test scenarios (Kruskal-Wallis test, H\u2009=\u20092.10 for lateral error, p\u2009=\u20090.99; H\u2009=\u20098 for angular error, p\u2009=\u20090.76), underscoring the system\u2019s reliability across diverse conditions (see Statistical Information). These results highlight the robustness and adaptability of the route-centric MB model in dynamic environments, confirming its potential applicability in a variety of navigation contexts.\n\nIn classical single-MBON familiarity models, memory capacity (m) is defined by an error probability (Perror), the chance of confusing an unfamiliar visual pattern with a learned one39. With our chosen parameters (N\u2009=\u200915,\u00a0000,\u00a0\u03ba\u2009=\u20090.01), theoretical estimates predict a memory capacity of m\u2009=\u2009346 KC activity patterns stored for a 1% error probability equivalent to roughly 38m of route in a cluttered environment39. However, such binary classification metrics fail to capture the complexity of our route-centric lateralized MBON steering mechanism.\n\nTo better quantify our model\u2019s steering-specific memory performance, we propose an empirical metric (Plerror), defined as the proportion of visual patterns incorrectly activating the opposite MBON (e.g., images associated with a leftward orientation producing lower familiarity on the left MBON than on the right MBON, and vice versa). Therefore, we define a steering-specific memory capacity (see Fig.\u00a09, Methods section and Supplementary Fig.\u00a0S8).\n\na Error proportion Plerror (defined as cases where the current visual pattern activates the incorrect lateralized MBON) as a function of route length and visual patterns learned, from outdoor experiments conducted on day one. b Route length that our MB architecture can store, maintaining an error proportion below 1%, plotted against the number of neurons and k-WTA parameter. The dataset is from a 250\u2009m outdoor route (real), and extrapolation is made on two couples of parameter (because it did not reach the 1% before 250\u2009m, see Supplementary Fig.\u00a0S8). Under our current network parameters (N\u2009=\u200915,\u00a0000,\u00a0\u03ba\u2009=\u20090.01), our route memory capacity with a 1% error probability corresponds to approximately 65\u2009m.\n\nUnder our metric, during extended route-following experiments in a semi-urban setting (55\u2009m, 430 unique KC activity patterns, Fig. 6), our network achieved 0.7% of error, below the critical threshold of 1% confusion probability (Fig. 9a). Further analysis of memory scalability using a larger dataset (up to 250\u2009m; Supplementary Fig.\u00a0S8) indicated that under our current network parameters (N\u2009=\u200915,\u00a0000,\u00a0\u03ba\u2009=\u20090.01), a 1% error probability yields an estimated 500 patterns, corresponding to about 65\u2009m of stored route in this conditions. A basic linear extrapolation indicated that with a larger network (N\u2009=\u2009100,\u00a0000, \u03ba\u2009=\u20090.005), routes as long as 600 m could be reliably encoded at the error threshold of 1% (Fig.\u00a09b).",
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+            ]
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+        {
+            "section_name": "Discussion",
+            "section_text": "We introduced a fully embodied, biologically grounded route-following system that unifies route-centric lateralized visual memory, panoramic input encoding, and neuromorphic control within a real-world robotic platform. Unlike prior ant-inspired models, which remained limited to short-range tasks or simulations, our model delivers continuous, one-shot learning and stable bi-directional navigation of visual routes \u2014 using only a single 800-pixel sensor, four MBONs, and light computational resources. These results mark a significant step forward in insect-inspired embodied cognition for real-world robotic autonomy.\n\nThe angular error between the agent\u2019s head direction and the dynamic local route orientation (i.e., route-centric, defined in the Methods as the Frenet frame56) emerged as both a challenge during exploitation\u2014where the system tends to minimize this error\u2014and a cue during learning, where the categorization process depends on its polarity. Our model demonstrated homing behavior using either a 180\u00b0 shift in visual oscillation or by inverting motor gains, thus enabling forward and backward movements with only a single foodward learning route. In addition, visual place memories stored in supplementary MBONs, paired with a motivational control system, allowed the robot to recognize route endpoints and modulate motor gains, halting movement or reversing foraging motivation. With a single learning pass in one direction, the agent could follow the route forward, backward, and in reverse, controlled by oscillation parameters and motivational cues. Only motivational rules required adjustment to switch between route following, homing, and shuttling, underscoring the model\u2019s flexibility.\n\nCompared to earlier ant-inspired familiarity-based models, generally limited to short, indoor routes or stop-and-scan strategies, our system demonstrates practical advantages in scalability, efficiency, and real-world adaptability19,20,21,22,23,24. Our memory footprint and command computation time are significantly lower than those reported in panoramic visual route-following methods13, which require 3 megabytes per kilometer and 400\u2009ms per control update. In contrast, our model operates at 0.3 megabytes per kilometer and produces commands within 75\u2009ms on a lightweight embedded board\u2014enabling real-time operation in constrained platforms. In addition, it achieves competitive performance compared to snapshot-based visual route-following methods that use odometry15.\n\nThis route-centric lateralized MB model distinguishes itself through reduced time and space complexity for route direction processing compared to perfect memory, snapshot, and insect-based visual compass approaches. Whereas time and space complexity increase with the number of images in perfect memory or snapshot models, our MB model maintains constant space complexity, relying only on the synaptic matrix size KCtoMBON. In addition, in contrast to visual compass approaches, where computational complexity scales with in-silico scan range and resolution during exploitation (\\({{\\mathcal{O}}}(n)\\)), our MB model maintains a constant factor (\\({{\\mathcal{O}}}(1)\\)) since in-silico scanning is only required during learning. For instance, while an insect-based visual compass scanning a \u2009\u00b1\u200945\u00b0 range at 1\u00b0 resolution requires 90 comparisons per image, our model requires only two comparisons, eliminating the need for angular scanning in exploitation. Notably, our model produced commands five times faster than the insect-based visual compass approach on the same robot platform21,22.\n\nOur contribution also aligns well with current biological observations, particularly highlighting the effectiveness of latent learning, where continuous learning bypass the need to control \u201cwhen to learn\u201d32,45. The opposed event-triggered and snapshot-based learning models producing place learning15,27 where used here only to recognize the place of interests, such as the nest and the feeder, to switch motivation, but were not engaged for route guidance. Also, our MB model prioritized body orientation within the route frame rather than splitting the visual field23,49, aligning with biological observations in ants with unilateral visual impairment, showing that these insects store and recognize fundamentally binocular views50. Interestingly, the linear relationship observed between familiarity measures and route-centric angular error during exploitation closely mirrors experimental findings in ants with nest-centric models44. This relationship enabled us to demonstrate the asymptotic stability of the system within a defined domain, ensuring the consistent and predictable behavior essential for a robotic navigation model57.\n\nFurthermore, oscillatory learning behavior mirrors ant behavior, where initial routes involve slow, rotational movements, transitioning to direct paths on subsequent journeys40. These oscillations typically fall within \u2009\u00b1\u2009100\u00b0, with peaks around \u2009\u00b1\u200945\u00b0 in unfamiliar terrain41,43. The robot\u2019s ability to slow down and produce emerging mechanical oscillation upon entering unfamiliar areas (see Fig.\u00a05a, b and Supplementary Movie\u00a01) are consistent with such naturalistic behaviors. Finally, Antcar\u2019s homing capability was maintained even when navigating backward, closely mirroring ant behavior while dragging food51,52,53,58. Overall, our attempt to integrate multiple MBONs, oscillations, \u201cturn back and look\u201d behavior, and motivational control mechanisms echoes insect mechanisms2,38, and the resulting expression when implemented in the robot echoes insect behaviors.\n\nThis study addresses several core needs identified in research on embodied neuromorphic intelligence6,8, such as robustness to visual changes, adaptability to real-world environments, and support for extended route learning. Our algorithm\u2019s efficiency allows computational power for additional tasks, making it valuable in GPS-compromised or SLAM-disrupted scenarios (Simultaneous Localization And Mapping). The robot\u2019s low-resolution, wide-angle vision proves resilient against moving objects that often disrupt SLAM. Our model is particularly effective in dynamic environments or scenarios where traditional odometry\u2014whether visual, inertial, step-counting, or wheel-rotation\u2014is unreliable. It can serve as a low-resource backup system (running on a 4-core CPU) alongside other processes, or be integrated with additional sensors to enhance state estimation robustness59,60.\n\nInterestingly, the semi-random encoding process, specifically the PNtoKC synaptic projections, introduces a \u201cfail-secure\u201d memory-sharing mechanism. If synaptic weights for encoding differ, memory sharing becomes inaccessible, an advantageous feature for swarm robotics or cross-robot memory sharing. Future research could enhance this approach but also transitioning this model to a spiking neural network on neuromorphic hardware could further enhance computational efficiency and biological fidelity11. In addition, incorporating obstacle avoidance61,62, would improve performance in dynamic environments.\n\nOur upward-facing fisheye camera provides a 360\u00b0 view at minimal cost, and in silico rotation keeps the learning route straight. However, if the ground is not planar, in silico rotation may not accurately represent physical rotation, thus learn an image that the robot will never encounter. Moreover, bypassing image unwrapping and calibration speeds computation but reduces the influence of distal cues, especially in large open fields where the horizon is severely deformed and can appear uniform. Interestingly, salt lake ants in such environments have developed enhanced horizontal resolution and accuracy, and build artificial visual cues near the nest entrance63.\n\nA reduced visual field, as seen in more general cases, may preclude in silico scanning, necessitating an estimation of the angular error between the road frame and the agent. Collett et al.64 proposed that ants use route segment odometry for navigation, suggesting a potential alternative. In insects, dopaminergic neurons (DAN) modulate MBON synapses from Kenyon cell inputs in response to motor stimuli, effectively acting as a \u201csupervisor\u201d for sensory cue categorization65. There are plenty of feedback from motor areas towards the MB (both DANs and MBON)66 that could enable to orchestrate visual memory formation, for instance, based on whether the current body orientation is left or right from a goal compass direction45. Similarly, our model\u2019s left-right classification functionally mimics the effect of dopaminergic feedbacks (onto MB), which activity would be based on whether the current body orientation is left or right from the local route heading.\n\nOur approach does not cover beeline homing post-foraging, or search behaviors near points of interest, although these could be added by adding path integration mechanisms67 or using the current visual mechanism but adding \u201clearning walk\u201d behaviors around places of interest45. Although anti-Hebbian learning effectively improves familiarity discriminability by sparsifying KCtoMBON synapses, there is a theoretical limit to this benefit. Excessive sparsification would lead to memory saturation (dramatic forgetting), where the MBON output no longer discriminates between familiar and unfamiliar inputs. Therefore, it suggests an opportunity for further exploration by adjusting KCs numbers or connectivity by testing different MB learning mechanisms with feedback or prediction error68.\n\nFinally, our system\u2019s memory capacity metric (500 patterns) is higher than the theoretical estimation from Ardin et al. (346 patterns)39. This discrepancy may arises because the theoretical model assumes random, independent KC activations, whereas in continuous route learning, KC activations are correlated and structured. In addition, our empirical error calculation depends on our visual preprocessing, hardware and the semi-urban environment. Also, the memory capacity error computed here can be linked to the sparsity of the KCtoMBON synaptic weight, avoiding a possible dramatic forgetting when all the KCs are used (i.e., the KCtoMBON vector is 0). To extend route length while reducing error, we could increase the number of KCs (see Fig.\u00a09); however, this may slow processing due to larger matrices\u2014though the impact may be minimal on a GPU. Alternatively, incorporating additional pairs of MBONs for different route segments could enable longer and multiple route memories without affecting processing time and, therefore, considering an extrapolated memory footprint of only 0.3 megabytes per kilometer. Also, expanding the number of MBONs, akin to the 100 in honey bees69, along with a mechanism (such as a context-based selection) to dynamically activate the appropriate MBON pair would enable more complex motivational states, multi-route memory storage, and broader navigational abilities70.\n\nInspired by the neuroethology of ants, our route-centric, lateralized MB model provides an effective bridge between theoretical insights and practical application in insect-inspired robotic navigation. This egocentric architecture demonstrates how biologically plausible neural circuits can support robust, scalable, and adaptive behavior in real-world robots\u2014using accessible hardware, panoramic input, and minimal computing resources. These results reinforce the promise of neuromorphic approaches for embodied autonomy and broaden opportunities for both robotic systems and experimental studies in comparative cognition.",
+            "section_image": []
+        },
+        {
+            "section_name": "Methods",
+            "section_text": "This section describes the methodology used in the present study, focusing on the Encoding, Learning, and Exploitation processes of the proposed MB model (Figs.\u00a02b\u2013d and 10). We also provide details on the hardware setup, control architecture, and stability analysis.\n\nThe network includes four MBONs fitted during the exploration phase. For visualization, the EP, AP, and KCtoMBON connections are reshaped into matrix-like formats. KCtoMBON synapses are initially fully connected prior to learning.\n\nInspired by the visual system of ants71, the model encoded real-world images into sparse, binary neural representations to efficiently handle visual input.\n\nThe encoding function (Figs.\u00a02b, 10 and Supplementary Note\u00a05) processed panoramic images from a camera with a 220\u00b0 vertical and 360\u00b0 horizontal field of view. This wide field of view enabled the camera to capture from slightly below the horizon to nearly directly below itself. To enhance natural contrast, the green channel of each image was selected71, followed by Gaussian smoothing (\u03c3\u2009=\u20093 pixels) to reduce noise. The chosen \u03c3 corresponds to an acceptance angle of about 4.\u00a04\u00b0 (\u03c3\u2009+\u2009FOV/r), slightly larger than the estimated visual acceptance angle of the Melophorus species72. The image was then downsampled to a low-resolution 32\u2009\u00d7\u200932 pixel thumbnail (0.145 pixel per degree), approximating the visual resolution of ants at 7.1\u00b0 between adjacent photoreceptors63. Next, a Sobel filter extracted edges, mimicking lateral inhibition as seen in insect optical lobes73. These processed images were flattened into n\u2009=\u2009800 Visual Projection Neurons (\\({{\\bf{PN}}}\\,\\in \\,{{\\mathbb{R}}}^{n}\\)), comparable to the number of ommatidia in Cataglyphis ants. These processing steps, with the aim of mimicking the output of the optic lobes, are described in detail in Supplementary Note\u00a05 and in Fig.\u00a010.\n\nThe PNs were further expanded into Kenyon Cells (KCs) using a fixed, sparse pseudo-random binary synaptic matrix (PNtoKC, equation (1)). Each KC received input from four PNs, enhancing the visual encoding\u2019s discriminative power within the MB, forming an Excitatory Post Synaptic Projection (EP) vector (see equation (2) and Fig.\u00a010).\n\nSo, the product\n\nwill be an N-dimensional vector, i.e., \\({{\\bf{EP}}}\\in {{\\mathbb{R}}}^{N}\\). The EP vector size was set to N\u2009=\u200915,\u00a0000 for the route MBONs (MBONR and MBONL), while for place-specific MBONs (MBONN and MBONF), which required fewer images, N was set to 5000.\n\nA \u03ba-Winner-Take-All (WTA) mechanism was applied to capture the highest contrasts, creating a high-dimensional, sparsified binary vector (see Fig.\u00a010). This vector, referred to as the Action Potential (AP, equation (3)), consequently activated only 1% of KCs (\u03ba\u2009=\u20090.01), giving Nu\u2009=\u2009N*\u03ba active neurons, such that:\n\nWhere i is the neurons number, and AP \u2208 {0, 1}N. This final binary representation served as the encoded visual input to be learned. All parameters were predefined by literature and experimental tests, but not further optimized.\n\nThe learning process is governed by synaptic depression through anti-Hebbian learning. For each MBONs, their synaptic weight vector (KCtoMBON) dynamically adjusted their binary weight based on input from the AP layer.\n\nWhere KCtoMBON \u2208 {0, 1}N. At the beginning, for each MBONs, their KCtoMBON vector are fully connected (i.e., all AP neuron are connected to the MBONs). During learning, each time the KCtoMBON have the same weight as the current AP (1), the respective synaptic connection is depressed (weight from 1 to 0) in the designed KCtoMBON (equation (4)). For the route, the KCtoMBON vector is designed (therefore depressed) according to the route-centric left or right looking direction (equation (4)). The model assumed the robot perfectly aligned to the route being learned. The body rotation was estimated as \\({\\hat{\\theta }}_{e}={\\theta }_{{{\\rm{e}}}}+{\\theta }_{c}\\), where therefore \u03b8e\u2009=\u20090 during learning, and \u03b8c is the image rotation angle. The encoded binary image (AP) was learn in one MBONs based on the polarity of \\({\\hat{\\theta }}_{e}\\), such that:\n\nWhere Learn() is the function in equation (4). The simulated oscillatory movements during learning were obtained by rotating each captured image in steps, creating a sweep of rotations (\u03b8c) described by the following function:\n\nwhere A represents the oscillation amplitude, \u0394\u03b8 the step size, and \u03d5 the phase shift. The step size was fixed at \u0394\u03b8\u2009=\u20095\u00b0, with A\u2009=\u200945\u00b0 for route MBONs and A\u2009=\u200930\u00b0 for place MBONs. The phase shift was \u03d5\u2009=\u2009180\u00b0 only for the homing task (Fig.\u00a07). The place MBONs learning was triggered by an external stimulus, specified by the robot operator.\n\nSynaptic weights (KCtoMBON) were stored in CSR format (Compressed Sparsed Row), achieving significant data compression to 148 kilobits independently of the route length (from 6\u2009m to 55\u2009m), reducing memory requirements by 99.97% from cumulative image storage. This self-supervised model continuously learned visual input at high throughput without memory overload, as only novel views (i.e., newly recruited KCs) modulated synapses. Several panoramic views were learned to define the start and finish areas in their respective MBONs, serving as motivational cues.\n\nDuring exploitation, the model calculated familiarity scores (\u03bb) by comparing the current input (AP) with each MBON\u2019s synaptic weight matrix (KCtoMBON):\n\nThis familiarity score, ranging from 0 (unfamiliar) to 1 (familiar), was used to assess route alignment. The lateralized difference in familiarities between the left and right MBONs (\u03bbdiff, equation (8) and Fig.\u00a010), which indicates whether the current view is more oriented to the left or right of the route, guided the robot\u2019s steering angle (\u03c6). Meanwhile, the maximum familiarity (\\({\\lambda }_{\\max }\\)), representing how familiar the current view is, modulated its speed (v).\n\nThus, the control input U was defined as:\n\nHere, Kv and K\u03c6 are proportional gains that control linear and angular velocities, while the saturation function (sat()) establishes a minimum throttle level, ensuring minimum speed even at low familiarity levels to allow the robot to turn (due to his mechanical constraint). The motivational state (M) regulated transitions between behaviors, based on familiarity thresholds within place-specific MBONs. During route following, M was consistently set to 1. In homing experiments, where the objective was to stop at the nest, M initially started at 1 and switched to 0 once the familiarity of the nest-specific MBON (\u03bbN) fell below a fixed threshold (p\u2009=\u20090.2), signaling arrival at the nest. For shuttling tasks, M alternated between values of 1 and \u00a0\u2212\u20091 as the robot reached each route extremity, driven by a familiarity threshold of the two place-specific MBONs (\u03bbN and \u03bbF).\n\nStability in mobile agents, biological or robotic, is essential for reliable, predictable behavior. In non-linear\u00a0control theory, an agent\u2019s motion is generally modeled as \\(\\dot{x}=f({{\\bf{x}}},{{\\bf{U}}})\\), where x is the state vector (e.g., position or velocity), U is the control input, and f describes system dynamics. A desired equilibrium point xe is achieved by defining a control input Ue such that f(xe,\u00a0Ue)\u2009=\u20090, allowing the system to maintain stability and return to equilibrium after disturbances. Stability is typically assessed using a Lyapunov function57, which ensures the system converges to a stable state over time.\n\nIn contrast to conventional control approaches, we applied a neuroethologically inspired control input derived from ant behavior and assessed its stability via an a posteriori Lyapunov analysis. The robot\u2019s motion was modeled in a Frenet frame, a moving reference frame coincident with the nearest point on the route, to minimize lateral and angular errors, defined by x\u2009=\u2009[d,\u00a0\u03b8e]. Empirical data for stability assessment was collected in indoor and outdoor environments (paths of approximately 6 meters with 855 learned images each), providing distinct visual contexts (Figs.\u00a02, 3). The robot\u2019s equations of motion from a global to the Frenet frame are ref. 74:\n\nwhere s is the arc length along the route, d is the lateral error, and \u03b8e is the angular error.\n\nThis kinematic model, along with by empirical observations (Fig.\u00a03), enabled us to establish an asymptotically stable domain for lateral and angular errors (d and \u03b8e), ensuring reliable route-following performance even with minor disturbances. The full theoretical stability proof and derivations of the model in the Frenet frame are provided in the Supplementary Note\u00a03 and 4.\n\nThe experiments were conducted using Antcar (Figs.\u00a01 and 2a), a PiRacer AI-branded car-like robot. Antcar features four wheels, with two rear drive wheels powered by 37-520 DC motors (12V, 1:10 reduction rate) and a front steering mechanism controlled by an MG996R servomotor (9kg/cm torque, 4.8V). The robot\u2019s chassis measures 13\u2009\u00d7\u200924\u2009\u00d7\u200919.6\u2009cm and is powered by three rechargeable 18650 batteries (2600\u2009mAh, 12.6\u2009V output). Antcar\u2019s primary sensor is a 220\u00b0 Entaniya\u2122 fisheye camera, mounted upward to capture panoramic images at 160\u2009\u00d7\u2009160px\u2009\u00d7\u20093 resolution, processed using OpenCV on a Raspberry Pi 4 Model B (Quad-core Cortex-A72, 1.8\u2009GHz, 4GB RAM), running Ubuntu 20.04. Note that there was no closed-loop control on the wheel rotation speed. Raspberry Pi manages real-time performance and controls the motors through a custom ROS architecture.\n\nReal-time communication is facilitated by ROS Noetic, either via Wi-Fi (indoor) or a 4G dongle (outdoor). The robot can be controlled manually using a keyboard, joystick or with a GPS waypoint, but in autonomous visual-only mode, it follows its own internal control law. Control inputs\u2014steering angle (\u03c6) and throttle (v) are processed using the PyGame library. Real-time data visualization and post-experiment monitoring are achieved via Foxglove.\n\nAntcar has a maximum velocity of 1.5 m/s and a maximum steering angle of 1 rad, with a wheelbase of 0.15\u2009m. The robot\u2019s configuration states q\u2009=\u2009(x,\u00a0y,\u00a0\u03b8) were tracked using different systems. Indoor experiments utilized eighteen Vicon\u2122 motion capture cameras, with infrared markers on Antcar providing precise tracking at 50\u2009Hz with 1\u2009mm accuracy. Outdoor experiments employed a GPS-RTK system with a SparkFun GPS-RTK Surveyor, providing 14\u2009mm accuracy at 2\u2009Hz (GPS-RTK stands for Global Positioning System - Real-Time Kinematic). Ground speed and angular speed were calculated through position differentiation. The base station used for GPS corrections was a Centipede LLENX station located at 24\u2009km (Marseille Provence Airport) from the experiment site in Marseille. Note that the ground truth acquisition system was run on the Raspberry Pi along with the MB model.\n\nLateral error was calculated by finding the nearest point on the learning route using the Euclidean distance, with the shortest distance representing the absolute lateral error. Angular error was defined as the absolute difference in heading between the nearest learning route point and the current position. The euclidean distance between the agent and the nest or feeder areas was calculated to estimate the distance when the robot switched behavior (i.e familiarity dropped below the threshold).\n\nTo compute our memory capacity and Plerror, we used a 250\u2009m dataset (Supplementary Fig.\u00a0S8). The metric was computed over the operating area defined by the learning oscillation. The computation was performed incrementally: for each new learned image (rotated from \u00a0\u2212\u200945\u00b0 to 45\u00b0 in 5\u00b0 steps), all previously encountered images were tested (rotated from \u00a0\u2212\u00a045\u00b0 to 45\u00b0 in 1\u00b0 steps), we didn\u2019t take into account the value between \u2212\u20091\u00b0 and 1\u00b0. For each tested image i, the familiarity difference \u03bbdiff\u2009[i] was calculated. An error indicator ei was then defined by comparing the sign of \u03bbdiff\u2009[i] with that of the heading error \u03b8e[i]:\n\nFinally, the cumulative mean error up to test image i is given by:\n\nThe errors used for statistics were recorded at each command decision timing. Due to non-normality in error values (with outliers retained), Box-Cox transformations were applied to stabilize variance across experiments, reducing the impact of outliers caused by indoor obstacles that hid the robot from the motion capture system or by GPS-RTK inaccuracies outdoors. The groups was compared using the Kruskal-Wallis test75, and median values are reported with median absolute deviation (MAD), as median \u00a0\u00b1 MAD. The package Python SciPy76 was used for the statistics. The overall medians and bivariate distribution plots were weighted by the number of measurements per experiment for the Fig.\u00a08.",
+            "section_image": [
+                "https:////media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41467-025-62327-3/MediaObjects/41467_2025_62327_Fig10_HTML.png"
+            ]
+        },
+        {
+            "section_name": "Data availability",
+            "section_text": "The dataset, including image banks and experimental data, is available at Figshare: https://doi.org/10.6084/m9.figshare.2770810577.",
+            "section_image": []
+        },
+        {
+            "section_name": "Code availability",
+            "section_text": "The code for the MB model, dataset analysis, and figure generation is available on GitHub: https://doi.org/10.5281/zenodo.1578347278. The ROS Python code is available upon request.",
+            "section_image": []
+        },
+        {
+            "section_name": "References",
+            "section_text": "Franceschini, N. Small brains, smart machines: From fly vision to robot vision and back again. In Proceedings of the IEEE 102, 751\u2013781 (2014).\n\nWebb, B. & Wystrach, A. Neural mechanisms of insect navigation. Curr. Opin. Insect Sci. 15, 27\u201339 (2016).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDenuelle, A. & Srinivasan, M. V. A sparse snapshot-based navigation strategy for uas guidance in natural environments. In Proceedings of the IEEE International Conference on Robotics and Automation (ICRA) (2016).\n\nGlick, P. E., Balaram, J. B., Davidson, M. R., Lyons, E. & Tolley, M. T. The role of low-cost robots in the future of spaceflight. Sci. Robot. 9, eadl1995 (2024).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nYang, G.-Z. et al. The grand challenges of Science Robotics. Sci. Robot. 3, eaar7650 (2018).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nde Croon, G. C., Dupeyroux, J., Fuller, S. B. & Marshall, J. A. Insect-inspired ai for autonomous robots. Sci. Robot. 7, eabl6334 (2022).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMangan, M. et al. A virtuous cycle between invertebrate and robotics research: Perspective on a decade of Living Machines research. Bioinspir. Biomim. 18, 035005 (2023).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBartolozzi, C., Indiveri, G. & Donati, E. Embodied neuromorphic intelligence. Nat. Commun. 13, 1024 (2022).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWebb, B. Robots in invertebrate neuroscience. Nature 417, 359\u2013363 (2002).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nFranz, M. O. & Mallot, H. A. Biomimetic robot navigation. Robotics Auton. Syst. 30, 133\u2013153 (2000).\n\nSandamirskaya, Y., Kaboli, M., Conradt, J. & Celikel, T. Neuromorphic computing hardware and neural architectures for robotics. Sci. Robot. 7, eabl8419 (2022).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nSimon, M., Broughton, G., Rou\u010dek, T., Rozsyp\u00e1lek, Z. & Krajn\u00edk, T. in Performance Comparison of Visual Teach and Repeat Systems for Mobile Robots. (Springer International Publishing, Cham, 2023).\n\nStelzer, A., Vayugundla, M., Mair, E., Suppa, M. & Burgard, W. Towards efficient and scalable visual homing. Int J Robot Res 37, 225\u2013248 (2018).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nNourizadeh, P., Milford, M. & Fischer, T. Teach and repeat navigation: A robust control Approach. In 2024 IEEE International Conference on Robotics and Automation (ICRA) 2909\u20132916 (2024).\n\nVan Dijk, T., De Wagter, C. & De Croon, G. C. H. E. Visual route following for tiny autonomous robots. Sci. Robot. 9, eadk0310 (2024).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMangan, M. & Webb, B. Spontaneous formation of multiple routes in individual desert ants (Cataglyphis velox). Behav. Ecol. 23, 944\u2013954 (2012).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKohler, M. & Wehner, R. Idiosyncratic route-based memories in desert ants, Melophorus bagoti: How do they interact with path-integration vectors? Neurobiol. Learn. Mem. 83, 1\u201312 (2005).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWystrach, A., Schwarz, S., Schultheiss, P., Beugnon, G. & Cheng, K. Views, landmarks, and routes: how do desert ants negotiate an obstacle course? J. Comp. Physiol. A 197, 167\u2013179 (2011).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKodzhabashev, A. & Mangan, M. Route Following Without Scanning. (Springer International Publishing, Cham, 2015).\n\nKnight, J. C., Sakhapov, D., Domcsek, N. & McDonald Dewar, A. D. Insect-Inspired Visual Navigation On-Board an Autonomous Robot: Real-World Routes Encoded in a Single Layer Network. In Proceeding of the 2019 Conference on Artificial Life of Artificial Life Conference. (2019).\n\nGattaux, G., Vimbert, R., Wystrach, A., Serres, J. R. & Ruffier, F. Antcar: Simple route following task with ants-inspired vision and neural model. Preprint at https://hal.science/hal-04060451v1(2023).\n\nGattaux, G., Wystrach, A., Ruffier, F. & Serres, J. Enhancing ant-inspired visual compass with focused visual scan in a compact robot. In 2025 IEEE 7th International Conference on AI Circuits and Systems (AICAS) 110\u2013114 (2025).\n\nLu, Y., Cen, J., Alkhoury Maroun, R. & Webb, B. Insect-inspired Embodied Visual Route Following. J. Bio. Eng. 22, 1167\u20131193 (2025).\n\nJesusanmi, O. O. et al. Investigating visual navigation using spiking neural network models of the insect mushroom bodies. Front. Physiol. 15, 1379977 (2024).\n\nArticle\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nCaron, G., Marchand, E. & Mouaddib, E. M. Photometric visual servoing for omnidirectional cameras. Auton. Robots 35, 177\u2013193 (2013).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nCartwright, B. A. & Collett, T. S. Landmark learning in bees: Experiments and models. J. Comp. Physiol. A 151, 521\u2013543 (1983).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nM\u00f6ller, R. & Vardy, A. Local visual homing by matched-filter descent in image distances. Biol. Cybern. 95, 413\u2013430 (2006).\n\nArticle\u00a0\n    MathSciNet\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nZeil, J., Hofmann, M. I. & Chahl, J. S. Catchment areas of panoramic snapshots in outdoor scenes. J. Opt. Soc. Am. A 20, 450 (2003).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWystrach, A., Cheng, K., Sosa, S. & Beugnon, G. Geometry, features, and panoramic views: ants in rectangular arenas. J. Exp. Psychol. Anim. Behavi. Process. 37, 420 (2011).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nGaffin, D. D. & Brayfield, B. P. Autonomous Visual Navigation of an Indoor Environment Using a Parsimonious, Insect Inspired Familiarity Algorithm. PLOS ONE 11, e0153706 (2016).\n\nArticle\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nPhilippides, A., Baddeley, B., Cheng, K. & Graham, P. How might ants use panoramic views for route navigation? J. Exp. Biol. 214, 445\u2013451 (2011).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBaddeley, B., Graham, P., Husbands, P. & Philippides, A. A model of ant route navigation driven by scene familiarity. PLoS Comput. Biol. 8, e1002336 (2012).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWystrach, A., Beugnon, G. & Cheng, K. Ants might use different view-matching strategies on and off the route. J. Exp. Biol. 215, 44\u201355 (2012).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLinsker, R. Self-organization in a perceptual network. Computer 21, 105\u2013117 (1988).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWystrach, A., Mangan, M., Philippides, A. & Graham, P. Snapshots in ants? new interpretations of paradigmatic experiments. J.Exp. Biol. 216, 1766\u20131770 (2013).\n\nPubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nHeisenberg, M. Mushroom body memoir: From maps to models. Nat. Rev. Neurosci. 4, 266\u2013275 (2003).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nEichler, K. et al. The complete connectome of a learning and memory centre in an insect brain. Nature 548, 175\u2013182 (2017).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nAso, Y. et al. Mushroom body output neurons encode valence and guide memory-based action selection in Drosophila. ELife 3, e04580 (2014).\n\nArticle\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nArdin, P., Peng, F., Mangan, M., Lagogiannis, K. & Webb, B. Using an Insect Mushroom Body Circuit to Encode Route Memory in Complex Natural Environments. PLOS Comput. Biol. 12, e1004683 (2016).\n\nArticle\u00a0\n    ADS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nHaalck, L. et al. CATER: Combined animal tracking & environment reconstruction. Sci. Adv. 9, https://doi.org/10.1126/sciadv.adg2094 (2023).\n\nDeeti, S., Cheng, K., Graham, P. & Wystrach, A. Scanning behaviour in ants: An interplay between random-rate processes and oscillators. J. Comp. Physiol. A (2023).\n\nWystrach, A., Philippides, A., Aurejac, A., Cheng, K. & Graham, P. Visual scanning behaviours and their role in the navigation of the australian desert ant melophorus bagoti. J. Comp. Physiol. A 200, 615\u2013626 (2014).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nClement, L., Schwarz, S. & Wystrach, A. An intrinsic oscillator underlies visual navigation in ants. Curr. Biol. 33, 411\u2013422 (2023).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWystrach, A., Le Mo\u00ebl, F., Clement, L. & Schwarz, S. A lateralised design for the interaction of visual memories and heading representations in navigating ants. Preprint at https://doi.org/10.1101/2023.03.09.531867 (2020).\n\nWystrach, A. Neurons from pre-motor areas to the Mushroom bodies can orchestrate latent visual learning in navigating insects. Preprint at https://doi.org/10.1101/2023.03.09.531867 (2023).\n\nSt\u00fcrzl, W., Zeil, J., Boeddeker, N. & Hemmi, J. M. How wasps acquire and use views for homing. Curr. Biol. 26, 470\u2013482 (2016).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nPaul, Furgale Timothy D., Barfoot Visual teach and repeat for long\u2010range rover autonomy. J. Field Robot. 27, 534\u2013560 (2010).\n\nZeil, J. Visual homing: an insect perspective. Curr. Opin. Neurobiol. 22, 285\u2013293 (2012).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nSteinbeck, F. et al. Familiarity-taxis: A bilateral approach to view-based snapshot navigation. Adapt. Behav. 32, 407\u2013420 (2024).\n\nSchwarz, S., Clement, L., Haalck, L., Risse, B. & Wystrach, A. Compensation to visual impairments and behavioral plasticity in navigating ants. Proc. Natl. Acad. Sci. USA 121, e2410908121 (2024).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nArdin, P. B., Mangan, M. & Webb, B. Ant homing ability is not diminished when traveling backwards. Front. Behav. Neurosci. 10, https://doi.org/10.3389/fnbeh.2016.00069 (2016).\n\nPfeffer, S. E. & Wittlinger, M. How to find home backwards? Navigation during rearward homing of Cataglyphis fortis desert ants. J. Exp. Biol. 219, 2119\u20132126 (2016).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nSchwarz, S., Clement, L., Gkanias, E. & Wystrach, A. How do backward-walking ants (Cataglyphis velox) cope with navigational uncertainty? Anim. Behav. 164, 133\u2013142 (2020).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nFreas, C. A. & Spetch, M. L. Terrestrial cue learning and retention during the outbound and inbound foraging trip in the desert ant, cataglyphis velox. J. Comp. Physiol. A 205, 177\u2013189 (2019).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nJocher, G., Qiu, J. & Chaurasia, A. Ultralytics YOLO. https://github.com/ultralytics/ultralytics (2023).\n\nFrenet, F. Sur les courbes \u00e0 double courbure. J. Math Pures Appl.17, 437\u2013447 (1852).\n\n\n                    Google Scholar\u00a0\n                \n\nLyapunov, A. M. The general problem of the stability of motion. Int. J. Control 55, 531\u2013534 (1992).\n\nArticle\u00a0\n    MathSciNet\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWebb, B. The internal maps of insects. J. Exp. Biol. 222, jeb188094 (2019).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDelarboulas, P., Gaussier, P., Caussy, R. & Quoy, M. Robustness study of a multimodal compass inspired from hd-cells and dynamic neural fields. In Proceedings 13th International Conference on Simulation of Adaptive Behavior, SAB 2014, Castell\u00f3n, Spain, July 22-25, 2014 (2014).\n\nSun, X., Yue, S. & Mangan, M. A decentralised neural model explaining optimal integration of navigational strategies in insects. ELife 9, e54026 (2020).\n\nArticle\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nSchoepe, T. et al. Finding the gap: Neuromorphic motion-vision in dense environments. Nat. Commun. 15, 817 (2024).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nSun, X., Fu, Q., Peng, J. & Yue, S. An insect-inspired model facilitating autonomous navigation by incorporating goal approaching and collision avoidance. Neural Netw. 165, 106\u2013118 (2023).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nZollikofer, C. P., Wehner, R. & Fukushi, T. Optical scaling in conspecific cataglyphis ants. J. Exp. Biol. 198, 1637\u20131646 (1995).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nCollett, T. S. & Collett, M. Route-segment odometry and its interactions with global path-integration. J.f Comp. Physiol. A 201, 617\u2013630 (2015).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nAso, Y. et al. The neuronal architecture of the mushroom body provides a logic for associative learning. Elife 3, e04577 (2014).\n\nArticle\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBrezovec, B. E. et al. Mapping the neural dynamics of locomotion across the drosophila brain. Curr. Biol. 34, 710\u2013726 (2024).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nStone, T. et al. An anatomically constrained model for path integration in the bee brain. Curr. Biol. 27, 3069\u20133085 (2017).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWebb, B. Beyond prediction error: 25 years of modeling the associations formed in the insect mushroom body. Learn. Mem. 31, a053824 (2024).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nRybak, J. & Menzel, R. Anatomy of the mushroom bodies in the honey bee brain: the neuronal connections of the alpha-lobe. J. Comp. Neurol. 334, 444\u2013465 (1993).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nSommer, S., Von Beeren, C. & Wehner, R. Multiroute memories in desert ants. Proc. Natl. Acad. Sci. USA 105, 317\u2013322 (2008).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nAksoy, V. & Camlitepe, Y. Spectral sensitivities of ants\u2013a review. Anim. Biol. 68, 55\u201373 (2018).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nSchwarz, S., Mangan, M., Zeil, J., Webb, B. & Wystrach, A. How ants use vision when homing backward. Curr. Biol. 27, 401\u2013407 (2017).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWystrach, A., Dewar, A., Philippides, A. & Graham, P. How do field of view and resolution affect the information content of panoramic scenes for visual navigation? A computational investigation. J. Comp. Physiol. A 202, 87\u201395 (2016).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nApplonie, R. & Jin, Y.-F. A novel steering control for car-like robots based on lyapunov stability. In Proceedings 2019 American Control Conference (ACC) 2396\u20132401 (2019).\n\nKruskal, W. H. & Wallis, W. A. Use of ranks in one-criterion variance analysis. J. Am. Stat. Assoc. 47, 583\u2013621 (1952).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nVirtanen, P. et al. Scipy 1.0: fundamental algorithms for scientific computing in python. Nat. Methods 17, 261\u2013272 (2020).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nGattaux, G. G., Wystrach, A., Serres, J. R. & Ruffier, F. Dataset for \u201croute-centric ant-inspired memories enable panoramic route following\u201d. https://doi.org/10.6084/m9.figshare.27708105 (2025).\n\nGattaux, G. G., Wystrach, A., Serres, J. R. & Ruffier, F. Code for \u201croute-centric ant-inspired memories enable panoramic route following\u201d. https://doi.org/10.5281/zenodo.15783472 (2025).\n\nDownload references",
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+        },
+        {
+            "section_name": "Acknowledgements",
+            "section_text": "The authors thank David Wood for revising the English in this study, Guillaume Caron for providing the camera reference,\u00a0St\u00e9phane Viollet for the GPS, and Thomas Gaillard, Cl\u00e9ment Serrasse, and Hamidou Diallo for their assistance during the robotic tests. G.G.G. was supported by a doctoral fellowship grant from Aix Marseille University (amU) and the French Ministry of Defense (AID - Agence Innovation D\u00e9fense, agreement #A01D22020549 ARM/DGA /AID). G.G.G., J.R.S. and F.R. were also supported by Aix Marseille University and the CNRS Institutes (Biology, Informatics, as well as Engineering). A.W. was supported by ERC Consolidator Grant RESILI-ANT no. 101125881. The facilities for the experimental tests has been mainly provided by ROBOTEX 2.0 (Grants ROBOTEX ANR-10-EQPX-44-01 and TIRREX ANR-21-ESRE-0015).",
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+            "section_name": "Author information",
+            "section_text": "Aix Marseille Univ, CNRS, ISM, Marseille, France\n\nGabriel G. Gattaux,\u00a0Julien R. Serres\u00a0&\u00a0Franck Ruffier\n\nUniv Toulouse, CRCA, CBI, UMR CNRS-UPS 5169, Toulouse, France\n\nAntoine Wystrach\n\nInstitut Universitaire de France, IUF, Paris, France\n\nJulien R. Serres\n\nENSTA|IP Paris, CNRS, Lab-STICC, Brest, France\n\nFranck Ruffier\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nG.G.G., A.W., J.R.S., and F.R. designed this research work; G.G.G., A.W., J.R.S., and F.R. got funding for this study; G.G.G. performed experiments, collected and visualized the data; G.G.G., A.W., J.R.S., and F.R. analyzed data; G.G.G. wrote the first full draft. All authors reviewed the results and approved the final version of the manuscript.\n\nCorrespondence to\n                Antoine Wystrach or Franck Ruffier.",
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+            "section_text": "Gattaux, G.G., Wystrach, A., Serres, J.R. et al. Route-centric ant-inspired memories enable panoramic route-following in a car-like robot.\n                    Nat Commun 16, 8328 (2025). https://doi.org/10.1038/s41467-025-62327-3\n\nDownload citation\n\nReceived: 22 November 2024\n\nAccepted: 14 July 2025\n\nPublished: 24 September 2025\n\nVersion of record: 24 September 2025\n\nDOI: https://doi.org/10.1038/s41467-025-62327-3\n\nAnyone you share the following link with will be able to read this content:\n\nSorry, a shareable link is not currently available for this article.\n\n\n\n\n                            Provided by the Springer Nature SharedIt content-sharing initiative\n                        ",
+            "section_image": [
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+            "section_image": []
+        }
+    ]
+}

0996185957de22ec96c13ddd4eeca9080a098f778fc62996a2333ee389185663/metadata.json

@@ -0,0 +1,144 @@
+{
+    "title": "Secure wireless communication of brain\u2013computer interface and mind control of smart devices enabled by space-time-coding metasurface",
+    "pre_title": "Secure wireless communication of brain-computer interface and mind control of smart devices enabled by space-time-coding metasurface",
+    "journal": "Nature Communications",
+    "published": "25 August 2025",
+    "supplementary_0": [
+        {
+            "label": "Supplementary Information",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-63326-0/MediaObjects/41467_2025_63326_MOESM1_ESM.pdf"
+        },
+        {
+            "label": "Description of Additional Supplementary Files",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-63326-0/MediaObjects/41467_2025_63326_MOESM2_ESM.pdf"
+        },
+        {
+            "label": "Supplementary Movie 1",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-63326-0/MediaObjects/41467_2025_63326_MOESM3_ESM.mp4"
+        },
+        {
+            "label": "Supplementary Movie 2",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-63326-0/MediaObjects/41467_2025_63326_MOESM4_ESM.mp4"
+        },
+        {
+            "label": "Transparent Peer Review file",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-63326-0/MediaObjects/41467_2025_63326_MOESM5_ESM.pdf"
+        }
+    ],
+    "supplementary_1": NaN,
+    "supplementary_2": NaN,
+    "source_data": [],
+    "code": [],
+    "subject": [
+        "Electrical and electronic engineering",
+        "Metamaterials"
+    ],
+    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
+    "preprint_pdf": "https://www.researchsquare.com/article/rs-4860006/v1.pdf?c=1756206415000",
+    "research_square_link": "https://www.researchsquare.com//article/rs-4860006/v1",
+    "nature_pdf": "https://www.nature.com/articles/s41467-025-63326-0.pdf",
+    "preprint_posted": "22 Aug, 2024",
+    "research_square_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Brain-computer interface (BCI) provides an interconnected pathway between human brain and external devices and paves a potential route for mind manipulations. However, most of existing BCI technologies are based on simple signal transmission and independent of other interface devices, owing to the considerations of reliability and safety of human brain\u2019s information interaction in the complicated wireless environment. To address the formidable limitation, we present a brain space-time-coding metasurface (BSTCM) system to deeply fuse the visual stimulation and electromagnetic manipulation for reliable and secure information transfer between human brain and external devices. Here, we innovatively integrate the BCI flashing frame and electromagnetic encoding sequence in the BSTCM system, and the STC metasurface ensures the secure wireless communications by using the harmonic-encrypted beams. We design and fabricate a proof-of-principle demonstration system and experimentally show that the proposed wireless BCI scheme could establish a remote but safeguarded paradigm for human-machine interactions, intelligent metasurfaces, and potential applications in metaverse, as a prominently scrutinized domain in the future 6G wireless communications.Physical sciences/Engineering/Electrical and electronic engineeringPhysical sciences/Optics and photonics/Optical materials and structures/MetamaterialsPhysical sciences/Materials science/Materials for optics/MetamaterialsSpace-time-coding metasurfacebrain-computer interfacesecure wireless communicationhuman-machine interactions",
+            "section_image": []
+        },
+        {
+            "section_name": "Additional Declarations",
+            "section_text": "There is NO Competing Interest.",
+            "section_image": []
+        },
+        {
+            "section_name": "Supplementary Files",
+            "section_text": "SupplementMaterials.pdfSupplementaryVideos.zipSupplementary Videos",
+            "section_image": []
+        }
+    ],
+    "nature_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Brain\u2013computer interface (BCI) provides an interconnected pathway between the human brain and external devices and paves a potential route for mind manipulations. However, most existing BCI technologies are based on simple signal transmission and are independent of other interface devices, with limited consideration for the reliability and security of the human brain\u2019s information interaction in complicated wireless environments. Here, we propose a deep fusion coding scheme that combines the BCI visual stimulation coding with metasurface space-time coding at the physical layer, enabling reliable and secure information transfers between the human brain and external devices. A brain space-time-coding metasurface platform is designed to implement a secure wireless communication system by using harmonic-encrypted beams. We design and fabricate a proof-of-principle prototype and experimentally show that the proposed wireless BCI scheme can establish a remote but safeguarded paradigm for human\u2013machine interactions and intelligent metasurfaces, providing a potential direction in future secure wireless communications.",
+            "section_image": []
+        },
+        {
+            "section_name": "Introduction",
+            "section_text": "Brain\u2013computer interface (BCI) has emerged as a cutting-edge technology in human\u2013machine interaction and demonstrates promising applications such as brain-controlled spelling input1,2, medical rehabilitation, and equipment control3,4. Electroencephalography (EEG) signals remain the predominant input signal modality in BCI systems, with notable implementations including motor imagery5, P3006, and steady-state visually evoked potential (SSVEP)7. The SSVEP-based BCI systems utilize the brain\u2019s SSVEP response to the fixed-frequency visual stimuli for mind recognition and interaction8, offering a significant advantage of a high information transfer rate. Recently, some high-performance BCI systems have been proposed9,10,11,12,13,14, and the advancement of 6G wireless communication technology has significantly expanded the potential applications of BCIs. Hence, ensuring high information security and privacy preservation15 for the BCI users and devices becomes imperative when facilitating intelligent interactions within the constructed communication environment.\n\nHowever, most existing BCI systems lack in-depth research in terms of security. Wireless transmission of brain signals in the BCI systems is vulnerable to theft and attacks, potentially leading to inaccurate control commands and unauthorized privacy breaches. Although some methodologies have been proposed to enhance the security and privacy in BCIs16,17,18, the encryption mechanisms specifically tailored to these systems remain largely unexplored. Moreover, visual stimulation is often isolated from back-end information processing, lacking deep integration and interaction. With the increasing demand for secure BCI systems, it is essential to develop intelligent interactions in a secure and reliable communication environment. The frequency-dependent SSVEP responses and programmable harmonic characteristics of space-time-coding (STC) metasurfaces have notable similarities. Therefore, the STC metasurfaces can be used as a promising method that not only provides visual stimulation but also enhances the security of the BCI systems at the physical layer, owing to their powerful ability to flexibly manipulate electromagnetic (EM) waves in both time and space domains19.\n\nThe metasurfaces are composed of specific unit structures arranged in periodic or quasi-periodic arrays, which can flexibly control the EM waves at the subwavelength scale and yield a large number of unusual physical phenomena and novel devices20,21,22,23. The proposal of digital coding and programmable metasurfaces has established a profound connection between the EM fields and digital information under the control of a high-speed field programmable gate array (FPGA)24. Recently, the exploration of STC metasurfaces has sparked a surge of research interest due to the excellent ability to manipulate the EM waves and process digital information in both temporal and spatial dimensions25,26,27,28,29, resulting in many novel physical phenomena that cannot be realized by the traditional spatially modulated metasurfaces. More importantly, the utilization of STC metasurfaces holds the capability to precisely control the amplitudes, phases, and polarizations at different harmonic frequencies independently by specially designing the STC matrices30, which opens up avenues to develop advanced communication schemes with enhanced efficiency and reliability31,32,33. Hence, the STC metasurface is a potential candidate for deep information modulation and interaction in the SSVEP-based BCI system owing to its capability to flexibly manipulate the EM waves and interact with the frequency-dependent visual stimulation.\n\nHere, we propose a deep fusion coding scheme that combines SSVEP visual stimulation coding with metasurface coding for secure information interactions at the physical layer. To implement this scheme, we present a brain space-time-coding metasurface (BSTCM) platform that seamlessly integrates the visual stimulation for SSVEP-based BCIs with the information interaction to the external environment, improving the system\u2019s compactness and reliability. To enhance BCI security, we propose a secure, encrypted wireless communication system that integrates the physical layer security with the cryptography encryption method. Specifically, the transmitted information is encrypted into two ciphertexts, which are respectively sent to two users through two independent harmonic frequency channels constructed by the BSTCM system. Experimental results demonstrate a high bit error rate (BER) of nearly 50% for the Eves and a secrecy capacity of approximately 1.9\u2009dB, validating the security of the encrypted wireless communication system. Finally, smart device control is presented by using the BSTCM system, realizing intelligent human\u2013machine interactions. The proposed BSTCM establishes a paradigm of human\u2013machine interactions and secure wireless communications.",
+            "section_image": []
+        },
+        {
+            "section_name": "Results",
+            "section_text": "The proposed deep fusion coding method combines the BCI visual stimulation coding with the metasurface coding for secure information interactions at the physical layer, as presented in Fig.\u00a01a. The brain signals can be induced by low-frequency flickering visual stimuli (4\u201350\u2009Hz), while the STC metasurface produces a series of harmonic frequencies, revealing notable similarities in the frequency domain. The visual stimulation is crucial for eliciting the distinct oscillatory patterns necessary for user-intent decoding, and the BCI system would be inoperative without it. Since the metasurface\u2019s switching frequency is significantly higher than the flicker frequency, we fuse the STC signals into high-level intervals of low-frequency visual stimuli, where two signals are temporally synthesized to generate the cohesive BSTCM signals that support both visual flicker and EM manipulation. This integration enables the seamless fusion of the two coding mechanisms, as illustrated in Fig.\u00a01a. To implement this fusion coding, an integrated BSTCM platform for both visual stimulation and EM-wave modulation is presented in Fig.\u00a01, which comprises an STC metasurface and a BCI device. The metasurface element includes a meta-structure for EM-wave regulation and a light-emitting diode (LED) stimulator for visual stimuli. The corresponding EEG signals can be accurately captured by a head-worn EEG cap when the user focuses on the LEDs flickering at distinct frequencies. Then, the brain\u2019s intention can be recognized as different commands through the classification process of EEG signals, and the commands are transmitted to the STC metasurface, where the metasurface coding is fused with the visual stimuli to generate BSTCM control signals. This simultaneously supports visual stimulation and EM-wave modulation, opening up a wide range of potential applications.\n\na The schematic diagram of fusing visual stimulation coding with metasurface coding. The STC metasurface can correctly support the visual stimuli for the SSVEP-based brain computer interface (BCI) and facilitate information interaction with the external environment. Here, \\({f}_{{SSVEP}}\\) represents the four target visual stimulation frequencies, and \\({f}_{0}\\) denotes the switching frequency of STC signals. b The BSTCM system integrates the STC metasurface into the SSVEP-based BCI systems, and an encrypted wireless communication system is realized. In this way, smart devices can be controlled by the human mind.\n\nThe detailed flow diagram of the BSTCM system is shown in Fig.\u00a02. The target flickering stimuli, characterized by four distinct frequencies (8.5\u2009Hz, 10\u2009Hz, 11.5\u2009Hz, and 7\u2009Hz), are supported by the STC metasurface integrated with LEDs. The interaction process begins with the user wearing an EEG cap and sitting in front of the STC metasurface. Four visual flickering stimuli with distinct frequencies are presented to the user for selection. These visual stimuli are employed to elicit specific BCI signals, while an EEG amplifier collects the BCI signals (see Supplementary Note\u00a01 for details). Then, the BCI signals are classified into four different interaction commands, each corresponding to one of the aforementioned visual stimulation frequencies. The interaction commands are sent to the STC metasurface, and the corresponding STC signals are generated. A fusion operation is conducted to fuse the STC signals and visual stimulation signals, hence generating the corresponding BSTCM signals. These BSTCM signals drive the STC metasurface to simultaneously maintain the visual stimuli of the fixed frequency and manipulate the EM waves. Finally, the BSTCM system is used to construct independent physical channels at harmonic frequencies, enabling secure wireless communication and remote control of smart devices. This integrated platform not only ensures high mobility and system compactness by reducing the external connections but also achieves real-time bidirectional interaction. This approach highlights a fusion of BCI and STC metasurface technologies to realize secure, efficient, and intelligent human\u2013computer interaction systems. By deeply fusing the visual encoding and metasurface STC signals, the BSTCM platform ensures that every module fulfills a specific function while remaining inseparable from the rest. Specifically, the extracted complex EEG signals can be precisely recognized using a machine learning method, an FPGA can fuse the low-frequency visual stimuli with high-frequency STC signals, and the STC metasurface can be controlled to generate the harmonic-encrypted EM beams. They collectively form a cohesive framework that seamlessly handles the human brain's intention and secure data transmission, ensuring real-time adaptation, robust security, and user-driven interaction. Ultimately, the BSTCM system allows individuals to customize and modulate EM waves via cognitive intent, expanding the EM functionalities while enhancing the flexibility and interactivity in the human-machine systems.\n\nThe user generates the BCI signals by gazing at visual stimuli, which are processed and classified into different commands by the machine learning method. These commands are then sent to the STC metasurface, which fuses the low-frequency visual stimuli signals and high-frequency STC signals to form different BSTCM signals in Fig.\u00a01a. The fusion method can simultaneously maintain the visual stimuli of the fixed frequency and manipulate the EM waves. The BSTCM platform supports brain-driven interactive functions with the external environment, enabling secure wireless communications and remote smart-device controls via the frequency- and space-multiplexed physical channels.\n\nThe STC metasurface enables precise control of the propagation direction and harmonic power distribution of the EM waves in both spatial and frequency domains. By harnessing the abundant harmonic modulation capabilities and integrating the advantages of human brain intelligence, the BSTCM system facilitates the implementation of a secure, encrypted wireless communication system and enables smart device control by the human mind. In the encrypted wireless communication system, the XOR-based encryption encoding method is employed to encrypt the target information34,35,36. In fact, the target information is encrypted into two secret ciphertexts. As schematically demonstrated in Fig.\u00a01b, a legal transmitter (Alice) equipped with an EEG cap intentionally transfers two secret ciphertexts to two legal receivers (Bob and Carol) at two different harmonic frequency channels based on the encrypted communication. The eavesdropper (Eve) cannot decrypt the transmitted information unless she simultaneously obtains two ciphertexts, and knows the encryption mechanism, which are nearly impossible. Hence, the proposed system ensures high security and concealment by encrypting the secret information into two ciphertexts and transmitting these ciphertexts through two harmonic frequency channels. Ingeniously camouflaged as an LED stimulator, the STC metasurface can effectively obstruct the Eve from detecting the information interaction. The proposed encrypted wireless communication system integrates the physical layer security with the cryptography encryption method, enhancing the system security. Furthermore, the proposed system facilitates the remote control of smart devices, enabling users to control devices directly through the user\u2019s brain intention without the need for physical actions.\n\nConventional SSVEP classification and recognition algorithms include canonical correlation analysis37, filter bank canonical correlation analysis38, task-related component analysis1, support vector machine39, and convolutional neural network (CNN)40. However, some limitations still exist in the above-mentioned algorithms. In this study, we present a robust deep learning-based algorithm for the recognition of the SSVEP component, which is seamlessly integrated into the signal recognition stage of the proposed system (refer to Supplementary Note\u00a02). As depicted in Fig.\u00a03a, the raw BCI signals undergo a comprehensive pre-processing pipeline to extract the key frequency features for SSVEP signal recognition. This pipeline filters the signals using a filter bank consisting of four Chebyshev Type I bandpass filters, isolating four distinct sub-bands with specified frequency ranges to mitigate the interference and enhance the signal quality. Subsequent application of the fast Fourier transform (FFT) to these sub-bands reveals their amplitude spectra, highlighting the frequency components of the SSVEP signals. To further refine the spectral information, a weighted summation process is used to assign weight factors to each sub-band based on their indices, emphasizing the contribution of lower frequency components. The resulting signal amplitude spectrum (SigSpec) encapsulates the essential frequency characteristics of the SSVEP signals, serving as the foundation for subsequent feature extraction and classification processes.\n\na The comprehensive workflow from raw BCI signal acquisition to the final signal recognition outcome. b The conversion of signal spectra (SigSpec) into eight distinct feature graphs through the outer product operation with the pre-calculated reference spectra (RefSpec). c The lightweight classification model, in which four convolutional and two fully connected layers were employed. d An example of frequency responses of the SSVEP signals for the four target frequencies, showing distinctive amplitude peaks corresponding to different frequencies.\n\nFurthermore, we employ an innovative feature extraction technique to perform outer product operations between the SigSpec and pre-computed reference spectra (RefSpec), derived from the SSVEP signals with known frequencies, as described in Fig.\u00a03b. This operation yields eight feature graphs (sized by 160\u2009\u00d7\u2009160 pixels), each representing the interaction between two input SSVEP signal channels (O1 and O2) and the reference signals corresponding to the four target frequencies. A discernible square grid pattern appears in the feature graph corresponding to the frequency of the anticipated classification result (refer to Supplementary Notes\u00a03\u20135). These feature graphs are then processed by a lightweight CNN-based classification model, which incorporates four convolutional layers and two linear layers, as shown in Fig.\u00a03c and Supplementary Fig.\u00a012. The feature graphs are initially processed through a convolutional input layer. Subsequently, a MaxPooling operation with a 2\u2009\u00d7\u20092 kernel is applied after the data are activated by the ReLU function. To facilitate the propagation of original data, a residual connection is strategically integrated between the second and third convolutional layers. Each convolutional layer is followed by the same 2\u2009\u00d7\u20092 MaxPooling operation and ReLU activation. Once the convolutional layers extract spatial feature vectors from the feature graphs, a series of two consecutive linear layers is employed to classify the feature vectors into four distinct target frequencies. Finally, an output layer with sigmoid activation reshapes the model\u2019s output into four confidence scores. After training 300 epochs, the model achieved a classification accuracy of 96.67% on the validation set, with precision and recall rates over 90%. These results highlight the effectiveness of the proposed deep learning-based algorithm for the SSVEP signal recognition (see Supplementary Notes\u00a06 for additional details).\n\nFigure\u00a04a showcases the detailed configuration of the 1-bit STC metasurface element integrated with an LED, which consists of three metallic layers and multiple substrate layers. The top metallic layer has two slotted rectangular patches with a width of w\u2009=\u20097.3\u2009mm and a length of l\u2009=\u200911\u2009mm, in which the middle slot has a width of w1\u2009=\u20091.5\u2009mm and a length of l1\u2009=\u20097\u2009mm. The outer metal frame with a width of 0.15\u2009mm is used to weaken the coupling effect between elements. The top F4B dielectric substrate has a relative permittivity of 2.65 and a loss tangent of 0.003 with the thickness h\u2009=\u20093\u2009mm and period p\u2009=\u200919\u2009mm. Two PIN diodes are serially loaded in the middle of two rectangular patches, and the two rectangular patches are connected with metallic bars, serving as positive and negative poles, in which two inductors are used as radio-frequency (RF) chokes to effectively isolate the RF signal from direct current (DC). To enable simultaneous visual stimulation and EM modulation in Fig.\u00a04a, an LED serving as visual stimulation is placed outside the metal patch to avoid affecting the scattering properties of meta-atoms and share the same voltage signals with the PIN diode. To evaluate the performance of the 1-bit meta-atom, full-wave simulations are conducted using the commercial software CST Microwave Studio. As shown in Fig.\u00a04b, c, the scattering characteristics of the meta-atom can be altered by switching the states of two PIN diodes corresponding to distinct RLC equivalent circuit models, hence realizing the 1-bit phase regulation. The diodes with the OFF state are assigned as coding \u201c0\u201d, and the ON state as coding \u201c1\u201d. When the meta-atom is subjected to normal illumination by a y-polarized plane wave, a phase difference of 180\u00b0 between \u201c0\u201d and \u201c1\u201d states is observed at approximately 6.9\u2009GHz, and both states exhibit reflective amplitudes exceeding \u22121 dB, indicating excellent performance of the 1-bit programmable meta-atom. Hence, the designed meta-atom can be used to build the 1-bit STC metasurface. The STC metasurface is composed of 32\u2009\u00d7\u200932 elements, and segmented into four partitions, with each region consisting of 16\u2009\u00d7\u200916 elements. In these partitions, LEDs are operated at four distinct frequencies (8.5\u2009Hz, 10\u2009Hz, 11.5\u2009Hz, and 7\u2009Hz) and implemented to evoke four distinct SSVEP signals. The detailed prototype design, modeling, and characterization are given in Methods and Supplementary Note\u00a09.\n\na The geometrical structure of the STC metasurface element. b, c The reflective amplitude and phase of the element, respectively. d\u2013f The optimized STC matrices for different scattering angles at different harmonic frequencies. g\u2013i The far-field results correspond to the optimized STC matrices. j\u2013m The encoding schemes for the transmitting symbol \u201c0\u201d and \u201c1\u201d for two users: the symbols \u2018\u201c0\u201d and \u201c1\u201d for Users 1 (j, k); the symbols \u201c0\u201d and \u201c1\u201d for Users 2 (l, m). n The detailed configuration of four visual stimulation regions on the STC metasurface.\n\nTo establish a dual-user encrypted wireless communication system, we implement an amplitude-shift keying (ASK) modulation scheme using the STC metasurface, enabling simultaneous encrypted transmissions via space and frequency multiplexing. The control voltages, originating from the FPGA, are applied to the PIN diodes, enabling periodic switching to the reflection phases of the 1-bit STC element with a time period of \\({T}_{0}=1/{f}_{0}\\). Consequently, each STC element possesses a periodic time-coding sequence and constitutes part of an STC matrix, making it possible to flexibly control the EM waves in both space and time domains. The flexibility of STC matrices can generate a series of new harmonic spectra at the frequency interval of \\({f}_{0}\\), which are further optimized with specific requirements (see Supplementary Notes\u00a07 and 8). The space-time modulation enables abundant harmonic characteristics to construct harmonic-based encrypted wireless communications. Using the 2D STC matrices, we can modulate the EM waves to steer to the desired directions for target users. The STC matrices encompass 16 rows of elements, each possessing periodic time-coding sequences with 11 intervals. As illustrative examples, three radiation patterns corresponding to three STC matrices (M0, M1, and M2) are shown in Fig.\u00a04. The radiation pattern of the optimized STC matrix M1 in Fig.\u00a04e is strategically manipulated to yield a main beam with a deflected angle of \u03b8\u2009=\u2009\u221215\u00b0 at the +1st harmonic frequency, as showcased in Fig.\u00a04h. Similarly, the radiation pattern of the STC matrix M2 (Fig.\u00a04f) is optimized to direct the beam towards the angle \u03b8\u2009=\u2009+30\u00b0, in correspondence with the \u22121st harmonic frequency, as demonstrated in Fig.\u00a04i. Furthermore, the time-invariant STC matrix M0 (Fig.\u00a04d) facilitates the positioning of main beam towards a direction of \u03b8\u2009=\u20090\u00b0, associated with the fundamental frequency, as illustrated in Fig.\u00a04g. The harmonic energy could be further enhanced in the future by optimizing STC coding strategies using advanced algorithms. As an example of ASK modulation scheme, the left panels (\\({f}_{1}\\)\u2009=\u20098.5\u2009Hz and \\({f}_{2}\\)\u2009=\u200910\u2009Hz) of the STC metasurface are utilized to send the digital symbols \u201c0\u201d and \u201c1\u201d to User 1 at the position of \u03b8\u2009=\u2009\u221215\u00b0 when the transmitting information is encoded as binary data streams. The right panels (\\({f}_{3}\\)\u2009=\u200911.5\u2009Hz and \\({f}_{4}\\)\u2009=\u20097\u2009Hz) of the STC metasurface are utilized to send the digital symbols \u201c0\u201d and \u201c1\u201d to User 2 at the position of \u03b8\u2009=\u2009+30\u00b0. Experiments are carried out in a microwave anechoic chamber to measure the far-field radiation patterns of the STC metasurface, as illustrated in Supplementary Notes\u00a010 and 11. Hence, the good experimental results demonstrate that two frequency-dependent communication channels are constructed, providing a solid foundation for the physical layer security.\n\nConstrained by the requirement of the SSVEP-based BCI to gather data and detect EEG signals at a single frequency, a viable encoding strategy is proposed to reduce the symbol error rate (SER), as depicted in Fig.\u00a04j\u2013m. The transmission of digital symbols \u201c0\u201d and \u201c1\u201d is achieved by encoding a sequence of repeated data frames, with every set of 4 frames serving as the synchronous frames. In the encoding scheme, the first bit \u201c1\u201d serves as the start bit, signaling the initiation of the transmission process. The second bit signifies the harmonic frequency (+1st or \u22121st) used for transmission, and the third bit corresponds to the transmission of the data itself. Finally, the fourth bit functions as the stop bit, indicating the end of transmitting one data frame. Based on the encoding process, the digital symbols \u201c0\u201d and \u201c1\u201d for User 1 are encoded as the repeated data frames \u201cM1\u2013M0\u2013M0\u2013M0\u2013M1\u2013M0\u2013M0\u2013M0\u2026\u201d and \u201cM1\u2013M0\u2013M1\u2013M0\u2013M1\u2013M0\u2013M1\u2013M0\u2026\u201d. Similarly, the digital symbols \u201c0\u201d and \u201c1\u201d for User 2 are encoded as the repeated data frames \u201cM2\u2013M2\u2013M0\u2013M0\u2013M2\u2013M2\u2013M0\u2013M0\u2026\u201d and \u201cM2\u2013M2\u2013M2\u2013M0\u2013M2\u2013M2\u2013M2\u2013M0\u2026\u201d, respectively. Hence, the STC matrix M1 operating with a switching frequency \\({f}_{0}\\), is precisely injected into the region of high amplitude associated with the flicker frequencies \\({f}_{1}\\) and \\({f}_{2}\\), as illustrated in Fig.\u00a04j, k. The STC matrices are updated when the information is sent to User 1 via the BSTCM system. Similarly, the STC matrix M2 with a period switch frequency \\({f}_{0}\\), undergoes injection into the high amplitude attributed to the flicker frequencies \\({f}_{3}\\) and \\({f}_{4}\\), as displayed in Fig.\u00a04j, k, representing the transmission of information to User 2. Remarkably, the update of STC matrices does not affect the flickering frequency of LEDs used for SSVEP stimuli, ensuring that BCI signals can be synchronously detected and recognized. Hence, the BCI operator can freely transmit different information by staring at different visual stimuli of the STC metasurface according to the above-mentioned encoding method.\n\nIn the proposed encrypted wireless communication system, the transmitted information is randomly encrypted into two ciphertexts using a fully algorithmic method without human involvement. These ciphertexts are then securely sent to two designated users through different harmonic communication channels controlled by the BSTCM platform. Under this encrypted method, the original information is recovered by XOR-based stacking of two visual shared keys (VSKs), wherein each pixel of the secret message is encrypted into two sub-pixels for two distinct users. As illustrated in Fig.\u00a05a, VSK1 is randomly generated, and VSK2 is subsequently derived through the XOR operation. Notably, neither share alone contains any discernible details regarding the original secret, thereby ensuring that the disclosure of a single VSK does not compromise the confidentiality of the underlying message. As an illustrative example in Fig.\u00a05a, the secret image \u201cH\u201d, consisting of a grid of 5\u2009\u00d7\u20095 black pixels (digital \u201c1\u201d) and white pixels (digital \u201c0\u201d), is encrypted into two VSKs composed of 5\u2009\u00d7\u20095 sub-pixels based on the presented encryption method, where VSK1 is randomly generated and VSK2 is subsequently derived through the XOR operation. Consequently, neither VSK1 nor VSK2 alone contains sufficient information to reveal the original secret information. When the BCI operator (Alice) sequentially transmits the two bitstream sequences of two VSKs to two legal users (Bob and Carol) by the human mind, she freely gazes at the visual stimuli of the four STC metasurface regions based on the properties of the SSVEP-based BCI system. As a result, different EEG signals are generated and classified into four commands, which are then sent to the FPGA to produce the corresponding four BSTCM signals, as illustrated in Fig.\u00a04j\u2013m. Each gaze from the BCI operator corresponds to transmitting a single pixel of the VSK. Due to the neural response time constraints and the required high classification accuracy, the system\u2019s data transmission rate is about 0.25\u2009bps, which can be further improved with advanced technology (refer to Supplementary Note\u00a017). By employing the proposed BSTCM system to construct two harmonic frequency-dependent physical channels (+1st and \u22121st harmonics), two VSKs (VSK1 and VSK2) are sequentially delivered to the respective legal users through these channels. During decryption, the two VSKs corresponding to each secret are XOR-based to recover the original information. The details of encryption and decryption methods can be found in Supplementary Note\u00a012. The target image in question can be decrypted through the XOR operation of two VSKs, realizing a robust level of information security. In the future, the encryption scheme can be expanded to include more users, further enhancing the BSTCM system\u2019s security.\n\na The encrypted encoding scheme for the secret image \u201cH\u201d. b The experimental scenarios of the encrypted wireless communication system, in which the operator, equipped with an EEG cap, transmits the encrypted information to two users via the BSTCM platform, respectively. c The receiving signals corresponding to the encoding scheme in Fig.\u00a04j\u2013m. The top panel displays the raw received signals, whereas the bottom panel shows the corresponding signals processed by the FFT method. d, e The decoded information of VSKs (VSK1 and VSK2) from the receiving signals is based on the encrypted coding scheme. f The correct transmitting information is decoded by the acquired VSK1 and VSK2.\n\nTo validate the encrypted communication scheme, we experimentally set up an encrypted wireless communication system using the BSTCM, as demonstrated in Fig.\u00a05b. The prototype of 1-bit STC metasurface is used to construct the encrypted communication system, as shown in Supplementary Fig.\u00a015. A commercial BCI device (actiCHamp of Brain Product GmbH company) composed of an EEG cap and amplifier is used to acquire the EEG signals when the operator stares at different partitions on the STC metasurface. The corresponding EEG signals can be accurately recognized by the proposed deep learning algorithm. The detailed description of the algorithm is provided in Supplementary Note\u00a06. A linearly polarized horn antenna, connected to a signal generator (Keysight E8267D), is placed at a vertical distance of 4\u2009m away from the metasurface center to excite a monochromatic plane wave at the frequency of 6.9\u2009GHz. The receiving terminals are composed of two horn antennas (serving as two users) and a spectrum analyzer (Keysight N9040D), which is used to demodulate the received signal. Two receiving horn antennas are located at the angles of \u03b8\u2009=\u2009\u221215\u00b0 and \u03b8\u2009=\u2009+30\u00b0 with relative to the metasurface normal, respectively. In the transmission process, the information undergoes encryption, resulting in the generation of two harmonic-based ciphers texts according to the encryption scheme. The transmission process is achieved by ensuring that the BCI operator maintains direct visual focus on the STC metasurface in alignment with the binary cipher texts. In addition, the system enables prompt acquisition, recognition, and translation of EEG signals into appropriate control signals of the FPGA, which in turn drive the STC metasurface. As a result, the accurate transmission of binary cipher texts is accomplished, facilitating reliable and efficient communications between the BCI operator and the intended recipients.\n\nIn the receiving process, the radiated signals propagating through free space are received individually by the two horn antennas, and these signals are subsequently demodulated using the spectrum analyzer. As shown in Fig.\u00a05c, the demodulated signals represent four encoding schemes that correspond to different digital symbols (\u201c0\u201d or \u201c1\u201d) for the two users and are then processed to the decoded results shown in Fig.\u00a05d by the FFT method. The decoded results clearly exhibit four repeated data frames, providing strong evidence to support the capability of the proposed system to recover the transmitting information successfully. Hence, two binary cipher texts are transmitted to two specific users by the BCI operator based on the proposed wireless communication system. The transmitted information is received, and the measured results are comprehensively showcased in Supplementary Note\u00a013 and Supplementary Video\u00a01. By employing the encoding method described earlier, the data streams corresponding to the specific users are extracted from the received signals, as depicted in Fig.\u00a05e, f. Subsequently, these data streams are decrypted accurately by the method outlined in Supplementary Note\u00a012. The deciphered information is displayed in Fig.\u00a05g. To verify the security performance of the BSTCM system, we measured the signal-to-noise ratio (SNR) and BER results. The SNR for two legal users is measured as approximately 22\u2009dB, while the SNR for an illegal user is less than 5\u2009dB. The security capacity is calculated as approximately 1.9\u2009dB. Furthermore, the BERs of the illegal user are measured to be approximately 50% when the illegal user eavesdrops separately from both the spatial and frequency domains (refer to Supplementary Note\u00a015 for additional details). These results validate the robustness and effectiveness of the proposed system in ensuring a high level of security and confidentiality, demonstrating its resilience against unauthorized interception and its capability to safeguard the secret information during transmission.\n\nTo experimentally verify the performance of the proposed BSTCM system, we conducted experiments to show the remote control capabilities of smart devices through human intention, which holds significant potential to enhance the quality of life for individuals with disabilities. The system flowchart depicted in Fig.\u00a06a outlines the key steps involved in the experimental setup. Initially, distinct EEG signals can be generated when the BCI operator stares at different visual stimuli of the STC metasurface. The EEG signals are acquired and subsequently processed by the BSTCM system for command recognition. The recognized commands are then translated to update the STC matrices of the metasurface by an FPGA. The four partitions of the STC metasurface are controlled by an FPGA to generate different beams at four deflected angles corresponding to the four harmonic frequencies, enabling the remote control of smart devices. Notably, the main beam at the \u22122nd harmonic frequency exhibits a pronounced peak in the direction of \u03b8\u2009=\u2009+10\u00b0, corresponding to the device assigned to User 3. Conversely, the main beam at the +2nd harmonic frequency demonstrates a strong peak at \u03b8\u2009=\u2009\u221245\u00b0, corresponding to the device assigned to User 1. As displayed in Fig.\u00a06c, d, the measured radiation patterns exhibit good consistency with theoretical predictions corresponding to the STC matrices. Additionally, the main beams were deflected at the other two angles (\u221215\u00b0 and 30\u00b0) using the +1st and \u22121st harmonic frequencies (Users 2 and 4), as shown in Fig.\u00a04h, i. The excellent performance of harmonic beam manipulation demonstrates that the system can effectively utilize harmonic frequencies to construct four independent physical channels, significantly enhancing the physical layer security. The receiving terminals are composed of four horn antennas, four RF energy detectors (LMH2110), four Microcontroller Unit (MCU) modules (Arduino), and four LED modules (serve as smart devices), as depicted in Fig.\u00a06b. The RF energy from harmonic beams captured by the detectors can be converted into DC voltages, which are subsequently fed into the MCU modules. Once the corresponding DC voltage is detected, the MCU modules send the control commands to activate the corresponding LED module, thereby implementing the remote control of the smart devices. The experimental setup is shown in Fig.\u00a06b, where the STC metasurface is illuminated by a monochromatic frequency signal of 6.9\u2009GHz.\n\na The system architecture of wireless remote control. b The experimental scenarios of the wireless remote-control system by the human brain. c, d The theoretical and experimental results for far-field patterns at \\(\\pm\\)2nd harmonic frequencies. e The variations between the input power of the detectors and the output voltage with respect to the different distances between the receiving antenna and the metasurface center. f The temporal waveform of the output voltages from four detectors when the operator lights up four devices in sequence.\n\nTo verify the robustness of the brain-control smart devices system, the position of the receiving antenna is sequentially placed at different distances from the metasurface center while maintaining specific harmonic direction angles with respect to the metasurface normal. The detection of RF energy from the emitted harmonic beams is carried out across varying distances, and the corresponding DC voltages can be accurately converted by the RF detectors, as illustrated in Fig.\u00a06e (see Supplementary Note\u00a014 for details). We observe that the RF energies of four users relatively decrease, and the converted DC voltages also decrease accordingly as the distance increases. To guarantee the attainment of the far-field region and maintain system stability, the four receiving antennas are positioned at a distance of approximately 300\u2009cm from the metasurface. Consequently, the detection voltage threshold is set as 0.15\u2009V, 0.4\u2009V, 0.4\u2009V, and 0. 2\u2009V in the MCU modules, respectively. We recorded a video of the brain-controlled multiple smart devices, as presented in Supplementary Movie\u00a02. The sequence diagrams shown in Fig.\u00a06f provide a clear visual representation of the sequential control process, where the smart devices (LED modules) are successively controlled through human intention using the BSTCM system. The experiment proves the feasibility of brain-controlled smart devices. By harnessing the power of BCI technology, individuals can exert control over smart devices without needing physical interaction. The BSTCM system enables seamless and intuitive manipulations of various smart devices, facilitating greater independence and convenience for people in daily life. The experimental results serve as a compelling validation supporting the significant benefits that the BSTCM can offer in improving the quality of life for individuals facing physical challenges.",
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+            ]
+        },
+        {
+            "section_name": "Discussion",
+            "section_text": "We presented a deep fusion coding scheme that combines the visual stimulation coding with the metasurface coding, and developed an integrated BSTCM platform to enable simultaneous visual stimulation and EM manipulation. The proposed system harnesses the human brain's intelligence and the flexible EM-control capabilities of the STC metasurface, enabling the information interaction within the EM field to establish reliable and stable communication environments. Furthermore, we demonstrated a secure, encrypted wireless communication system that combines the physical layer security and the cryptography encryption method, enhancing the system security. Finally, remote control of smart devices was illustrated by the BSTCM system, realizing intelligent human\u2013machine interactions. The proposed BSTCM, integrating the EM manipulation capability with the intelligence of the human brain, provides a paradigm for the interactions among human-machine interfaces and the future 6G wireless communication applications.",
+            "section_image": []
+        },
+        {
+            "section_name": "Methods",
+            "section_text": "A metasurface prototype was fabricated by the standard printed circuit board (PCB) process. The entire STC metasurface is composed of 32\\(\\times\\)32 digital elements and an effective size of 608\\(\\times\\)608\u2009mm2. For the convenience of processing and welding, the entire metasurface was disassembled into 8 sub-metasurfaces with 8\\(\\times\\)16 digital elements and an effective size of 152\\(\\times\\)304\u2009mm2. A total number of 2\\(\\times\\)32\\(\\times\\)32 PIN diodes (SMP1320-079LF from SKYWORKS) and RF inductors of 10 nH were elaborately welded on the metasurfaces with the surface mount technology, which is a mature engineering method to weld small components on PCB using the batch solder-reflow processes in a dedicated machine. Meanwhile, an LED is embedded into each metasurface element.\n\nAs depicted in Fig.\u00a02a, the SSVEP-BCI is delineated into three discrete distinct stages: the preparation stage, the signal acquisition stage, and the signal recognition stage. The EEG data in this study were acquired using the actiCHamp EEG amplifier manufactured by Brain Products GmbH. This amplifier offers a maximum capacity of 64 channels, 24-bit precision, and a sampling rate of 100\u2009kHz. It exhibits a high common mode rejection ratio (CMRR) of 100, making it suitable for capturing and detecting SSVEP signals effectively. This study uses a standard 10\u201320 EEG cap to obtain the signal. Since SSVEP is a local potential that predominantly originates from the occipital lobe7, the O1 and O2 electrodes located on the occipital region were selected for EEG data acquisition, with a reference electrode placed at the vertex (Cz) region. The sample time in this study was set to 4\u2009s. With a sampling rate of 512\u2009Hz and excluding the reference electrode data, each sample yielded 4096 sampling points (4\u2009s\u2009\u00d7\u2009512\u2009Hz\u2009\u00d7\u20092 channels). Square wave signals were utilized to present visual stimuli on the LEDs of the STC metasurface units, which emitted the red light, thereby ensuring adequate visual contrast. To minimize the harmonic interference, four target visual stimulus frequencies were: top-left at 8.5\u2009Hz, bottom-left at 10\u2009Hz, top-right at 11.5\u2009Hz, and bottom-right at 7\u2009Hz. To mitigate mutual interference between two closely spaced flickering stimuli pairs, the frequencies 7\u2009Hz and 8.5\u2009Hz, as well as 10\u2009Hz and 11.5\u2009Hz, were placed diagonally opposite to one another. The example of the collected brain wave signal data for four target frequencies is shown in Supplementary Fig.\u00a01. Data processing and model training were conducted in Python and PyTorch environments. Signal processing primarily involved utilizing the scipy package for filtering and FFT calculations. Given that neither the absolute value of the EEG signal nor its temporal characteristics were pertinent to this study, all sampled signals were linearly transformed to have a mean of zero and a standard deviation of one.\n\nInitially, a dataset comprising 240 instances of raw SSVEP signals was collected from two participants. Subsequently, a subset consisting of 80 instances of randomly selected raw signals was employed to create RefSpec. The remaining 160 instances of raw signals were randomly selected to serve as training and validation datasets for classification model training. The two subsets have an equal number of signals across four stimulus frequencies. As for the training and validation dataset, a subset of 60 instances was extracted from the initial subset of 160 instances to serve as the validation set. The remaining 100 instances underwent a data augmentation process, which resulted in an expanded dataset of 1700 instances. These augmented instances constituted the training set, which was then utilized to train the model for 300 epochs. The validation operation was executed every two training epochs.",
+            "section_image": []
+        },
+        {
+            "section_name": "Data availability",
+            "section_text": "The data supporting the findings of this study are presented in the paper and the Supplementary Information file.",
+            "section_image": []
+        },
+        {
+            "section_name": "Code availability",
+            "section_text": "The code that supports the findings of this study are available from the corresponding author upon request.",
+            "section_image": []
+        },
+        {
+            "section_name": "References",
+            "section_text": "Nakanishi, M. et al. Enhancing detection of SSVEPs for a high-speed brain speller using task-related component analysis. IEEE Trans. Biomed. Eng. 65, 104\u2013112 (2018).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBin, G. et al. SSVEP-based brain\u2013computer interfaces: time, frequency, and code modulations [Research Frontier]. IEEE Comput. Intell. Mag. 4, 22\u201326 (2009).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLi, Y. Q., Pan, J. H., Wang, F. & Yu, Z. L. A Hybrid BCI system combining P300 and SSVEP and its application to wheelchair control. IEEE Trans. Biomed. Eng. 60, 3156\u20133166 (2013).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMuller-Putz, G. R. & Pfurtscheller, G. Control of an electrical prosthesis with an SSVEP-based BCI. IEEE Trans. Biomed. Eng. 55, 361\u2013364 (2008).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nAl-Saegh, A., Dawwd, S. A., Abdul-Jabbar, J. M. Deep learning for motor imagery EEG-based classification: a review. Biomed. Signal Process. Control 63, 102172 (2021).\n\nLenhardt, A., Kaper, M. & Ritter, H. J. An adaptive P300-based online brain\u2013computer interface. IEEE Trans. Neural Syst. Rehabil. Eng. 16, 121\u2013130 (2008).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nVialatte, F.-B., Maurice, M., Dauwels, J. & Cichocki, A. Steady-state visually evoked potentials: focus on essential paradigms and future perspectives. Prog. Neurobiol. 90, 418\u2013438 (2010).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nNiu, Y. et al. Improving SSVEP-BCI system interaction efficiency: design recommendations for shape of visual stimuli and number of auxiliary stimuli. Int. J. Human Comput. Interact. 40, 3427\u20133448 (2024).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWillett, F. R., Avansino, D. T., Hochberg, L. R., Henderson, J. M. & Shenoy, K. V. High-performance brain-to-text communication via handwriting. Nature 593, 249\u2013254 (2021).\n\nArticle\u00a0\n    ADS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nRoy A. M. Adaptive transfer learning-based multiscale feature fused deep convolutional neural network for EEG MI multiclassification in brain\u2013computer interface. Eng. Appl. Artif. Intell. 116, 105347 (2022).\n\nMa, Q. et al. Directly wireless communication of human minds via non-invasive brain\u2013computer-metasurface platform. eLight 2, 11 (2022).\n\nWandelt, S. K. et al. Representation of internal speech by single neurons in human supramarginal gyrus. Nat. Hum. Behav. 8, 1136\u20131149 (2024).\n\nXiao, Q. et al. Electromagnetic Brain\u2013Computer\u2013Metasurface Holography (ACS Photonics, 2023).\n\nZhu, R. et al. Remotely mind-controlled metasurface via brainwaves. eLight 2, 10 (2022).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDang, S., Amin, O., Shihada, B. & Alouini, M.-S. What should 6G be?. Nat. Electron. 3, 20\u201329 (2020).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBrocal, F. Brain\u2013computer interfaces in safety and security fields: risks and applications. Safety Sci. 160, 106051 (2023).\n\nBhalerao, S., Ansari, I. A. & Kumar, A. Protection of BCI system via reversible watermarking of EEG signal. Electron. Lett. 56, 1389\u20131392 (2020).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBernal, S. L., Celdr\u00e1n, A. H., P\u00e9rez, G. M., Barros, M. T. & Balasubramaniam, S. Security in brain\u2013computer interfaces. ACM Comput. Surv. 54, 1\u201335 (2021).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWei, M., Zhao, H., Galdi, V., Li, L. & Cui, T. J. Metasurface-enabled smart wireless attacks at the physical layer. Nat. Electron. 6, 610\u2013618 (2023).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nPendry, J. B. Negative refraction makes a perfect lens. Phys. Rev. Lett. 85, 3966\u20133969 (2000).\n\nArticle\u00a0\n    ADS\u00a0\n    PubMed\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nPendry, J. B., Schurig, D. & Smith, D. R. Controlling electromagnetic fields. Science 312, 1780\u20131782 (2006).\n\nArticle\u00a0\n    ADS\u00a0\n    MathSciNet\u00a0\n    PubMed\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLiu, R. et al. Broadband ground-plane cloak. Science 323, 366\u2013369 (2009).\n\nArticle\u00a0\n    ADS\u00a0\n    PubMed\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nSmith, D. R. & Kroll, N. Negative refractive index in left-handed materials. Phys. Rev. Lett. 85, 2933\u20132936 (2000).\n\nArticle\u00a0\n    ADS\u00a0\n    PubMed\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nCui, T. J., Qi, M. Q., Wan, X., Zhao, J. & Cheng, Q. Coding metamaterials, digital metamaterials and programmable metamaterials. Light.: Sci. Appl. 3, e218 (2014).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nZhang, L. et al. Space-time-coding digital metasurfaces. Nat. Commun. 9, 4334 (2018).\n\nArticle\u00a0\n    ADS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWu, H. et al. Harmonic information transitions of spatiotemporal metasurfaces. Light Sci. Appl 9, 198 (2020).\n\nArticle\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWu, G.-B., Dai, J. Y., Cheng, Q., Cui, T. J. & Chan, C. H. Sideband-free space\u2013time-coding metasurface antennas. Nat. Electron. 5, 808\u2013819 (2022).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nZhang, L. et al. A wireless communication scheme based on space- and frequency-division multiplexing using digital metasurfaces. Nat. Electron. 4, 218\u2013227 (2021).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nShaltout, A. M., Shalaev, V. M. & Brongersma, M. L. Spatiotemporal light control with active metasurfaces. Science 364, eaat3100 (2019).\n\nWu, G.-B. et al. A universal metasurface antenna to manipulate all fundamental characteristics of electromagnetic waves. Nat. Commun. 14, 5155 (2023).\n\nZhao, J. et al. Programmable time-domain digital-coding metasurface for non-linear harmonic manipulation and new wireless communication systems. Natl Sci. Rev. 6, 231\u2013238 (2019).\n\nArticle\u00a0\n    PubMed\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDai, J. Y. et al. Wireless communication based on information metasurfaces. IEEE Trans. Microw. Theory Tech. 69, 1493\u20131510 (2021).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nTang, W. et al. Wireless communications with programmable metasurface: new paradigms, opportunities, and challenges on transceiver design. IEEE Wirel. Commun. 27, 180\u2013187 (2020).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nChen, T.-H. & Tsao, K.-H. Visual secret sharing by random grids revisited. Pattern Recognit. 42, 2203\u20132217 (2009).\n\nArticle\u00a0\n    ADS\u00a0\n    MATH\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nYang, C.-N. New visual secret sharing schemes using probabilistic method. Pattern Recognit. Lett. 25, 481\u2013494 (2004).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWang, D., Yi, F. & Li, X. Probabilistic visual secret sharing schemes for grey-scale images and color images. Inf. Sci. 181, 2189\u20132208 (2011).\n\nArticle\u00a0\n    MathSciNet\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBin, G., Gao, X., Yan, Z., Hong, B. & Gao, S. An online multi-channel SSVEP-based brain\u2013computer interface using a canonical correlation analysis method. J. Neural Eng. 6, 046002 (2009).\n\nChen, X., Wang, Y., Gao, S., Jung, T.-P. & Gao, X. Filter bank canonical correlation analysis for implementing a high-speed SSVEP-based brain\u2013computer interface. J. Neural Eng. 12, 046008 (2015).\n\nSingla, R., Khosla, A. & Jha, R. Influence of stimuli colour in SSVEP-based BCI wheelchair control using support vector machines. J. Med. Eng. Technol. 38, 125\u2013134 (2014).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDing, W. et al. Filter bank convolutional neural network for short time-window steady-state visual evoked potential classification. IEEE Trans. Neural Syst. Rehabil. Eng. 29, 2615\u20132624 (2021).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDownload references",
+            "section_image": []
+        },
+        {
+            "section_name": "Acknowledgements",
+            "section_text": "The work is supported by the National Natural Science Foundation of China (62288101, T.J.C., 92167202, T.J.C., 62301147, T.J.C., and 72171044, Y.F.N.), the National Key Research and Development Program of China (2022YFA1404903, T.J.C.), the Major Project of Natural Science Foundation of Jiangsu Province (BK20212002, T.J.C., and BK20210209, T.J.C.), Special Fund for Key Basic Research in Jiangsu Province (BK20243015, T.J.C.), the Natural Science Foundation of Jiangsu Province (BK20230822, T.J.C.), the State Key Laboratory of Millimeter Waves, Southeast University, China (K201924, T.J.C.), the Fundamental Research Funds for the Central Universities (2242023K5002, T.J.C., 2242018R30001, T.J.C., and 2242022R20017, T.J.C.), the 111 Project (111-2-05, T.J.C.), Young Elite Scientists Sponsorship Program by CAST (2022QNRC001, Q.M.), Jiangsu joint laboratory of multidimensional perceptual information technology (BM2022017, T.J.C.), the China Postdoctoral Science Foundation (2021M700761, Q.M.), and ZhiShan Scholar Program of Southeast University (2242022R40004, Y.F.N.).",
+            "section_image": []
+        },
+        {
+            "section_name": "Author information",
+            "section_text": "These authors contributed equally: Qiang Xiao, Lin Han Fan, Qian Ma.\n\nState Key Laboratory of Millimeter Waves and Institute of Electromagnetic Space, Southeast University, Nanjing, China\n\nQiang Xiao,\u00a0Qian Ma,\u00a0Yu Ming Ning,\u00a0Ze Gu,\u00a0Long Chen,\u00a0Jian Wei You\u00a0&\u00a0Tie Jun Cui\n\nJiangsu Joint Laboratory of Multidimensional Perceptual Information Technology, Nanjing, China\n\nQiang Xiao\u00a0&\u00a0Qian Ma\n\nSchool of Mechanical Engineering, Southeast University, Nanjing, China\n\nLin Han Fan\u00a0&\u00a0Ya Feng Niu\n\nState Key Laboratory of Advanced Optical Communication Systems and Networks, Department of Electronics, Peking University, Beijing, China\n\nLianlin Li\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nT.J.C. suggested the designs and supervised the work, in consultation with Q.M., Y.F.N., Q.X., and J.W.Y. conceived the idea and carried out the theoretical analysis and numerical simulations. Q.X., L.H.F., Y.M.N., and Z.G. built the system and performed the experimental measurements. Q.X., L.H.F., and L.C. performed the data analysis. Q.X. and L.H.F. wrote the manuscript. Q.M., L.L., J.W.Y, Y.F.N., and T.J.C. reviewed the manuscript. All authors discussed the theoretical aspects and numerical simulations, interpreted the results, and reviewed the manuscript.\n\nCorrespondence to\n                Qian Ma, Ya Feng Niu or Tie Jun Cui.",
+            "section_image": []
+        },
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+            "section_name": "Ethics declarations",
+            "section_text": "The authors declare no competing interests.",
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+        },
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+            "section_name": "Peer review",
+            "section_text": "Nature Communications thanks Chung-Tse Wu and the other anonymous reviewer(s) for their contribution to the peer review of this work. A peer review file is available.",
+            "section_image": []
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+            "section_name": "About this article",
+            "section_text": "Xiao, Q., Fan, L.H., Ma, Q. et al. Secure wireless communication of brain\u2013computer interface and mind control of smart devices enabled by space-time-coding metasurface.\n                    Nat Commun 16, 7914 (2025). https://doi.org/10.1038/s41467-025-63326-0\n\nDownload citation\n\nReceived: 06 August 2024\n\nAccepted: 15 August 2025\n\nPublished: 25 August 2025\n\nVersion of record: 25 August 2025\n\nDOI: https://doi.org/10.1038/s41467-025-63326-0\n\nAnyone you share the following link with will be able to read this content:\n\nSorry, a shareable link is not currently available for this article.\n\n\n\n\n                            Provided by the Springer Nature SharedIt content-sharing initiative\n                        ",
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+{
+    "title": "Intrinsic metal-support interactions break the activity-stability dilemma in electrocatalysis",
+    "pre_title": "Intrinsic metal-support interactions break the activity-stability dilemma in electrocatalysis",
+    "journal": "Nature Communications",
+    "published": "01 October 2025",
+    "supplementary_0": [
+        {
+            "label": "Supplementary Information",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-63397-z/MediaObjects/41467_2025_63397_MOESM1_ESM.pdf"
+        },
+        {
+            "label": "Description of Additional Supplementary Files",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-63397-z/MediaObjects/41467_2025_63397_MOESM2_ESM.pdf"
+        },
+        {
+            "label": "Supplementary Data 1",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-63397-z/MediaObjects/41467_2025_63397_MOESM3_ESM.txt"
+        },
+        {
+            "label": "Supplementary Movie 1",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-63397-z/MediaObjects/41467_2025_63397_MOESM4_ESM.mp4"
+        },
+        {
+            "label": "Supplementary Code 1",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-63397-z/MediaObjects/41467_2025_63397_MOESM5_ESM.txt"
+        },
+        {
+            "label": "Transparent Peer Review file",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-63397-z/MediaObjects/41467_2025_63397_MOESM6_ESM.pdf"
+        }
+    ],
+    "supplementary_1": NaN,
+    "supplementary_2": NaN,
+    "source_data": [
+        "/articles/s41467-025-63397-z#ref-CR69"
+    ],
+    "code": [
+        "/articles/s41467-025-63397-z#MOESM5"
+    ],
+    "subject": [
+        "Electrocatalysis",
+        "Heterogeneous catalysis",
+        "Hydrogen energy"
+    ],
+    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
+    "preprint_pdf": "https://www.researchsquare.com/article/rs-5208867/v1.pdf?c=1759403192000",
+    "research_square_link": "https://www.researchsquare.com//article/rs-5208867/v1",
+    "nature_pdf": "https://www.nature.com/articles/s41467-025-63397-z.pdf",
+    "preprint_posted": "26 Nov, 2024",
+    "research_square_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Electrocatalysis plays a central role in clean energy conversion and sustainable technologies. However, the trade-off between activity and stability of electrocatalysts significantly hinders their practical applications, notably in the oxygen evolution reaction (OER) for producing hydrogen and solar fuels. Here we report a steam-assisted synthesis armed with machine learning screening of an integrated ruthenium-titanium-manganese electrode, featuring intrinsic metal-support interactions. These atomic-scale interactions with self-healing capabilities radically address the activity-stability dilemma across all pH levels. Consequently, our electrode achieved high mass activities, 48.5, 112.8 and 74.6 times those of benchmark ruthenium oxides in acidic, neutral and alkaline conditions, respectively; and stable operation for up to 3,000 hours, a multi-fold improvement in stability over the reported advanced catalysts. The breakthrough in activity-stability limitations highlights the potential of intrinsic metal-support interactions for enhancing electrolysis and other heterogeneous catalysis.Physical sciences/Materials science/Materials for energy and catalysis/ElectrocatalysisPhysical sciences/Chemistry/Electrochemistry/Electrocatalysis",
+            "section_image": []
+        },
+        {
+            "section_name": "Additional Declarations",
+            "section_text": "There is NO Competing Interest.",
+            "section_image": []
+        },
+        {
+            "section_name": "Supplementary Files",
+            "section_text": "SupplementaryInformation.pdfSupplementary InformationSupplementaryVideo1.mp4Supplementary Video 1",
+            "section_image": []
+        }
+    ],
+    "nature_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Electrocatalysis plays a central role in clean energy conversion and sustainable technologies. However, the trade-off between activity and stability of electrocatalysts largely hinders their practical applications, notably in the oxygen evolution reaction for producing hydrogen and solar fuels. Here we report a steam-assisted synthesis armed with machine learning screening of an integrated Ru/TiMnOx electrode, featuring intrinsic metal-support interactions. These atomic-scale interactions with self-healing capabilities radically address the activity-stability dilemma across all pH levels. Consequently, the Ru/TiMnOx electrode demonstrate enhanced mass activities\u201448.5\u00d7, 112.8\u00d7, and 74.6\u00d7 higher than benchmark RuO2 under acidic, neutral, and alkaline conditions, respectively. Notably, it achieves stable operation for up to 3,000\u2009h, representing a multi-fold stability improvement comparable to other state-of-the-art catalysts. The breakthrough in activity-stability limitations highlights the potential of intrinsic metal-support interactions for enhancing electrocatalysis and heterogeneous catalysis in diverse applications.",
+            "section_image": []
+        },
+        {
+            "section_name": "Introduction",
+            "section_text": "The global energy crisis and climate issues urgently call for the development of sustainable green energy technologies1,2,3. Electrocatalysis is key to clean energy conversion, driving multiple sustainable processes for future technologies1,2,3,4,5. However, the dilemma between the catalytic activity and the stability imposes fundamental limitations on the practical applications6,7,8,9. Typically, the oxygen evolution reaction (OER) is crucial in various renewable energy conversion and storage systems7,8,9,10,11,12,13,14, especially for hydrogen (H2) production through water electrolysis (WE)2,3,4,5,7,8,9,10,12. The activity-stability tradeoff in OER, arising from the formation of highly active yet soluble Mx+ species, greatly hinders large-scale WE deployment15,16,17. Therefore, overcoming these conventional constraints has been a long-pursued goal in OER and other catalysis research, yet remains extremely challenging.\n\nTo date, supported metal catalysts (SMCs) have been regarded as promising candidates for electrocalysis and heterogeneous catalysis17,18,19. By manipulating active metal species at nanoscale or even atomic scale, maximal intrinsic activity can be achieved17,18,19,20,21,22. Unfortunately, the inherently high surface free energy in atomic-scale metal species often drives atom aggregation and activity loss17,18,21,23. Previous studies have focused on modulating the metal-support interactions to prevent metal dissolution in SMCs17,18,19,20,21,22,23. Strategies such as post-treatment24,25,26,27, defect engineering28,29,30,31,32,33 and cation exchange4,15,34,35 have been employed to strengthen these interactions. However, these strategies typically involve support growth and metal loading through a stepwise bond-breaking and reformation process15,24,28,29,30,31,32. The resultant extrinsic metal-support interactions still fails to address the activity-stability dilemma fundamentally. Furthermore, most reported SMCs are in powder form and require binder coating for electrode preparation, thereby compromising catalyst-substrate adhesion and charge transfer efficiency4,15,28,29,30,31,32,33,34,35. Growing SMCs directly on the substrate offers potential for achieving both intrinsic metal-support and catalyst-substrate interactions, leading to a radical enhancement in stability without compromising activity. Prior studies have not experimentally resolved atomic-scale metal-support interactions, particularly with regard to OER under pH-universal conditions.\n\nIn this work, we develop a one-step chemical steam deposition (CSD) strategy to fabricate a Ru/TiMnOx electrode with atomic-scale metal-support interactions. This integrated structure overcomes the activity-stability trade-off in pH-universal OER. The key to the CSD strategy was the introduction of potassium permanganate (KMnO4) to obtain gaseous Ru species, ensuring atomic/molecular-scales reaction for achieving intrinsic interactions. Using machine learning, the optimal composition balancing both activity and stability metrics has been screened. The best-performing Ru0.24/Ti0.28Mn0.48O electrode exhibited high mass activities, ~49, 113, and 75 times those of RuO2 under acidic, neutral, and alkaline conditions, respectively; and outstanding long-term durability for up to 3,000\u2009h. Our findings demonstrate a machine learning-guided steam deposition strategy for atomic-level synthesis of nano-metal oxides, enabling tunable interfacial properties applicable across pH-universal conditions",
+            "section_image": []
+        },
+        {
+            "section_name": "Results",
+            "section_text": "A one-pot chemical steam deposition (CSD) strategy was developed to fabricate an integrated Ru/TiMnOx electrode (Fig.\u00a01a, Methods, Supplementary Figs.\u00a01 and 2, and Supplementary Discussion\u00a01). Under hydrothermal conditions, solution-derived RuO4 and KMnO4 volatilized into gas phases. These precursors then reacted with the Ti substrate, enabling Ru embedding at nanoscale within TiMnOx lattices. KMnO4 played a pivotal role in the CSD strategy, not only as a Mn source but also as a strong oxidant that oxidizes Ru3+ into RuO4 gas precursors. RuO4, acting as a gaseous reactant, directly diffused to the Ti substrate surface in molecular form and rapidly accumulated through physical adsorption or chemical interactions. Upon reaching local supersaturation at the Ti interface, RuO4 underwent immediate reduction and nucleated on the substrate surface, forming an interlayer dominated by Ru nanoclusters36,37. As the reaction progressed, the RuO4 concentration near the substrate decreased due to rapid consumption, shifting the reaction mechanism from diffusion-controlled kinetics (fast reduction under high-concentration conditions) to surface reaction-controlled kinetics (slow deposition at low concentrations)38,39. Concurrently, KMnO4 participated as a co-deposition agent under critical conditions, competing with RuO4 for reduction40,41. This phenomenon could potentially explain the suppression of Ru nanocluster formation while enabling atomic-level incorporation of Ru into the TiMnOx lattice. Consequently, these collective processes likely contributed to the formation of the catalytic layer with atomically dispersed Ru species, which constituted the dominant component of Ru/TiMnOx. To validate the CSD synthesis mechanism, we devised an apparatus that ensures the exclusive production of gas-phase products throughout the hydrothermal process. By positioning the Ti substrate onto apparatuses of diverse dimensions, Ru/TiMnOx with distinct electrode areas were successfully fabricated (Supplementary Fig.\u00a02). This strategy provides the initial demonstration of scalable steam-assisted hydrothermal synthesis for nanomaterials.\n\na Schematic illustration of the one-step synthesis of Ru/TiMnOx. b X-Ray diffraction (XRD) patterns of Ru/TiMnOx with different Ru, Ti, and Mn ratios. c Overall machine learning diagram, showing the steps of experimentation, feature extraction, and validation. d, e Predicted OER overpotential (\u03b7) and deactivation rate (\u0394E) with various ternary compositions.\n\nEmploying the CSD strategy, we synthesized Ru/TiMnOx electrodes with varying compositions. As the Ru ratio increases (Fig.\u00a01b, from bottom to top), the peak of Ru/TiMnOx located at 59.3\u00b0 shifts to a lower angle. This low-angle shift aligns with Bragg\u2019s law, indicating an expansion of the lattice parameters due to the substitutional incorporation of Ru atoms into the TiMnOx matrix, where Ru ions replaced smaller Mn and Ti ions42,43. Subsequently, we evaluated their OER performance based on both experimental overpotential (\u03b7) and deactivation rate (\u0394E) indicators (Supplementary Fig.\u00a03 and Supplementary Table\u00a01). Given the requirement for an ideal catalyst to exhibit concurrently high activity and stability, we employed machine learning analysis to predict the OER performance of Ru/TiMnOx using both activity and stability indicators as inputs (Fig.\u00a01c, Supplementary Fig.\u00a04 and Supplementary Table\u00a02). The OER \u03b7 and \u0394E of catalysts with different Ru-Ti-Mn ratios are presented in a ternary composition diagram with the molar ratios among the constituent elements on the vertices (Fig.\u00a01d, e). The regions exhibiting the lowest \u03b7 and \u0394E were highlighted in yellow circles, with their overlapping areas indicating the optimal composition range, specifically (Ru-Ti-Mn: 0.20\u20130.50, 0.20\u20130.30, 0.25\u20130.50). The predicted lowest overpotential to drive a current density of 10\u2009mA\u2009cm\u22122 is 163.0\u2009mV, corresponding to a ratio of 0.26: 0.26: 0.48 (Ru: Ti: Mn).\n\nBased on machine learning predictions, an optimized Ru-Ti-Mn electrode was obtained via the CSD strategy. The crystal structure of Ru/TiMnOx was characterized by X-ray diffraction (XRD) analysis (Fig.\u00a02a and Supplementary Table\u00a03). The absence of characteristic peaks corresponding to Ru species in the XRD pattern suggests that Ru species are highly dispersed on the support15. The Ru-Ti-Mn ratio of the Ru/TiMnOx was determined from the refined occupancies to be ~0.24:0.28:0.48, which is consistent with the machine learning prediction and the data obtained from inductively coupled plasma optical emission spectrometry (ICP-OES; Supplementary Fig.\u00a05). Transmission electron microscopy (TEM) image and corresponding elemental mapping (Fig.\u00a02b) verified a homogeneous distribution of Ru, Mn and Ti. Subsequently, focused ion beam (FIB) milling was employed to prepare cross-sectional slices of the Ru/TiMnOx on the Ti substrate, enabling direct observation of interfacial structures (Supplementary Figs.\u00a06\u20138). Cross-sectional spherical aberration-corrected high-angle annular dark-field scanning TEM (HAADF\u2013STEM) imaging combined with elemental mapping revealed two layers: (i) an interlayer adjacent to the Ti substrate, where Ru predominantly existed as nanoclusters embedded within Ti-rich oxide domains, and (ii) a catalytic layer (accounting for ~80% of the total thickness) with highly dispersed Ru single-atoms uniformly distributed throughout the TiMnOx matrix. Notably, Mn species exhibited preferential surface enrichment, while Ru and Ti demonstrated complete penetration across the entire oxide film.\n\na Rietveld refinement analysis of XRD patterns of Ru/TiMnOx and its crystal structure (inset). b TEM image of Ru/TiMnOx and corresponding elemental mapping profile. c, e Aberration-corrected HAADF-STEM images of Ru/TiMnOx. d Inverse-fast Fourier-transform (IFFT) image for (c). f 3D surface plot for (c). g, h Magnified images of (f) and the corresponding STEM intensity profiles presented to directions labeled with \u03b1 and \u03b2 boxes.\n\nFurthermore, HADDF-STEM characterization was performed on ultrasonically dispersed Ru/TiMnOx fragments, which were preferentially exfoliated from the outer catalytic layer (Fig.\u00a02c\u2013e and Supplementary Fig.\u00a09). The analysis confirmed the atomic-level incorporation of Ru into the TiMnOx lattice. Additionally, lattice fringes with interplanar spacings of 0.23\u2009nm and 0.25\u2009nm were observed, corresponding to the (020) and (111) planes of cubic Ru/TiMnOx, respectively. The observed crystal structure agreed well with the XRD Rietveld refinement results. The 3D surface plots displayed varying peak heights, where relatively higher peaks correlated with Ru atoms (Fig.\u00a02f\u2013h). The line intensity and weight fraction profiles (Fig.\u00a02g, h and Supplementary Fig.\u00a09c,d) further demonstrated the atomic-level embedding of Ru into the TiMnOx lattice within the dominant catalytic layer, which is a prerequisite for achieving intrinsic metal-support interactions. To highlight the significance of these interactions for OER performance, Ru/MnOx and TiMnOx catalysts were synthesized (Supplementary Figs.\u00a010\u201312 and Supplementary Table\u00a04).\n\nThe OER performances of the as-prepared Ru/TiMnOx electrodes were evaluated in electrolytes with different pH values, including pH=0 (0.5\u2009M H2SO4), pH=7 (0.5\u2009M PBS), and pH=14 (1.0\u2009M KOH). Ru/MnOx, TiMnOx and commercial RuO2 (Com. RuO2) were used as references. The OER activities in these three electrolytes across the full pH range showed the same trend: Ru/TiMnOx\u2009>\u2009Ru/MnOx > Com. RuO2\u2009>\u2009TiMnOx (Fig.\u00a03a and Supplementary Fig.\u00a013). Notably, the overpotential of Ru0.24/Ti0.28Mn0.48O under 10\u2009mA\u2009cm\u22122 in acidic conditions (165.2\u2009mV) closely aligns with the prediction of Ru0.26/Ti0.26Mn0.48O (163.0\u2009mV) by machine learning, affirming the validity of the established model. Tafel analysis reveals fast reaction kinetics of Ru/TiMnOx across the investigated pH range (Supplementary Fig.\u00a013d\u2013f). Furthermore, Ru/TiMnOx showed high mass activities, 48.5, 112.8 and 74.6 times those of benchmark Com. RuO2 in acidic, neutral and alkaline conditions, respectively (Supplementary Fig.\u00a014 and Supplementary Table\u00a05). The same trend was also confirmed when the activity was evaluated using the electrochemically active surface area (ECSA) (Supplementary Figs.\u00a015\u201317), further highlighting the advantages of atomically dispersed Ru species in reducing the noble metal loading amount. The electrochemical impedance spectroscopy (EIS) analysis determined the enhanced charge transfer capabilities of Ru/TiMnOx (Supplementary Fig.\u00a018), revealing notably low charge transfer resistance. The radar charts (Fig.\u00a03b and Supplementary Fig.\u00a019) showed the outstanding OER performance of Ru/TiMnOx under pH-universal conditions from multiple perspectives. Its notable activities are attributed to optimized kinetics from atomically dispersed sites and enhanced mass transfer from an integrated structure. As illustrated in Supplementary Movie\u00a01, the Ru/TiMnOx electrode served directly as the anode for electrocatalytic water splitting, bypassing the use of binders. The rapid generation and detachment of oxygen bubbles on the electrode surface visually demonstrated the notable activity of Ru/TiMnOx.\n\na Linear sweep voltammetry (LSV) curves of Ru/TiMnOx, Ru/MnOx, TiMnOx, and commercial RuO2 (Com. RuO2) in 0.5\u2009M H2SO4 (pH = 0.3\u2009\u00b1\u20090.02), 0.5\u2009M PBS (pH = 7.1\u2009\u00b1\u20090.10) and 1.0\u2009M KOH (pH = 13.9\u2009\u00b1\u20090.03). Scan rate: 10\u2009mV\u2009s-1. b Radar plot comparing the OER performance of Ru/TiMnOx and the reference samples in 0.5\u2009M H2SO4 (pH\u00a0= 0.3\u00a0\u00b1\u20090.02). c\u2013e Chronopotentiometry curves of Ru/TiMnOx for OER at 10\u2009mA\u2009cm\u22122 in 0.5\u2009M H2SO4 (c), 0.5\u2009M PBS (d) and 1.0\u2009M KOH (e), respectively. The potentials of chronopotentiometry tests are not iR-corrected.\n\nIn addition to high OER activity, good stability is another crucial prerequisite for catalysts to realize practical applications. The OER stability in acidic and neutral conditions is particularly challenging5,7,8,44. We investigated OER durability at 10\u2009mA\u2009cm\u22122geo (Fig.\u00a03c\u2013e and Supplementary Fig.\u00a020), a widely adapted benchmark criterion in literature. Specifically, in 0.5\u2009M H2SO4, the overpotential (without iR compensation) of Ru/TiMnOx increased from 175\u2009mV to 185\u2009mV in a 1000\u2009h test, to 198\u2009mV in a 2000\u2009h test, and 205\u2009mV in a 3000\u2009h test (Fig.\u00a03c). The average increase in overpotential was 0.01\u2009mV\u2009h-1; this is over 1698 times slower than that of the Com. RuO2 (16.9\u2009mV\u2009h\u22121) (Supplementary Fig.\u00a020a). To date, no catalyst, especially Ru-based materials, has matched such performance of Ru/TiMnOx under acidic OER conditions (Supplementary Table\u00a06). This stability was also notable in both neutral and alkaline conditions (Fig.\u00a03d, e, Supplementary Tables\u00a07 and 8), particularly under the challenging neutral conditions5,44, where it attained a duration of 1500\u2009h (Fig.\u00a03d). Furthermore, Ru/TiMnOx demonstrated notable long-term stability under high current density across the entire pH range. It can stably drive a current density of 100\u2009mA\u2009cm\u22122 for 220\u2009h under acidic conditions, 120\u2009h under neutral conditions, and 140\u2009h under alkaline conditions, respectively (Supplementary Fig.\u00a021). These results demonstrate its potential for practical applications in water electrolysis devices. As a proof of concept, both the integrated proton exchange membrane water electrolyzer (PEMWE) and anion exchange membrane water electrolyzer (AEMWE) utilizing Ru/TiMnOx electrodes were constructed to evaluate the performance under conditions that are representative of practical applications. The devices achieved industrial-grade OER performance, delivering a current density of 1.0\u2009A\u2009cm\u22122 at cell voltages of 1.66\u2009V (PEMWE) and 1.72\u2009V (AEMWE), respectively (Supplementary Figs.\u00a022 and 23). These operational efficiencies outperformed those reported for state-of-the-art catalysts and commercial RuO2 benchmarks, as evidenced by the substantially higher potentials (1.94\u2009V and 1.99\u2009V) to reach equivalent current densities under comparable conditions (Supplementary Table\u00a09). Besides, RuO2-based systems exhibited activity decay within 3000\u2009min (PEMWE) and 6000\u2009min (AEMWE) at 200\u2009mA\u2009cm\u22122, whereas Ru/TiMnOx-based electrolyzers maintained stable operation for over 11,000\u2009min and 10,000\u2009min, respectively. These findings further highlights the competitive advantage of Ru/TiMnOx in OER at high current densities, demonstrating its great potential for scalable water electrolysis technologies. In summary, the performance of Ru/TiMnOx for pH-universal OER demonstrated a multi-fold improvement over other advanced OER electrocatalysts (Supplementary Tables\u00a06\u20139). Surprisingly, we observed periodic increases and decreases in voltage during the long-term stability tests (see inset in Fig.\u00a03c\u2013e, Supplementary Figs.\u00a021 and 24). We believe that periodic potential fluctuations are linked to the long-term stability of Ru/TiMnOx. Next, a thorough examination of the intrinsic metal-support interactions was conducted to elucidate its impact on OER performance.\n\nThe electronic configuration and the coordination structure of Ru, Ti and Mn in Ru/TiMnOx were investigated using X-ray photoelectron spectroscopy (XPS) and synchrotron X-ray absorption spectroscopy (XAS). Deconvolution of the Ru 3d spectra revealed oxidation states of metallic Ru0 and oxidized Ru4+ in Ru/TiMnOx and Ru/MnOx45,46,47. For Ru/TiMnOx, the Ru0 component accounted for only ~14% of the total Ru content, whereas in Ru/MnOx, the Ru0 fraction was ~60% (Supplementary Table\u00a010). The minimal Ru0 content in Ru/TiMnOx likely originated from trace Ru nanoclusters, while the predominant Ru0 in Ru/MnOx indicated extensive aggregation of Ru nanoparticles due to weaker metal-support interactions. Notably, compared to RuO2, the Ru 3d5/2 binding energies in Ru/TiMnOx and Ru/MnOx exhibited negative shifts of 0.05\u2009eV and 0.10\u2009eV, respectively (Supplementary Fig.\u00a025a and Supplementary Table\u00a010). This observation indicates a lower Ru oxidation state in both Ru/TiMnOx and Ru/MnOx compared to the stoichiometric Ru(IV) in RuO2, with Ru/TiMnOx displaying a much higher Ru valence than Ru/MnOx. In the Mn 2p spectra, the electronic structure of TiMnOx aligned closely with MnO2, suggesting a Mn(IV)-dominant configuration15,16 (Supplementary Fig.\u00a025b and Supplementary Table\u00a011). Conversely, the Mn 2p3/2 binding energies of Mn3+ for Ru/TiMnOx and Ru/MnOx showed negative shifts of 0.79\u2009eV and 0.11\u2009eV relative to TiMnOx, respectively. These shifts correlate with a reduced Mn oxidation state in the ternary oxides, with Ru/MnOx exhibiting a marginally higher Mn valence compared to Ru/TiMnOx. Ti oxidation states were further elucidated through high-resolution Ti 2p spectra. Both Ru/TiMnOx and TiMnOx exhibited dual Ti3+/Ti4+ character, indicating mixed-valence Ti species in these oxides (Supplementary Fig.\u00a025c and Supplementary Table\u00a012)48,49,50,51,52. Collectively, the XPS results reveal strong electronic interactions among Ru, Mn, and Ti in Ru/TiMnOx. The observed binding energy shifts reflected synergistic charge transfer processes, where Ru served as an electron reservoir while Mn and Ti participated in redox-active cycling. These findings provide critical insights into the electronic structure-property relationships governing the catalytic behavior of these multi-metallic oxides, particularly in electrochemical energy conversion applications. Additionally, in-depth XPS analysis was performed to verify changes in elemental composition and valence states within Ru/TiMnOx (Supplementary Fig.\u00a026). As the etching depth increased, a negative shift in the Ru 3\u2009d binding energy was observed (Supplementary Fig.\u00a026a), concomitant with an increase in the Ru0/Ru4+ ratio from 0.17 (catalytic layer) to 0.26 (interlayer) (Supplementary Fig.\u00a026b and Supplementary Table\u00a013). This trend confirmed the accumulation of metallic Ru0 species at the catalyst-substrate interface, as corroborated by HAADF-STEM cross-sectional imaging, which revealed Ru0 nanoclusters within the interlayer (Supplementary Fig.\u00a08). Concurrently, the elemental depth profile demonstrated a gradual increase in Ru content and a decrease in Mn/Ti concentrations. These observations aligned with cross-sectional elemental mapping, further validating the elemental distribution within the catalytic layer. The Mn species in the lattice are known to enhance the OER activity of the oxide3,4,34, while the Ti species are believed to improve the OER stability, especially in acidic conditions32,53. This metal distribution potentially facilitates bulk Ru migration to replenish surface active sites upon dissolution, contributing to enhanced stability. The cross-sectional imaging (Supplementary Figs.\u00a06\u20138) and depth-resolved XPS analysis (Supplementary Fig.\u00a026 and Supplementary Table\u00a013) collectively provided evidence supporting the as-proposed growth mechanism of Ru/TiMnOx: RuO4 supersaturation first triggered Ru0 nanocluster formation at the interlayer, followed by atomic Ru incorporation into TiMnOx upon precursor depletion, ultimately forming the dominant component of catalytic layer.\n\nNext, the structural and electronic structure stability of Ru/TiMnOx was investigated. HADDF-STEM images demonstrated that the structure of Ru/TiMnOx remained stable after long-term OER stability test in 0.5\u2009M H2SO4 (Supplementary Fig.\u00a027). Subsequent ICP-MS analysis confirmed that the Ru/TiMnOx sample retained over 90% of Ru and Mn content after stability testing, exhibiting only trace ion leaching (Supplementary Fig.\u00a028). Notably, the Ru retention rate in Ru/TiMnOx was 1.67 times and 2.29 times higher than those of Ru/MnOx and Com. RuO2 reference samples, respectively. The electronic structure stability was then verified through XPS, as no marked changes in the valence states of Ru and Mn in Ru/TiMnOx were observed after OER stability testing (Supplementary Figs.\u00a029 and 30). In contrast, a distinct positive shift in the Ru 3\u2009d binding energy was observed in both Ru/MnOx and Com. RuO2. Notably, the Ru0/Ru4+ ratio in Ru/TiMnOx remained nearly unchanged (from 0.17 to 0.16), whereas that in Ru/MnOx drastically decreased from 1.48 to 0.41 (Supplementary Table\u00a010). These results, combined with ICP-MS findings, indicated that the active sites in Ru/TiMnOx were protected from excessive oxidation-induced dissolution, whereas Ru in the comparison samples underwent severe oxidation and leaching deactivation.\n\nTo elucidate the origin of the high OER performance in Ru/TiMnOx, we systematically conducted XAS analysis on Ru, Mn and Ti to clarify its coordination structure (Fig.\u00a04, Supplementary Figs.\u00a031-40 and Supplementary Tables\u00a014-17). The K-edge X-ray absorption near-edge spectroscopy (XANES) spectra of Ru, Mn, and Ti reveal that the oxidation states of Ru, Ti, and Mn in Ru/TiMnOx lay between those of metal foils and +4-valent metal oxides (Fig.\u00a04a, Supplementary Figs.\u00a031, 33 and 35). Notably, the oxidation state of Ru in Ru/TiMnOx was determined to be +3.0, which is higher than that observed in Ru/MnOx (+\u20091.1). Conversely, the oxidation state of Mn exhibited an opposing trend, with a valence of +3.1 in Ru/TiMnOx, slightly lower than that in the Ru/MnOx (\u2009+\u20093.8). These findings are in good agreement with the oxidation state trends identified through XPS analysis, further validating the strong interactions between Ru, Mn and Ti in Ru/TiMnOx. The extended X-ray absorption fine-structure (EXAFS) analysis further elucidated the metal coordination environment in Ru/TiMnOx. The Ru K-edge Fourier-transform (FT) EXAFS spectra (Fig.\u00a04b) indicated dominant coordination of Ru centers with oxygen (Ru-O), while the Ru-Ru scattering path, arising from interlayer Ru nanoclusters36,54, is consistent with the metallic Ru0 component identified in XPS analysis. Notably, a unique Ru-O-M signal (where M represents Ru, Mn or Ti) emerged at ~3.3\u2009\u00c5, distinct from both RuO2 reference and Ru/MnOx control sample (Supplementary Table\u00a014). The FT-EXAFS and wavelet transform (WT) patterns of Mn and Ti also confirmed the formation of M1-O-M2 (where M1 and M2 represent different metallic species among Ru, Mn, or Ti) bridging bonds, demonstrating the presence of strong intrinsic interactions within Ru/TiMnOx (Fig.\u00a04c and Supplementary Figs.\u00a032\u201336). Since Ti-based bridging bonds are conducive to stabilizing active species32,53, Ti stabilizes the active sites through Ti-O-M bonds, underscoring its critical role in maintaining structural integrity and catalytic performance.\n\na, b Ru K-edge XANES spectra (a) and Fourier transforms (FT) of k2-weighted Ru K-edge of EXAFS spectra (b) of Ru/TiMnOx and Ru/MnOx, with Ru foil and RuO2 as references. c, FT k2-weighted Mn K-edge EXAFS spectra of Ru/TiMnOx and Ru/MnOx, with Mn foil, Mn2O3 and MnO2 as references. d FT k2-weighted Ru K-edge EXAFS spectra of Ru/TiMnOx, Ru/TiMnOx-OER-10 and Ru/TiMnOx-OER-20, with Ru foil and RuO2 as references. e The plot of coordination number (CN) and radial distance (R) fitted from Ru K-edge EXAFS spectra (see Supplementary Table\u00a014 for details). f Wavelet transforms for the k2-weighted EXAFS signals at Ru K-edge of RuO2, Ru/TiMnOx, Ru/TiMnOx-OER\u221210 and Ru/TiMnOx-OER-20. k (\u00c5\u22121): Wave vector in momentum space; R (\u00c5): radial distance of coordination shells.\n\nTo elucidate the evolution of the active site, in-situ XAS measurements of Ru/TiMnOx were conducted in the 0.5\u2009M H2SO4 electrolytic environment (Supplementary Fig.\u00a039 and 40, Supplementary Table\u00a017). The Mn K-edge XANES spectra demonstrated a reversible behavior of unoccupied Mn orbitals: upon applying a positive voltage bias (\u2009+\u2009V), the white-line intensity exhibited an initial increase followed by complete recovery to its original state upon voltage reversal (-V), indicative of dynamic reconstruction of Mn 3\u2009d electronic states (Supplementary Fig.\u00a039a). Furthermore, the Mn-O bond length displayed reversible structural modulation: starting from the initial value of ~1.89\u2009\u00c5, it underwent elongation to ~1.90\u2009\u00c5 under +V bias and subsequent contraction to ~1.85\u2009\u00c5 upon -V restoration (Supplementary Fig.\u00a039c and Supplementary Table\u00a017). This reversible bond length variation, combined with its orbital state recovery, provided evidence for the self-healing ability of the Mn-O bond.\n\nWe hypothesized that this reversibility guarantees the stability of Ru/TiMnOx. To investigate the self-healing behavior in the OER process, we firstly monitored changes in electrolyte concentration during electrolysis at 10\u2009mA\u2009cm\u22122 in 0.5\u2009M H2SO4. Nearly no Ti was detected in the time-dependent ICP-OES tests (Supplementary Fig.\u00a041). By contrast, Ru and Mn concentrations initially increased for 600\u2009min then stabilized at ~20 and ~25 ppb, respectively, correlating with potential fluctuations period. The fluctuation period of the potential driving OER during the stability test is ~20\u2009h (with the voltage increasing during the first ~10\u2009h and then decreasing over the subsequent ~10\u2009h, see Supplementary Fig.\u00a024 for details). To elucidate the structural self-healing mechanism of Ru/TiMnOx, we comprehensively characterized samples collected at 10.83\u2009h (denoted as Ru/TiMnOx-OER-10) and 20.63\u2009h (denoted as Ru/TiMnOx-OER-20) using XAS (Fig.\u00a04d\u2013f, Supplementary Figs.\u00a042 and 43). XANES analysis revealed a reversible oxidation state modulation of Ru: starting from +3.0 in the fresh catalyst, the valence state increased to +3.7 after ~10\u2009h of electrolysis, then decreased to +2.7 by ~20\u2009h (Supplementary Fig.\u00a042). This dynamic redox cycling suggested inherent self-healing capability of Ru centers, effectively maintaining the high catalytic activity. It is noteworthy that the strong interaction between the bridging O atom and proton induced local crystal lattice distortion55. This structural perturbation manifested as an initial elongation of the Ru-O-M bond length (from 3.31\u2009\u00c5 to 3.34\u2009\u00c5), accompanied by a simultaneous reduction in coordination number (CN) from 3.9 to 2.6 within the first ~10\u2009h, followed by complete recovery to the original geometric parameters after ~20-h electrolysis (Fig.\u00a04e and Supplementary Table\u00a014). The temporary decrease in CN reflects partial lattice distortion56, while the subsequent recovery indicates structural self-healing through dynamic bond reconfiguration. Such dynamic behavior demonstrated the reconstruction of long-range coordination order, thereby re-establishing its catalytic activity for OER in the subsequent period. By combining time-dependent ICP and XAS characterizations, the self-healing mechanism of Ru/TiMnOx was proposed to involve the following processes: Ti stabilizes the crystalline framework, trace amounts of Ru/Mn dissolve and redeposit, accompanied by the restoration of both compositional and coordination structures (Fig.\u00a05a). This self-healing processes not only explain the observed potential oscillations but also fundamentally guarantee Ru/TiMnOx\u2019s long-term stability in OER applications.\n\na Schematic illustration for the self-healing behavior of integrated Ru/TiMnOx electrode. b In-situ Raman spectra of integrated Ru/TiMnOx electrode in 0.5\u2009M H2SO4 electrolyte under different external applied potential (OCP\u22121.75\u2009V vs. RHE). c 2D in-situ Raman contour image enlarged from (b). d, e In-situ ATR-FTIR spectra recorded in the potential range of OCP\u22121.85\u2009V vs. RHE for Ru/TiMnOx in 0.5\u2009M H2SO4 electrolyte. f, g In-situ differential electrochemical mass spectrometry (DEMS) signals of O2 products for Ru/TiMnOx in 0.5\u2009M H2SO4 (H218O) (f) and 0.5\u2009M H2SO4 (H216O) (g).\n\nThen, the structural evolution of catalyst was tracked by in-situ electrochemical Raman spectroscopy (Fig.\u00a05b, c and Supplementary Fig.\u00a044). As the potential increased from open circuit potential (OCP) to 1.75\u2009V vs. RHE, a blue-shift was observed in the Mn-O vibrational peaks (Fig.\u00a05b). According to Hooke\u2019s law57,58, this blue-shift are attributed to the substitution of Mn by Ru during the OER. Notably, the A1g mode at ca. 666\u2009cm-1 gradually vanished as the potential increased, indicating the deprotonation of Ru-O-Mn59,60. When the potential cycled back to OCP, this peak intensity returned to initial level (Fig.\u00a05c). The combined time-dependent ICP-OES and in-situ spectroscopy results coincide with the hypothesis that the Ru/TiMnOx can self-repair during the OER process, thereby ensuring long-term catalytic efficiency.\n\nTo experimentally investigate the OER mechanism, in-situ attenuated total reflectance Fourier transform infrared (ATR-FTIR) spectroscopy was conducted on Ru/TiMnOx, allowing for tracking the changes in surface reaction intermediates (Fig.\u00a05d, e, Supplementary Figs.\u00a045 and 46). In addition to an absorption peak at ca. 3,619\u2009cm-1 (Fig.\u00a05e, O-H stretching mode), distinctive absorption peaks at 1117\u2009cm-1 and 1100\u2009cm-1 were also observed (Fig.\u00a05d and Supplementary Fig.\u00a046). The central peak (1089\u2009cm-1) and shoulder peak (1100\u2009cm-1) signify the formation of O-O bonds15,61. Specifically, the linearly bonded superoxol species (*-O-O) and the oxygen bridges between metal sites (*-O-O-*), respectively15,62,63. This feature agrees with the advanced oxide path mechanism (OPM) pathway which break through the theoretical activity limit in the traditional adsorbate evolution mechanism (AEM) and avoid the structure collapse in the lattice oxygen oxidation mechanism (LOM)7,15,34,35,61. Additionally, these peak intensities returned to their initial levels when the potential decreased to OCP, reinforcing the reversibility of Ru/TiMnOx. To experimentally confirm this OPM pathway, in-situ differential electrochemical mass spectrometry (DEMS) with isotopic labeling measurements was conducted (Fig.\u00a05f, g, Supplementary Figs.\u00a047 and 48). Initially, the Ru/TiMnOx were subjected to three LSV cycles in 0.5\u2009M H2SO4 (H218O) (Supplementary Fig.\u00a048a). For the OPM-type OER, the adsorbed 16O species on neighboring metal sites may couple to form 32O2, which were detected during the initial 18O-labeling process for Ru/TiMnOx (Fig.\u00a05f). Next, the electrocatalyst was thoroughly washed with H216O deionized water and then operated in the 0.5\u2009M H2SO4 (H216O) electrolyte (Supplementary Fig.\u00a048b). The captured 36O2 signals (Fig.\u00a05g), resulting from the coupling of adjacent 18O adsorbates, corroborate the OPM-related pathway in Ru/TiMnOx15.\n\nThe density functional theory (DFT) calculations were conducted to gain insight into the origin of the enhanced OER performance for Ru/TiMnOx. According to the XRD refinement and TEM analysis, Ru/TiMnOx (100) and Ru/MnOx (110) slab models were constructed with formulas of Ru0.24/Ti0.28Mn0.48O and Ru0.56/Mn0.44O2, respectively (Fig.\u00a06a, Supplementary Figs.\u00a049 and 50, Supplementary Data\u00a01). Based on the Bader charge analysis, the average charge of Ru in Ru/TiMnOx was found to be +0.55 e, which is lower than that of RuO2 (+1.68 e). The charge density difference of Ru/TiMnOx and Ru/MnOx further indicated a shift of electron cloud from O to M in the M-O covalent bond (Fig.\u00a06b and Supplementary Figs.\u00a051\u201353). This observation indicates that the electron transfer from Mn/Ti to Ru through the bridging O atom (Obri) results from the intrinsic metal-support interactions. To quantify the covalency of the M-O bond, the partial density of states (PDOS) calculations were employed (Fig.\u00a06d and Supplementary Fig.\u00a054). The energy of the Ru d-band center (\u025bd) for Ru/TiMnOx (-1.167\u2009eV) was more appropriate for adsorbate-catalyst surface interaction compared to Ru/MnOx (-1.936\u2009eV) and RuO2 (-1.110\u2009eV)43. Furthermore, the gap between the Ru/Mn \u025bd and O 2p band center (\u025bp) is greatly enlarged in Ru/TiMnOx, with values of 2.31\u2009eV and 0.98\u2009eV for Ru-O and Mn-O, respectively. Consequently, the covalency of M-O bonds in Ru/TiMnOx is lower than in Ru/MnOx and RuO2. It is well-established that weaker M-O covalency boosts catalyst stability by inhibiting the LOM mechanism during OER, thereby accounting for the long-term stability of Ru/TiMnOx64,65,66. The enhanced stability of Ru/TiMnOx was also evidenced by its high de-metallization energies for Ru and Mn (Fig.\u00a06c and Supplementary Table\u00a018). Specifically, the de-metallization energy of Ru in Ru/TiMnOx is 0.174\u2009eV greater than in RuO2 and 0.462\u2009eV greater than in Ru/MnOx. Next, we conducted mechanistic studies targeting the OER process. The preferred reaction pathways were determined by investigating the OER paths based on OPM and AEM (Fig.\u00a06e and Supplementary Figs.\u00a055\u201358). For Ru/MnOx, the formation of *OOH was identified as the rate-determining step (RDS), characterized by a significant free energy barrier of 1.957\u2009eV. Comparatively, the RDS for Ru/TiMnOx via the OPM pathway is 1.511\u2009eV, 0.952\u2009eV lower than that of the AEM, indicating a thermodynamic preference for the OPM. Therefore, theoretical calculations reveal that Ru-Obri-Ti/Mn bonds in Ru/TiMnOx modulate charge distribution and orbital overlap, optimizing the OER pathway.\n\na Ru0.24/Ti0.28Mn0.48O structure with the value of computed bader charge and bond length. b Filled contour plot of the cross-section of differential charge density for Ru0.24/Ti0.28Mn0.48O (100). c Demetallization energies of Ru from RuO2; Ru and Mn from Ru/MnOx and Ru/TiMnOx, respectively. d Schematic diagram of the band structures of Ru/TiMnOx, Ru/MnOx and RuO2 based on PDOS analysis. e The free energy diagrams for preferred OER paths on the surfaces of Ru/MnOx and Ru/TiMnOx. RDS denotes rate-determining step.",
+            "section_image": [
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+            ]
+        },
+        {
+            "section_name": "Discussion",
+            "section_text": "In summary, the concept of intrinsic metal-support interactions has been established and validated, addressing a critical challenge in breaking the activity-stability tradeoff for electrolysis. The Ru/TiMnOx exhibited low overpotential of 165.2\u2009mV at 10\u2009mA\u2009cm\u22122, aligning well with machine learning predictions and thereby avoiding traditional trial-and-error approaches. Its mass activities exceed benchmark Ru oxides by ~49, 113, and 75 times under acidic, neutral, and alkaline conditions, respectively; while maintaining 3000-h stability at pH=0. Our findings offer a potential pathway to modulate intrinsic metal-support interactions, thereby mitigating the activity-stability tradeoff in electrocatalysis.",
+            "section_image": []
+        },
+        {
+            "section_name": "Methods",
+            "section_text": "The integrated Ru/TiMnOx electrode was prepared through a chemical steam deposition (CSD) strategy which combines the concept of chemical vapor deposition (CVD) and the conditions of hydrothermal reaction (see Fig.\u00a01a, Supplementary Figs.\u00a01 and 2, and Supplementary Discussion\u00a01 for details). In detail, the entire CSD process can be completed in one step, and its mechanism were dissected into the following three steps: firstly, potassium permanganate (KMnO4, Aladdin 99.99%, AR, grade) in aqueous solution oxidized ruthenium(III) chloride hydrate (RuCl3\u00b7xH2O, Alfa Aesar, 99.99%, AR, grade) to RuO4 gas. Secondly, under hydrothermal conditions, RuO4 gas, along with KMnO4 steam, underwent spontaneous redox reactions with the Ti foam (TF, thickness 600 \u03bcm, Tianjin Eilian Electronics & technology Co. ltd). Finally, the resulting Ru/TiMnOx deposited in-situ on the Ti substrate. Before synthesis, a Ti foam piece (1.0\u2009\u00d7\u20096.0\u2009cm) was etched in hydrochloric acid (HCl, 18\u2009wt%, Sinopharm Chemical Reagent Co., Ltd.) at 90\u2009\u00b0C for 15\u2009min. Synthesis of Ru0.24/Ti0.28Mn0.48O involved the following steps: (1) Preparation of a redox-active precursor by dissolving 27.0\u2009mg RuCl3\u2022xH2O and 79.0\u2009mmol KMnO4 in 10.0\u2009mL deionized water; (2) Immersion of a pre-etched TF substrate into the solution within a Teflon-lined autoclave; (3) Hydrothermal reaction at 140\u2009\u00b0C (3\u2009h) to concurrently generate the Ti-Mn-O matrix and immobilize Ru species, uniquely yielding gas-phase reaction products from the critical interaction between KMnO4 and RuO4 during hydrothermal nucleation; (4) Post-synthesis washing (deionized water) and vacuum drying (60\u2009\u00b0C) of the TF-supported Ru0.24/Ti0.28Mn0.48O. The material obtained from the reaction occurring above the liquid level was identified as Ru0.24/Ti0.28Mn0.48O, and its physical representation corresponds to the black portion on the Ti substrate (Supplementary Fig.\u00a02a). To validate the CSD synthesis mechanism, we devised an apparatus that ensures the exclusive production of gas-phase products during the hydrothermal process (Supplementary Fig.\u00a02). Specifically, the Ti substrates were placed on hollow supports with different heights (4.5, 5 and 5.5\u2009cm) to ensure sufficient gas reaction. Furthermore, we successfully scaled up the support size in proportion to the dimensions of the hydrothermal reactor, thereby obtaining integrated Ru/TiMnOx electrodes with surface areas of 4.00, 6.25, and 12.25\u2009cm\u00b2, demonstrating the scalability of the CSD. The Ru mass loading of Ru/TiMnOx was 0.14\u2009mg\u2009cm\u22122.\n\nFor comparison, Ru/MnOx, TiMnOx and commercial RuO2 (denoted as Com. RuO2) samples were synthesized. The synthesis conditions for TiMnOx were identical to those employed for Ru/TiMnOx, with the sole exception being that TiMnOx was derived via a liquid-phase reaction occurring within the liquid medium during the hydrothermal process. TiMnOx corresponds to the gray portion on the Ti substrate depicted in Supplementary Fig.\u00a02a. The Ru/MnOx powder was prepared using the same hydrothermal method as Ru/TiMnOx, without adding a Ti substrate. The RuO2 catalyst on TF was fabricated by the following steps: a dispersion was prepared by mixing 50\u2009\u03bcL of ethanol, 5\u2009\u03bcL of nafion, 15\u2009\u03bcL of deionized water, and 10\u2009mg of RuO2 (Alfa Aesar). Subsequently, the dispersion was dropwise added and dispersed onto the TF, with the added quantity determined according to the loading mass of Ru. The Ru mass loadings of Ru/MnOx and Com. RuO2 were 0.35\u2009mg\u2009cm\u22122 and 0.52\u2009mg\u2009cm\u22122, respectively.\n\nTo find the optimal ratio combination of Ru, Mn, and Ti, a powerful and widely used machine learning model, the back-propagation neural network, was employed. In this experiment, five-fold cross-validation was used to optimize the number of layers and the initial learning rate. Three-layer, five-layer, and seven-layer back-propagation networks were considered (excluding the input layer). The activation function of the last layer is linear and all the other layers are rectified linear unit. The number of neurons for the three-layer neural network was (128, 32, 2), for the five-layer network was (128, 64, 32, 16, 2), and for the seven-layer network was (128, 64, 64, 32, 32, 16, 2). The initial learning rates considered were 1e-2, 1e-3, 1e-4, and 1e-5. The loss function was the weighted mean squared error of \u03b7 and the degradation rate (\u0394E), with the weight of \u03b7 set to be twice that of the \u0394E in order to emphasize the importance of \u03b7. The Adaptive Moment Estimation optimizer, also known as Adam, was used with 1000 epochs. Finally, based on the cross-validation results, a five-layer back-propagation network with an initial learning rate of 1e-4 was selected. To minimize the impact of randomness, ten training runs were performed, and the one with the smallest mean squared error was chosen as the final model. The data sources, training process and the detailed parameters are shown in Supplementary Figs.\u00a03 and 4, Supplementary Tables\u00a01 and 2, and Supplementary Code\u00a01.\n\nMultiscale structural and chemical profiling of the samples included: (1) Topographical and elemental distribution analysis via field-emission scanning electron microscopy (FE-SEM, JSM-7500) integrated with energy-dispersive X-ray spectroscopy (EDS); (2) Atomic-resolution lattice imaging by aberration-corrected transmission electron microscopy (FE-TEM, Titan Themis G2F20) in high-angle annular dark-field scanning TEM mode (HAADF-STEM); (3) Nanoscale compositional mapping using scanning transmission electron microscopy (STEM, Tecnai G2F30) at 300\u2009kV accelerating voltage; (4) Crystalline phase identification through powder X-ray diffraction (XRD, Rigaku SmartLab) with Cu K\u03b1 radiation (\u03bb\u2009=\u20091.5418\u2009\u00c5), scanning at 2\u00b0/min; (5) Surface speciation and oxidation states quantified by X-ray photoelectron spectroscopy (XPS, ESCALAB 250Xi) with monochromatic Al K\u03b1 source (1486.6\u2009eV), calibrated against adventitious carbon (C 1\u2009s, 284.8\u2009eV). Depth profiling was further conducted via alternating cycles of argon ion sputtering (Ar+) and XPS spectral acquisition, enabling layer-by-layer characterization of composition gradients from the surface to the substrate interface. The focused ion beam (FIB) was used for Ru/TiMnOx cross-sectional imaging using FEI Helios G4. The metal concentration in electrolytes were characterized by the inductively coupled plasma optical emission spectrometry (ICP-OES) measurement (iCAP 7400, Thermo, Waltham, USA). Since Ru/TiMnOx was grown in situ on a Ti substrate, the dissolution of the solid did not allow for the measurement of the Ti content in the Ru/TiMnOx. To ascertain the relative elemental proportions within the Ru/TiMnOx material, we implemented an ultrasonic dispersion technique to disperse the Ru/TiMnOx in an aqueous medium, subsequently quantifying the elemental composition of the resultant solution through ICP-OES. This approach circumvented interference from the Ti substrate, enabling accurate measurement of Ru and Mn concentrations. Synchrotron-based X-ray absorption spectroscopy studies were conducted at the Shanghai Synchrotron Radiation Facility (SSRF, beamline BL14W1). Ru K-edge and Mn K-edge spectra were collected using a 4-channel silicon drift detector (Bruker 5040). Samples were prepared as 1\u2009cm diameter pellets sealed with Kapton tape. Reference standards (Ru foil, RuO2, Mn foil, Mn2O3, MnO2) were measured in transmission mode for valence state calibration. Data processing, including background subtraction, normalization, and EXAFS fitting, was executed using the IFEFFIT package (Athena and Artemis modules)67,68. Fourier transforms of \u03c7(k) data employed a Hanning window (dk\u2009=\u20091.0\u2009\u00c5-1), with structural parameters refined via least-squares fitting for conversion into radial distance space (R-space). By taking the first derivative (d\u03bc/dE) of the normalized-XAS of Ru and Mn K-edge, the E0 value was obtained corresponding to the first maximum point. Subsequently, the linear relationship between E0 and valence state is established using references with known valence states (Ru foil and RuO2 for Ru; Mn foil, Mn2O3 and MnO2 for Mn). Finally, the valence state of the target elements in unknown samples were determined by comparing their measured E0 values to the relationship.\n\nIn-situ XAS for Mn K-edge was performed at the Canadian Light Source. Before the in-situ XAS test, a micro-electrochemical cell was fabricated with Ru/TiMnOx as the anode (\u2009~\u20091.0\u2009cm2), 0.5\u2009M H2SO4 as electrolyte. The micro-electrochemical cell was connected to an electrochemical station (Biologic). The working electrode was firstly tested without H2SO4 electrolyte and applied voltage, named as ex-situ. Then, the voltages (1.45\u2009V vs. RHE and -0.13\u2009V vs. RHE) were applied, corresponding to current densities of 15\u2009mA\u2009cm\u22122 and -15 mA cm\u22122, respectively. The catalyst was stabilized for 15\u2009min prior to XAS measurements at each potential. The in-situ XAS spectra of Mn were recorded in transmission mode for 120\u2009seconds, and then the X-ray beam was blocked for 20\u2009min to minimize potential beam damage. During the test, all obtained spectra were calibrated using Mn foil as a reference. The spectra were analyzed using Athena software. In-situ Raman spectroscopy was performed using a Renishaw inVia Raman microscope and a CHI650E electrochemical workstation. The working electrode of Ru/TiMnOx was immersed in the 0.5\u2009M H2SO4 electrolyte through the wall of the in-situ cell, with its plane perpendicular to the laser. Pt and Ag/AgCl were used as the counter electrode and reference electrode, respectively. The potential was gradually increased from OCP to 1.75\u2009V vs. RHE and then gradually decreased back to the initial value, with a stabilization period of 300\u2009seconds at each potential level. For the electrochemical in-situ attenuated total reflectance Fourier transform infrared (ATR-FTIR) measurements, a silicon crystal coated with an Au film was used in the internal reflection mode. The spectra were recorded on a Thermo Nicolet Nexus 670 spectrometer, with a CHI650E electrochemical workstation employed. Pt and Ag/AgCl were used as the counter electrode and reference electrode, respectively. Before data collection, a voltage was applied to the working electrode for 20\u2009min to test for receiving a reliable signal. Then, the potential was gradually increased from OCP to 1.85\u2009V vs. RHE and then gradually decreased back to the initial value. The in-situ differential electrochemical mass spectrometry (DEMS) system is similar to the system recently reported by the Lee group15. The in-situ DEMS system consisted of two interconnected vacuum chambers, including a mass spectrometer chamber with a high vacuum and a second chamber with a mild vacuum. The working electrode was an Au film sputtered on a porous polytetrafluoroethylene membrane. After obtaining powder catalysts through ultrasonic treatment of integrated Ru/TiMnOx electrode, the catalyst ink was prepared and dropped onto the Au film. The electrochemical cell was a three-electrode system with volume of ~3\u2009mL. Before the electrochemical measurements, all the electrolytes were purged with high-purity Ar to remove the dissolved oxygen. Before data collection, a voltage was applied to the working electrode for 718\u2009s to test for receiving a reliable signal. The Ru/TiMnOx were subjected to three LSV cycles in the potential range of 1.17-1.72\u2009V vs. RHE at a scan rate of 10\u2009mV\u2009s-1 in 0.5\u2009M H2SO4 (H218O), while the mass signals of 32O2, 34O2 and 36O2 were recorded. Then, five consecutive CV cycles (1.17-1.72\u2009V vs. RHE) were applied for labeling the catalyst surface with 18O. The catalysts were thoroughly washed with H216O deionized water to remove surface-adsorbed H218O and then operated in the 0.5\u2009M H2SO4 (H216O) electrolyte. Before data collection, a voltage was applied to the working electrode for 767\u2009s to test for receiving reliable signals. Again, the gaseous products were monitored by the mass spectrometer.\n\nAll electrochemical experiments were conducted using a BioLogic VSP-300 potentiostat equipped with iR compensation module. A conventional three-electrode cell was employed, comprising: working electrode (as-synthesized integrated RuTiMnOx electrode: geometric area: 1\u2009cm2; thickness: 600 \u03bcm), counter electrode (Pt plate: 1\u2009cm2 effective area; positioned parallel to the working electrode) and reference electrode (Ag/AgCl in saturated KCl). The Ag/AgCl reference electrode was calibrated against a secondary pre-validated master electrode (Tianjin Eilian Electronics & technology Co. ltd) using a dual-reference-electrode setup. Both electrodes were immersed in saturated KCl solution, and the open-circuit potential (OCP) was recorded, ensuring potential stability within \u00b1 5\u2009mV. The electrolytes were freshly prepared and promptly utilized. Linear sweep voltammetry (LSV) was performed at a scan rate of 10\u2009mV\u2009s-1 from 0.0 to 2.0\u2009V vs. RHE. The potential was converted to the reversible hydrogen electrode (RHE) scale using the Eq. (1):\n\nThe LSV curves were corrected with 95 % iR (i, current; R, resistance) compensation. The chronopotentiometric tests, conducted under iR-free conditions at a constant current density of 10\u2009mA\u2009cm\u22122, were performed in an H-type water electrolysis cell with the anode and cathode separated by a Nafion 117 membrane. A Nafion 117 membrane (DuPont, thickness: 183 \u03bcm) was sequentially washed by 5\u2009wt% H2O2, electrolyte, and deionized water for 30\u2009min, 60\u2009min, and 30\u2009min, respectively. The active area of Nafion 117 membrane is 19.6\u2009cm\u22122. Nyquist plots derived from electrochemical impedance spectroscopy (EIS) were acquired using a BioLogic VSP-300 potentiostat under open-circuit conditions, with a sinusoidal perturbation amplitude of 5\u2009mV applied across the frequency domain from 100\u2009kHz to 0.01\u2009Hz. Measurements were conducted in 0.5\u2009M H2SO4 (pH = 0.3\u2009\u00b1\u20090.02), 0.5\u2009M PBS (pH = 7.1\u2009\u00b1\u20090.10) and 1.0\u2009M KOH (pH = 13.9\u2009\u00b1\u20090.03) electrolytes.\n\nFor PEMWE tests, a cation exchange membrane (DuPont, Nafion\u2009117) was used as the membrane electrolyte. The membrane electrode assembly (MEA) was prepared by pressing the cathodes (20% Pt/C sprayed on the Nafion 117 membrane) and anodes (Ru/TiMnOx). During the test, the cell was maintained at 60\u2009\u00b0C, and the pre-heated deionized water was fed to the anode by a peristaltic pump. For AEMWE tests, the anion exchange membrane (FAA-3\u201350) was pre-treated in 1.0\u2009M KOH for over 24\u2009h and cleaned with deionized water. The commercial Raney Ni mesh was used as the cathode while the Ru/TiMnOx was used as the anode. 1.0\u2009M KOH was used as an electrolyte at a temperature of 60\u2009\u00b0C. All the data of PEMWE and AEMWE were not iR corrected and displayed as raw data.\n\nThe electrochemically accessible surface area (ECSA) was quantified using the double-layer capacitance method, as defined by (2):\n\nWhere Cdl is electrode-specific double-layer capacitance and Cs is the specific capacitance of the sample. Cdl was derived from cyclic voltammetry (CV) scans in the non-faradaic region (0.2\u2009~\u20090.3\u2009V vs. RHE) with six scan rates (20, 40, 60, 80, 100, 120\u2009mV\u2009s-1). The charging current (ic) was measured at 0.25\u2009V vs. RHE and plotted against scan rate (v). The slope of the linear regression yielded Cdl according to Eq. (3):\n\nThe mass activity (jmass) was determined using Eq. (4):\n\nWhere mRu is the calculated Ru mass loading based on the results of ICP-OES analysis, Ageo is the geometric area and jgeo is the geometric current density.\n\nAll DFT calculations were conducted by Vienna Ab initio Simulation Package (VASP) with projected augmented wave (PAW) pseudopotentials. The generalized gradient approximation (GGA) functional of Perdew-Burke-Ernzerhof (PBE) was applied as the exchange-correlation functional. The kinetic cutoff energy of plane wave was set at 520\u2009eV. The DFT\u2009+\u2009U approach was applied with Ueff\u2009=\u20093.9 for Mn to treat the strong on-site Coulomb interaction of localized electrons.The supercell of Ru/MnTiOx, Ru/MnOx and RuO2 contained 64, 96, 48 atoms respectively. The Brillouin zone in reciprocal space was sampled by a gamma-centered k-point grid of 2\u2009\u00d7\u20092\u2009\u00d7\u20092 during structural optimization. The slab model of Ru/MnTiOx had four layers, containing 18 Ru atoms, 34 Mn atoms, 20 Ti atoms and 72\u2009O atoms. The Ru/MnOx (110) slab model had 96 atoms, including 18 Ru atoms, 14 Mn atoms and 64\u2009O atoms. The slab models are used for calculations of OER and demetallization energies. The demetallization energies were obtained by the following Eq. (5):\n\nwhere Etot is the total energy of the slab model, Eatom is the energy of a single atom and Evac is the slab model energy with a vacancy formed by removing the single atom.\n\nThe computational hydrogen electrode (CHE) approach was applied to calculate the energy barrier in OER process. Adsorbate evolution mechanism (AEM) and oxide path mechanism (OPM) were both considered. The overpotential in AEM was evaluated using the following steps (6)\u2013(9):\n\nOPM was shown in the following steps (10)\u2013(14):\n\n*OH, *O, and *OOH are the reaction intermediates adsorbed on the catalyst surface. The catalyst surface was represented by slab models in calculation. Then, the free energy of each OER step was calculated according to the following Eq. (15):\n\nwhere \u0394ZPE is the zero-point energy, \u0394E is the change in the total ground-state energy, T is temperature (298\u2009K), \u0394S is the change in entropy and \u0394GU\u2009=\u2009eU, U is the electrode potential. The zero point energies and entropies of the intermediates were obtained by calculating the vibrational frequencies.",
+            "section_image": []
+        },
+        {
+            "section_name": "Data availability",
+            "section_text": "All data supporting this study is available in the article and the Supplementary Information. Source Data file has been deposited in Figshare under accession code DOI link69.",
+            "section_image": []
+        },
+        {
+            "section_name": "Code availability",
+            "section_text": "The Python code written in this paper for screening the most appropriate catalyst metal ratio is provided in the Supplementary Code\u00a01.",
+            "section_image": []
+        },
+        {
+            "section_name": "References",
+            "section_text": "Seh, Z. W. et al. Combining theory and experiment in electrocatalysis: insights into materials design. Science 355, eaad4998 (2017).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nRam, R. et al. Water-hydroxide trapping in cobalt tungstate for proton exchange membrane water electrolysis. Science 384, 1373\u20131380 (2024).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nChong, L. et al. La-and Mn-doped cobalt spinel oxygen evolution catalyst for proton exchange membrane electrolysis. Science 380, 609\u2013616 (2023).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLi, A. et al. Atomically dispersed hexavalent iridium oxide from MnO2 reduction for oxygen evolution catalysis. Science 384, 666\u2013670 (2024).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nYang, S. et al. The mechanism of water oxidation using transition metal-based heterogeneous electrocatalysts. Chem. Soc. Rev. 53, 5593\u20135625 (2024).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLyu, Z. et al. Biphase Pd Nanosheets with atomic-hybrid RhOx/Pd amorphous skins disentangle the activity-stability trade-off in oxygen reduction reaction. Adv. Mater. 36, 2314252 (2024).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nRong, C., Dastafkan, K., Wang, Y. & Zhao, C. Breaking the activity and stability bottlenecks of electrocatalysts for oxygen evolution reactions in acids. Adv. Mater. 35, 2211884 (2023).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWang, Q. et al. Long-term stability challenges and opportunities in acidic oxygen evolution electrocatalysis. Angew. Chem. Int. Ed. 135, e202216645 (2023).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nZhang, Y. L. et al. Engineering Co-N-Cr cross-interfacial electron bridges to break activity-stability trade-off for superdurable bifunctional single atom oxygen electrocatalysts. Angew. Chem. Int. Ed. 63, e202400577 (2024).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nHan, N. et al. Lowering the kinetic barrier via enhancing electrophilicity of surface oxygen to boost acidic oxygen evolution reaction. Matter 7, 1330\u20131343 (2024).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLi, W. et al. Defect engineering for fuel-cell electrocatalysts. Adv. Mater. 32, 1907879 (2020).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nYang, Y. et al. Anion-exchange membrane water electrolyzers and fuel cells. Chem. Soc. Rev. 51, 9620\u20139693 (2022).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nSun, W. et al. A rechargeable zinc-air battery based on zinc peroxide chemistry. Science 371, 46\u201351 (2021).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKondori, A. et al. A room temperature rechargeable Li2O-based lithium-air battery enabled by a solid electrolyte. Science 379, 499\u2013505 (2023).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLin, C. et al. In-situ reconstructed Ru atom array on \u03b1-MnO2 with enhanced performance for acidic water oxidation. Nat. Catal. 4, 1012\u20131023 (2021).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWu, Z.-Y. et al. Non-iridium-based electrocatalyst for durable acidic oxygen evolution reaction in proton exchange membrane water electrolysis. Nat. Mater. 22, 100\u2013108 (2023).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nGloag, L., Somerville, S. V., Gooding, J. J. & Tilley, R. D. Co-catalytic metal-support interactions in single-atom electrocatalysts. Nat. Rev. Mater. 9, 173\u2013189 (2024).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nYang, J., Li, W., Wang, D. & Li, Y. Electronic metal-support interaction of single-atom catalysts and applications in electrocatalysis. Adv. Mater. 32, 2003300 (2020).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLi, Y., Zhang, Y., Qian, K. & Huang, W. Metal-support interactions in metal/oxide catalysts and oxide\u2013metal interactions in oxide/metal inverse catalysts. ACS Catal. 12, 1268\u20131287 (2022).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nHu, S. & Li, W.-X. Sabatier principle of metal-support interaction for design of ultrastable metal nanocatalysts. Science 374, 1360\u20131365 (2021).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nShan, J. et al. Metal-metal interactions in correlated single-atom catalysts. Sci. Adv. 8, eabo0762 (2022).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nYang, C. et al. Metal alloys-structured electrocatalysts: metal-metal interactions, coordination microenvironments, and structural property-reactivity relationships. Adv. Mater. 35, 2301836 (2023).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWang, Y. et al. Advanced electrocatalysts with single-metal-atom active sites. Chem. Rev. 120, 12217\u201312314 (2020).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nChen, S. et al. Defective TiOx overlayers catalyze propane dehydrogenation promoted by base metals. Science 385, 295\u2013300 (2024).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBeck, A. et al. Controlling the strong metal-support interaction overlayer structure in Pt/TiO2 catalysts prevents particle evaporation. Angew. Chem. Int. Ed. 62, e202301468 (2023).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nChen, H. et al. Photoinduced strong metal-support interaction for enhanced catalysis. J. Am. Chem. Soc. 143, 8521\u20138526 (2021).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nXin, H. et al. Overturning CO2 hydrogenation selectivity with high activity via reaction-induced strong metal-support interactions. J. Am. Chem. Soc. 144, 4874\u20134882 (2022).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nPeng, B. et al. Embedded oxide clusters stabilize sub-2 nm Pt nanoparticles for highly durable fuel cells. Nat. Catal. 7, 818\u2013828 (2024).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nZhai, P. et al. Engineering single-atomic ruthenium catalytic sites on defective nickel-iron layered double hydroxide for overall water splitting. Nat. Commun. 12, 4587 (2021).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nHejazi, S. et al. On the controlled loading of single platinum atoms as a Co-catalyst on TiO2 anatase for optimized photocatalytic H2 generation. Adv. Mater. 32, 1908505 (2020).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nJ. Chang et al. Synthesis of ultrahigh-metal-density single-atom catalysts via metal sulfide-mediated atomic trapping. Nat. Synth. https://doi.org/10.1038/s44160-024-00607-4 (2024).\n\nZhao, S. et al. Constructing regulable supports via non-stoichiometric engineering to stabilize ruthenium nanoparticles for enhanced pH-universal water splitting. Nat. Commun. 15, 2728 (2024).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nRong, C. et al. Electronic structure engineering of single-atom Ru sites via Co-N4 sites for bifunctional pH-universal water splitting. Adv. Mater. 34, 2110103 (2022).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLiu, W. et al. Extremely active and robust Ir-Mn dual-atom electrocatalyst for oxygen evolution reaction by oxygen-oxygen radical coupling mechanism. Angew. Chem. Int. Ed. 136, e202411014 (2024).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nChang, J. et al. Oxygen radical coupling on short-range ordered Ru atom arrays enables exceptional activity and stability for acidic water oxidation. J. Am. Chem. Soc. 146, 12958\u201312968 (2024).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nZhou, Y. et al. Lattice-confined Ru clusters with high CO tolerance and activity for the hydrogen oxidation reaction. Nat. Catal. 3, 454\u2013462 (2020).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nHan, H.-J. et al. Chemical vapor deposition of Ru thin films with an enhanced morphology, thermal stability, and electrical properties using a RuO4 precursor. Chem. Mater. 21, 207\u2013209 (2009).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nSabzi, M. et al. A review on sustainable manufacturing of ceramic-based thin films by chemical vapor deposition (CVD): reactions kinetics and the deposition mechanisms. Coatings 13, 188 (2023).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nZaera, F. Mechanisms of surface reactions in thin solid film chemical deposition processes. Coord. Chem. Rev. 257, 3177\u20133191 (2013).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDin, R.-U. et al. Steam assisted oxide growth on aluminium alloys using oxidative chemistries: Part I Microstructural investigation. Appl. Surf. Sci. 355, 820\u2013831 (2015).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDin, R.-U., Gudla, V.-C., Jellesen, M.-S. & Ambat, R. Accelerated growth of oxide film on aluminium alloys under steam: part I: effects of alloy chemistry and steam vapour pressure on microstructure. Surf. Coat. Tech. 276, 77\u201388 (2015).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nHu, W. et al. Doping Ti into RuO2 to accelerate bridged-oxygen-assisted deprotonation for acidic oxygen evolution reaction. Adv. Mater. 37, 2411709 (2025).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nZhong, X. et al. Stabilization of layered lithium-rich manganese oxide for anion exchange membrane fuel cells and water electrolysers. Nat. Catal. 7, 546\u2013559 (2024).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nZhang, L. et al. Sodium-decorated amorphous/crystalline RuO2 with rich oxygen vacancies: a robust pH-universal oxygen evolution electrocatalyst. Angew. Chem. Int. Ed. 133, 18969\u201318977 (2021).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nYin, H. et al. Dual active centers bridged by oxygen vacancies of ruthenium single-atom hybrids supported on molybdenum oxide for photocatalytic ammonia synthesis. Angew. Chem. Int. Ed. 61, e202114242 (2022).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nYou, M. et al. In-situ growth of ruthenium-based nanostructure on carbon cloth for superior electrocatalytic activity towards HER and OER. Appl. Catal. B 317, 121729 (2022).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nThalluri, S.-M. et al. Enhancing alkaline hydrogen evolution reaction on Ru-decorated TiO2 nanotube layers: synergistic role of Ti3+, Ru single atoms, and Ru nanoparticles. Energy Environ. Sci. 8, e12864 (2025).\n\nCAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nPowar, N.-S. et al. Unravelling the effect of Ti3+/Ti4+ active sites dynamic on reaction pathways in direct gas-solid-phase CO2 photoreduction. Appl. Catal. B 352, 124006 (2024).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWang, K. et al. Highly active ruthenium sites stabilized by modulating electron-feeding for sustainable acidic oxygen-evolution electrocatalysis. Energy Environ. Sci. 15, 2356\u20132365 (2022).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDeng, L. et al. Valence oscillation of Ru active sites for efficient and robust acidic water oxidation. Adv. Mater. 35, 2305939 (2023).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nQin, Q. et al. Atomically dispersed vanadium-induced Ru-V dual active sites enable exceptional performance for acidic water oxidation. Angew. Chem. Int. Ed. 137, e202413657 (2025).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDeka, N. et al. On the operando structure of ruthenium oxides during the oxygen evolution reaction in acidic media. ACS Catal. 13, 7488\u20137498 (2023).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLi, Y. et al. Integrating interactive Ir atoms into titanium oxide lattice for proton exchange membrane electrolysis. Adv. Mater. 37, 2407386 (2025).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nChen, Y. et al. Metastabilizing the ruthenium clusters by interfacial oxygen vacancies for boosted water splitting electrocatalysis. Adv. Energy Mater. 14, 2400059 (2024).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nPan, X. et al. Electric-field-assisted proton coupling enhanced oxygen evolution reaction. Nat. Commun. 15, 3354 (2024).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nFeng, W. et al. Proton exchange membrane water splitting: advances in electrode structure and mass-charge transport optimization. Adv. Mater. 37, 2416012 (2025).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDuan, X. et al. Simultaneously constructing active sites and regulating Mn-O strength of Ru-substituted perovskite for efficient oxidation and hydrolysis oxidation of chlorobenzene. Adv. Sci. 10, 2205054 (2023).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nYu, Z. et al. Defective Ru-doped \u03b1-MnO2 nanorods enabling efficient hydrazine oxidation for energy-saving hydrogen production via proton exchange membranes at near-neutral pH. Chem. Eng. J. 470, 144050 (2023).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWen, Y. et al. Introducing Br\u00f8nsted acid sites to accelerate the bridging-oxygen-assisted deprotonation in acidic water oxidation. Nat. Commun. 13, 4871 (2022).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nYang, C. et al. Mn-oxygen compounds coordinated ruthenium sites with deprotonated and low oxophilic microenvironments for membrane electrolyzer-based H2-Production. Adv. Mater. 35, 2303331 (2023).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nSong, H. et al. RuO2-CeO2 lattice matching strategy enables robust water oxidation electrocatalysis in acidic media via two distinct oxygen evolution mechanisms. ACS Catal. 14, 3298\u20133307 (2024).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWang, B. et al. In situ structural evolution of the multi-site alloy electrocatalyst to manipulate the intermediate for enhanced water oxidation reaction. Energy Environ. Sci. 13, 2200\u20132208 (2020).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nVivek, J. P., Berry, N. G., Zou, J., Nichols, R. J. & Hardwick, L. J. In situ surface-enhanced infrared spectroscopy to identify oxygen reduction products in nonaqueous metal-oxygen batteries. J. Phys. Chem. C. 121, 19657\u201319667 (2017).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nPing, X. et al. Locking the lattice oxygen in RuO2 to stabilize highly active Ru sites in acidic water oxidation. Nat. Commun. 15, 2501 (2024).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMiao, X. et al. Quadruple perovskite ruthenate as a highly efficient catalyst for acidic water oxidation. Nat. Commun. 10, 3809 (2019).\n\nArticle\u00a0\n    ADS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nHwang, J. et al. Perovskites in catalysis and electrocatalysis. Science 358, 751\u2013756 (2017).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nRavel, B. et al. Data analysis for X-ray absorption spectroscopy using IFEFFIT. J. Synchrotron Rad. 12, 537\u2013541 (2005).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nZabinsky, S. I. et al. Multiple-scattering calculations of X-ray-absorption spectra. Phys. Rev. B 52, 2995\u20133009 (1995).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nL. Zhou, M. Yang, Y. Liu, F. Kang & R. Lv, Intrinsic metal-support interactions break the activity-stability dilemma in electrocatalysis, Figshare, https://doi.org/10.6084/m9.figshare.27233385 (2025).\n\nDownload references",
+            "section_image": []
+        },
+        {
+            "section_name": "Acknowledgements",
+            "section_text": "This work is supported by the National Natural Science Foundation of China (Grant No. 52371228 (R.L.) and 52302302 (M.Y.)), the National Key Research and Development Program of China (Grant No. 2021YFA1200800 (R.L.)), Xishan-Tsinghua Program for Deep Integration of Industry-University-Research (Grant No. 20242002205) and Tsinghua University-Toyota Joint Research Center for Hydrogen Energy and Fuel Cell Technology of Vehicles (grant to R.L.). We thank R. X. Zhou and Y. F. Li for technical support, and Q. M. Yuan and G. S. Liao for experimental assistance.",
+            "section_image": []
+        },
+        {
+            "section_name": "Author information",
+            "section_text": "These authors contributed equally: Lingxi Zhou, Menghao Yang.\n\nState Key Laboratory of New Ceramic Materials, School of Materials Science and Engineering, Tsinghua University, Beijing, China\n\nLingxi Zhou\u00a0&\u00a0Ruitao Lv\n\nShanghai Key Laboratory for R&D and Application of Metallic Functional Materials, School of Materials Science and Engineering, Tongji University, Shanghai, China\n\nMenghao Yang\u00a0&\u00a0Yihong Liu\n\nInstitute of Materials Research and Shenzhen Geim Graphene Center, Tsinghua Shenzhen International Graduate School, Tsinghua University, Shenzhen, China\n\nFeiyu Kang\n\nKey Laboratory of Advanced Materials (MOE), School of Materials Science and Engineering, Tsinghua University, Beijing, China\n\nFeiyu Kang\u00a0&\u00a0Ruitao Lv\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nR.L., and L.Z., conceived the original idea. R.L., supervised the project. L.Z., carried out machine learning, catalyst synthesis, materials characterization, catalytic tests and related data processing. M.Y., and Y.L., carried out DFT calculations. L.Z., M.Y., Y.L., and F.K., co-wrote the manuscript. All authors contributed to data analysis, scientific discussion and commented the manuscript.\n\nCorrespondence to\n                Ruitao Lv.",
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+        },
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+            "section_text": "Zhou, L., Yang, M., Liu, Y. et al. Intrinsic metal-support interactions break the activity-stability dilemma in electrocatalysis.\n                    Nat Commun 16, 8739 (2025). https://doi.org/10.1038/s41467-025-63397-z\n\nDownload citation\n\nReceived: 14 November 2024\n\nAccepted: 19 August 2025\n\nPublished: 01 October 2025\n\nVersion of record: 01 October 2025\n\nDOI: https://doi.org/10.1038/s41467-025-63397-z\n\nAnyone you share the following link with will be able to read this content:\n\nSorry, a shareable link is not currently available for this article.\n\n\n\n\n                            Provided by the Springer Nature SharedIt content-sharing initiative\n                        ",
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0b7608bc251c8024ae493244379344108add8b6da42c8277a7031cc03e69c3fc/metadata.json

@@ -0,0 +1,152 @@
+{
+    "title": "The negligible role of carbon offsetting in corporate climate strategies",
+    "pre_title": "The negligible role of carbon offsetting in corporate climate strategies",
+    "journal": "Nature Communications",
+    "published": "10 September 2025",
+    "supplementary_0": [
+        {
+            "label": "Supplementary Information",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-62970-w/MediaObjects/41467_2025_62970_MOESM1_ESM.pdf"
+        },
+        {
+            "label": "Description of Additional Supplementary Files",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-62970-w/MediaObjects/41467_2025_62970_MOESM2_ESM.pdf"
+        },
+        {
+            "label": "Supplementary Data 1",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-62970-w/MediaObjects/41467_2025_62970_MOESM3_ESM.xlsx"
+        },
+        {
+            "label": "Reporting Summary",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-62970-w/MediaObjects/41467_2025_62970_MOESM4_ESM.pdf"
+        },
+        {
+            "label": "Transparent Peer Review file",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-62970-w/MediaObjects/41467_2025_62970_MOESM5_ESM.pdf"
+        }
+    ],
+    "supplementary_1": NaN,
+    "supplementary_2": NaN,
+    "source_data": [
+        "/articles/s41467-025-62970-w#MOESM3",
+        "https://github.com/n-stolz/nature_comms_negligible_role_carbon_offsetting.git",
+        "https://github.com/n-stolz/nature_comms_negligible_role_carbon_offsetting.git",
+        "https://doi.org/10.5281/zenodo.15634074"
+    ],
+    "code": [
+        "https://github.com/n-stolz/nature_comms_negligible_role_carbon_offsetting.git"
+    ],
+    "subject": [
+        "Business",
+        "Industry"
+    ],
+    "license": "http://creativecommons.org/licenses/by/4.0/",
+    "preprint_pdf": "https://www.researchsquare.com/article/rs-5355499/v1.pdf?c=1757674135000",
+    "research_square_link": "https://www.researchsquare.com//article/rs-5355499/v1",
+    "nature_pdf": "https://www.nature.com/articles/s41467-025-62970-w.pdf",
+    "preprint_posted": "24 Nov, 2024",
+    "research_square_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Carbon credits feature prominently in corporate climate strategies and have sparked public debate about their potential to delay companies' internal decarbonisation. While industry reports claim that credit purchasers decarbonise faster, rigorous evidence is missing. Here, we provide an in-depth analysis of 89 multinational companies\u2019 historical emissions reductions and climate target ambitions. Based on self-reported sustainability data and more than 400 sustainability reports, we find no significant difference between companies that purchased credits and those that did not. Voluntary offsetting is not a central part of most companies\u2019 climate strategies, and many pass these credits' costs and purchase decisions directly onto their customers. While the companies within our sample retired 1/4th of all carbon credits in 2022, the top five offsetters' expenditures on voluntary emission offsetting are, on average, only 1 percent relative to their capital expenditures. For most companies, carbon credits are, therefore, unlikely to crowd out internal decarbonisation measures. Yet, we document that for large-scale offsetters like Delta Air Lines or easyJet, carbon credit purchases competed with financing internal decarbonisation efforts.Scientific community and society/Business and industry/IndustryScientific community and society/Business and industry/Business",
+            "section_image": []
+        },
+        {
+            "section_name": "Additional Declarations",
+            "section_text": "There is NO Competing Interest.",
+            "section_image": []
+        }
+    ],
+    "nature_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Carbon credits feature prominently in corporate climate strategies and have sparked public debate about their potential to delay companies\u2019 internal decarbonisation. While industry reports claim that credit purchasers decarbonise faster, rigorous evidence is missing. Here, we provide an in-depth analysis of 89 multinational companies\u2019 historical emission reductions and climate target ambitions. Based on self-reported environmental data and more than 400 sustainability reports, we find no significant difference between the climate strategies of companies that purchased credits and those that did not. Voluntary offsetting is not a central part of most companies\u2019 climate strategies, and many pass credit costs directly onto their customers. While the companies within our sample retired one-fourth of all carbon credits in 2022, the top five offsetters\u2019 expenditures on voluntary emission offsetting are, on average, only 1 percent relative to their capital expenditures. For most companies, carbon credits are, therefore, unlikely to crowd out internal decarbonisation measures. Yet, we document that for large-scale offsetters in the airline industry, carbon credit purchases competed with financing internal decarbonisation measures.",
+            "section_image": []
+        },
+        {
+            "section_name": "Introduction",
+            "section_text": "Companies have faced increasing pressure from policymakers, consumers, civil society, and investors to reduce emissions. In response to the Paris Agreement, governments have consistently tightened their climate policies1. This regulatory shift has increased investors\u2019 concerns about transition risk, prompting them to demand credible climate strategies from the companies in their portfolio2. However, media and non-governmental organisations (NGOs) that monitor corporate emission targets3 frequently expose cases of greenwashing4,5.\n\nIn response to the growing pressure, half of the Forbes Global 2000 companies have set net zero targets3. However, no globally accepted, binding standard for setting credible net zero targets exists. This gap has been filled by private initiatives like the Science-Based Targets initiative (SBTi), which provides standards on the emission coverage and ambition of net zero targets. SBTi also offers guidelines for how companies can compensate for residual emissions once they have reduced most of their emissions6.\n\nMany companies use or plan to use carbon credits from the voluntary carbon markets to offset parts of their emissions on their path to net zero7. Carbon credits are the \u201creduction, avoidance or removal of a unit of greenhouse gas (GHG) emissions by one entity, purchased by another entity to counterbalance a unit of GHG emission by that other entity\"8. These voluntary emission practices and the claims derived from emission offsetting (e.g. carbon neutral, net zero)9 are prominently featured in the public debate about decarbonisation10,11,12. However, carbon credits\u2019 role in corporate climate strategies remains unclear.\n\nInsights from political economy, stakeholder theory, and legitimacy theory suggest that when civil society, politicians, and other stakeholders pressure companies, they may engage in voluntary social or environmental disclosure to shore up support13,14. However, these strands of literature typically do not predict or assess whether such action translates into improved corporate climate performance. Companies may engage in voluntary environmental disclosure to achieve a variety of objectives: they may aim to inform the public about superior environmental performance relative to peers, to reshape the company\u2019s image without substantial change, to shift the focus of the discourse, or to influence stakeholder expectations about the company\u2019s actions13,15. In the context of voluntary carbon offsetting, companies may retire carbon credits to signal superior environmental performance or enhance their public image without substantially advancing internal decarbonisation. Alternatively, corporate emission offsetting, as a form of corporate social responsibility, may be driven by altruistic motives16 that have not been previously captured in the literature.\n\nPurchasing carbon credits instead of pursuing\u00a0potentially more effective internal decarbonisation can be conceptualised as a moral hazard. Moral hazard occurs when actors take on higher risks or engage in socially suboptimal behaviour because they are shielded from the consequences of their actions17. Therefore, there is a risk that emission offsetting leads to moral hazard when companies neglect internal and value chain emission reductions because the improved public perception achieved through emission offsetting shields them from the risk of reputational damage, public scrutiny, or governmental regulation.\n\nThere is mixed evidence regarding the relationship between corporate carbon management practices and subsequent emission reductions. While some studies demonstrate a positive relationship between corporate carbon disclosure and emission reductions18,19, others find this link only among emission-intensive companies20. Conversely, to our knowledge, no study to date has established a significant relationship between adopting reporting guidelines, such as the Global Reporting Initiative (GRI) and improved corporate emission performance21,22. Further, the impact of corporate climate strategies on emission reductions remains ambiguous. For example, there is limited evidence around the relationship between the mere presence of corporate climate targets and subsequent decarbonisation23, though more ambitious targets are associated with greater emission reductions23,24. Recent findings suggest that only a comprehensive mix of corporate climate instruments (e.g., absolute emission targets, internal carbon prices, value chain engagement) is linked to absolute emission reductions25.\n\nWhile research on companies\u2019 use of carbon credits is still nascent, research on renewable energy attributes (REAs), another market-based carbon accounting tool, is more advanced. REAs allow companies to verify and claim the purchase of renewable energy, directly reducing market-based scope 2 emissions under the Greenhouse Gas Protocol and Science-Based Targets initiative (SBTi)26. Unlike voluntary carbon credits, REAs can be counted towards SBTi goals. Ascui et al.27 show that companies using REAs tend to increase their scope 1 and 2 emissions without improving energy efficiency compared to peers who do not use them, which indicates their potential to induce moral hazard27. Additionally, setting targets for market-based scope 2 emissions and achieving them by purchasing REAs might undermine the integrity of SBTi because these certificates do not lead to real emission reductions28,29,30.\n\nIn contrast to the well-documented role of REAs in corporate climate performance, research on carbon credits is still nascent. Recent industry reports claim that companies engaging in emission offsetting decarbonise faster than their peers31,32,33. These industry reports argue that by voluntarily offsetting emissions, companies put a price on greenhouse gas emissions, creating a financial incentive for faster internal decarbonisation33. In addition, Engler et al.34 show that emission offsetting does not crowd out investment in decarbonisation for German small- to medium-sized companies but complements pro-environmental activities34.\n\nHowever, growing evidence challenges voluntary carbon markets\u2019 overall positive climate effect. A range of studies show that emission reductions associated with carbon credits are systematically overestimated35. Also, large-scale offsetters tend to source cheap and low-quality carbon credits36. Beyond these issues, the industry reports supporting the claim that emission offsetters decarbonise faster than their peers do not control for company size and do not examine whether carbon credit spending might crowd out investments in internal decarbonisation31,32,33. Further, scientific findings on the corporate usage of carbon credits are not based on observed corporate emission performance but capture explanatory variables like perceived climate-related risks, presence of any climate target and environmental management systems34. However, these findings cannot be generalised to multinational companies in hard-to-abate sectors, which constitute the largest buyer group37.\n\nHere, we analyse the emission offsetting behaviour of 89 multinational companies in the oil and gas (O&G), automobile manufacturing, and airline sectors. The companies in the sample constitute 24% of carbon credits retired in the voluntary carbon market in 2022. We focus on multinational companies in hard-to-decarbonise sectors since those companies are characterised by high emissions, low profits per ton of emitted carbon dioxide38, and weak climate targets37. We compiled a dataset on the corporate usage of voluntary carbon credits by combining several sources. First, we utilised data from CDP on corporate greenhouse gas emissions, carbon credit retirements, and emission targets. Second, we cross-verified the carbon credit retirement data with the largest registries (Verra, Gold Standard, CDM). Third, we compiled a dataset of qualitative information on corporate emission offsetting between 2014 and 2023, analysing over 400 corporate sustainability and annual reports. Our analysis proceeds in two stages. First, we evaluate if emission offsetting is associated with more ambitious decarbonisation efforts by companies compared to peers that do not engage in emission offsetting. We measure decarbonisation ambition with two metrics: the change in scope 1 emissions between the CDP reporting cycles 2018 and 2023 as a retrospective indicator and the ambition of emission reduction targets as a forward-looking metric. Second, we examine the role of emission offsetting in corporate climate strategies by analysing carbon credit expenditures and their usage details.\n\nWe find no significant difference in climate strategy between companies that offset emissions and those that do not. The reason for the non-significant relationship is likely the low expenditures on emission offsetting relative to companies\u2019 capital expenditures, the low overall share of offset emissions relative to total company emissions, and the non-binding nature of voluntary emission offsetting. However, we find that carbon credit expenditures compete with financing internal decarbonisation efforts for large-scale offsetting campaigns. We argue that voluntary emission offsetting is not associated with accelerated corporate decarbonisation and that the role of carbon credits in corporate climate strategies is overstated in the public discourse.",
+            "section_image": []
+        },
+        {
+            "section_name": "Results",
+            "section_text": "We find no significant relationship between the number of carbon credits a company retired in CDP\u2019s 2023 reporting period and the historical change in scope 1 emissions or with the ambition of their emission targets (see Fig.\u00a01).\n\nThe graph displays the estimated regression coefficients (\\({\\hat{\\beta }}_{i}\\)), with error bars representing their 95% confidence intervals (CI) with \\({\\text{CI}}_{{\\beta }_{i},0.95}=\\left[{\\hat{\\beta }}_{i}-{t}^{*}\\cdot \\,\\text{SE}\\,({\\hat{\\beta }}_{i}),{\\hat{\\beta }}_{i}+{t}^{*}\\cdot \\,\\text{SE}\\,({\\hat{\\beta }}_{i})\\right]\\) and t* the critical value from the t-distribution. In (a), positive regression coefficients indicate a negative relationship between the explanatory variables (on y-axis) and decarbonisation speed (x-axis), suggesting that as the explanatory variables increase, we observe a decreased decarbonisation speed. In (b), positive regression coefficients indicate a positive relationship between the explanatory variables (y-axis) and climate target ambition (x-axis), suggesting that as the explanatory variables increase, we observe an increased climate target ambition. The sectoral categorical variables are relative to the aviation sector, and the geographic categorical variables are relative to headquarters in Asia. The label of retired carbon credits is written in bold as it represents the study\u2019s primary outcome variable of interest.\n\nThe only significant association with the change of scope 1 emissions over the study period is that companies in the oil and gas sector reduced their emissions more slowly than companies in the aviation sector (significance level \u03b1\u2009=\u20090.05, Fig.\u00a01a). However, this relationship is not robust to leaving single observations out of the regression (see Supplementary Information Fig.\u00a0S1a, b). Nevertheless, there is no significant association between the number of carbon credits retired and the change in scope 1 emissions.\n\nConversely, the variation in climate target ambition until 2050 is significantly correlated with sector and location. Companies headquartered in Europe set more ambitious climate targets than their peers in other regions. Conversely, oil and gas companies are associated with setting targets that are less ambitious than those of companies in other sectors. However, we find no significant association between the number of retired carbon credits and climate target ambition.\n\nThese findings suggest that the number of carbon credits a company retires is unrelated to its past emission reductions and climate target ambition. This conclusion holds across various robustness checks (see Supplementary Information Tables\u00a0S3\u2013S8). Below, we explore the reasons for these findings.\n\nThere are two opposing lines of argument about how the purchase of carbon credits can influence companies\u2019 emission trajectories. Some argue that buying carbon credits diverts resources from internal decarbonisation, thereby delaying it39. Others argue that the cost of carbon credits is a voluntary penalty for greenhouse gas emissions, which incentivises companies to accelerate decarbonisation33. Our findings support none of these views since we find a non-significant relationship between offsetting and emission trajectories and climate target ambition.\n\nTo delve deeper into potential reasons behind our findings, we estimate the magnitude of emission offsetting costs relative to companies\u2019 investments in their assets and mandatory emission costs. Therefore, we estimate companies\u2019 carbon credit and emission trading scheme costs and compare them to their reported capital expenditures. Compared to their capital expenditures (CAPEX), companies allocate relatively small amounts of funds to emission offsetting (see Fig.\u00a02). The companies with the largest CAPEX share spent on carbon credits are easyJet (2.7%) and Delta Air Lines (1.8%). In the oil and gas sector, Eni (0.14 \u22120.38%) and Shell (0.10 \u22120.25%) follow. In the automobile manufacturing sector, Volkswagen Group (0.13\u22120.20%) and Mercedes-Benz Group (0.07 \u22120.13%) spend the largest share of funds on offsetting. Overall, the distribution of corporate spending on emission offsetting is long-tailed, meaning that few companies spend a lot on credits while the majority spend little.\n\nMinimum estimates (blue) are based on the lowest reported carbon credit price among companies in the sample (easyJet) for 2022, and maximum estimates (red) are based on data from Ecosystem Marketplace (2023)60. Reported CAPEX shares (green) indicate that companies reported total spending for carbon credits in 2022. The figure includes the 15 companies with the highest share of funds spent on carbon credits relative to their CAPEX.\n\nSimilarly, European companies face much higher costs under compliance Emission Trading Schemes (ETS) - such as EU-ETS, UK-ETS, and Switzerland-ETS - compared to their spending on carbon credits (see Fig.\u00a03). However, there is substantial variation between sectors. For example, easyJet, despite being an outlier in carbon credit spending, spent 9.9\u2009times more money on compliance emission trading than on voluntary emission offsetting. In the oil and gas sector, Eni had to allocate ~33.1\u2009times more to compliance emission trading, while Shell only spent ~6.7\u2009times more. An exception to this trend is the BMW Group, which spent more on voluntary offsetting - 2.3\u2009times their compliance emission trading costs - since they could cover their emissions with excess allowances from past years40.\n\nSources: Retired carbon credits and ETS allowances from the CDP database40, average ETS prices from World Bank46, Carbon credit price estimates from Ecosystem Marketplace (2023)60. *Easyjet directly reports spending on carbon credits in their 2022 annual report.\n\nIn addition to the financial commitment of offsetting emissions, which emissions a company offsets, who pays for the carbon credits, and the permanence of the decision to offset emissions likely affect the role of carbon credits in companies\u2019 decarbonisation strategies. We find that the role of emission offsetting in corporate climate strategies varies between companies (see Fig.\u00a04). Companies that purchase large quantities of carbon credits typically follow one of two approaches: they either offset a fixed portion of their emissions (e.g. Delta Air Lines, easyJet, and Volkswagen Group) or offset residual emissions to meet specific emission targets (e.g. Shell, Eni, and Inpex). In contrast, companies that purchase fewer carbon credits typically only offer them to their customers during the checkout (e.g. Deutsche Lufthansa, Air France - KLM, Ryanair Holding, International Consolidated Airlines Group) or offset their business travel (e.g. Deutsche Lufthansa, International Consolidated Airlines Group).\n\nOverview of offsetting purpose for companies that reported >100,000 retired credits in CDP's 2023 survey between 2014 and 2023.The information is based on companies' sustainability and annual reports.\n\nWe find that all airlines and oil and gas companies that reported the retirement of >100,000 carbon credits in the CDP 2023 survey either provide customers the option to voluntarily offset their purchases at checkout or to buy pre-offset fossil products. It is common practice for airlines to offer the option to offset emissions during the flight booking process (e.g. easyJet post-2022, Deutsche Lufthansa, International Consolidated Airlines, Ryanair Holdings, Air France - KLM). Similarly, oil and gas companies regularly sell pre-offset fossil products (e.g. Shell, BP, Eni, Inpex, TotalEnergies). Therefore, despite their relatively low expenditure on carbon credits, many companies pass these credits\u2019 costs and purchase decisions directly onto their customers.\n\nBesides large variability in the usage of carbon credits for emission offsetting, companies regularly change their offsetting strategy. Over the past decade, many companies have expanded the use cases for emission offsetting. However, the largest two emission offsetters, Delta Air Lines and easyJet, stopped their large-scale offsetting campaign in 2022. Also, BP changed its offsetting strategy in 2020, ceasing to use carbon credits to reach its zero net growth target41.\n\nGiven the large variety in companies\u2019 approaches to emission offsetting (Fig.\u00a04), it is unclear how substantial the number of retired carbon credits is compared to companies\u2019 overall greenhouse gas emissions. We find that only easyJet (78.2%) and Delta Air Lines (43.7%) retire carbon credits accounting for substantial portions of their total scope 1, 2, and 3 emissions (see Fig.\u00a05a). Deutsche Lufthansa offsets the third highest share of scope 1, 2 and 3 emissions (1.5%) despite ranking 11th in the number of retired carbon credits in the sample and only offsetting employee business travel and offering voluntary offsets to customers (see Fig.\u00a04). Among oil and gas companies, Eni (1.4%) and BP (0.7%) offset the largest shares of their emissions, while in the automobile manufacturing sector, Volkswagen Group (1.1%) and BMW (0.7%) offset the most.\n\nShare of scope 1, 2, and 3 emissions (a) and of scope 1 and 2 emissions (b) that companies voluntarily offset based on emission reporting during the 2023 CDP reporting cycle40. Location-based scope 2 emissions are used.\n\nThe picture changes substantially when focusing solely on scope 1 and location-based\u00a0scope 2 emissions. The three automobile manufacturers that offset their emissions, Volkswagen Group (50.3%), BMW (45.2%), and Mercedes-Benz Group (40.3%), emerge among the largest five offsetters of scope 1 and 2 emissions (see Fig.\u00a05b). These offset shares rise further when considering market-based scope 2 emissions since BMW and Mercedes-Benz Group offset their full scope 1 and market-based scope 2 emissions. However, even limited to scope 1 and 2 emissions, oil and gas companies offset minor emission shares. Shell (9.8%) has the largest share of offset scope 1 and 2 emissions in the oil and gas sector, followed by Eni (7.5%) and BP (7%).\n\nDespite clear indications that voluntary emission offsetting contributes, on average, little to meaningful decarbonisation efforts (see Fig.\u00a01) due to low investment levels (see Fig.\u00a02) and low persistence of emission offsetting in corporate climate strategies (see Fig.\u00a04), it is unclear if voluntary emission offsetting competes with internal decarbonisation investment in some cases. Among companies engaging in emission offsetting, we identify two key pathways through which offsetting may compete with internal decarbonisation efforts.\n\nThe first pathway is the investment effect. In this pathway, companies allocate a fixed budget for decarbonisation, which includes both the purchase of carbon credits and investments in internal emission reduction measures. Every dollar spent on carbon credits reduces the funds available for investments in operations or value chain decarbonisation. As a result, carbon credit purchases compete with investments in operations or value chain decarbonisation, potentially replacing internal decarbonisation efforts.\n\nThe second pathway is the target effect. Here, companies use carbon credits as part of their strategy to meet emission reduction targets. Since purchasing carbon credits is often cheaper and easier than implementing structural changes, companies may opt to purchase carbon credits instead of implementing more substantial internal decarbonisation initiatives to meet their targets. Therefore, as for the investment effect, the target effect might indirectly lead to competition between investments in internal decarbonisation and carbon credit expenditures.\n\nWe find evidence for the investment effect, where investments in decarbonisation are crowded out due to the allocation of funds to carbon offsetting for Delta Air Lines and easyJet. These two companies are the outliers, spending the largest CAPEX ratios on carbon credits (see Fig.\u00a02). Delta Air Lines set a fixed budget of USD 1\u2009billion over 10\u2009years for decarbonisation measures, including both carbon credits and investments in internal decarbonisation initiatives42. After 3\u2009years, Delta spent USD 284\u2009million on carbon credits, leaving only USD 16\u2009million for internal decarbonisation initiatives, assuming an annual budget of USD 100\u2009million over 10\u2009years (see Table\u00a01). Although easyJet did not communicate a fixed decarbonisation budget, after stopping their large-scale offsetting campaign, they announced that they would use the funds formerly committed to emission offsetting for internal decarbonisation measures, indicating that large-scale offsetting competed with internal decarbonisation investments.\n\nIn the oil and gas sectors, we observe the target effect, where emission offsetting is treated as a substitute for emission reductions. Shell, Eni, and Inpex include carbon credits in their emission reduction targets (see Table\u00a01), allowing them to meet their targets either by reducing emissions or by retiring carbon credits. While Eni communicates how many carbon credits they plan to use to achieve their emission targets43, it is unclear how many carbon credits Shell44 and Inpex45 plan to use for achieving their emission targets.",
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+        },
+        {
+            "section_name": "Discussion",
+            "section_text": "Our analysis of 89 multinational companies, covering around one-fourth of all carbon credits retired in 2022, reveals no significant difference in climate performance or ambition between companies that offset their emissions and those that do not. This conclusion holds for historical emission performance (CDP 2018-2023 survey) and forward-looking climate target ambition. Contrary to the findings by industry reports31,32,33 and Engler et al. (2023)34, companies in hard-to-decarbonise sectors appear to purchase and retire carbon credits primarily in response to external pressure. Given that most companies in our sample spend little and inconsistently on carbon credits, it appears that carbon credit purchases are a strategy to maintain or restore legitimacy without accelerating decarbonisation relative to their peers.\n\nCompared to their overall capital expenditures, companies allocate very little funds to emission offsetting (Fig.\u00a02). Even the two outliers, easyJet and Delta Air Lines, spend less than 3% relative to their CAPEX on carbon credits. Also, compared to compliance emission trading schemes, the costs of voluntary carbon offsetting are relatively low where such schemes exist. For instance, the five European companies that retired the most carbon credits spent, on average, 5.7% of their compliance carbon expenditures on voluntary carbon credits. Therefore, even reallocating these funds to internal decarbonisation efforts would likely have minimal impact on overall emission reductions. This illustrates that despite its prominence in the public debate on corporate climate strategies, voluntary emission offsetting plays only a minor role in shaping these strategies. Hence, its importance is overstated in public discourse since it imposes minimal financial burden on companies and requires little commitment to climate change mitigation since companies can cease these activities at any time.\n\nConversely, companies operating under European emission trading schemes already pay substantial costs for their emissions. Unlike voluntary carbon markets, these compliance schemes are mandatory, and carbon allowances trade at substantially higher prices than carbon credits on the voluntary carbon markets46. Consequently, they are more suitable for making a business case for corporate decarbonisation.\n\nAlthough, on average, there is no statistically significant association between voluntary emission offsetting and companies\u2019 environmental performance, qualitative evidence suggests two potential ways emission offsetting could compete with internal decarbonisation. The first is the investment effect, which arises when companies allocate a shared decarbonisation budget for both carbon credit purchases and internal decarbonisation. Here, internal decarbonisation initiatives directly compete with spending on carbon credits. The second is the target effect, which occurs when companies allow emission offsetting to reach climate targets, offering a low-cost alternative to internal decarbonisation. However, the long-term impact of these effects on emission trajectories remains unclear. In practice, companies may increase their decarbonisation budgets once they realise that more funds are necessary. For instance, after committing USD 1 billion to decarbonisation in 2020, Delta Air Lines acknowledged in 2023 that additional resources would be required to achieve their emission reduction targets47. Moreover, access to emission offsetting could allow companies to achieve more ambitious climate targets than companies that do not use offsets for residual emissions.\n\nThe lack of significant correlation between the number of retired carbon credits and environmental performance suggests that voluntary carbon offsetting has historically not been associated with moral hazard. However, there is qualitative evidence that some oil and gas companies, like Shell, Eni, and Inpex, plan to integrate voluntary emission offsetting into their climate targets. Although we cannot assess whether these companies genuinely plan to reduce their emissions, this approach could result in moral hazard if companies purchase carbon credits that do not entail promised emission reductions rather than actively reduce their emissions. In such a scenario, the use of carbon credits could reflect the same type of moral hazard previously observed in the context of renewable energy attributes, where the claimed benefits fall short of real emission reductions. Lastly, some compliance pricing mechanisms, such as the Colombian and South African carbon taxes or the Korean and Californian ETSs, permit companies to use carbon credits sourced from voluntary carbon markets to meet part of their obligations48. Hence, if companies reduce their compliance emission costs by retiring carbon credits, this can be associated with moral hazard.\n\nOur findings entail several recommendations for policymakers. Voluntary emission offsetting is not associated with positive corporate environmental performance. Therefore, it is not a reliable alternative to regulatory measures, such as compliance carbon pricing. Policymakers should, therefore, focus on strengthening regulatory mechanisms to ensure substantial corporate contributions to emission reductions. Moreover, companies in emission-intensive sectors typically offset only small portions of their total scope 1, 2, and 3 emissions and allocate minimal funds to purchasing carbon credits. This highlights the importance of policies such as the European Union\u2019s directive to empower consumers for the green transition through better protection against unfair practices and through better information49, which aims to prevent companies from making excessive environmental claims.\n\nWhile we find clear indications that carbon credits play a minor role in corporate climate strategies, the study has potential limitations. First, we only consider a limited number of companies in three hard-to-abate sectors. Therefore, we might not identify small effect sizes of carbon credit usage on the change in scope 1 emissions and climate target ambition. However, few companies in hard-to-decarbonise sectors purchase substantial quantities of carbon credits and report on the details of their credit purchases and emissions. In hard-to-decarbonise sectors like cement, steel, and cargo shipping, no major company offset substantial shares of their emissions during the latest CDP reporting year40. Therefore, the effect of voluntary offsetting cannot be evaluated for those sectors. Second, we rely on self-reported company data, which are often criticised for their lack of credibility and comparability between companies. To limit the influence of reported data, we validated offsetting data with publicly available carbon credit registries and manually checked if outliers in our dataset were plausible.\n\nOverall, the system of voluntary offsetting emissions is not associated with improved corporate sustainability performance. Most companies allocate minimal funds to voluntary carbon credits, which, even if redirected toward internal decarbonisation, would likely have little impact on their overall environmental performance. Further, the flexibility for companies to discontinue or alter their offsetting strategies at any time indicates that emission offsetting does not entail a solid commitment to decarbonising operations and value chains. Therefore, voluntary carbon offsetting should not be considered an indicator of superior corporate environmental performance. Instead, the public discourse on corporate decarbonisation should focus on progress in internal and value chain decarbonisation initiatives.",
+            "section_image": []
+        },
+        {
+            "section_name": "Methods",
+            "section_text": "Our main data source for numerical sustainability data is the CDP (formerly known as Carbon Disclosure Project) reporting cycle 2023. CDP has collected climate impact disclosure from companies since 2002. Scholars frequently use CDP data to study corporate climate performance over time50,51,52,53. In addition, we use financial data from S&P Capital IQ.\n\nThe study includes 89 oil and gas, airlines, and automobile manufacturing companies. These sectors are well-suited for investigating the role of voluntary emission offsetting, as they are characterised by high emissions and include some of the largest emission offsetting companies. In contrast, other hard-to-decarbonise industries, such as steel, cement, and maritime shipping, rarely engage in voluntary offsetting40. The sample includes all passenger airlines and automobile manufacturers that disclose their emissions to CDP. Further, we selected the 40 companies with the highest scope 1 emissions from the oil and gas sector due to the large number of companies in the CDP dataset. PJSC Lukoil was excluded from the analysis due to substantial structural changes in the Russian gas industry during the study period. Consequently, the final sample consists of 39 oil and gas companies, 27 passenger airlines, and 23 automobile manufacturers.\n\nWe use data from CDP\u2019s 2023 survey wave to obtain (1) companies\u2019 scope 1, 2 and 3 emissions, (2) carbon credit retirement data (number of credits and project types), (3) emission targets, and (4) purchased allowances under emission trading schemes. Companies\u2019 reporting years in the 2023 CDP survey wave end between 31. March 2022 and 31. March 2023, with the majority (70 companies) reporting for the calendar year 2022. In addition to the 2023 survey wave, we use CDP\u2019s 2018 survey wave to obtain historical scope 1 and 2 emission data. Since 36 companies in our sample did not participate in CDP\u2019s emission disclosure in 2018, we complement the data with information from corporate sustainability or annual reports. For nine companies (Ko\u00e7 Holding, San Miguel Corporation, Copa Holding, Kinder Morgan, Wizz Air Holding, Grupo Aeromexico, NFI Group, Hawaiian Holding, and Chorus Aviation), we have not found scope 1 emission data for 2018.\n\nTo improve data reliability, we cross-validate carbon credit retirement data with the largest voluntary carbon market registries of Verra, Gold Standard, and CDM. While the CDM was introduced to enable industrialised countries to reach their emission targets under the Kyoto Protocol, CDM credits can also be retired for voluntary purposes. If a company\u2019s cumulative credit retirements in those carbon market registries are larger than what the company reports to CDP, we use the registry data. Discrepancies between CDP data and registry data happen predominantly in cases where companies offset emissions for fossil products sold to clients (e.g. Inpex Corporation and PETRONAS).\n\nWe define the historical emission performance as the ratio of scope 1 emissions reported in the CDP survey waves 2023 and 2018. We do not include scope 2 emissions since 20 companies in the sample did not report scope 2 emissions in 2017, and 13 further companies reported scope 2 emissions in 2017 without disclosing whether they used the location-based or market-based accounting approach. Further, location-based scope 2 emissions are heavily influenced by grid-emission factors, while market-based scope 2 emissions can be lowered through the purchase of renewable energy attributes that have been shown to have little effect on renewable energy expansion28,29. To ensure robustness, we present findings that include changes in combined scope 1 and 2 emissions in the supplementary information (Table\u00a0S4). Further, we do not consider scope 3 emissions since current reporting practices do not allow for meaningful cross-organisational comparison54. We exclude Mercedes-Benz Group from the emission analysis due to the spin-out of Daimler Truck in December 2021. Further, we exclude Inpex Corporation from the emission analysis since it is an outlier with a 1085% increase in scope 1 over the study time. In the\u00a0supplementary information we illustrate with a leave-one-out cross-validation that Inpex Corporation is the only data point that influences the results substantially (see Supplementary Information Fig.\u00a0S1).\n\nWe perform ordinary least squares (OLS) regression using the python package statsmodels (version 0.14.1) to estimate the association between retired carbon credits and the change in historical emission reductions. We control for companies\u2019 sizes, industrial sectors, and continents of headquarters. We estimate:\n\nwhere i indexes the companies, Yi is a company\u2019s ratio of scope 1 emissions reported in the CDP survey waves 2023 and 2018, Xi is the number of carbon credits a company retired in CDP\u2019s 2023 reporting cycle, Ci are the control variables, and \u03f5i represents the error term, capturing unobserved factors affecting Yi. We control for revenue, sector, and continent of headquarters. We convert the categorical variables for the sector (automobile, oil and gas, and airlines) and the continent of headquarters (Asia, Europe, Latin America, and North America) into binary indicator columns (i.e. one-hot encoding). That means in the regression, each categorical variable equals 1 if a company belongs to a specific sector or is headquartered in a particular region and 0 otherwise. To avoid multicollinearity, we excluded the sectoral category \u201cAirlines\" and the geographical category \u201cAsia\" from the regression. These omitted categories serve as the reference groups against which the effects of other categories are compared.\n\nIt is difficult to compare climate target ambition due to differences in scope, base years and target years. Therefore, corporate climate targets must be harmonised before they can be directly compared across companies55. Here we calculate the ambition for each emission scope (scope 1, 2, and 3) and then add the ambitions weighted with the relative importance of that scope for a specific industry (relative importance\u2009=\u2009avg. share of total emissions for scope n in industry X).\n\nWe use the following assumptions and simplifications to construct the target emission trajectories between 2020 and 2050 in line with previous studies that compared climate targets across organisations:\n\nBetween intermediate targets, emission trajectories are linear55.\n\nEmissions that are not covered by any target remain unchanged55,56\n\nWe only consider company-wide targets, not product targets - e.g. when a company sells oil and gas but only has a target for their oil operation, we do not regard it since a reduction in oil emissions could be compensated by increased gas production. The only exception is when there are product-level targets for all main products of a company (e.g. separate targets for oil and gas operation). This assumption helps to avoid the difficulties of aggregating product-level emission-intensity targets for integrated energy companies that often sell different energy and non-energy products56 by constructing a company-wide intensity metric.\n\nIn line with SBTi\u2019s net zero standard6, we accept both absolute and intensity targets. If, for the same year, intensity and absolute targets are given, we use the absolute target. While other studies also accept absolute and intensity targets55,56, in contrast to Bolay et al. (2022), we do not use the associated expected change in absolute emissions for intensity targets that companies need to report to CDP. Instead, we directly use the targeted change in emission intensity to construct a company\u2019s emission trajectory. The deviation from previous studies is due to low data quality for the expected change in absolute emissions for intensity targets. Often, it is unclear if companies correctly use positive and negative numbers to indicate expected increases or decreases in absolute emissions. Further, it is not possible to verify the data since this data is typically not reported in annual or sustainability reports. To verify that companies that use intensity targets do not systematically set more ambitious climate targets, we show in the\u00a0Supplementary Information that the share of a company\u2019s target that is covered by intensity targets is not significantly correlated with its target ambition (Table\u00a0S5) and, therefore, does not bias the result reported in the regression analysis.\n\nWe assign an ambition score for each subtarget by comparing planned emission trajectories with emission reductions in line with the annual average of all 1.5 degree Celsius warming emission scenarios from IPCC\u2019s Sixth Assessment Report57 Studies that evaluated climate targets compare target ambitions either to emission trajectories58 or to targeted average annual change in emissions55,56. We choose to compare companies based on the targeted cumulative emissions until 2050 instead of targeted average annual changes in emissions since not only the average change in emissions but also the shape of the emission trajectory is directly linked to global warming. The choice of the reference emission trajectory is not relevant for the regression results since it is the same constant that is deducted from each observation and, hence, does not influence the regression coefficients. Further, we do not use different reference emission trajectories per sector or geography to avoid biasing our regression results. Instead, we explicitly control for geography and sector in the regression.\n\nFigure\u00a06 illustrates how we translate emission targets to emission trajectories and target ambition for the example company A. Company A\u2019s emission target only covers 90% of its emissions. Therefore, we assume that 10% of emissions remain unchanged. First, we construct the emission trajectory between the base year and target years, assuming emissions decline linearly. Second, we set 2020 as the reference year where emissions are at 100%. Finally, we quantify the target ambition as the area between the targeted company emission trajectory and the average of IPCC\u2019s 1.5 degree Celsius warming emission scenarios:\n\nIllustration of emission target quantification for company A. The red area is the magnitude of ambition. Since the targeted emission trajectory is higher than the 1.5\u00b0 degree trajectory, the ambition is negative.\n\nPositive target ambition values indicate targets surpassing the reference scenario\u2019s ambition, negative target ambition values fall short of the reference scenario\u2019s ambition, and values of zero indicate an exact match with the average of IPCC\u2019s 1.5 degree Celsius warming emission scenarios.\n\nWe perform OLS using the python package statsmodels (version 0.14.1) to estimate the effect size of using carbon credits on the companies\u2019 climate target ambitions. We estimate:\n\nwhere i indexes the companies, Yi is a company\u2019s climate target ambition (eq. (2)), Xi is the number of carbon credits a company retired in CDP\u2019s 2023 reporting cycle, Ci are the control variables, and \u03f5i represents the error term, capturing unobserved factors affecting Yi. We control for revenue, sector, continent of headquarters, and share of emissions covered by intermediate targets on the path to net zero. We convert the categorical variables for the sector (automobile, oil and gas, and airlines) and the continent of headquarters (Asia, Europe, Latin America, and North America) into binary indicator columns (i.e. one-hot encoding). That means in the regression, each categorical variable equals 1 if a company belongs to a specific sector or is headquartered in a particular region and 0 otherwise. We include the share of emissions covered by intermediate targets (i.e. emission targets that are no net zero targets) to avoid systematically favouring companies that set only long-term net zero targets without intermediate goals. For instance, a company with a net zero target for 2050 but no intermediate targets would appear to have higher target ambition than the exemplary company depicted in Fig.\u00a06, as the red area decreases without Target 1.\n\nBesides the quantitative evaluation of how many carbon credits companies retire, we qualitatively evaluate how companies use carbon credits over time using the qualitative data analysis software Atlas.ti. We manually scanned through 488 corporate sustainability and annual reports for the years 2014\u22122023 using the search words \u201coffset\", \u201ccarbon credit\", \u201ccarbon market\", \u201ccompensate\", and \u201ccompensation\". We assigned codes when the text passage revealed the purpose of voluntary carbon credit retirement. We tagged 522 text passages on carbon credit usage in 238 distinct documents.\n\nWe manually classify the use case of carbon credits into five categories:\n\nRetirement to meet emission targets: Companies plan to use carbon credits to reach an emission target. The quantity of retired carbon credits depends on the gap to target completion.\n\nOffsetting fixed portion of emissions: Companies define a fixed portion of their emissions to offset (e.g. scope 1, scope 2, specific product).\n\nEmployees\u2019 business travel\n\nCustomer Offsetting: Companies either offer customers the service to purchase carbon credits during checkout (mostly business to consumer) or offer pre-offset products (both business to consumer and business to business).\n\nOther: Offset usage that does not fit in other categories. These are often pilot projects to source carbon credits in preparation for compliance schemes or fixed-term marketing events.\n\nPrices companies pay for carbon credits are not publicly available at a granular level. Therefore, we estimate feasible price ranges by using the lowest prices reported by companies (USD 3.72 by easyJet59) in our sample as the low end of the price range and average credit prices 2022 by project type reported by Ecosystem Marketplace60 as the upper end of the price range. Using Ecosystem Marketplace\u2019s data as an upper bound is a feasible assumption for the upper end of the feasible price range since companies in our sample are multinational companies purchasing relatively large quantities of carbon credits. Therefore, we assume these companies do not pay prices above the market average. We estimate the lower (boundarylow) and upper (boundaryhigh) boundary of the feasible carbon credit cost range for company i purchasing carbon credits from project type n as:\n\nTo put the costs of carbon credits in perspective, we compare them with companies\u2019 CAPEX and costs of emission allowances under compliance emission trading schemes. CAPEX, which represents the funds a company spends to buy or improve assets, helps assess whether carbon credit costs are substantial enough to compete with investments in internal decarbonisation. Additionally, by comparing these costs to compliance emission pricing mechanisms, we evaluate whether carbon offsetting incentivises companies to accelerate decarbonisation efforts beyond existing regulation.\n\nWe estimate the costs for emission allowances in European emission trading schemes (EU-ETS, UK-ETS, and Switzerland-ETS) by multiplying the number of allowances a company purchased under a specific ETS with average allowance prices in 2022. Companies disclose the number of allocated allowances, purchased allowances, and overall emissions under ETSs in the CDP survey40. Average ETS prices in 2022 are based on the World Bank\u2019s carbon pricing database (EU ETS: USD 86.52, UK ETS: USD 98.99; Switzerland: 65.59 USD)46. The only exception is easyJet, which does not disclose the number of purchased allowances in the CDP report. Here we determine the number of purchased emission allowances as the difference between scope 1 emissions under the different ETSs disclosed to CDP40 and publicly available information on allocated emission allowances61,62,63.\n\nFurther information on research design is available in the\u00a0Nature Portfolio Reporting Summary linked to this article.",
+            "section_image": [
+                "https:////media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41467-025-62970-w/MediaObjects/41467_2025_62970_Fig6_HTML.png"
+            ]
+        },
+        {
+            "section_name": "Data availability",
+            "section_text": "All relevant data to reproduce plots can be found in our\u00a0supplementary data and under https://github.com/n-stolz/nature_comms_negligible_role_carbon_offsetting.git. The data used in this article includes data points from CDP. The reproduction of any part of the CDP data by any third party is prohibited.\n\nThe data can be cited as: Niklas Stolz and Benedict Probst, The negligible role of carbon offsetting in corporate climate strategies, https://github.com/n-stolz/nature_comms_negligible_role_carbon_offsetting.git, https://doi.org/10.5281/zenodo.15634074, 2025.",
+            "section_image": []
+        },
+        {
+            "section_name": "Code availability",
+            "section_text": "All relevant code can be found under https://github.com/n-stolz/nature_comms_negligible_role_carbon_offsetting.git.",
+            "section_image": []
+        },
+        {
+            "section_name": "References",
+            "section_text": "Stechemesser, A. et al. Climate policies that achieved major emission reductions: global evidence from two decades. Science 385, 884\u2013892 (2024).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nvan Benthem, A. A., Crooks, E., Giglio, S., Schwob, E. & Stroebel, J. The effect of climate risks on the interactions between financial markets and energy companies. Nat. Energy 7, 690\u2013697 (2022).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nNet Zero Tracker. Net Zero Tracker Net Zero Stocktake 2023. https://zerotracker.net/analysis/net-zero-stocktake-2023 (2023).\n\nIvanova, I. Delta Faces Lawsuit Alleging Its \u201ccarbon-neutral\" Claim Is Greenwashing. https://www.cbsnews.com/news/delta-lawsuit-cabon-neutral-greenwashing-carbon-offsets/ (2023).\n\nTaft, M. A Trojan Horse Of Legitimacy: Shell Launches A \u2018climate Tech\u2019 Startup Advertising Jobs In Oil And Gas. https://www.theguardian.com/us-news/2024/feb/26/shell-climate-tech-startup-onward-oil-gas-jobs-greenwashing (2024).\n\nSBTi. SBTi Corporate Net-Zero Standard v1.1 https://files.sciencebasedtargets.org/production/files/Legacy_Net-Zero-Standard_v1.1.pdf (2023).\n\nFankhauser, S. What next on net zero? One Earth 4, 1520\u20131522 (2021).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDiemen, R. V. Annex I: Glossary. In Climate Change 2022\u2014Mitigation of Climate Change, 1793\u20131820 (Cambridge University Press, 2023).\n\nTrouwloon, D., Streck, C., Chagas, T. & Martinus, G. Understanding the use of carbon credits by companies: a review of the defining elements of corporate climate claims. Glob. Chall. 7, 2200158 (2023).\n\nArticle\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLakhani, N. This Article Is More Than 2\u2009Months Old Corporations Invested In Carbon Offsets That Were \u2018likely Junk\u2019, Analysis Says. https://www.theguardian.com/environment/article/2024/may/30/corporate-carbon-offsets-credits (2024).\n\nStanway, D. Greenpeace Accuses China Oil And Gas Firms Of \u2019greenwashing\u2019 LNG Purchase. https://www.reuters.com/sustainability/climate-energy/greenpeace-accuses-china-oil-gas-firms-greenwashing-lng-purchases-2023-11-27/ (2023).\n\nDurfrasne, G. Why Carbon Offsetting Undermines Climate Targets - Joint NGO Statement. https://newclimate.org/sites/default/files/2024-07/Joint-CSO-Statement-Offsetting.pdf (2024).\n\nGray, R., Kouhy, R. & Lavers, S. Corporate social and environmental reporting: a review of the literature and a longitudinal study of UK disclosure. Account. Audit. Account. J. 8, 47\u201377 (1995).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nPatten, D. M. The relation between environmental performance and environmental disclosure: a research note. Account. Organ. Soc. 27, 763\u2013773 (2002).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLindblom, C. K. The Implications Of Organizational Legitimacy For Corporate Social Performance And Disclosure. https://www.scirp.org/reference/referencespapers?referenceid=1905311 (1994).\n\nKotek, K., Schoenberg, A. M. & Schwand, C. CSR behavior: between altruism and profit maximization. In Innovation Management and Corporate Social Responsibility: Social Responsibility as Competitive Advantage (ed. Altenburger, R.) 159\u2013169 (Springer International Publishing, 2018).\n\nBaker, T. On the genealogy of moral hazard. Tex. Law Rev. 75, 237\u2013292 (1996).\n\n\n                    Google Scholar\u00a0\n                \n\nQian, W. & Schaltegger, S. Revisiting carbon disclosure and performance: legitimacy and management views. Br. Account. Rev. 49, 365\u2013379 (2017).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDownar, B., Ernstberger, J., Reichelstein, S., Schwenen, S. & Zaklan, A. The impact of carbon disclosure mandates on emissions and financial operating performance. Rev. Account. Stud. 26, 1137\u20131175 (2021).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nHsueh, L. Voluntary climate action and credible regulatory threat: evidence from the carbon disclosure project. J. Regul. Econ. 56, 188\u2013225 (2019).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nHaque, F. & Ntim, C. G. Executive compensation, sustainable compensation policy, carbon performance and market value. Br. J. Manag. 31, 525\u2013546 (2020).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBelkhir, L., Bernard, S. & Abdelgadir, S. Does GRI reporting impact environmental sustainability? a cross-industry analysis of CO2 emissions performance between GRI-reporting and non-reporting companies. Manag. Environ. Qual. Int. J. 28, 138\u2013155 (2017).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDahlmann, F., Branicki, L. & Brammer, S. Managing carbon aspirations: the influence of corporate climate change targets on environmental performance. J. Bus. Ethics 158, 1\u201324 (2019).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nIoannou, I., Li, S. X. & Serafeim, G. The effect of target difficulty on target completion: the case of reducing carbon emissions. Account. Rev. 91, 1467\u20131492 (2016).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKlaa\u00dfen, L., Lohm\u00fcller, C. & Steffen, B. Assessing corporate climate action: corporate climate policies and company-level emission reductions. PLOS Clim. 3, e0000458 (2024).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWorld Resources Institute & World Business Council for Sustainable Development. The Greenhouse Gas Protocol: A Corporate Accounting and Reporting Standard, Revised Edition. https://ghgprotocol.org/corporate-standard (2024).\n\nAscui, F., Brander, M., Cojoianu, T. & Li, Q. Moral hazard and the market-based method: does using REAs affect corporate emissions performance? Acad. Manag. Proc. 2021, 15686 (2021).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBj\u00f8rn, A., Lloyd, S. M., Brander, M. & Matthews, H. D. Renewable energy certificates threaten the integrity of corporate science-based targets. Nat. Clim. Change 12, 539\u2013546 (2022).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBrander, M., Gillenwater, M. & Ascui, F. Creative accounting: a critical perspective on the market-based method for reporting purchased electricity (scope 2) emissions. Energy Policy 112, 29\u201333 (2018).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nGillenwater, M., Lu, X. & Fischlein, M. Additionality of wind energy investments in the U.S. voluntary green power market. Renew. Energy 63, 452\u2013457 (2014).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nEcosystem Marketplace. All in on Climate: The Role of Carbon Credits in Corporate Climate Strategies. https://www.ecosystemmarketplace.com/publications/2023-em-all-in-on-climate-report/ (2023).\n\nSylvera. Carbon Credits: Permission to Pollute, or Pivotal for Progress? - Does Investment In Carbon Credits Hinder Decarbonization Among The World\u2019s Largest Companies?. https://www.sylvera.com/reports/carbon-credits-and-decarbonization (2023).\n\nMSCI. Corporate Emission Performance and the Use of Carbon Credits. https://www.msci.com/research-and-insights/paper/corporate-emissions-performance-and-the-use-of-carbon-credits (2023).\n\nEngler, D., Gutsche, G., Simixhiu, A. & Ziegler, A. On the relationship between corporate CO2 offsetting and pro-environmental activities in small- and medium-sized firms in Germany. Energy Econ. 118, 106487 (2023).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nProbst, B. S. et al. Systematic assessment of the achieved emission reductions of carbon crediting projects. Nat. Commun. 15, 9562 (2024).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nTrencher, G., Nick, S., Carlson, J. & Johnson, M. Demand for low-quality offsets by major companies undermines climate integrity of the voluntary carbon market. Nat. Commun. 15, 6863 (2024).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBerger-Schmitz, Z., George, D., Hindal, C., Perkins, R. & Travaille, M. What explains firms\u2019 net zero adoption, strategy and response? Bus. Strategy Environ. 32, 5583\u20135601 (2023).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nH\u00f6gelund, R. & Mitchel-Larson, E. Bridging The Ambition Gap: A Framework For Scaling Corporate Funds For Carbon Removal And Wider Climate Action. https://carbongap.org/wp-content/uploads/2022/11/Ambition_Gap_Report_Nov22.pdf (2022).\n\nOck, H. L. The Promise Of Voluntary Carbon Markets Unlocking Finance For The Global South May Be A Myth. https://newclimate.org/news/the-promise-of-voluntary-carbon-markets-unlocking-finance-for-the-global-south-may-be-a-myth (2024).\n\nCDP. CDP: Public Climate Change Dataset 2023. https://www.cdp.net/en/disclose/question-bank/climate-change (2023).\n\nBP. Reimagining Energy for People and Our Planet. https://www.bp.com/content/dam/bp/business-sites/en/global/corporate/pdfs/sustainability/group-reports/bp-sustainability-report-2020.pdf (2020).\n\nDelta. 2020 ESG Report. https://www.delta.com/content/dam/delta-www/about-delta/corporate-responsibility/2020-esg-report.pdf (2020).\n\nEni. Eni for a Just Trainsition 2023. https://www.eni.com/content/dam/enicom/documents/eng/sustainability/2023/eni-for-2023-just-transition-eng.pdf (2023).\n\nShell. Sustainability Report 2023. https://www.shell.com/sustainability/reporting-centre/reporting-centre-archive/_jcr_content/root/main/section_2106585602/tabs/tab/text_copy/links/item0.stream/1742906426699/4ef5cfa607e5e308ad8a68fc3ddffbe6342f8fa8/shell-sustainability-report-2023.pdf (2023).\n\nInpex. Sustainability Report 2022. https://www.sustainability-report.inpex.co.jp/2022/en/services/downloads.html (2022).\n\nWorld Bank Group. State and Trends of Carbon Pricing Dashboard. https://carbonpricingdashboard.worldbank.org/compliance/price (2023).\n\nDelta. ESG Report 2023. https://esghub.delta.com/content/esg/en/2023/home.html (2023).\n\nUNFCCC. Regional Climate Week Asia-Pacific - The Role of Carbon Credits. https://unfccc.int (2023).\n\nEuropean Parliament & Council. Directive (EU) 2024/825 of the European Parliament and of the Council of 28 February 2024 amending Directives 2005/29/EC and 2011/83/EU As Regards Empowering Consumers For The Green Transition Through Better Protection Against Unfair Practices And Through Better Information. https://eur-lex.europa.eu/eli/dir/2024/825/oj/eng (2024).\n\nDamert, M., Paul, A. & Baumgartner, R. J. Exploring the determinants and long-term performance outcomes of corporate carbon strategies. J. Clean. Prod. 160, 123\u2013138 (2017).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDoda, B., Gennaioli, C., Gouldson, A., Grover, D. & Sullivan, R. Are corporate carbon management practices reducing corporate carbon emissions? Corp. Soc. Responsib. Environ. Manag. 23, 257\u2013270 (2016).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nCallery, P. J. The influence of strategic disclosure on corporate climate performance ratings. Bus. Soc. 62, 950\u2013988 (2023).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nGallego-\u00c1lvarez, I., Garc\u00eda-S\u00e1nchez, I. M. & da Silva Vieira, C. Climate change and financial performance in times of crisis. Bus. Strategy Environ. 23, 361\u2013374 (2014).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKlaa\u00dfen, L. & Stoll, C. Harmonizing corporate carbon footprints. Nat. Commun. 12, 6149 (2021).\n\nArticle\u00a0\n    ADS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBolay, A.-F., Bj\u00f8rn, A., Weber, O. & Margni, M. Prospective sectoral GHG benchmarks based on corporate climate mitigation targets. J. Clean. Prod. 376, 134220 (2022).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDietz, S., Gardiner, D., Jahn, V., & Noels, J. Carbon Performance Assessment Of Oil & Gas Producers: Note On Methodology. https://www.transitionpathwayinitiative.org/publications/uploads/2024-carbon-performance-assessment-of-oil-and-gas-producers-note-on-methodology.pdf (2021).\n\nByers, E. et al. AR6 Scenarios Database. https://iiasa.ac.at/models-tools-data/ar6-scenario-explorer-and-database (2022).\n\nBj\u00f8rn, A., Lloyd, S. & Matthews, D. From the Paris agreement to corporate climate commitments: evaluation of seven methods for setting \u2018science-based\u2019 emission targets. Environ. Res. Lett. 16, 054019 (2021).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nGwyn Topham. Easyjet To Offset Carbon Emissions From All Its Flights. https://www.theguardian.com/business/2022/sep/26/easyjet-will-stop-offsetting-carbon-emissions-from-planes-roadmap-net-zero (2019).\n\nEcosystem-Marketplace. 2023 State of the Voluntary Carbon Markets Report: Paying for Quality. https://www.ecosystemmarketplace.com/publications/state-of-the-voluntary-carbon-market-report-2023/ (2023).\n\nDepartment for Energy Security & Net Zero. UK ETS Aviation Allocation Table for the 2021 to 2025 Allocation Period. https://www.gov.uk/csv-preview/67da8abc594182179fe087ee/uk-ets-aviation-allocation-table-march-2025.csv (2024).\n\nFederal Office for the Environment. Emissions Trading System for Aircraft Operators. https://www.bafu.admin.ch/bafu/en/home/topics/climate/info-specialists/reduction-measures/ets/aviation.html (2024).\n\nEuropean Commission. Commission Decision of 13 December 2021 on instructing the Central Administrator of the European Union Transaction Log to enter the national aviation allocation tables of Belgium, Bulgaria, Czechia, Denmark, Germany, Estonia, Ireland, Greece, Spain, France, Croatia, Italy, Cyprus, Latvia, Lithuania, Luxembourg, Hungary, Malta, Netherlands, Austria, Poland, Portugal, Romania, Slovenia, Slovakia, Finland and Sweden into the European Union Transaction Log 2022/C 74/04. https://eur-lex.europa.eu/legal-content/EN/TXT/?uri=uriserv%3AOJ.C_.2022.074.01.0006.01.ENG&toc=OJ%3AC%3A2022%3A074%3ATOC (2022).\n\neasyJet. Annual Report 2022. https://s203.q4cdn.com/522538739/files/shareholder_docs/2023/annual-report-2022.pdf (2022).\n\nDownload references",
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+        },
+        {
+            "section_name": "Acknowledgements",
+            "section_text": "Niklas Stolz is part of SPEED2ZERO, a Joint Initiative co-financed by the ETH Board. We would like to express our gratitude to Lambert Schneider, Malte Toetzke, and Volker Hoffmann for their valuable input and insightful discussions that contributed to the development of this work.",
+            "section_image": []
+        },
+        {
+            "section_name": "Funding",
+            "section_text": "Open access funding provided by Swiss Federal Institute of Technology Zurich.",
+            "section_image": []
+        },
+        {
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+            "section_text": "Group for Sustainability and Technology, ETH Zurich, 8092, Zurich, Switzerland\n\nNiklas Stolz\u00a0&\u00a0Benedict S. Probst\n\nNet Zero Lab, Max Planck Institute for Innovation and Competition, Munich, Germany\n\nBenedict S. Probst\n\nCambridge Centre for Environmental, Energy and Natural Resource Governance, University of Cambridge, Cambridge, UK\n\nBenedict S. Probst\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nN.S. designed and led the implementation of the study and collected and analysed the data. N.S. and B.S.P. developed the methodology and wrote the manuscript.\n\nCorrespondence to\n                Niklas Stolz.",
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+            "section_text": "Stolz, N., Probst, B.S. The negligible role of carbon offsetting in corporate climate strategies.\n                    Nat Commun 16, 7963 (2025). https://doi.org/10.1038/s41467-025-62970-w\n\nDownload citation\n\nReceived: 04 November 2024\n\nAccepted: 05 August 2025\n\nPublished: 10 September 2025\n\nVersion of record: 10 September 2025\n\nDOI: https://doi.org/10.1038/s41467-025-62970-w\n\nAnyone you share the following link with will be able to read this content:\n\nSorry, a shareable link is not currently available for this article.\n\n\n\n\n                            Provided by the Springer Nature SharedIt content-sharing initiative\n                        ",
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0c0fdd1f1980a187e682cbf3e5e869fcf82f48c1168f402cd0132e7122adb5fe/metadata.json

@@ -0,0 +1,152 @@
+{
+    "title": "Direct bandgap quantum wells in hexagonal Silicon Germanium",
+    "pre_title": "Direct bandgap quantum wells in hexagonal Silicon Germanium",
+    "journal": "Nature Communications",
+    "published": "19 June 2024",
+    "supplementary_0": [
+        {
+            "label": "Supplementary Information",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-024-49399-3/MediaObjects/41467_2024_49399_MOESM1_ESM.pdf"
+        },
+        {
+            "label": "Reporting Summary",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-024-49399-3/MediaObjects/41467_2024_49399_MOESM2_ESM.pdf"
+        },
+        {
+            "label": "Lasing Reporting Summary",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-024-49399-3/MediaObjects/41467_2024_49399_MOESM3_ESM.pdf"
+        },
+        {
+            "label": "Peer Review File",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-024-49399-3/MediaObjects/41467_2024_49399_MOESM4_ESM.pdf"
+        }
+    ],
+    "supplementary_1": NaN,
+    "supplementary_2": NaN,
+    "source_data": [
+        "https://doi.org/10.5281/zenodo.10839570"
+    ],
+    "code": [
+        "https://www.vasp.at/",
+        "https://doi.org/10.5281/zenodo.10839570"
+    ],
+    "subject": [
+        "Nanowires",
+        "Quantum optics",
+        "Semiconductor lasers",
+        "Silicon photonics"
+    ],
+    "license": "http://creativecommons.org/licenses/by/4.0/",
+    "preprint_pdf": "https://www.researchsquare.com/article/rs-3875137/v1.pdf?c=1718881689000",
+    "research_square_link": "https://www.researchsquare.com//article/rs-3875137/v1",
+    "nature_pdf": "https://www.nature.com/articles/s41467-024-49399-3.pdf",
+    "preprint_posted": "09 Feb, 2024",
+    "research_square_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Silicon is indisputably the most advanced material for scalable electronics, but it is a poor choice for active photonic applications, due to its indirect band gap. The recently developed hexagonal (hex-)Si1\u2212xGex semiconductor features a direct bandgap at least for x > 0.65, and the realization of quantum heterostructures would unlock new opportunities for advanced optoelectronic devices based on the SiGe system. Here, we demonstrate the synthesis and characterization of direct bandgap quantum wells (QW)s realized in the hex-Si1\u2212xGex system. Photoluminescence experiments on hex-Ge/Si0.2Ge0.8 QWs demonstrate quantum confinement in the hex-Ge segment with type-I band alignment, showing light emission up to room temperature. Moreover, the tuning range of the QW emission energy can be extended using hex-Si1\u2212xGex/Si1\u2212yGey QWs with additional Si in the well. These experimental findings are supported with ab initio bandstructure calculations. A direct bandgap with type-I band alignment is pivotal for the development of novel low-dimensional light emitting devices based on hex-Si1\u2212xGex alloys, which have been out of reach for this material system until now.Physical sciences/Nanoscience and technology/Nanoscale materials/NanowiresPhysical sciences/Optics and photonics/Optical materials and structures/Silicon photonicsPhysical sciences/Nanoscience and technology/Nanoscale devices/Nanophotonics and plasmonicsPhysical sciences/Optics and photonics/Lasers, LEDs and light sources/Semiconductor lasers",
+            "section_image": []
+        },
+        {
+            "section_name": "Additional Declarations",
+            "section_text": "There is NO Competing Interest.",
+            "section_image": []
+        },
+        {
+            "section_name": "Supplementary Files",
+            "section_text": "HexGeSiGeQWsExtendedData.pdf",
+            "section_image": []
+        }
+    ],
+    "nature_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Silicon is indisputably the most advanced material for scalable electronics, but it is a poor choice as a light source for photonic applications, due to its indirect band gap. The recently developed hexagonal Si1\u2212xGex semiconductor features a direct bandgap at least for x\u2009>\u20090.65, and the realization of quantum heterostructures would unlock new opportunities for advanced optoelectronic devices based on the SiGe system. Here, we demonstrate the synthesis and characterization of direct bandgap quantum wells realized in the hexagonal Si1\u2212xGex system. Photoluminescence experiments on hex-Ge/Si0.2Ge0.8 quantum wells demonstrate quantum confinement in the hex-Ge segment with type-I band alignment, showing light emission up to room temperature. Moreover, the tuning range of the quantum well emission energy can be extended using hexagonal Si1\u2212xGex/Si1\u2212yGey quantum wells with additional Si in the well. These experimental findings are supported with ab initio bandstructure calculations. A direct bandgap with type-I band alignment is pivotal for the development of novel low-dimensional light emitting devices based on hexagonal Si1\u2212xGex alloys, which have been out of reach for this material system until now.",
+            "section_image": []
+        },
+        {
+            "section_name": "Introduction",
+            "section_text": "Electronic devices based on silicon have been the driver for the revolution in information technology witnessed today. However, with their standard cubic-diamond crystal structure, silicon, germanium, and SiGe-alloys are all indirect band gap semiconductors, impeding the use of silicon-based materials for lasers and optical amplifiers for integrated photonics1. Several strategies have been investigated for integrating light emitting materials on silicon, including III-V2,3, GeSn4,5,6,7,8,9, strained Ge7,10, and SiGe quantum wells and dots11,12,13,14,15,16,17, but remain challenging due to various reasons. When transformed into the hexagonal crystal structure, the hex-Si1\u2212xGex alloys18 are direct bandgap semiconductors with the fundamental bandgap at the \u0393-point. The hex-Si1\u2212xGex compositional family shows tunable light emission from 1.8\u2009\u03bcm to 3.4\u2009\u03bcm and features a nanosecond radiative lifetime18. As such, hex-Si1\u2212xGex stands out in the field of group IV photonics as a direct bandgap semiconductor with a relatively large energy difference between the direct and indirect conduction band minima, up to 0.3 eV for hex-Ge19,20. Additional favorable properties of hex-Si1\u2212xGex include its low surface recombination velocity21, large theoretical Land\u00e9 g-factor of 1822, and the potential to fabricate structures from nuclear spin-free isotopes23, which is important for applications in quantum information.\n\nQuantum confinement in direct bandgap semiconductors has stood at the cradle of many photonic devices such as single photon quantum dot (QD) emitters24,25,26,27, quantum well (QW) lasers28,29 and colloidal QD LED display technology30,31,32. These direct bandgap low dimensional structures have been responsible for major advances in science and constitute a toolbox for many optoelectronic and quantum photonic devices33,34, allowing for tunable and narrow band emission, and the concentration of charge carriers.\n\nHere, we show the synthesis of hex-SiGe quantum wells, and we demonstrate quantization of the energy levels with type-I band alignment between the hex-Si1\u2212xGex well (0.9\u2009<\u2009x\u2009<\u20091.0) and the hex-Si1\u2212yGey barrier (0.7\u2009<\u2009y\u2009<\u20090.8). We observe broad tunability of the QW emission from 3.4\u2009\u03bcm for hex-Ge/Si0.2Ge0.8 to 2.0\u2009\u03bcm for hex-Si0.1Ge0.9/Si0.3Ge0.7, which may be further extended down towards 1.5\u2009\u03bcm, the limits of which are a subject of future investigations. Most notably, we confirm direct bandgap emission from the QWs by observing a subnanosecond photoluminescence lifetime, comparable with direct bandgap emission in bulk hex-SiGe. Our experimental data are complemented by ab initio density functional theory and quasiparticle calculations of the bandstructure of hex-Ge/Si0.25Ge0.75 QWs, showing a direct bandgap with a large directness, defined to be the separation between the \\(\\bar{\\Gamma }\\) minimum and the nearest indirect conduction band minimum. Theory confirms a type-I heterostructure and carrier confinement in the hex-Ge layers, with almost identical valence and conduction band offsets. Our hex-Ge/Si0.2Ge0.8 QWs thus can serve as a textbook example demonstrating quantum confinement.",
+            "section_image": []
+        },
+        {
+            "section_name": "Results",
+            "section_text": "We have embedded coaxial hex-Ge quantum wells in hex-Si0.2Ge0.8 barriers, grown epitaxially on the \\(\\{1\\overline{1}00\\}\\) m-plane facets of wurtzite (WZ) GaAs core nanowires (NWs)18,35, as shown in Fig.\u00a01a. The goal is to create a QW of hex-Ge, as shown in Fig.\u00a01b. A Scanning Electron Microscopy (SEM) image in Fig.\u00a01c illustrates the dimensions of the resulting structures. The Ge/Si0.2Ge0.8 shells in these NWs are doped with arsenic, at a doping level below 2.5\u2009\u00d7\u20091018\u2009cm\u22123 (See \u201cMethods\u201d for details about the growth).\n\na Schematic illustration of the GaAs/Si0.2Ge0.8/Ge/Si0.2Ge0.8 core-multishell nanowires. All interfaces are orthogonal to \\(\\langle 1\\overline{1}00\\rangle\\) directions. b Schematic band alignment of the different materials. The electrons and holes are confined in the hex-Ge layer due to type-I alignment with the surrounding hex-Si0.2Ge0.8, as will be proven in this manuscript. Approximate values of the bandgap and offsets are given. c 30-degree tilted scanning electron micrograph of a NW array. Within these NWs, a (12\u2009\u00b1\u20093) nm Ge/Si0.2Ge0.8 QW is embedded.\n\nThe Ge/Si0.2Ge0.8 QWs are characterized by cross-sectional Scanning Transmission Electron Microscopy (STEM) along two different zone axes. When imaged along the [0001] zone axis, the Ge/Si0.2Ge0.8 QW is visible as a hexagon, an example is given in Fig.\u00a02a, and other data is shown in Fig.\u00a0S2. We note that the Si0.2Ge0.8 barrier has composition fluctuations, Si-rich spokes connect the corners of the GaAs with the outer corners of the NW36. Moreover, as highlighted in the inset of Fig.\u00a02a, the thickness of the Ge QW varies between the different facets. Fluctuations in QW thickness on different facets have also been reported for other material systems37,38, possibly resulting in charge carrier localization in the thickest well39. The QW thickness varies between 10 and 30\u00a0nm by changing the growth time, as shown in Fig.\u00a02b, while the Si0.2Ge0.8 barrier thickness always exceeds 50\u00a0nm. For each sample, we observe a distribution of thicknesses, mainly due to the facet-to-facet fluctuation within one NW, which is larger than the deviation in average QW thickness between different NWs of the same sample. The probability distribution is bimodal for some samples, with two different Ge QW thicknesses that are most likely. However, the bimodal distribution does not appear for all samples, and therefore the average is taken as a measure of the QW thickness.\n\na False-colored HAADF-STEM image of a cross-sectional lamella, viewing the Ge QW along the [0001] zone axis. Inset shows that Ge QWs on neighboring facets have different thicknesses. b Growth rate curve for Ge/Si0.2Ge0.8 QWs. The thicknesses of individual facets, all measured in images acquired along the [0001] zone axis, are indicated with the colored data points. Colored areas show approximate probability distributions, obtained from these data points by Kernel smoothing. c False-colored HAADF-STEM image of a cross-sectional lamella, viewing the QW along the \\([11\\overline{2}0]\\) zone axis. The core of the NW is on the left. Locations with local hexagonal (ABABA, blue), cubic (ABCA, green), and twinned cubic boundary (ABCBA, pink) stacking are indicated with circles. The pink arrow highlights a defect that starts in the Ge QW. d X-ray diffraction reciprocal space map around the hexagonal \\([10\\overline{1}5]\\) reflection. The peak position does not match Vegard\u2019s rule (dashed line), indicating pseudomorphic strain relaxation.\n\nWhen imaged along the \\([11\\overline{2}0]\\) zone axis, the Ge/Si0.2Ge0.8 QW is visible as a vertical stripe in TEM (Fig.\u00a02c). The thickness of the QW is not constant along the length of the NW (Fig.\u00a0S3), and the roughness on the \\(\\{1\\overline{1}00\\}\\) interface between Ge/Si0.2Ge0.8 is estimated from Fig.\u00a02c to be a few nm. Additionally, the \\([11\\overline{2}0]\\) zone axis allows to distinguish between hexagonal and cubic stacking. The hexagonal stacking is not continuous along the [0001] direction but is segmented due to the inclusion of cubic defects. Most of these are I3 defects, which nucleate either on the GaAs-Si0.2Ge0.8 interface or at random positions in the shell40,41. An example is indicated with the arrow in Fig.\u00a02c. A statistical analysis of the atomic stacking shows a broad distribution in the length of segments with the hexagonal stacking (Fig.\u00a0S4a, b). In contrast, only narrow segments of coherent cubic stacking are observed.\n\nX-ray diffraction (XRD) is used to study the crystalline quality and lattice constants from a large ensemble of NWs. The diffraction spectra of all samples are similar, indicating comparable crystalline quality between samples (Fig.\u00a0S4c, d). A reciprocal space map around the hexagonal \\([10\\overline{1}5]\\) reflection shows a single peak (Fig.\u00a02d), despite the 0.8% lattice mismatch between Ge and Si0.2Ge0.8. Increasing the Ge thickness does not significantly influence the lattice parameters of the NWs (Fig.\u00a0S5a). Instead, the c-lattice constant depends on the thickness of the Si0.2Ge0.8 barriers (Fig.\u00a0S5b). These observations indicate that there is pseudomorphic strain relaxation in the Ge/Si0.2Ge0.8 structures.\n\nThe Si0.2Ge0.8 barriers have smaller lattice constants than the Ge QW, and the Ge is therefore compressed along the \\(\\langle 11\\overline{2}0\\rangle\\) and \u30080001\u3009 directions. Pseudomorphic strain relaxation in the Ge QW results in an increased lattice constant along the \\(\\langle 1\\overline{1}00\\rangle\\) direction. This radial relaxation becomes more pronounced if the Ge thickness is increased, as confirmed by the Geometric Phase Analysis (GPA) of TEM images (Fig.\u00a0S5c, d).\n\nThe optical properties of the Ge/Si0.2Ge0.8 QW samples have been studied by low-temperature photoluminescence (PL) as a function of the QW thickness in Fig.\u00a03a. We observe that the emission energy consistently blueshifts with decreasing QW growth time demonstrating increasing quantum confinement with decreasing thickness. Moreover, all QW emission peaks are positioned between the emission originating from the bulk hex-Ge and hex-Si0.2Ge0.8 reference samples, thus providing experimental evidence for type-I band alignment. We note that for type-II band alignment, one would expect emission below the energy of (strained) bulk hex-Ge42. The width of the QW emission peaks is larger than that of the reference samples, and for some samples, multiple peaks have been observed; this is probably due to fluctuations in QW thickness and, for the wider QWs, the presence of the second confined level. The intensity of the QW emission exceeds that of the reference sample (see Fig.\u00a0S6a), indicating that many carriers diffuse towards the QWs. The relation between emission energy and QW thickness is shown in Fig.\u00a03b, showing a blueshift with decreasing thickness, consistent with a shift due to confinement energy in a QW.\n\na Ge/Si0.2Ge0.8 PL spectrum for varying growth time at low temperature (T\u2009\u2248\u20094 K) and low excitation density (P\u226465\u2009W cm\u22122), b The PL emission versus the QW thicknesses tQW determined from TEM, together with the confinement energy predicted from theory shifted up by 60 meV to account for the difference in the theoretical and experimental bandgap of the hex-Ge. The dashed line shows the confinement energies using a simple finite QW model. We also include the reference spectra of bulk-Ge and the bulk Si0.2Ge0.8 barrier as horizontal lines with the FWHM of the spectra shown as horizontal gray bars. Error bars in tQW are the standard deviations presented in Fig.\u00a02b and error bars in the peak energy indicate the FWHM of the emission spectrum.\n\nThe optoelectronic properties of the Ge/Si0.2Ge0.8 QWs are investigated in more detail by power- and temperature-dependent photoluminescence spectroscopy. We focus here on two specific samples: (i) a relatively thin (10\u2009\u00b1\u20094) nm QW showing single peak emission with strong confinement and (ii) a thick (24\u2009\u00b1\u20097) nm QW with small confinement energy and a large separation between the confinement level in the QW and the barrier, as shown in Fig.\u00a04. Besides the emission being between the hex-Ge reference and the Si0.2Ge0.8 barrier, as mentioned before, we observe that the emission peak energy of the (10\u2009\u00b1\u20094) nm QW is nearly independent of both the excitation density in Fig.\u00a04a and the temperature in Fig.\u00a04b. We highlight the (absence of) shift with excitation density in Fig.\u00a04c. At low excitation densities a minor\u2009<\u20095 meV blueshift is observed, followed by a redshift at high excitation. These shifts are likely due to Burstein-Moss band-filling (blueshift) and bandgap renormalization (redshift). Importantly, we do not observe the significant blueshift with increasing excitation density expected for a type-II QW structure43. The absence of such a blueshift provides additional evidence for a type-I band offset. Similar trends have been observed for the other QW samples. The spectra of the thick (24\u2009\u00b1\u20097) nm QW sample are plotted in Fig.\u00a04d as a function of excitation density. At low excitation density, we observe a single emission peak, while with increasing excitation density, the sample evolves from a single to a double peak shape. We attribute the presence of the second peak at increased excitation density to either distinct QW thicknesses e.g., at different facets of the nanowire shells or to the observation of the HH2-C2 transition within the wide quantum well. The behavior of the high energy peak becomes dominant at intermediate excitation densities, while the lower energy peak increases at the highest excitation densities. This could indicate a different density of states of the subbands44, but a detailed analysis is beyond the scope of the present paper. The light-in light-out (LILO) curves for the QWs and the Si0.2Ge0.8 barrier reference sample are introduced in Fig.\u00a04g. While we observe sublinear behavior, the slopes of (0.69\u2009\u00b1\u20090.01) and (0.66\u2009\u00b1\u20090.01) for the (24\u2009\u00b1\u20097) nm and (10\u2009\u00b1\u20094) nm QWs respectively exceed the slope of the barrier reference sample (0.59\u2009\u00b1\u20090.02) (observed for all QW samples shown in Fig.\u00a0S6b). Pure radiative (non-radiative) recombination is expected to yield a slope of 1 (2). A LILO slope below unity is due to an increasing loss of carriers at high excitation, which is most likely due to carrier overflow into cubic insertions, or due to Auger recombination. This behavior deserves further study.\n\na The (10\u2009\u00b1\u20094) nm (2.5 min) low temperature (T\u2009\u2248\u20094\u2009K) QW photoluminescence spectrum as a function of excitation density showing a constant lineshape over two orders of magnitude with the peak position in between the bulk-Ge and Si0.2Ge0.8 barrier reference measurements, b The (10\u2009\u00b1\u20094) nm QW showing a near constant lineshape through temperature with the tail states becoming slightly more significant as the peak intensity quenches at higher temperatures. c The emission peak energy of the (10\u2009\u00b1\u20094) nm QW shows a nearly constant magnitude through excitation density. Initially the peak blueshifts due to band-filling of the QW and then redshift around 100\u2009W cm\u22122, likely due to Bandgap renormalization. d The (24\u2009\u00b1\u20097) nm (9 min) QW spectrum evolves from a single to a double peak with increasing excitation density due to band-filling. Additionally, if the lowest and highest excitation density spectra are compared, we observe no significant shift in the position of the low energy peak. e The (24\u2009\u00b1\u20097) nm QW sample as a function of temperature showing emission up to room temperature. f The Arrhenius plot of the QWs and Si0.2Ge0.8 barrier reference samples measured at an excitation density of 0.88 kW cm\u22122. It can be seen that the temperature behavior of the QWs exceeds the bulk hex-Si0.2Ge0.8 reference. g The Light-In Light-Out (LILO) curves of the QWs and SiGe barrier reference samples measured at 4 K. The slopes of (0.69\u2009\u00b1\u20090.01) and (0.66\u2009\u00b1\u20090.01) for the (24\u2009\u00b1\u20097) nm and (10\u2009\u00b1\u20094) nm QWs respectively exceed the (0.59\u2009\u00b1\u20090.02) of the bulk hex-Si0.2Ge0.8 reference.\n\nWe present the PL as a function of temperature in Fig.\u00a04e. Notably, room temperature emission from an ensemble of NWs with a single coaxial hex-Ge/Si0.2Ge0.8 QW is demonstrated. In the range T\u2009=\u20092.4\u2013100\u2009K, the relative magnitude of the higher energy peak increases, which is likely due to the de-trapping of carriers from the potential landscape due to alloy fluctuations in the Si0.2Ge0.8 barrier, allowing more carriers to diffuse to the QW, while the lower energy QW level is already fully occupied. Above 250 K the low energy peak again becomes more dominant, which is likely due to a higher probability of thermal emission from the higher energy QW level into the barrier, while also allowing the carriers to be even more mobile to find the lowest energy states. The temperature dependence of the integrated PL intensity is shown in Fig.\u00a04f and shows a monotonous decay of the intensity with temperature. This shows that the emission is not phonon-activated, which is a strong indication for direct bandgap emission18. Moreover, the intensity of the QW emission outperforms the emission of the bulk hex-Si0.2Ge0.8 reference sample at elevated temperatures (observed for all QW samples shown in Fig.\u00a0S6c), which is an important advantage for devices e.g., a hex-Ge/Si0.2Ge0.8 QW laser. From the thermal quenching results we estimate the band offset and effective mass of the most shallow confined charge carrier from the activation energies in Fig.\u00a0S6d of three of the widest (approximately infinite) QW samples which are found to be Eoffset\u2009=\u2009(100\u2009\u00b1\u200930)meV and m*\u2009=\u2009(0.03\u2009\u00b1\u20090.02)m0 respectively, which is close to the predicted band offset and effective mass of our ab initio bandstructure calculations presented below.\n\nHaving confirmed quantum confinement and wavelength tunability of emission from the hex-Ge/Si0.2Ge0.8 QWs, we subsequently like to demonstrate type-I confinement in hex-Si0.1Ge0.9/Si0.3Ge0.7 QWs that emit light at even higher energy by making use of alloys with a larger bandgap18. These hex-Si0.1Ge0.9/Si0.3Ge0.7 QWs are realized as coaxial nanowire shells, similar to those presented in Fig.\u00a01. A cross-sectional view of the (5\u2009\u00b1\u20091) nm Si0.1Ge0.9/Si0.3Ge0.7 QW is presented in Fig.\u00a05a, and an overview of all studied Si0.1Ge0.9/Si0.3Ge0.7 QWs is presented in Fig.\u00a0S7. There are two main differences compared to the Ge/Si0.2Ge0.8 system studied. Additional radial contrast lines, which do not terminate at the NW corners, are recognizable in the TEM image. These lines correspond to dislocations, whose occurrence is correlated with the lattice mismatch between the WZ GaAs core and the hex-Si1\u2212xGex shell. Secondly, there is a compositional gradient in the Si1\u2212xGex barrier, where the Si concentration increases with increasing distance to the GaAs core (see Fig.\u00a0S8). Both effects arise from the lattice mismatch in this system, which is either relaxed through dislocations or mitigated by forming a self-assembled compositional gradient buffer layer.\n\na False-colored HAADF-STEM of a cross-sectional lamella, viewing the (5\u2009\u00b1\u20091) nm (5 min) Si0.1Ge0.9/Si0.3Ge0.7 QW in the [0001] zone axis. b Background corrected photoluminescence spectra for varying QW growth time at low temperature (\u2009\u2248\u20094 K) and high excitation density\u2009<\u20090.88 kW cm\u22122. Reference spectra of bulk Si0.1Ge0.9 and Si0.3Ge0.7 are included. c The PL emission versus the QW thicknesses tQW determined from TEM. Spectra of the Si0.1Ge0.9 well and Si0.3Ge0.7 barrier alloys are included as horizontal lines with the FWHM of the spectra as horizontal gray bars. A simple finite QW model is calculated for this heterostructure which shows reasonable agreement with the experiment. Error bars in tQW are the standard deviations presented in Fig.\u00a0S7e and error bars in the peak energy indicate the FWHM of the emission spectrum. d Initial QW lifetime measured using TCSPC for the (5\u2009\u00b1\u20091) nm QW for varying laser fluence with the error bars indicating the standard deviation determined fitting the initial decays presented in Fig.\u00a0S9b.\n\nThe photoluminescence emission from the hex-Si0.1Ge0.9/Si0.3Ge0.7 QW is between the emission of the bulk Si0.1Ge0.9 well material, and the barrier material, as shown in (Fig.\u00a05b), signifying a type-I band offset also for these compositions. We again fit the observed QW emission energies with the conventional finite QW model, showing qualitative agreement in Fig.\u00a05c. This suggests that the band alignment of the broader family of the hex-Si1\u2212xGex/Si1\u2212yGey QWs is of type-I nature.\n\nWe emphasize that the observation of efficient direct bandgap emission is not obvious since theoretical DFT calculations predict18 a radiative lifetime of 20\u2009\u03bcs for hex-Ge. If true, this would comprise the well material of our hex-Ge/SiGe QWs. To obtain experimental evidence for direct bandgap emission, we measure the carrier recombination lifetime using a Time-Correlated Single Photon Counting (TCSPC) system employing a Superconducting Nanowire Single Photon Detector (SNSPD) for the (5\u2009\u00b1\u20091) nm QW (Single nanowire spectrum shown in Fig.\u00a0S9a). We measure the PL lifetime at a lattice temperature of 4 K where the nonradiative recombination rate is expected to vanish since the nonradiative recombination is a thermally activated process by \\({\\tau }_{nr}^{-1}={\\tau }_{nr}^{-1}{e}^{-{E}_{a}/kT}\\). For our QWs, this behavior is experimentally observed as a constant PL-intensity below a temperature of 10 K and at an excitation density of 0.88 kW cm\u22122 in Fig.\u00a04f. We measure the PL decay time under pulsed excitation conditions where the radiative limit is maintained up to much higher temperature as shown by Fadaly et al.18, implying that the measured PL decay time should be equal to the radiative lifetime at 4 K. We present the carrier recombination lifetime in Fig.\u00a05d for varying laser fluence. Importantly, we observe an initial carrier lifetime of\u2009\u2248\u20091 ns for the lowest fluence (Full time decays are provided in Fig.\u00a0S9b), confirming direct bandgap emission. We note that the observation of a decreasing recombination lifetime with increasing excitation density provides additional evidence for radiative recombination governed by 1/\u03c4rad\u2009=\u2009B(n0\u2009+\u2009\u0394n)(p0\u2009+\u2009\u0394p)/\u0394p\u2009\u2248\u2009B\u0394n for high excitation (\u0394n\u2009=\u2009\u0394p\u2009>\u2009>\u2009n0,\u2009p0), in which B is the coefficient for radiative recombination, n0,\u2009p0 are the doping concentrations and \u0394n,\u2009\u0394p are the photoexcited carrier concentrations. On the other hand, the observations in Fig.\u00a05d cannot be explained by a nonradiative recombination mechanism since nonradiative recombination centers get saturated at high excitation, thus increasing the lifetime. We conclude that the observed nanosecond radiative recombination lifetime falls within the same range as that reported by Fadaly et al.18,45 for bulk hex-SiGe nanowires and confirms direct bandgap emission in Si0.1Ge0.9/Si0.3Ge0.7 QWs.\n\nTo examine the band alignment of the experimentally realized hex-Ge/Si0.2Ge0.8 and Si0.1Ge0.9/Si0.3Ge0.7 single QWs, we first calculate the electronic band structure of hex-Ge/Si0.25Ge0.75 multi-quantum well (MQW) structures, with \\((1\\overline{1}00)\\) interfaces, as superlattices (see Fig.\u00a06a). The ab initio calculations are based on Density Functional Theory (DFT) for optimized atomic geometries and an approximate quasiparticle (QP) electronic structure approach to the band structures (see \u201cMethods\u201d for details). The band structures of the different materials and heterostructures are aligned employing their branch points (BPs)46. The Ge/Si0.25Ge0.75 MQW system is the closest approximation of the experimentally realized Ge/Si0.2Ge0.8 QWs, which still allows modeling of the alloy barriers by ordered arrangements of a single Si and three Ge atoms in one Lonsdaleite unit cell. The increase of the average Si incorporation by 5% compared to the experiment increases the barrier heights by approximately 0.05 eV, but has a vanishing effect on the confinement for both carrier types. Within the calculations, the Si0.25Ge0.75 barrier thickness is kept constant at 2\u00a0nm, i.e., 12 monolayers along the \\([1\\overline{1}00]\\) direction, while the Ge well thickness is varied between 4 and 15\u00a0nm. This barrier thickness is sufficient to prevent tunneling of electron and hole wave functions through the barriers47. As a consequence, the Ge layers in the MQW system are electronically decoupled, and the Ge layers can thus be treated as isolated single QWs. The use of thin Si0.25Ge0.75 barriers in the modeling only affects the strain distribution, which is different for the thick Si0.2Ge0.8 barriers in the experiment. This effect is accounted for by applying an external biaxial strain to the Ge/Si0.25Ge0.75 MQW structure of -0.6% and -0.91% along the \\([11\\overline{2}0]\\) and [0001] directions respectively, based on the X-ray diffraction experiments on the realized Ge/Si0.2Ge0.8 QWs (Fig.\u00a0S5a). The studied heterostructure is allowed to relax along the \\([1\\overline{1}00]\\) direction, tending towards\u00a0an \u22480.3% expansion in the well and \u22480.1% contraction in the Si0.25Ge0.75 barrier.\n\na Hexagonal Ge/Si0.25Ge0.75 heterostructure with \\((1\\overline{1}00)\\) interfaces. b Bulk hexagonal Brillouin zone (BZ) and its projection onto the two-dimensional BZ of the \\((1\\overline{1}00)\\) interface. c Direct bandgap band structure of hexagonal 4 nm Ge/ 2 nm Si0.25Ge0.75 multiple quantum well structure (black lines) and bulk Si0.25Ge0.75 (gray area) projected onto the two-dimensional Brillouin zone. The horizontal red line indicates the branching points of the two systems used as energy zero for alignment. d Energies of the lowest electron and highest hole subband at \\(\\bar{\\Gamma }\\) versus Ge thickness in the Ge/Si0.25Ge0.75 heterostructures studied. They are compared with the lowest conduction and highest valence band of the bulk Si0.25Ge0.75 barrier material, see the \u201cMethods\u201d section for an explanation. Dashed lines indicate the extrapolated band-states at infinite Ge well thickness. For comparison, also the energy position of the lowest indirect conduction band minimum outside \\(\\bar{\\Gamma }\\) (dot-dashed line) is given.\n\nThe QP band structure of a (superlattice with a) 4\u00a0nm thick Ge layer is displayed in Fig.\u00a06b, c, clearly showing a direct bandgap with a \\(\\bar{\\Gamma }\\) minimum approximately 0.3 eV below the lowest indirect conduction band minimum which appears near the corner point \\(\\overline{{{{{{{{\\rm{M}}}}}}}}}\\) of the Brillouin zone boundary. We plot the band structure of the MQW together with a background illustrating the projected band structure of the strained Si0.25Ge0.75 bulk. The two band structures are aligned by their BPs. The bands of the Ge/Si0.25Ge0.75 MQW, within the fundamental gap of the projected Si0.25Ge0.75 band structure, describe subbands of electrons and holes, whose wave functions are both localized in the Ge layers. The localization of both the electron and hole wave functions in the Ge well (Fig.\u00a0S10a) clearly indicates type-I band alignment. The type-I behavior is confirmed by the energies for the highest hole subbands and lowest-energy electron subbands at the \\(\\bar{\\Gamma }\\) point, which are presented versus the Ge layer thickness in Fig.\u00a06d. Corresponding band structures for MQW structures with thicker Ge layers are displayed in Fig.\u00a0S10b. Combining this data with the calculated band structure for bulk (strained) hex-Ge, serving as infinitely thick QW, allows us to extract the quantization effects, more precisely the confinement energies of the lowest n\u2009=\u20091 electron and hole levels directly from ab initio band structure calculations. While only one level appears in the narrow QW with a thickness of 4\u00a0nm, a second and third confined level appear in finite QWs starting from a thickness of 8 nm (Fig.\u00a0S10b).\n\nThe band offsets in the conduction band and the valence band of 0.13\u20130.15 eV are nearly equal (Fig.\u00a0S10c). The band offsets can be employed as barrier heights in simplified rectangular finite QW models for electrons and holes. The ab initio confinement energy of electrons (holes) in the QW vary from 72 (36) to 31 (8) meV for thicknesses of 4 and 15\u00a0nm, respectively. These values are much smaller than the offsets, and one therefore may approximate the system as an infinite QW. For the lowest n\u2009=\u20091 levels, the finite band offsets \u0394Ec/h, and the mentioned ab initio confinement energies \u03f5e/h in the finite rectangular-well model allows the extraction of the effective electron/hole masses according to48\n\nas me\u2009\u2248\u20090.05\u2009m0 and mh\u2009\u2248\u20090.13\u2009m0 averaged over all studied QWs. These values are close to those as 0.076 m0 and 0.055 m0 which have been calculated for unstrained bulk hex-Ge along the \\([1\\overline{1}00]\\) direction19. Computations without external strain result in much smaller confinement energies, which indeed are closely related to the bulk effective masses of unstrained hex-Ge.",
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+            ]
+        },
+        {
+            "section_name": "Discussion",
+            "section_text": "The experimental values for the bandgaps of the 4, 6, 8, 11 and 15\u00a0nm Ge/Si0.2Ge0.8 QWs are compared with the calculated results (black dots) in Fig.\u00a03b. For properly comparing theory with experiment, the theoretical bandgaps are shifted with +60 meV to match the calculated bandgap of the hex-Ge well (\u2009\u2248\u20090.30 eV)19 with the experimentally observed bandgap of bulk hex-Ge (\u2009\u2248\u20090.36 eV)18. This shift remains within the error margin of the ab initio DFT calculations (\u2009\u2248\u20090.1 eV or 25%49). Based on the theoretically calculated band offsets and effective masses19,50,51, the emission energy versus thickness is also calculated using a conventional finite QW model (dashed line)52. This simple model is useful to calculate the emission energies for any QW thickness and composition when reasonable values for the band offsets and carrier masses are available and detailed QP calculations are computationally unfeasible.\n\nA qualitative agreement between theory and experiment is obtained, but the experimental emission energies are all higher than the theoretical values. We identify three possible reasons for the deviation between experiment and theory. (1) The Ge QW thicknesses, measured from TEM images, are slightly overestimated (see Fig.\u00a0S3). (2) We do not include an additional confinement energy due to quantization along the length of the NW, due to the inclusion of cubic stacking faults. The alignment between cubic and hexagonal stacking is expected to be of type-I47,53, and every hexagonal segment with a direct bandgap is thus bound by cubic barriers with larger bandgap (Fig.\u00a0S4a). The exact increase of confinement due to the cubic insertions is ambiguous and subject of future investigations. (3) Likely a few percent Si is incorporated in the wells due to interdiffusion of Si between the Si0.2Ge0.8 and the Ge wells, which elevates their bandgap since the bandgap of hex-Si1\u2212xGex alloys is larger than that of hex-Ge18. Moreover, interdiffusion of Si results in a less steep potential at the QW-Barrier interface, which might also increase the confinement energies.\n\nIn conclusion, we have grown coaxial hex-Ge/Si0.2Ge0.8 and Si0.1Ge0.9/Si0.3Ge0.7 QWs showing direct bandgap light emission. We experimentally confirm efficient direct bandgap emission by the temperature dependence of the integrated PL versus temperature as well as by the observed carrier lifetime of\u2009\u2248\u20091 ns at 4 K, where the recombination is purely radiative. The direct bandgap is confirmed by ab initio DFT and approximate quasiparticle calculations showing a high directness, implying that the indirect minima are 0.3 eV above the \\(\\bar{\\Gamma }\\) minimum. In addition, we observe clear quantum confinement combined with type-I band alignment. Importantly, both analyses of the thermal quenching observed in the Arrhenius pots as the theoretical calculations demonstrate nearly equal conduction and valence band offsets. Although our hex-Ge/Si0.2Ge0.8 QWs are lattice mismatched and feature strongly anisotropic effective masses, our results can still be properly described by a simple finite QW model. In this paper, we studied hex-Si1\u2212xGex/Si1\u2212yGey nanowire QWs, but our findings are expected to equally apply to future planar hex-Si1\u2212xGex/Si1\u2212yGey QWs compatible with Si-photonics circuits. Our results are unlocking the hex-Si1\u2212xGex/Si1\u2212yGey system for different low-dimensional devices for photonics and quantum information, such as quantum well lasers, optical amplifiers and single photon sources using Si1\u2212xGex alloys.",
+            "section_image": []
+        },
+        {
+            "section_name": "Methods",
+            "section_text": "The nanowires are grown on commercially available GaAs (111)B oriented (n-doped with Si) substrates. The substrates are cleaned with an NH4OH treatment before e-beam exposure, for which an PMMA-A2 photoresist is used. The e-beam exposure patterns 300\u2009x\u2009300\u00a0nm squares with a pitch of 4 \u03bcm. The resist is developed after e-beam exposure with a solution of MIBK/IPA, followed by an Au deposition of 6\u00a0nm by e-beam evaporation. The resist is removed in a lift-off process with PRS3000, acetone and IPA. Final steps before growth involve an oxygen plasma treatment to remove organic residues, followed by an NH4OH treatment to remove surface oxides. The epitaxial growth of WZ GaAs NWs is done in a close-coupled shower head Metal Organic Vapor-Phase Epitaxy (MOVPE) reactor and follows the recipe detailed in Fig.\u00a0S1a. The total flow through the reactor is 8.2 liters per minute. The obtained wurtzite (WZ) GaAs NWs can have stacking fault densities as low as 4 per \u03bcm.\n\nRemoval of the Au catalyst is done by wet-chemical etching in a diluted cyanide solution (KCN:H2O - 1:10) for 17 min. KCN residues are removed by rinsing in H2O for 20 min. The rinsing is immediately followed by a NH4OH treatment to remove oxides from the NW sidewalls. The samples are immersed in IPA for 30 seconds, after which the samples are ready to be dried through centrifugation. The samples with GaAs NWs are placed inside the MOVPE reactor to clean the sidefacets of the NWs, according to the recipe detailed in Fig.\u00a0S1b. The GaAs shell growth during this step is negligible.\n\nThe samples are taken out of the reactor, and the reactor kit is changed to a kit dedicated to the growth of Si1\u2212xGex alloys. Extensive coating recipes are used to ensure minimal contamination from previous GaAs runs. Earlier work on hex-Si1\u2212xGex showed a high As-doping level in the order of 9\u2009\u00d7\u20091018\u2009cm\u22123 as deduced by Atom Probe Tomography (APT) measurements18. Equivalent samples as those presented in this study still have unintentional doping from arsenic, but the level is reduced below the detection limit of APT, so it is below 2.5\u2009\u00d7\u20091018\u2009cm\u22123, likely due to the extensive coating runs.\n\nSamples with WZ GaAs cores are reintroduced in the reactor. Different recipes are used for hex-Ge/Si0.2Ge0.8 and Si0.1Ge0.9/Si0.3Ge0.7 samples, as detailed in Fig.\u00a0S1c\u2013d. For hex-Ge/Si0.2Ge0.8 QWs, the first step is an anneal in an H2 atmosphere, which improves the GaAs-Si0.2Ge0.8 interface. The initial Si0.2Ge0.8 shell is grown in 90 min. However, a large fraction of these 90 min is the incubation time, which is a growth delay before the shell starts to grow. The initial shell typically has a thickness of 10\u201320 nm. The precursor flows to the reactor are stopped, leaving the sample in an H2 atmosphere for 5 min, and this time is used to lower the flows of GeH4 and Si2H6. Growth of the Ge QW follows a similar procedure. Both flows are stopped, and the reactor is flushed for 5 min with H2 to remove residual Si2H6.\n\nFor hex-Si0.1Ge0.9/Si0.3Ge0.7 QWs, the initial barrier is grown in a single step (Fig.\u00a0S1d). The remainder of the recipe is comparable to the hex-Ge/Si0.2Ge0.8 QWs.\n\nTransmission Electron Microscopy (TEM) studies were performed using a probe corrected JEOL ARM 200F, operated at 200\u2009kV. All images were acquired at low camera length (8 cm, 68-280 mrad) to minimize the contribution of strain and diffraction contrast.\n\nEnergy dispersive X-ray Spectroscopy (EDS) studies were performed using a 100 mm2 Centurio EDS silicon drift detector. Quantification of the EDS spectra was done using the Cliff-Lorimer model. The accuracy of EDS quantification was previously confirmed by determining the composition of a single sample, corresponding to MOVPE input Si0.10Ge0.90, with both EDS-STEM and Atom Probe Tomography (APT)18.\n\nCross-sectional TEM samples of nanowires were prepared using a Focused Ion Beam (FIB) FEI Nova Nanolab 600i Dualbeam system. For this, the NWs were initially swiped from the growth substrate to a piece of Si and then arranged to lie parallel to each other with the aid of a micromanipulator. These NWs were covered with the use of electron-beam induced C and Pt deposition to minimize the ion beam damage in following steps. Afterwards, the NWs were embedded in ion-beam induced Pt deposition. The lamella was cut out by milling with 30 kV Ga ions and thinned down with subsequent steps of 30, 16, and 5 kV ion milling in order to minimize the Ga-induced damage in the regions imaged with TEM.\n\nThe QW thickness is mainly determined from images along the [0001] zone axis. QWs of which the thickness could not be measured accurately, due to varying QW position or width within the thickness of the TEM lamella, are excluded from the analysis.\n\nThe stacking sequence within the Ge/Si0.2Ge0.8 QWs is obtained from Scanning Transmission Electron Microscopy (STEM) images. Within each image, we count the number of planes that have surrounding hexagonal segments. A segment of i\u2009=\u20091,\u20092,\u20093 planes would represent segments of 2,\u20093,\u20094 consecutive neighboring monolayers (ABA,ABAB,ABABA) respectively. Over multiple images, we count how many times we observe a segment that contains i hexagonal stacked planes, which we call \\({N}_{i}^{Hex}\\). Similar reasoning holds for the segments with coherent cubic stacking. The distribution of the hexagonal and cubic segment lengths (\\({N}_{i}^{Hex}\\) and \\({N}_{i}^{Cub}\\)) respectively, are shown in Fig.\u00a0S4a.\n\nThe hexagonality \\({F}_{i}^{Hex}\\), i.e., the percentage of the NW that has local hexagonal stacking of at least i planes, as\n\nFor i\u2009=\u20091, above equation calculates the fraction of the NW that is made from hexagonal segments that are at least 1 plane long. Longer segments are also included, and weighted according to their length. Higher-order degrees of hexagonality are calculated using larger values of i, which are shown in Fig.\u00a0S4b. The minimum length of a segment with hexagonal stacking, to still have a direct bandgap, is not yet precisely determined.\n\nLocal variations of the lattice constant are measured with Geometric Phase Analysis (GPA), utilizing STEM images at atomic resolution. We used a custom, in-house developed toolbox to perform the GPA analysis. The GPA tool calculates the local diffraction pattern, using a 2D-Fourier transformation. Changes of the diffraction spots, due to changes in the local lattice constant, are used to calculate the strain with respect to a reference area. With the 2D-Fourier transformation, it is possible to measure the strain in the horizontal and vertical direction of each image. If the QW is imaged along the [0001] zone axis, this corresponds to the strain in the azimuthal and radial directions of the NW geometry. This reference area is defined within each TEM image, in this case, to be within the inner Si0.2Ge0.8 layer.\n\nThe X-ray diffraction measurements were made with a Bruker Discover D8. The incidence beam is filtered with a Ge monochromator for the Cu K-\u03b1 radiation (1.5406 \u00c5). The incidence beam is collimated with a nozzle of 2 mm in diameter. The diffracted beam is measured with a 2D detector, without any optics in between. The 2D detector is used to collect diffracted X-rays with an in-plane angle perpendicular to 2\u03b8 of\u2009\u00b1\u20090.36\u00b0.\n\nReciprocal space maps (RSMs) covering the cubic twin [331] until the hexagonal \\([10\\bar{1}6]\\) reflection are measured in a single scan. The RSMs are aligned such that the angular coordinates [\u03c9,\u20092\u03b8] of the GaAs [224] substrate reflection correspond exactly to the theoretical values of [61.3474\u00b0,\u200983.7524\u00b0].\n\nThe hexagonal lattice constants of the NWs are obtained by fitting the RSMs around the \\([10\\bar{1}5]\\) reflection with a 2D Gaussian profile. The uncertainty in the peak position of this Gaussian is used to calculate the uncertainty in the lattice constants.\n\nAsymmetrical crystal truncation rods are obtained by taking a line scan along Qz through the RSMs. The intensity at Qx\u2009=\u20091.816 \u00c5\u22121 is integrated along the \u03c9-direction within a region of \u03c9\u2009\u00b1\u20091.\u20095\u00b0. The range is chosen to collect both the substrate and NW reflections, which occur at slightly different Qx due to the difference in the in-plane lattice constant.\n\nThe asymmetrical crystal truncation rod allows the separation of the hexagonal and the cubic reflections. Hence, it is used as a probe for the amount of hexagonal stacked material within the NWs. One of the main problems with XRD is that it is quite insensitive to the I3 stacking fault, which is the most common defect in the hex-Si1\u2212xGex. Consider two hexagonal stacked domains ABAB and BABA, which are aligned along the [0001] axis, separated by either a single \u201cA\u201d plane, i.e., perfect hexagonal stacking, or by a single \u201cC\u201d plane, corresponding to the I3 stacking fault. The only difference between the two configurations is that the I3 defect transforms the local stacking from ABABABABA to ABABCBABA. The two hexagonal domains separated by an I3 defect still interfere constructively, since the I3 defect has no burgers vector40. Therefore, we believe that an I3 defect does not broaden any peak in XRD54. The I3 stacking, however, should result in a lower intensity of the diffraction signal since there are fewer lattice planes contributing to constructive interference. The relative intensity of the hexagonal peaks between samples is therefore used as a probe for the amount of I3 defects.\n\nTo do so, peaks with a Voigt profile are fitted to the asymmetrical crystal truncation rods. Near the hex-\\([10\\overline{1}5]\\) peak, two peaks are fitted. One around Qz\u2009\u2248\u20094.82 \u00c5\u22121, which we attribute to signal coming from the core-shell NWs, and one around Qz\u2009\u2248\u20094.78 \u00c5\u22121, which we attribute to bulk-like WZ GaAs, that parasitically grows on the GaAs substrate around the base of the NW. After Si1\u2212xGex shell growth, this bulk-like WZ GaAs maintains a lattice constant close to WZ GaAs, while the lattice constant from the NW is shifted towards Si1\u2212xGex. The obtained hex-\\([10\\overline{1}5]\\) peak areas are normalized to the [224] substrate reflection, to account for small imperfections in the alignment between the samples. Moreover, the \\([10\\overline{1}5]\\) peak areas are divided by the volume of the NWs. These volumes are calculated from the length and diameter, as extracted from SEM images. When normalized in this manner, all GaAs-Si1\u2212xGex core-shell NW samples give a similar number within a factor of 1.5 (Fig.\u00a0S4d).\n\nThe (macro) PL measurements were performed using a Thermo Scientific iS50R step-scan Fourier Transform InfraRed Spectrometer (FTIR). The as-grown NW samples are introduced to the setup by placing them in a LHe cooled Oxford Instruments HiRes2 continuous-flow cryostat which can be temperature controlled using the integrated heater governed by an Oxford Instruments MercuryiTC. The samples are excited using a Quasi-continuous wave (Quasi-CW) 976\u00a0nm laser, focused on the sample by a 2.1\u2009cm focal distance off-axis parabolic Au mirror to an\u2009\u2248\u2009100\u2009\u03bcm spot and the collected photoluminescence is measured using the internal Mercury Cadmium Telluride (MCT) detector of the FTIR. The excitation laser was filtered out using a germanium window (1950\u00a0nm) or a 1650\u00a0nm long pass filter. To extract the NW response from the black-body radiation background, the laser is modulated using a 38\u2009kHz square wave generated by a Siglent SDG1032X Arbitrary Waveform Generator (AWG) and the signal is finally demodulated using a Zurich Instruments MFLI Lock-in Amplifier (LIA). To improve the stability of the modulation frequency, the AWG was locked to the oscillator in the LIA using the 10 MHz clock signal reference.\n\nFor Fig.\u00a03, the QW and reference samples were measured at the lowest excitation density that still gave an acceptable Signal-to-noise ratio, being 3, 13, 50, 39, 6, 9 and 13\u2009W\u2009cm\u22122 for the 9, 6, 4, 3, 2.5, 2 and 1.5\u2009min QWs and 64 and 2\u2009W\u2009cm\u22122 for the bulk hex-Si0.2Ge0.8 and hex-Ge reference samples respectively and lightly smoothed for clarity using a 21 point, linear Savitzky-Golay filter. The finite quantum well model added to Fig.\u00a03b was calculated using the bulk effective masses for the well and interpolated effective masses between bulk hex-Ge (me\u2009\u2248\u20090.079\u2009m0,\u2009mh\u2009\u2248\u20090.055\u2009m0)19 and hex-Si for the barrier (me\u2009=\u20090.122\u2009m0,\u2009mh\u2009=\u20090.213\u2009m0)50. The bandgap energy EWell was determined from the experimental 0.354 eV emission peak of the hex-Ge reference spectrum increased by 13 meV to account for the shift due to strain from the QP calculations and EBarrier\u2009=\u20090.570\u2009eV was determined from the peak energy of the hex-Si0.2Ge0.8 reference spectrum, the reference spectra are shown in Fig.\u00a03a. The band-offsets were assumed to be symmetrical as indicated by the QP calculations Fig.\u00a0S10c and the experimental estimation Fig.\u00a0S6d.\n\nFor Fig.\u00a05, the QW and reference samples were measured at 0.88\u2009kW cm\u22122 for the 5 and 15\u2009min QWs and 0.88 and 0.42\u2009kW cm\u22122 for the bulk Si0.1Ge0.9 and Si0.3Ge0.7 reference samples respectively. The spectra were background corrected by fitting the sum of an exponential Urbach tail55,56 from the GaAs epitaxial substrate and a Gaussian peak spectrum for each spectrum, after which the exponential is subtracted. As the Si0.3Ge0.7 reference had a very low intensity even at high excitation density it was smoothed for clarity after the baseline correction using an 81 point, quadratic Savitzky-Golay filter. The spectra of the 5 min QW and Si0.3Ge0.7 reference after baseline correction are in agreement with the \u03bcPL spectra of single NWs mechanically transferred onto an Aluminum-Nitride (AlN) substrate shown in Fig.\u00a0S9. The finite quantum well model added to Fig.\u00a05c was calculated using interpolated bulk effective masses between hex-Ge (me\u2009=\u20090.076\u2009m0,\u2009mh\u2009=\u20090.055\u2009m0)19 and hex-Si (me\u2009=\u20090.122\u2009m0,\u2009mh\u2009=\u20090.213\u2009m0) for both the barrier and the well material, the band-offsets were assumed to be symmetric and determined from the experimental emission energies of the well and barrier reference samples shown in Fig.\u00a05b.\n\nThe single nanowire spectrum is investigated using a Time-Resolved Fourier-Transform-Infrared-Spectroscopy setup (TR-FTIR). This setup allows us to study the spectrally-resolved time decay of the photoluminescence of a sample. The as-grown hex-SiGe NWs samples are mechanically transferred on a planar AlN substrate and are introduced to the setup by placing them in a LHe cooled Oxford Instruments HiRes2 continuous-flow cryostat. The temperature is set to 4\u2009K using an Oxford Instruments MercuryiTC. The samples are optically excited using a femto-second pulsed mode-locked fiber laser (NKT ORIGAMI 10\u201340) with a wavelength of 1032\u00a0nm and repetition rate of 40\u2009MHz. A 36x/0.40NA Cassegrain objective is used to excite and collect the signal from the sample. The excitation/collection spot diameter on the sample is 3\u2009\u03bcm. The PL signal from the sample is sent through the Nireos GEMINI birefringent Fourier transform interferometer to acquire spectrally resolved photoluminescence and finally collected by a Superconducting Nanowire Single-Photon Detector (SNSPD) with a measurement window up to 2.35\u2009\u03bcm (Single Quantum EOS110). A 1350\u00a0nm long-pass filter is placed before the GEMINI module to block the excitation laser reflected on the sample. For the single NW lifetime measurement, the GEMINI interferometer is kept fixed at the zero path distance and the measurement is performed without acquiring spectral information from the NW signal.\n\nAll calculations were performed within the framework of Density Functional Theory (DFT) using the VASP software57,58 and the projector-augmented wave method59, with a plane-wave cutoff of 500 eV. The shallow 3d levels of Ge were treated as valence states. Geometry relaxations employed the Perdew-Becke-Ernzerhof exchange-correlation (XC) functional PBEsol60. Brillouin zone integrations were carried out with a \u0393-centered 12\u2009\u00d7\u200912\u2009\u00d7\u20096 k-point grid for lonsdaleite (2H) crystals. Quasiparticle band structures were computed using the MBJLDA XC potential of Tran and Blaha61, which combines the modified Becke-Johnson (MBJ) exchange62 with correlation in the local density approximation (LDA)63. Spin-orbit coupling (SOC) was consistently considered, as the resulting corrections to the band structure are crucial for Ge and alloys with a substantial Ge content. Branch point energies were calculated following the method of reference46, and they were applied whenever necessary to align energy levels of different materials and heterostructures. This approach was already validated for [0001] interfaces in reference47. The resulting band structures of hex-Ge and hex-SiGe alloys are consistent with previously published results19,20,64. Numerical differences between the reported findings here and those published earlier stem from the additional biaxial strain applied in this work to replicate experimental conditions, as discussed in the main text.\n\nIn our approach, the Ge layer thickness affects the lowest conduction band of the bulk Si0.25Ge0.75 barrier material (red solid line in Fig.\u00a06d). The structural optimization within the DFT approach of the studied MQW structures gives rise to mutual biaxial strains in the hex-Ge well layers as well as in the SiGe barrier layers in dependence of the layer thicknesses in addition to the significant \u201cexternal\u201d biaxial strain taken from the measurements. Despite this strong biaxial strain due to the assumed pseudomorphic growth of the hex-Ge/SiGe heterosystems on the wurtzite-GaAs core wires, the additional small strain distribution in the heterosystem only slightly affects the actual strong strain situation in the barrier material resulting in small band edge variations made visible in Fig.\u00a06d by a red (blue) line for electrons (holes). The accompanying changes of the QW barrier heights of less than 0.015\u2009eV hardly influence the carrier confinement in the lowest n\u2009=\u20091 levels in the QWs.\n\nFurther information on research design is available in the\u00a0Nature Portfolio Reporting Summary linked to this article.",
+            "section_image": []
+        },
+        {
+            "section_name": "Data availability",
+            "section_text": "The raw data generated in this study have been deposited in Zenodo: https://doi.org/10.5281/zenodo.10839570.",
+            "section_image": []
+        },
+        {
+            "section_name": "Code availability",
+            "section_text": "The VASP code used for electronic structure calculations can be acquired from the VASP Software GmbH at https://www.vasp.at/. The Python code used for the analysis of the growth and the photoluminesence experiments is provided as \u2018Source Code\u2019 files deposited in Zenodo: https://doi.org/10.5281/zenodo.10839570.",
+            "section_image": []
+        },
+        {
+            "section_name": "References",
+            "section_text": "Soref, R. The past, present, and future of silicon photonics. IEEE J. Sel. Top. Quantum Electron. 12, 1678\u20131687 (2006).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nShi, Y. et al. Time-resolved photoluminescence characterization of ingaas/gaas nano-ridges monolithically grown on 300 mm si substrates. J. Appl. Phys. 127, 101101 (2020).\n\nElshaari, A. W., Pernice, W., Srinivasan, K., Benson, O. & Zwiller, V. Hybrid integrated quantum photonic circuits. Nat. Photonics 14, 285\u2013298 (2020).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWirths, S. et al. Lasing in direct-bandgap GeSn alloy grown on Si. Nat. Photonics 9, 88\u201392 (2015).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nElbaz, A. et al. Ultra-low-threshold continuous-wave and pulsed lasing in tensile-strained GeSn alloys. Nat. Photonics 14, 375\u2013382 (2020).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKim, Y. et al. Short-wave infrared cavity resonances in a single GeSn nanowire. Nat. Commun. 14, 4393 (2023).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nArmand Pilon, F. T. et al. Lasing in strained germanium microbridges. Nat. Commun. 10, 2724 (2019).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nZhou, Y. et al. Electrically injected GeSn lasers on Si operating up to 100 K. Optica 7, 924\u2013928 (2020).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nChr\u00e9tien, J. et al. Room temperature optically pumped GeSn microdisk lasers. Appl. Phys. Lett. 120, 051107 (2022).\n\nArmand Pilon, F. T. et al. Investigation of lasing in highly strained germanium at the crossover to direct band gap. Phys. Rev. Res. 4, 033050 (2022).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKuo, Y. H. et al. Strong quantum-confined Stark effect in germanium quantum-well structures on silicon. Nature 437, 1334\u20131336 (2005).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nGatti, E. et al. Room temperature photoluminescence of ge multiple quantum wells with ge-rich barriers. Appl. phys. lett. 98, 031106 (2011).\n\nPezzoli, F. et al. Ge Crystals on Si Show Their Light. Phys. Rev. Appl. 1, 1\u20138 (2014).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nChaisakul, P. et al. Integrated germanium optical interconnects on silicon substrates. Nat. Photonics 8, 482\u2013488 (2014).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nStehouwer, L. E. A. et al. Germanium wafers for strained quantum wells with low disorder. Appl. Phys. Lett. 123, 92101 (2023).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nHutchins-Delgado, T. A. et al. Characterization of shallow, undoped Ge/SiGe quantum wells commercially grown on 8-in. (100) Si wafers. ACS Appl. Electron. Mater. 4, 4482\u20134489 (2022).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nChaisakul, P. et al. Recent progress on Ge/SiGe quantum well optical modulators, detectors, and emitters for optical interconnects. Photonics 6, 24 (2019).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nFadaly, E. M. T. et al. Direct-bandgap emission from hexagonal ge and sige alloys. Nature 580, 205\u2013209 (2020).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nR\u00f6dl, C. et al. Accurate electronic and optical properties of hexagonal germanium for optoelectronic applications. Phys. Rev. Mater. 3, 034602 (2019).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBorlido, P. et al. From pseudo-direct hexagonal germanium to direct silicon-germanium alloys. Phys. Rev. Mater. 5, 114604 (2021).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBerghuis, W. J. H. et al. Low surface recombination in hexagonal SiGe alloy nanowires: Implications for SiGe-based nanolasers. ACS Appl. Nano Mater. 7, 2343\u20132351 (2024).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nPulcu, Y., Koltai, J., Korm\u00e1nyos, A. & Burkard, G. Multiband k\u00b7 p theory for hexagonal germanium. Phys. Rev. B 109, 205202 (2024)\n\nScappucci, G. et al. The germanium quantum information route. Nat. Rev. Mater. 6, 926\u2013943 (2021).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMichler, P. et al. A quantum dot single-photon turnstile device. science 290, 2282\u20132285 (2000).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWang, J., Sciarrino, F., Laing, A. & Thompson, M. G. Integrated photonic quantum technologies. Nat. Photonics 14, 273\u2013284 (2020).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nSalter, C. L. et al. An entangled-light-emitting diode. Nature 465, 594\u2013597 (2010).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMcJunkin, T. et al. SiGe quantum wells with oscillating Ge concentrations for quantum dot qubits. Nat. Commun. 13, 7777 (2022).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nArakawa, Y. & Sakaki, H. Multidimensional quantum well laser and temperature dependence of its threshold current. Appl. Phys. Lett. 40, 939\u2013941 (1982).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nT\u00e4schler, P. et al. Femtosecond pulses from a mid-infrared quantum cascade laser. Nat. Photonics 15, 919\u2013924 (2021).\n\nArticle\u00a0\n    ADS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nCoe, S., Woo, W.-K., Bawendi, M. & Bulovi\u0107, V. Electroluminescence from single monolayers of nanocrystals in molecular organic devices. Nature 420, 800\u2013803 (2002).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWood, V. & Bulovi\u0107, V. Colloidal quantum dot light-emitting devices. Nano Rev. 1, 5202 (2010).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nPradhan, S. et al. High-efficiency colloidal quantum dot infrared light-emitting diodes via engineering at the supra-nanocrystalline level. Nat. Nanotechnol. 14, 72\u201379 (2019).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nHendrickx, N. W. et al. A four-qubit germanium quantum processor. Nature 591, 580\u2013585 (2021).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nPelucchi, E. et al. The potential and global outlook of integrated photonics for quantum technologies. Nat. Rev. Phys. 4, 194\u2013208 (2021).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nHauge, H. I. T., Conesa-Boj, S., Verheijen, M. A., Koelling, S. & Bakkers, E. P. Single-crystalline hexagonal silicon\u2013germanium. Nano Lett. 17, 85\u201390 (2017).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBergamaschini, R. et al. Prismatic ge-rich inclusions in the hexagonal sige shell of gap\u2013si\u2013sige nanowires by controlled faceting. Nanoscale 13, 9436\u20139445 (2021).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nSaxena, D. et al. Design and room-temperature operation of GaAs/AlGaAs multiple quantum well nanowire lasers. Nano Lett. 16, 5080\u20135086 (2016).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nSkalsky, S. et al. Heterostructure and Q-factor engineering for low-threshold and persistent nanowire lasing. Light. Sci. Appl. 9, 43 (2020).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nSonner, M. M. et al. Breakdown of corner states and carrier localization by monolayer fluctuations in radial nanowire quantum wells. Nano Lett. 19, 3336\u20133343 (2019).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nFadaly, E. M. T. et al. Unveiling planar defects in hexagonal group iv materials. Nano Lett. 21, 3619\u20133625 (2021).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nVincent, L. et al. Growth-related formation mechanism of I3-Type basal stacking fault in epitaxially grown hexagonal Ge-2H. Adv. Mater. Interfaces 9, 2102340 (2022).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nZheng, Z., Zu, X., Zhang, Y. & Zhou, W. Rational design of type-II nano-heterojunctions for nanoscale optoelectronics. Mater. Today Phys. 15, 100262 (2020).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDinu, M., Cunningham, J. E., Quochi, F. & Shah, J. Optical properties of strained antimonide-based heterostructures. J. Appl. Phys. 94, 1506\u20131512 (2003).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nSong, Y. et al. Splitting of valance subbands in the wurtzite c-plane InGaN/GaN quantum well structure. Appl. Phys. Lett. 93, 161910 (2008).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nvan Tilburg, M. A. J. et al. Polarized emission from hexagonal-silicon-germanium nanowires. J. Appl. Phys. 133, 065702 (2023).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nSchleife, A., Fuchs, F., R\u00f6dl, C., Furthm\u00fcller, J. & Bechstedt, F. Branch-point energies and band discontinuities of iii-nitrides and iii-/ii-oxides from quasiparticle band-structure calculations. Appl. Phys. Lett. 94, 012104 (2009).\n\nBelabbes, A., Botti, S. & Bechstedt, F. Band lineup at hexagonal SixGe1\u2212x/SiyGe1\u2212y alloy interfaces. Phys. Rev. B 106, 085303 (2022).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nHaug, H. & Koch, S. W.Quantum Theory of the Optical and Electronic Properties of Semiconductors (WORLD SCIENTIFIC, 2009).\n\nLi, W., Walther, C. F. J., Kuc, A. & Heine, T. Density functional theory and beyond for band-gap screening: performance for transition-metal oxides and dichalcogenides. J. Chem. Theory Comput. 9, 2950\u20132958 (2013).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDe, A. & Pryor, C. E. Electronic structure and optical properties of Si, Ge and diamond in the lonsdaleite phase. J. Phys. Condens. Matter 26, 045801 (2014).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nSink, J. & Pryor, C. Empirical tight-binding parameters for wurtzite group III-V(non-nitride) and IV materials. AIP Adv. 13, 025354 (2023).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nFox, M. & Ispasoiu, R. Quantum Wells, Superlattices, and Band-Gap Engineering. Springer Handbooks 1021\u20131040 (2007).\n\nKaewmaraya, T., Vincent, L. & Amato, M. Accurate estimation of band offsets in group IV polytype junctions: a first-principles study. J. Phys. Chem. C. 121, 5820\u20135828 (2017).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMcLaurin, M. B., Hirai, A., Young, E., Wu, F. & Speck, J. S. Basal plane stacking-fault related anisotropy in X-ray rocking curve widths of m-plane GaN. Jpn. J. Appl. Phys. 47, 5429 (2008).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nUrbach, F. The Long-Wavelength Edge of Photographic Sensitivity and of the Electronic Absorption of Solids. Phys. Rev. 92, 1324\u20131324 (1953).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKaiser, C. et al. A universal Urbach rule for disordered organic semiconductors. Nat. Commun. 12, 3988 (2021).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKresse, G. & Furthm\u00fcller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169 (1996).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKresse, G. & Furthm\u00fcller, J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Computational Mater. Sci. 6, 15\u201350 (1996).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 59, 1758 (1999).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nPerdew, J. P. et al. Restoring the density-gradient expansion for exchange in solids and surfaces. Phys. Rev. Lett. 100, 136406 (2008).\n\nArticle\u00a0\n    ADS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nTran, F. & Blaha, P. Accurate band gaps of semiconductors and insulators with a semilocal exchange-correlation potential. Phys. Rev. Lett. 102, 226401 (2009).\n\nArticle\u00a0\n    ADS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBecke, A. D. & Johnson, E. R. A simple effective potential for exchange. J. Chem. Phys. 124, 221101 (2006).\n\nKohn, W. & Sham, L. J. Self-consistent equations including exchange and correlation effects. Phys. Rev. 140, A1133 (1965).\n\nArticle\u00a0\n    ADS\u00a0\n    MathSciNet\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nSuckert, J. R., R\u00f6dl, C., Furthm\u00fcller, J., Bechstedt, F. & Botti, S. Efficient strain-induced light emission in lonsdaleite germanium. Phys. Rev. Mater. 5, 024602 (2021).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDownload references",
+            "section_image": []
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+            "section_name": "Acknowledgements",
+            "section_text": "We thank P.J. van Veldhoven and M.G. van Dijstelbloem for the technical support of the MOVPE reactor. We thank Orson A.H. van der Molen for the GPA analysis. This project received funding from the European Union\u2019s Horizon 2020 research and innovation program under grant agreement number 964191, Opto Silicon (W.H.J.P., M.M.J., S.B., F.B., J.E.M.H., and E.P.A.M.B.), the Dutch Organization for Scientific Research (NWO) in the Zwaartekracht Project, Grant No. 024.002.033 (M.A.J.T.), 739.017.002, (V.T.L.), and OCENW.M.21.052 (R.F.) and Solliance and the Dutch province of Noord-Brabant for funding the TEM facility.",
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+        },
+        {
+            "section_name": "Author information",
+            "section_text": "These authors contributed equally: Wouter H. J. Peeters, Victor T. van Lange, Abderrezak Belabbes.\n\nDepartment of Applied Physics, Eindhoven University of Technology, 5600 MB, Eindhoven, The Netherlands\n\nWouter H. J. Peeters,\u00a0Victor T. van Lange,\u00a0Max C. van Hemert,\u00a0Marvin Marco Jansen,\u00a0Riccardo Farina,\u00a0Marvin A. J. van Tilburg,\u00a0Marcel A. Verheijen,\u00a0Jos. E. M. Haverkort\u00a0&\u00a0Erik P. A. M. Bakkers\n\nDepartment of Physics, Sultan Qaboos University, P.O. Box 123, Muscat, Oman\n\nAbderrezak Belabbes\n\nInstitut f\u00fcr Festk\u00f6rpertheorie und -optik, Friedrich-Schiller-Universit\u00e4t Jena, Jena, Germany\n\nAbderrezak Belabbes,\u00a0Silvana Botti\u00a0&\u00a0Friedhelm Bechstedt\n\nEurofins Materials Science Netherlands BV, Eindhoven, The Netherlands\n\nMarcel A. Verheijen\n\nResearch Center Future Energy Materials and Systems of the University Alliance Ruhr and Interdisciplinary Centre for Advanced Materials Simulation, Ruhr University Bochum, Universit\u00e4tsstra\u00dfe 150, Bochum, Germany\n\nSilvana Botti\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nW.H.J.P., M.M.J. carried out the growth of hex-Si1\u2212xGex/Si1\u2212yGey quantum wells. W.H.J.P. analyzed the data. V.T.L. and M.C.H. carried out the photoluminescence spectroscopy and analyzed the optical data. R.F. and M.A.J.T. performed time-resolved spectroscopy on single quantum well nanowires. A.B. and F.B. performed the DFT calculations. W.H.J.P. performed the XRD measurements. W.H.J.P. and M.M.J. performed the FIB cuts, and M.A.V. performed the TEM analysis. S.B., F.B., J.E.M.H., and E.P.A.M.B. supervised the project. F.B. contributed to the interpretation of data, and W.H.J.P., V.T.L., F.B., J.E.M.H., and E.P.A.M.B. contributed to the writing of the manuscript. All authors discussed the results and commented on the manuscript.\n\nCorrespondence to\n                Erik P. A. M. Bakkers.",
+            "section_image": []
+        },
+        {
+            "section_name": "Ethics declarations",
+            "section_text": "The authors declare no competing interests.",
+            "section_image": []
+        },
+        {
+            "section_name": "Peer review",
+            "section_text": "Nature Communications thanks the anonymous reviewer(s) for their contribution to the peer review of this work. A\u00a0peer review file is available.",
+            "section_image": []
+        },
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+            "section_text": "Open Access  This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article\u2019s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article\u2019s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.\n\nReprints and permissions",
+            "section_image": []
+        },
+        {
+            "section_name": "About this article",
+            "section_text": "Peeters, W.H.J., van Lange, V.T., Belabbes, A. et al. Direct bandgap quantum wells in hexagonal Silicon Germanium.\n                    Nat Commun 15, 5252 (2024). https://doi.org/10.1038/s41467-024-49399-3\n\nDownload citation\n\nReceived: 02 February 2024\n\nAccepted: 04 June 2024\n\nPublished: 19 June 2024\n\nVersion of record: 19 June 2024\n\nDOI: https://doi.org/10.1038/s41467-024-49399-3\n\nAnyone you share the following link with will be able to read this content:\n\nSorry, a shareable link is not currently available for this article.\n\n\n\n\n                            Provided by the Springer Nature SharedIt content-sharing initiative\n                        ",
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+        "http://ring.gm.ingv.it",
+        "https://www.mathworks.com/products/matlab.html",
+        "https://www.python.org/"
+    ],
+    "code": [
+        "/articles/s41467-024-54094-4#ref-CR25",
+        "/articles/s41467-024-54094-4#ref-CR32"
+    ],
+    "subject": [
+        "Geophysics",
+        "Seismology"
+    ],
+    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
+    "preprint_pdf": "https://www.researchsquare.com/article/rs-4042694/v1.pdf?c=1731589582000",
+    "research_square_link": "https://www.researchsquare.com//article/rs-4042694/v1",
+    "nature_pdf": "https://www.nature.com/articles/s41467-024-54094-4.pdf",
+    "preprint_posted": "13 Mar, 2024",
+    "research_square_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Pump-probe experiments investigate the strain sensitivity of crustal elastic properties, showing nonlinear variations during the strain cycle. In the laboratory, pre-seismic reductions in seismic velocity indicate that asperity contacts within the fault zone begin to fail before macroscopic frictional sliding. The recognition of such effects in natural seismic-cycles has been challenging. By exploiting seasonal hydrological strains, we used a quasi-static natural pump-probe experiment to investigate the nonlinear response of crustal rocks and its role in seismic failure along the tectonically-active Irpinia Fault System (Southern Italy). By comparing 14-years-long series of spring discharge, strain, seismic velocity variations and earthquakes rate, we find that seismicity peaks during maximum hydrological forcing and minimum seismic velocity. Seasonal strains of ~10-6 are required for both earthquakes triggering and significant nonlinearity effects arising from modulus reduction. We suggest that, for faults in a critical state, cyclical softening may lead to failure and seasonal seismicity.Earth and environmental sciences/Solid Earth sciences/GeophysicsEarth and environmental sciences/Solid Earth sciences/Seismology",
+            "section_image": []
+        },
+        {
+            "section_name": "Additional Declarations",
+            "section_text": "There is NO Competing Interest.",
+            "section_image": []
+        },
+        {
+            "section_name": "Supplementary Files",
+            "section_text": "SupplementaryMaterial.docxSupplementary MaterialanimationFRAMES6.gifContinuos strain evolution",
+            "section_image": []
+        }
+    ],
+    "nature_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Pump-probe experiments investigate the strain sensitivity of crustal elastic properties, showing nonlinear variations during the strain cycle. In the laboratory, pre-seismic reductions in seismic velocity indicate that asperity contacts within the fault zone begin to fail before the macroscopic frictional sliding. The recognition of such effects in natural seismic-cycles has been challenging. Here we exploit seasonal hydrological strains, performing a natural analogue to a quasi-static laboratory pump-probe experiment to investigate the nonlinear strain sensitivity of crustal rocks and its role in seismic failure along the tectonically-active Irpinia Fault System (Southern Italy). By comparing 14-years-long series of spring discharge, strain, seismic velocity variations and earthquakes rate, we find that seismicity peaks during maximum hydrological forcing and minimum seismic velocity. Seasonal strains of ~10\u22126 are required for both earthquake triggering and significant nonlinearity effects arising from modulus reduction. We suggest that, for faults in a critical state, cyclical softening may lead to failure and seasonal seismicity.",
+            "section_image": []
+        },
+        {
+            "section_name": "Introduction",
+            "section_text": "While linear elasticity is widely employed in Earth science applications1, the heterogenous nature of geomaterials makes them to behave in a non-linear way, as it can be revealed by variations in elastic modulus2, hysteresis3, slow dynamics4, when rocks are subjected to strain perturbations5. Pump-probe experiments are nowadays widely used to quantify the non-linear behavior of rocks in laboratory2,5,6,7 and provide fundamental insights about the relationships between non-linear elastic parameters and physical properties of materials, such as damage7,8 or presence and amount of fluids9,10,11, among others2,6,12,13,14,15. All these variables have a key role in controlling the seismic cycle16,17 and the physics of earthquakes nucleation18,19. It has been suggested that progressive loading produces distributed microcracks that at some stage begin to coalesce onto a volumetric region of concentrated damage that, when a critical level is exceeded, experiences instability that leads to rupture17. In laboratory20 accelerated fault creep causes elastic moduli (and seismic velocity) reductions during the preparatory phase preceding failure, as asperity contacts begin to fail before macroscopic frictional sliding. This can be also related to rock damage. A temporary reduction in the fault core modulus could induce fault slip for a fault already near failure18. It is thus crucial to assess the non-linear response of crustal rocks by investigating behaviors associated with stress, pore pressure, permeability, material failure, and rock damage in the Earth in the same way as in laboratory2,20,21,22. The advent of ambient noise seismology23 offers to scientists the possibility to develop ad-hoc pump-probe experiments, measuring in-situ the velocity changes (\u03b4v/v) from estimates of the Green\u2019s function23 (the probe), excited by (the pump) natural (mainly tidal strains12,24) or man-made strain. These studies revealed significant non-linearity for shallow crustal rocks13, enhanced in complex settings such as fault systems8,25 and volcanic regions9,13.\n\nFollowing previous works on non-linearity8,12,24, \u03b2 represents the second order, quadratic, coefficient of the stress-strain elastic relationship5:\n\nwhere \u03c3 is the stress, M is the elastic modulus, \u03b5 is the strain and f indicates the hysteretic components dependent on strain and strain rate. The strain sensitivity \u03b25,24 of seismogenic rocks can be estimated through a quantitative comparison of strain \u03b5 vs \u03b4v/v curves5,24:\n\nwhere \u03b1 is an offset.\n\nA value of \u03b2 different from zero indicates non-linearity13,26 and increases with the degree of the material damage and density of cracks7. Negative values of the strain sensitivity \u03b2 have been interpreted in terms of decrease (increase) of seismic velocities under dilatational (contractional) strain operated by opening (closing)27 of preexisting cracks in the crust13.\n\nIn this study we perform a 14-years long-term analysis based on a natural analog of a pump-probe experiment to assess the non-linear behavior of the seismogenic volume in the Irpinia Fault Zone (IFZ, Fig.\u00a01), which hosted the largest (Ms 6.9) instrumentally recorded earthquake in Italy28. Here we measured \u03b4v/v induced by annual strain variations originating from recharging groundwater in karst aquifers29,30, that significantly extends the temporal tidal forcing employed in previous works14,24. We show that hydrological processes induce nearly periodic, anisotropic fluctuations of horizontal strain31,32 (which we used as a pump) associated with seasonal modulation of seismicity. We employ ambient seismic noise correlation23 to track the temporal evolution of \u03b4v/v in two sites (MCRV and CAFE, Fig.\u00a01; see \u201cMethods\u201d), representative of the variable hydrological forcing conditions, that we used as the probe to measure the non-linear elastic response of crustal rocks to strain fluctuations. Our analysis reveals a negative value for \u03b2 in agreement with previous natural12,13,24 and laboratory experiments2,7,21, related to seasonal cycling of material damage along the IFZ and associated with seasonal modulation of seismicity. Our results highlight the dependence of seasonal seismicity on the non-linear rock behavior, which calls to improve our understanding of the role of elastic non-linearity and its effect on frictional properties in controlling the triggering of earthquakes along major seismogenic faults8,33,34,35,36,37,38,39,40.\n\na Map of the study area. Global Positioning System velocities in a Tyrrhenian reference frame43. The trace of Irpinia70 is shown in red. Carbonate rocks are represented with green overlays. Background color-coding shows the secular tectonic strain rate (second invariant of the strain rate tensor). The inset shows the location of the study area in Italy. b Enlarged map (area enclosed by the black line in a) showing 2008\u20132022 seismicity from the Irpinia Seismic Network. Colored dots represent the considered declustered seismicity within the first 12\u2009km of depth and above the completeness magnitude, white dots represent other not-considered seismic events. Global Centroid Moment Tensor focal solution and surface projections of the three faults28 responsible for Ms 6.9, 1980 Irpinia earthquake with its focal mechanism; green patches enclose shallow carbonates rocks; c Time series of hydrological, seismological and geodetic observations. The upper panel shows the discharge measured at Caposele spring. Lower panels show velocity variations (green circles, inverted sign) for coda waves time lapse using empirical Green\u2019s functions reconstructed by autocorrelation of seismic noise recorded at MCRV and CAFE in the frequency band of 0.5\u2010 to 1\u2010Hz (blue dots) together with East components of displacement at the same stations (red circles); d conceptual model of the modulation of crustal deformation induced by variable hydraulic head in karst aquifers. \u03b5xx indicates the horizontal strain in the ENE-WSW direction.",
+            "section_image": [
+                "https:////media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41467-024-54094-4/MediaObjects/41467_2024_54094_Fig1_HTML.png"
+            ]
+        },
+        {
+            "section_name": "Results",
+            "section_text": "The Caposele spring29 provides a unique, 100-years-long, hydrological dataset of discharge (average ~4\u2009m3/s) from the karst aquifer of the Picentini Mountains (Fig.\u00a01) hosted in extensively fractured, 2\u20133\u2009km-thick, allochthonous, Mesozoic carbonates41. As no man-made modifications occur in its catchment, this spring is strictly controlled by climate trends29 and is regionally-representative of the variations of hydrological forcing operated by the karst aquifers with maximum/minimum recharge in May-July and November-January, respectively29,30. To investigate the effects of hydrological forcing on crustal elastic properties, we calculated the velocity variations \u03b4v/v from 14 years (January 2008-December 2021) of seismic data recorded at MCRV and CAFE stations (Fig.\u00a01). Both sites (with co-located seismic and GPS receivers) are located within the tectonically deforming belt along the Apennines (Fig.\u00a01a) but at variable distances from the IFZ and the karst aquifer. The recent microseismicity (local magnitude \u22120.4\u2009\u2264\u2009ML\u2009\u2264\u20093.7) occurring in the investigated region is characterized by normal fault mechanism42, in agreement with the regional strain field43 and the geometry and slip of the faults involved in the Ms 6.9, 1980 Irpinia earthquake28. We used ambient noise correlations from single station measurements to apply the Coda Wave interferometry method23 (CWI, see Methods) in a time-lapse of 10\u201350\u2009s after zero time (ballistic waves arrival time). The time series of \u03b4v/v (Fig.\u00a01c) at MCRV reveal up to ~0.2% velocity variations which closely tracks the evolution of spring discharge and the GPS horizontal displacement (Fig.\u00a01c). At MCRV we found that peaks of eastward displacement, which correspond to a transient, recoverable dilatational strain in the shallow crust across the karst aquifer31,32, are correlated with negative peaks in the velocity of seismic waves, similarly to observations in other Apenninic regions25,44. The opposite occurs for negative Eastward displacements with contractional strains and significant increase of seismic velocities. At CAFE, located outside the karst aquifer region but inside the actively-deforming tectonic belt (Fig.\u00a01a), we observe an order of magnitude smaller fractional seismic velocity change (~0.03%), and a GPS time series insensitive to seasonal variations, which document the absence of any relevant hydrological forcing. The seasonal velocity variations observed at MCRV are higher than those observed in other regions in the same tectonic environment25,44 and comparable to those occurring in volcanic regions9,45, where pronounced seasonal velocity variations9 are similarly detected, and where the presence of large amount of preexisting microcracks can be a common condition.\n\nTo assess the depth at which seismic velocity variations occur, we computed the depth sensitivity of surface waves46 for a local 1D velocity model47. The sensitivity of surface wave (see Methods) in the analyzed frequency band (0.5\u20131.0\u2009Hz25,) is concentrated in the first few kilometers of the crust (depth\u2009<\u20091.5\u2009km, see Fig.\u00a0S1), which include the thickness of highly-permeable, fractured carbonate rocks41 forming the karst aquifer. However, the theoretical depth sensitivity of the scattered body waves, computed as in ref. 25 considering a 3D sensitivity kernel formulation48 (see \u201cMethods\u201d), shows that the kernel is sensitive to a deeper volume in the crust than for surface waves (Fig.\u00a0S1). The uncertainty in the nature of scattered waves challenges a precise attribution of the velocity variations observed at MCRV, which could be related to both the shallow highly-permeable, fractured carbonate rocks and the deeper seismogenic volume. Improving the reliability of sensitivity kernels is crucial to address and solve the depth resolution problem49. Additionally, independent information is provided by time-dependent P and S wave tomographic models, with poorer intensity and temporal sensitivity but higher spatial resolution. These analyses show significant temporal variations of Vp/Vs ratio below 6\u2009km depth correlated with hydrological forcing50 supporting the hypothesis of significant nonlinear effects at similar depths.\n\nWe estimated the strain variations (positive extensional strain) induced by the hydrological cycle (Fig.\u00a02), by computing a 14 years-long time series of horizontal strain, that we modeled with a 3.5\u2009km-thick layer of elementary cuboid sources51 in the IFZ area (similar approach as in ref. 32, see \u201cMethods\u201d). To remove the long-term tectonic component and mitigate the temporal high-frequency noise and daily scatter, raw GPS time series have been initially detrended and low-pass filtered using a Gaussian filter (full-width 180 days). Two snapshots illustrating the regional NNE-SSW extension during wet periods and contraction in dry periods are reported in Fig.\u00a02a, b, respectively, while the horizontal dilatational strain at MCRV is reported in Fig.\u00a02c. The \u03b4v/v follows the evolution of strain, with positive \u03b4v/v for contractional strains and negative \u03b4v/v associated with extension (Fig.\u00a02c), consistent with previous natural12,24,52 and laboratory experiments2,21,27. We remark that in the two episodes (Fig. 2a, b) the displacement at MCRV is oriented respectively NE (Fig. 2a) and SW (Fig. 2b), suggesting that the horizontal dilatation induced by hydrological forcing occurs along a single axis during both the recharge/discharge phases. Figure\u00a02d represents the frequency of the compressional (left) and extensional (right) axis azimuth, coupled with the sign of the temporally coincident strain (top) and velocity variations (bottom) series. In particular, the frequency of the compressional (extensional) axis is counted when the dilatation is negative (positive). During summer, when strain is positive (red color), the extensional axis is oriented mostly W-NW, while during winter, when strain is negative (blue color), a similar orientation is shown by the compressive axis. The same happens when looking at velocity variations; during summer (winter) the velocity changes are negative (positive) and the extensional (compressional) axis is oriented mostly W-NW. We attribute the uniaxial strain fluctuation to an anisotropic poroelastic response53 of the crust due to hydrological forcing32 (hydraulic head \u2206h in karst aquifers). The horizontal strain \u03b5xx in the ENE-WSW direction (taken here as the x axis, see Supplementary Material for the complete derivation) can thus be expressed as:\n\nwhere \u03b1 is the Biot\u2019s coefficient, \u03c1w is water density, g is the gravity acceleration, E is the Young\u2019s modulus and \u03bd is the Poisson\u2019s coefficient. We test the validity of our model considering a realistic water table variation \u2206h\u2009=\u200920\u201340\u2009m32 and a reasonable range of upper crust poroelastic parameters for carbonate rocks (\\(E=60-80{GPa}\\), \\(\\nu=0.2-0.3\\), \\(\\alpha=0.6-0.8\\)54;). We estimate a strain variation in the order of \\(2-10\\times {10}^{-6}\\), whose lower bound is consistent with the range of observed non-tectonic strain variations within the decade-long time series (Fig.2c).\n\na, b Maps of distributed hydrological strain with calculated/observed GPS displacements. The complete, continuous strain evolution is shown in Supplementary Movie 1. The two frames display opposite conditions of groundwater recharge in karst aquifers (shown as green lines) and opposite dilatational patterns. Red, green, and blue circles in (a) indicate data points where series of dilatational strain, velocity variations, and spring discharge (shown in (c)) have been respectively calculated. c Time series of dilatational strain (red) calculated at MCRV compared with the co-located velocity variations (green), earthquake rate (black), and Caposele spring discharge (blue); d frequency of the azimuth of compressional axis (left) and extensional axis (right) coupled with the sign of the synchronized scalar of the strain (top panel) and velocity changes (bottom panel).\n\nThe observations summarized in Fig.\u00a02, together with our simplified poroelastic model, suggest a strong coupling between \u03b4v/v and strain in saturated crustal rocks. The oscillatory change in velocity with strain (Fig.\u00a02) is similar to observations in laboratory-scale experiments2,21, and can be exploited to study the nonlinear elastic response of crustal rocks following equation [2]. A comparison between \u03b4v/v and strain values (Fig.\u00a03a) shows a general inverse relationship (\u03b2\u2009=\u2009\u22120.64\u2009\u00d7\u200910\u22123) indicating that, on average, seismic waves are slower when rocks are extended during maximum hydrological forcing (May-July), that when compressed during minimum hydrological forcing (December-January). This mechanism is consistent with the opening and closing of cracks and pores6,13,52 with increasing stiffness of their internal contacts during compression27.\n\na seismic velocity variations (\u03b4v/v) plotted against dilatational strain, color-coded for annual phase (capital letters in the colorbar indicate each month). The black dashed line shows the best-fit regression line whose slope (\u03b2) represents the strain sensitivity of velocity variations. b same as (a) but color-coded for dilatational rate. c\u2013h specific annual cycles (year labeled on top left) color-coded for annual phase.\n\nThe observed sensitivity \u03b2 aligns with the values observed in previous works (\u22121\u2009\u00d7\u2009103\u2013105)12,13,24. We also observe a complex, non-unique correspondence between velocity variations and strain, attributed to the superposition of seasonal and multiyear forcing cycles31. This superposition results in annual trajectories with similar slopes but different cycle means along the \u03b4v/v axis (Fig.\u00a03c\u2013h). Additional information on the strain-rate dependency of seismic velocity variations can be inferred from the hysteretic behavior of \u03b4v/v and strains3,8. For annual cycles defining closed or semi-closed loops (Fig.\u00a03c\u2013h), we observe prevalent clockwise loops but no evidence that seismic velocities are systematically higher during extension (Fig.\u00a03b). We also do not observe a dependency of the cycles pattern upon strain magnitude.\n\nIt has been suggested3 that the mechanism controlling quadratic nonlinearity (i.e., \u03b2) is distinct from the mechanisms controlling additional nonlinear parameters (i.e., average softening and hysteresis). This distinction3,26 may depend on the primary deformation mode across the interfaces (cracks or pores) within the bond system. Longitudinal deformation perpendicular to cracks or low-aspect ratio pores would control \u03b2, whereas shear deformation across the interfaces being responsible for average softening and hysteresis.\n\nPossible factors arising from the calculation of strain that may affect the estimation of \u03b2 are two folds. The first is the spacing of geodetic stations (tens of kilometers), larger than the dimension of the karst aquifer (Fig.\u00a01), likely providing a lower boundary on the estimated strain. The second is the use of surface measurements of strain as representative of the actual values at depths (likely to be lower) where seismic velocity changes occur. These two factors, which cannot be easily quantified, have opposite effects and will probably affect the value of \u03b2 but not its sign.\n\nIt has been previously reported that seismicity along the IFZ is modulated at seasonal and multiannual time scales by hydrological forcing from the karst aquifers32. The low values of estimated hydrologically-induced stress variations32, corresponding to the observed seismicity modulation, suggest a critical state of stress for the faults within the actively deforming area, as observed in other actively-deforming regions where seismicity is triggered by small stress changes55. To investigate the relation between rock properties modulated by the hydrological forcing (strain and seismic velocity variations) and earthquake nucleation we declustered the seismic catalog along the IFZ (color-coded circles in Fig.1 c) and calculated the daily seismicity rates within 90-days moving windows (see Methods). This modulation is clearly displayed in the multiyear time series of Fig.\u00a02c (where all the different observables have been resampled and synchronized at a 0.04-year step), showing in-phase peaks of seismicity rate, \u03b4v/v, strain and spring discharge. We also observe that the three largest peaks of seismicity rates in 2009, 2013 and 2021 (Fig.\u00a02c), correspond to large seasonal increments in spring discharge (>2\u2009m3/s) and dilatational strain (>1\u2009\u00d7\u200910\u22126). We test the relationship between background seismicity and hydrological forcing (expressed as variations of dilatational strain or seismic velocity), following the approach of ref. 56 using a modified quantile-quantile plot (QQP). QQP tests for a specific relationship between hydrological forcing and seismicity rate rather than simply asking the question if earthquake occurrence is correlated with such forcing. In our case we plot the normalized cumulative fraction of earthquake rates that occurs at or below a given level of strain or seismic velocity against the normalized cumulative fraction of time that is spent at or below the same given level. To facilitate interpretation, we follow ref. 56 and modify the QQP plots to show excess or deficit of earthquakes by removing the 1:1 trend line. In the case of no correlation between the earthquake rate and hydrological forcing (either the strain or velocity variations), we expect to see a horizontal line because the fraction of earthquakes below a given level should be equivalent to the fraction of time spent at or below that level. If a point falls below the horizontal line, then there is a deficit of earthquakes up to the corresponding value compared with what is expected for time spent up to the corresponding value. If the point falls above, the opposite is true, which means we have an excess of earthquakes. We found (red lines in Fig.\u00a04a) a deficit of earthquakes for low values of the strain compared to the case in which there would be no correlation with the strain (e.g., in the case of a Poisson process). This indicates that seismicity and hydrologically-related strains are correlated with each other. Moreover, the curve is slightly skewed to the right (Fig.\u00a04a), showing that seismicity rate responds non-linearly to increasing strains explaining also the large response of seismicity to the largest strain increase in 2009, 2013 and 2021. As expected, the same analysis with velocity variations (Fig.\u00a04b), shows an opposite behavior and an excess of earthquakes during low values of seismic velocity. Therefore, earthquakes occurrence and velocity variations are anti-correlated. In this second case, the curve is also skewed to the left (Fig.\u00a04b), showing that seismicity rate also responds non-linearly to increasing velocity variations. The gray lines shown in Fig.\u00a04a, b display 100 random permutations of the observed catalog which are cloudily disposed around the horizontal line showing that, when the catalog is randomized, no correlation is present with either strain (Fig.\u00a04a) or seismic velocity variations (Fig.\u00a04b). By comparing the observed seismicity rate with synthetic rate histories containing both random and hydrological components, we could estimate the level of hydrological forcing in the real catalog (see Methods). Figure\u00a04(c\u2013f) shows that the observed nCDFs of the observed seismicity require ~40% contribution of hydrological forcing and an increasing effect of strain or seismic velocity variation to reproduce the observed skewness, i.e., a non-linear influence of strain or seismic velocity variations on the seismicity rate.\n\nThe vertical axis is a measure of excess or deficit of earthquakes at a given level of strain (in red, plots a, c, e) or velocity (in blue, plots b, d, f) based on the amount of time spent at or below that level. The horizontal axis is the normalized Cumulative Density Function (nCDF) of time-strain (or time-velocity). Gray lines show synthetic realizations (mean shown in yellow) with variable contribution and increasing effect of hydrological forcing.",
+            "section_image": [
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+            ]
+        },
+        {
+            "section_name": "Discussion",
+            "section_text": "We measured hydrologically-modulated velocity changes \u03b4v/v in the order of ~0.2% near the karst aquifers close to IFZ. Those variations are one order of magnitude smaller (~0.03%) at around 25\u2009km distance, where the amplitudes of horizontal transient displacements are negligible too (Fig.\u00a01c). Our primary observation shows that velocity is systematically slower during extension and higher during compressional strains resulting in a seasonally-controlled variation of the state of rock damage. Variations of elastic properties and their non-linear sensitivity to strain arise from the stiffness modification of the grain and fracture contacts. We thus propose that seasonal variations induce a weakening/healing process that cyclically affects the crust along the IFZ. The process we observe seems to be reversible, with a restoration of the initial conditions (and of the elastic properties), like a fault healing process57 by which the crust retrieves its original characteristics prior to the new damage episode. Geodetic strain allows us to precisely track the mechanism underlying the velocity variations, which is the cyclical crack opening/closing of NW-SE-oriented crack system in the direction of the regional direction of minimum horizontal stress.\n\nWe observe that significant non-linear seasonal variations of elastic properties of the crust along the IFZ are statistically correlated with earthquakes rate. We propose a model in which hydrological deformations promote earthquake failure by a mechanism involving dynamic nonlinear elasticity22. Seasonal variations of elastic properties cause a weakening that triggers the observed micro-seismicity, alternated to a healing process as the strain amplitudes decrease and seismic wave velocity increases with frictional contacts ageing20. In terms of frictional contacts, we may also interpret triggering as the onset of sliding of the faults, resulting from an abrupt decrease in the shear strength of the fault gouge by softening of frictional contacts. Necessary physical characteristics for this triggering mechanism require a weak fault in a critical state and dynamic strain amplitudes greater than about 10\u2212618, regardless of their frequency content58. Both requirements are satisfied along the IFZ where active tectonic strain is likely to keep faults close to failure and hydrological forcing provides sufficient oscillatory strains. For the recent background micro seismicity, no significant localization along the segments responsible for the 1980 Ms 6.9 earthquake is observed59 suggesting that a diffused triggering mechanism in the volume interested by hydrological forcing and resulting nonlinear reduction of elastic properties is more likely than an accelerated aseismic slip along major fault zones.\n\nLaboratory experiments22 show that modulus reduction increases progressively as the effective stress is reduced, implying that the system\u2019s elastic nonlinearity is strongly sensitive to increase in pore pressure. In agreement with the observed depth distribution of seismicity (Fig.\u00a0S1), the deeper parts of the crust, where pore pressure may be greater than hydrostatic, may thus be more sensitive to hydrological forcing with respect to the shallow crust where extensive fracturing maintains a hydrostatic profile. The observed relationship between seismicity triggering and modulus reduction (Fig.\u00a04e, f) also agrees with laboratory experiments18 showing the existence of an approximate strain threshold above which significant elastic nonlinearity is observed and earthquakes are easily triggered. Thus, our study suggests that the elastic nonlinearity of fault cores close to a critical state plays a major role in earthquake triggering and offers an alternative perspective beyond models based solely on the evolution of pore pressure or Coulomb stress. We speculate that regional weakening of active fault zones, over time scales relevant for earthquake nucleation, may also increase the likelihood of higher-magnitude ruptures on large fault systems.",
+            "section_image": []
+        },
+        {
+            "section_name": "Methods",
+            "section_text": "We computed the three-component (ZZ, EE, NN) autocorrelation using continuous seismic data recorded at the MCRV station located in the IFZ area, in Southern Italy (Fig.\u00a01a). The considered time window for this study is from January 2008 to December 2021. We rejected daily traces if they don\u2019t contain more than 20\u2009h of data available and to reduce transient signals, we carried out a one\u2010bit normalization.\n\nWe measured the velocity variations using the stretching technique60, which provides stable measurements25, by stacking 90 days using an 89-day overlap of correlations. The stack of the autocorrelation over the full-time period was used as the reference signal to compute relative velocity variations. This operation was performed for each component in the coda wave window starting at 10\u2009s from the arrival of ballistic waves and with a duration of 40\u2009s. The choice of this window allows to resolve changes of \u03b4v/v in the shallow crust25. Velocity variations of the three components are, then, combined weighting with squared correlation coefficients estimated after stretching. We then select the velocity variations with correlation coefficients above 0.85.\n\nIn Fig.\u00a01c we represent the comparison of the seismic velocity variation for the stations MCRV and CAFE, this latter being outside the carbonates and characterized by much smaller variations (around 34% compared to MCRV), demonstrating that the response of crust around MCRV is very peculiar and associated with the local characteristics of the complex IFZ.\n\nWe computed the depth sensitivity of surface waves (Fig.\u00a0S1c, d) as in ref. 46 for a local velocity model47 and for the frequency band 0.5\u20131.0\u2009Hz at which we computed the velocity variations. This frequency band has been selected as it is the optimal band used in the Apennines to have a good temporal resolution with high quality correlation while limiting the number of stacked days25,44,61. For autocorrelations, the better outcomes are observed for frequencies exceeding 0.5\u2009Hz62, because in Southern Europe seasonal variations in the distribution of noise sources reduce the quality of the correlations and thus limit time dependent analysis63, while frequencies higher than 1\u2009Hz are too much contaminated by anthropogenic noise. We also computed the theoretical depth sensitivity of the scattered body waves (Fig.\u00a0S1e) as in ref. 25, considering a 3D sensitivity kernel formulation48. We solved for the body wave depth sensitivity normalized to 30\u2009km depth with each layer 1\u2009km thick layer25. In our case we considered a coda time lapse 30\u2009s, representative of the time window 10\u201350\u2009s, and two free path (10,100\u2009km) as reference.\n\nContinuous surface displacements have been measured by permanent GPS stations of the RING network (http://ring.gm.ingv.it). For our analysis, we considered the time series of horizontal components corrected for the long-term tectonic trend and instrumental offset from January 2008 through December 2021 obtained following the procedure outlined in ref. 32. We calculate the time-dependent horizontal strain rate tensor at the surface by modeling the observed displacement with elementary cuboid sources extending to a depth of 3.5\u2009km51 following the approach described in ref. 32. The use of this modeling approach (fully described in ref. 51) to calculate the horizontal components of the \u201chydrological\u201d strain rate field is required by the need to regularize the sparse density coverage of the GPS stations and incorporate the geometry of the karst aquifers. The second invariant of the horizontal long-term, tectonic strain rate field shown in Fig.\u00a01a, has been obtained from the secular GPS velocity field of ref. 64 and using the VISR code65 to calculate a regular grid of the horizontal strain rate tensor.\n\nIFZ is monitored since 2007 by the Irpinia Near Fault Observatory (INFO), which includes the Irpinia Seismic Network (ISNet, http://isnet.unina.it, network code IX), composed of a total of 31 co-located tri-axial strong motion accelerometers and three-components short period or broad-band seismometers and 8 INGV seismic stations (https://eida.ingv.it/it/, virtual network _NFOIRPINA, network code IV). The period analyzed in the present study ranges from January 2008 through December 2021. The original data set consisted of 1898 events with local magnitude \u22120.4\u2009\u2264\u2009ML\u2009\u2264\u20093.7, and the seismicity is mostly concentrated at depths between 8 and 12\u2009km (Fig.\u00a01c, S1). To avoid biases associated to aftershocks, we declustered the earthquake catalog using the approach described in ref. 66, and its windowing technique, where a scan of the catalog within distance and time is performed with spatiotemporal windows as a function of the magnitude66. In this procedure, the first shock is not necessarily the largest shock in the sequence; thus, a small foreshock is the first event of an aftershock sequence. If a largest shock occurs in the series, this enlarges the window beyond the value used for the first shock66. Since the recorded seismicity may be affected by the detection capability of the network, we select events shallower than 12\u2009km with magnitude above the minimum magnitude of completeness (MC), i.e., the magnitude above which the network is assumed to reliably record all the events occurring in the region of interest, estimated at ML 1.1 for ISNet67. Then we computed the seismicity rate as the number of earthquakes occurring in 90-days moving windows. We also tested the sensitivity of the seismicity rate to the parameters of the windowing technique66 used for the declustering and we found that seismicity rate is not changed at all by varying the windows used (Fig.\u00a0S2, Supplementary Materials). We constructed the synthetic catalogs starting from the observed number of events occurring in the considered time interval and considering this number as resulting from the sum of an homogeneous Poisson process and a nonhomogeneous hydrological forcing. The nonhomogeneous contribution has been produced using the inversion method68 which involves firstly obtaining the cumulative distribution for the variable to be sampled (strain or seismic velocity). Cumulative distribution functions of the strain and seismic velocity variations (simple or squared to consider the case of linear and non-linear effects, respectively) are calculated from the respective time series and rearranged to give an expression for the variable of interest (strain or seismic velocity) in terms of its probability. The variable can then be sampled by inserting uniform random values between 0 and 1 into this expression for each event contributing to the nonhomogeneous part of the synthetic catalog. The same approach has been used to calculate the homogeneous Poissonian contribution to the synthetic catalogs randomly sampling the cumulative function of the exponential distribution which controls the distribution of time intervals between successive independent events in a Poisson process68. Synthetic seismicity rate histories (90-days moving windows) are then computed from the synthetic catalogs.",
+            "section_image": []
+        },
+        {
+            "section_name": "Data availability",
+            "section_text": "The seismic catalog can be downloaded at http://isnet.unina.it. Velocimetric continuous data are available at https://eida.ingv.it/it/. Raw GPS data (rinex files) are available at http://ring.gm.ingv.it. The time series of the discharge of Caposele spring has been provided by Approvviggionamento Idrico (DIRAP), Acquedotto Pugliese, S.p.a., Bari. The dataset of seismic velocity changes, geodetic strain, and seismicity rate, generated during the current study, is available from the corresponding author on reasonable request. Analysis was made using MATLAB (release 2023a, https://www.mathworks.com/products/matlab.html) and Python (https://www.python.org/). Correspondence and material requests should be addressed to S.T. at the following address: stefania.tarantino@ingv.it.",
+            "section_image": []
+        },
+        {
+            "section_name": "Code availability",
+            "section_text": "This study was performed using the Python package Obspy and uses workflows provided in ref. 25 and ref. 32 for velocity variations measurement and strain computation respectively.",
+            "section_image": []
+        },
+        {
+            "section_name": "References",
+            "section_text": "Zener, C. Elasticity and Anelasticity of Metals (The University of Chicago Press, 1948).\n\nRenaud, G., Le Bas, P.-Y. & Johnson, P. A. Revealing highly complex elastic nonlinear (anelastic) behavior of Earth materials applying a new probe: dynamic acoustoelastic testing. J. Geophys. Res. Solid Earth 117, n/a-n/a (2012).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nSimpson, J., Malcolm, A. E. & van Wijk, K. The effect of temperature on the nonlinear elasticity of a fault rock in dynamic acoustoelastic testing (DAET) experiments. Geophys. J. Int. 235, 554\u2013565 (2023).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLieou, C. K. C., Daub, E. G., Ecke, R. E. & Johnson, P. A. Slow dynamics and strength recovery in unconsolidated granular Earth materials: a mechanistic theory. J. Geophys. Res. Solid Earth 122, 7573\u20137583 (2017).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nOstrovsky, L. A. & Johnson, P. A. Dynamic nonlinear elasticity in geomaterials. La Riv. del. Nuovo Cim. 24, 1\u201346 (2001).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nRenaud, G., Call\u00e9, S. & Defontaine, M. Remote dynamic acoustoelastic testing: elastic and dissipative acoustic nonlinearities measured under hydrostatic tension and compression. Appl. Phys. Lett. 94, 011905 (2009).\n\nJin, J., Rivi\u00e8re, J., Ohara, Y. & Shokouhi, P. Dynamic acousto-elastic response of single fatigue cracks with different microstructural features: an experimental investigation. J. Appl. Phys. 124, 075303 (2018).\n\nDelorey, A. A., Guyer, R. A., Bokelmann, G. H. R. & Johnson, P. A. Probing the damage zone at parkfield. Geophys. Res. Lett. 48, e2021GL093518 (2021).\n\nWang, Q.-Y. et al. Seasonal crustal seismic velocity changes throughout Japan. J. Geophys. Res. Solid Earth 122, 7987\u20138002 (2017).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nClements, T. & Denolle, M. A. Tracking groundwater levels using the ambient seismic field. Geophys. Res. Lett. 45, 6459\u20136465 (2018).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMao, S., Lecointre, A., van der Hilst, R. D. & Campillo, M. Space-time monitoring of groundwater fluctuations with passive seismic interferometry. Nat. Commun. 13, 4643 (2022).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nTakano, T., Nishimura, T., Nakahara, H., Ohta, Y. & Tanaka, S. Seismic velocity changes caused by the Earth tide: ambient noise correlation analyses of small-array data. Geophys. Res. Lett. 41, 6131\u20136136 (2014).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nTakano, T., Nishimura, T., Nakahara, H., Ueda, H. & Fujita, E. Sensitivity of seismic velocity changes to the tidal strain at different lapse times: data analyses of a small seismic array at Izu\u2010Oshima Volcano. J. Geophys. Res. Solid Earth 124, 3011\u20133023 (2019).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDelorey, A. A., van der Elst, N. J. & Johnson, P. A. Tidal triggering of earthquakes suggests poroelastic behavior on the San Andreas Fault. Earth Planet Sci. Lett. 460, 164\u2013170 (2017).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDelorey, A. A., Bokelmann, G. H. R., Johnson, C. W. & Johnson, P. A. Estimation of the orientation of stress in the Earth\u2019s crust without earthquake or borehole data. Commun. Earth Environ. 2, 190 (2021).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBen-Zion, Y. Collective behavior of earthquakes and faults: continuum-discrete transitions, progressive evolutionary changes, and different dynamic regimes. Rev. Geophys. 46, RG4006 (2008).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBen-Zion, Y. & Zaliapin, I. Spatial variations of rock damage production by earthquakes in southern California. Earth Planet Sci. Lett. 512, 184\u2013193 (2019).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nJohnson, P. A. & Jia, X. Nonlinear dynamics, granular media and dynamic earthquake triggering. Nature 437, 871\u2013874 (2005).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nNiu, F., Silver, P. G., Daley, T. M., Cheng, X. & Majer, E. L. Preseismic velocity changes observed from active source monitoring at the Parkfield SAFOD drill site. Nature 454, 204\u2013208 (2008).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nScuderi, M. M., Marone, C., Tinti, E., Di Stefano, G. & Collettini, C. Precursory changes in seismic velocity for the spectrum of earthquake failure modes. Nat. Geosci. 9, 695\u2013700 (2016).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nRivi\u00e8re, J. et al. Frequency, pressure, and strain dependence of nonlinear elasticity in Berea Sandstone. Geophys Res Lett. 43, 3226\u20133236 (2016).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nTinti, E. et al. On the evolution of elastic properties during laboratory stick\u2010slip experiments spanning the transition from slow slip to dynamic rupture. J. Geophys. Res. Solid Earth 121, 8569\u20138594 (2016).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nShapiro, N. M. & Campillo, M. Emergence of broadband Rayleigh waves from correlations of the ambient seismic noise. Geophys. Res. Lett. 31, n/a-n/a (2004).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nHillers, G. et al. In situ observations of velocity changes in response to tidal deformation from analysis of the high\u2010frequency ambient wavefield. J. Geophys. Res. Solid Earth 120, 210\u2013225 (2015).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nPoli, P., Marguin, V., Wang, Q., D\u2019Agostino, N. & Johnson, P. Seasonal and coseismic velocity variation in the region of L\u2019Aquila from single station measurements and implications for crustal rheology. J. Geophys. Res. Solid Earth 125, e2019JB019316 (2020).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nSens-Sch\u00f6nfelder, C., Snieder, R. & Li, X. A model for nonlinear elasticity in rocks based on friction of internal interfaces and contact aging. Geophys. J. Int. https://doi.org/10.1093/gji/ggy414 (2018).\n\nGr\u00eat, A., Snieder, R. & Scales, J. Time-lapse monitoring of rock properties with coda wave interferometry. J. Geophys. Res. Solid Earth 111, n/a-n/a (2006).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBernard, P. & Zollo, A. The Irpinia (Italy) 1980 earthquake: detailed analysis of a complex normal faulting. J. Geophys. Res. 94, 1631 (1989).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLeone, G. et al. A hundred years of Caposele spring discharge measurements: trends and statistics for understanding water resource availability under climate change. Stoch. Environ. Res. Risk Assess. 35, 345\u2013370 (2021).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nFiorillo, F. Spring hydrographs as indicators of droughts in a karst environment.J. Hydrol. 373, 290\u2013301 (2009).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nSilverii, F., D\u2019Agostino, N., M\u00e9tois, M., Fiorillo, F. & Ventafridda, G. Transient deformation of karst aquifers due to seasonal and multiyear groundwater variations observed by GPS in southern Apennines (Italy). J. Geophys. Res. Solid Earth 121, 8315\u20138337 (2016).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nD\u2019Agostino, N. et al. Crustal deformation and seismicity modulated by groundwater recharge of karst aquifers. Geophys. Res. Lett. 45, 12,253\u201312,262 (2018).\n\nHeki, K. Snow load and seasonal variation of earthquake occurrence in Japan. Earth Planet Sci. Lett. 207, 159\u2013164 (2003).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nSaar, M. O. & Manga, M. Seismicity induced by seasonal groundwater recharge at Mt. Hood, Oregon. Earth Planet. Sci. Lett. 214, 605\u2013618 (2003).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBettinelli, P. et al. Seasonal variations of seismicity and geodetic strain in the Himalaya induced by surface hydrology. Earth Planet Sci. Lett. 266, 332\u2013344 (2008).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nCraig, T. J., Chanard, K. & Calais, E. Hydrologically-driven crustal stresses and seismicity in the New Madrid Seismic Zone. Nat. Commun. 8, 2143 (2017).\n\nArticle\u00a0\n    ADS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nJohnson, C. W., Fu, Y. & B\u00fcrgmann, R. Seasonal water storage, stress modulation, and California seismicity. Science 356, 1161\u20131164 (2017).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nHandwerger, A. L., Huang, M.-H., Fielding, E. J., Booth, A. M. & B\u00fcrgmann, R. A shift from drought to extreme rainfall drives a stable landslide to catastrophic failure. Sci. Rep. 9, 1569 (2019).\n\nArticle\u00a0\n    ADS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nHsu, Y.-J. et al. Synchronized and asynchronous modulation of seismicity by hydrological loading: a case study in Taiwan. Sci. Adv. 7, eabf7282 (2021).\n\nXue, L., Johnson, C. W., Fu, Y. & B\u00fcrgmann, R. Seasonal seismicity in the western branch of the East African Rift system. Geophys. Res. Lett. 47, e2019GL085882 (2020).\n\nAscione, A., Mazzoli, S., Petrosino, P. & Valente, E. A decoupled kinematic model for active normal faults: Insights from the 1980, MS = 6.9 Irpinia earthquake, southern Italy. Geol. Soc. Am. Bull. 125, 1239\u20131259 (2013).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDe Matteis, R. et al. Fault Delineation and regional stress direction from the analysis of background microseismicity in the Southern Apennines, Italy. Bull. Seismol. Soc. Am. 102, 1899\u20131907 (2012).\n\nD\u2019Agostino, N. Complete seismic release of tectonic strain and earthquake recurrence in the Apennines (Italy). Geophys. Res. Lett. 41, 1155\u20131162 (2014).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBarajas, A., Poli, P., D\u2019Agostino, N., Margerin, L. & Campillo, M. Separation of poroelastic and elastic processes of an aquifer from tectonic phenomena using geodetic, seismic, and meteorological data in the Pollino region, Italy. Geochem. Geophys. Geosyst. 22, e2021GC009742 (2021).\n\nBrenguier, F. et al. Mapping pressurized volcanic fluids from induced crustal seismic velocity drops. Science (1979) 345, 80\u201382 (2014).\n\nCAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nHerrmann, R. B. Computer programs in seismology: an evolving tool for instruction and research. Seismol. Res. Lett. 84, 1081\u20131088 (2013).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMatrullo, E., De Matteis, R., Satriano, C., Amoroso, O. & Zollo, A. An improved 1-D seismic velocity model for seismological studies in the Campania\u2013Lucania region (Southern Italy). Geophys J. Int 195, 460\u2013473 (2013).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nPacheco, C. & Snieder, R. Time-lapse travel time change of multiply scattered acoustic waves. J. Acoust. Soc. Am. 118, 1300\u20131310 (2005).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBarajas, A., Margerin, L. & Campillo, M. Coupled body and surface wave sensitivity kernels for coda-wave interferometry in a three-dimensional scalar scattering medium. Geophys. J. Int. 230, 1013\u20131029 (2022).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDe Landro, G. et al. Decade-long monitoring of seismic velocity changes at the Irpinia fault system (southern Italy) reveals pore pressure pulsations. Sci. Rep. 12, 1\u20139 (2022).\n\n\n                    Google Scholar\u00a0\n                \n\nBarbot, S., Moore, J. D. P. & Lambert, V. Displacement and stress associated with distributed anelastic deformation in a half\u2010space. Bull. Seismol. Soc. Am. 107, 821\u2013855 (2017).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nYamamura, K. et al. Long-term observation of in situ seismic velocity and attenuation. J. Geophys. Res. Solid Earth 108, 2317 (2003).\n\nSegall, P. & Lu, S. Injection-induced seismicity: Poroelastic and earthquake nucleation effects. J. Geophys. Res. Solid Earth 120, 5082\u20135103 (2015).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMavko, G., Kjartansson, E. & Winkler, K. Seismic wave attenuation in rocks. Rev. Geophys. 17, 1155 (1979).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nScholz, C. H. The Mechanics of Earthquakes and Faulting. (Cambridge University Press, 2019). https://doi.org/10.1017/9781316681473.\n\nDelorey, A. A. & Chen, T. Behavior of tidally triggered earthquakes depends on fluid conditions. Bull. Seismol. Soc. Am. 112, 2890\u20132901 (2022).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBrenguier, F. et al. Postseismic relaxation along the San Andreas fault at Parkfield from continuous seismological observations. Science 321, 1478\u20131481 (2008).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nGomberg, J. & Johnson, P. Dynamic triggering of earthquakes. Nature 437, 830\u2013830 (2005).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDe Landro, G. et al. High-precision differential earthquake location in 3-D models: evidence for a rheological barrier controlling the microseismicity at the Irpinia fault zone in southern Apennines. Geophys. J. Int. 203, 1821\u20131831 (2015).\n\nLobkis, O. I. & Weaver, R. L. Coda-wave interferometry in finite solids: recovery of P-to-S conversion rates in an Elastodynamic Billiard. Phys. Rev. Lett. 90, 254302 (2003).\n\nArticle\u00a0\n    ADS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMikhael, N., Poli, P. & Garambois, S. Non\u2010linear seismic velocity variations observed during a seismic swarm in the Alto Tiberina low angle normal fault from ambient noise correlation measurements. J. Geophys. Res. Solid Earth 129, e2023JB028232. (2024).\n\nHobiger, M., Wegler, U., Shiomi, K. & Nakahara, H. Single-station cross-correlation analysis of ambient seismic noise: application to stations in the surroundings of the 2008 Iwate-Miyagi Nairiku earthquake. Geophys J. Int 198, 90\u2013109 (2014).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nStehly, L., Delouche, E., Tomasetto, L. & Ranjan, P. Dynamic of seismic noise sources in the Mediterranean Sea: implication for monitoring using noise correlations. Comptes Rendus G\u00e9osci. 356, 1\u201324 (2024).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDaout, S. et al. Along-strike variations of strain partitioning within the Apennines determined from large-scale multi-temporal InSAR analysis. Tectonophysics 867, 230076 (2023).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nShen, Z., Wang, M., Zeng, Y. & Wang, F. Optimal interpolation of spatially discretized geodetic data. Bull. Seismol. Soc. Am. 105, 2117\u20132127 (2015).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nGardner, J. K. & Knopoff, L. Is the sequence of earthquakes in Southern California, with aftershocks removed, Poissonian? Bull. Seismol. Soc. Am. 64, 1363\u20131367 (1974).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nVassallo, M., Festa, G. & Bobbio, A. Seismic ambient noise analysis in Southern Italy. Bull. Seismol. Soc. Am. 102, 574\u2013586 (2012).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nZhuang, J. & Touati, S. Stochastic simulation of earthquake catalogs, community online resource for statistical seismicity analysis. http://www.corssa.org (2015).\n\nWessel, P. et al. The generic mapping tools version 6. Geochem. Geophys. Geosyst. 20, 5556\u20135564 (2019).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nGalli, P. & Peronace, E. New paleoseismic data from the Irpinia Fault. A different seismogenic perspective for southern Apennines (Italy). Earth Sci. Rev. 136, 175\u2013201 (2014).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDownload references",
+            "section_image": []
+        },
+        {
+            "section_name": "Acknowledgements",
+            "section_text": "This work has been supported by the INGV-Pianeta Dinamico Project MYBURP (Modulation of hydrology on stress buildup on the Irpinia Fault) and the PRIN-FLUIDS project: \u201cDetection and tracking of crustal fluid by multi-parametric methodologies and technologies\u201d of the Italian PRIN-MIUR programme (Grant no. 20174X3P29). P.P. has been supported by the European Research Council (ERC) under the European Union Horizon 2020 Research and Innovation Program (grant agreements 802777\u2014MONIFAULTS). Figures were generated with Generic Mapping Tools69.",
+            "section_image": []
+        },
+        {
+            "section_name": "Author information",
+            "section_text": "Istituto Nazionale di Geofisica e Vulcanologia, L\u2019Aquila, Italy\n\nStefania Tarantino\u00a0&\u00a0Maurizio Vassallo\n\nDepartment of Geoscience, University of Padova, Padova, Italy\n\nPiero Poli\n\nIstituto Nazionale Geofisica e Vulcanologia, Rome, Italy\n\nNicola D\u2019Agostino\n\nDepartment of Physics, University of Napoli, Napoli, Italy\n\nGaetano Festa\u00a0&\u00a0Aldo Zollo\n\nApprovvigionamento Idrico (DIRAP), Acquedotto Pugliese S.p.A, Bari, Italy\n\nGerardo Ventafridda\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nS.T., P.P., and N.D. conceived the methodology and wrote the first draft of the manuscript. S.T., P.P., N.D., G.F., and M.V. contributed to data preparation and analysis and to the interpretation of results. G.V. provided data of the Caposele spring. A.Z. contributed to the interpretation of results. All authors revised the final draft of the manuscript.\n\nCorrespondence to\n                Stefania Tarantino.",
+            "section_image": []
+        },
+        {
+            "section_name": "Ethics declarations",
+            "section_text": "The authors declare no competing interests.",
+            "section_image": []
+        },
+        {
+            "section_name": "Peer review",
+            "section_text": "Nature Communications thanks Andrew Delorey and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. A peer review file is available.",
+            "section_image": []
+        },
+        {
+            "section_name": "Additional information",
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+            "section_image": []
+        },
+        {
+            "section_name": "Rights and permissions",
+            "section_text": "Open Access  This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article\u2019s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article\u2019s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.\n\nReprints and permissions",
+            "section_image": []
+        },
+        {
+            "section_name": "About this article",
+            "section_text": "Tarantino, S., Poli, P., D\u2019Agostino, N. et al. Non-linear elasticity, earthquake triggering and seasonal hydrological forcing along the Irpinia fault, Southern Italy.\n                    Nat Commun 15, 9821 (2024). https://doi.org/10.1038/s41467-024-54094-4\n\nDownload citation\n\nReceived: 08 March 2024\n\nAccepted: 01 November 2024\n\nPublished: 13 November 2024\n\nVersion of record: 13 November 2024\n\nDOI: https://doi.org/10.1038/s41467-024-54094-4\n\nAnyone you share the following link with will be able to read this content:\n\nSorry, a shareable link is not currently available for this article.\n\n\n\n\n                            Provided by the Springer Nature SharedIt content-sharing initiative\n                        ",
+            "section_image": [
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0ea74b5c8de9b0e46fcdecaea8a66b6a4b59669369e79a3310d00aabe8f4f20a/metadata.json

@@ -0,0 +1,150 @@
+{
+    "title": "Maternal plasma cell-free RNA as a predictor of early and late-onset preeclampsia throughout pregnancy",
+    "pre_title": "Maternal Plasma Cell-Free RNA as a Predictor of Early and Late-Onset Preeclampsia Throughout Pregnancy",
+    "journal": "Nature Communications",
+    "published": "20 October 2025",
+    "supplementary_0": [
+        {
+            "label": "Supplementary information",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-64215-2/MediaObjects/41467_2025_64215_MOESM1_ESM.pdf"
+        },
+        {
+            "label": "Description of Additional Supplementary Files",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-64215-2/MediaObjects/41467_2025_64215_MOESM2_ESM.pdf"
+        },
+        {
+            "label": "Supplementary Data File 1",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-64215-2/MediaObjects/41467_2025_64215_MOESM3_ESM.xlsx"
+        },
+        {
+            "label": "Supplementary Data File 2",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-64215-2/MediaObjects/41467_2025_64215_MOESM4_ESM.xlsx"
+        },
+        {
+            "label": "Reporting Summary",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-64215-2/MediaObjects/41467_2025_64215_MOESM5_ESM.pdf"
+        },
+        {
+            "label": "Transparent Peer Review file",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-64215-2/MediaObjects/41467_2025_64215_MOESM6_ESM.pdf"
+        }
+    ],
+    "supplementary_1": NaN,
+    "supplementary_2": NaN,
+    "source_data": [],
+    "code": [
+        "https://github.com/marinaigual/ipremom-cfrna-preeclampsia-predictor/tree/main"
+    ],
+    "subject": [
+        "Pre-eclampsia",
+        "Predictive markers",
+        "RNA sequencing"
+    ],
+    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
+    "preprint_pdf": "https://www.researchsquare.com/article/rs-5684050/v1.pdf?c=1761044762000",
+    "research_square_link": "https://www.researchsquare.com//article/rs-5684050/v1",
+    "nature_pdf": "https://www.nature.com/articles/s41467-025-64215-2.pdf",
+    "preprint_posted": "16 Jan, 2025",
+    "research_square_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Early-onset (EOPE) and late-onset preeclampsia (LOPE) pose significant challenges to maternal and child health, highlighting the need for early, non-invasive risk identification. In this prospective longitudinal study, we followed 9,586 pregnant women, collecting blood samples each trimester: 9-14 weeks (T1), 18-28 weeks (T2), and after 28 weeks or at preeclampsia diagnosis (T3). Plasma cell-free RNA (cfRNA) signatures were analyzed in women who developed EOPE (n=42) or LOPE (n=43) and compared to matched normotensive controls (n=75). Mapping cfRNA origins and performing differential abundance analysis provided insights into multi-organ impacts, revealing distinct transcriptional features of EOPE and LOPE. We developed a first-trimester EOPE predictive model using 36 transcripts, achieving 83% sensitivity, 88% specificity, and an AUC of 0.85, detecting risk 18.0 weeks before onset. A second-trimester model based on 87 cfRNA transcripts, predicted EOPE 8.5 weeks prior to onset with 87% sensitivity, 84% specificity, and an AUC of 0.85. For LOPE model, detecting risk 14.9 weeks before onset, used 92 cfRNAs, with 86% sensitivity, 89% specificity, and an AUC of 0.88. EOPE models were enriched for decidua-associated transcripts, highlighting the maternal involvement in this subtype, while LOPE models showed diverse tissue responses, paving the way for improved subtype differentiation and tailored interventions to mitigate preeclampsia risks.Health sciences/Biomarkers/Predictive markersBiological sciences/Biological techniques/Sequencing/RNA sequencingBiological sciences/Computational biology and bioinformatics/Predictive medicine",
+            "section_image": []
+        },
+        {
+            "section_name": "Additional Declarations",
+            "section_text": "Table 1 is available in the Supplementary Files section.\nYes there is potential Competing Interest. N.C-M., M.I., T.G-G., C.S. are inventors on a patent application (EP24383276.3) covering methods for determining the risk of preeclampsia. N.C-M., T.C., M.I., C.G-A., N.B-G., A.G-D., E.O-D., A.V., T.G-G. are employees of iPremom Pregnancy Healthcare Diagnostics. C.S. is a founder of iPremom Pregnancy Healthcare Diagnostics",
+            "section_image": []
+        },
+        {
+            "section_name": "Supplementary Files",
+            "section_text": "Table1.xlsxTable 1. Maternal characteristics and pregnancy outcomes for the selected subset of participants.Supp.Table1.xlsxSupplementary Table 1. Gestational age at blood sample for patients and controls in the selected \u00a0subset of participants.Supp.Table2.xlsxSupplementary Table 2. Differentially abundant cfRNA transcripts at diagnosis in early-onset \u00a0preeclampsia patients compared to normotensive controls.Supp.Table3.xlsxSupplementary Table 3. Differentially abundant cfRNA transcripts at diagnosis in late-onset preeclampsia patients compared to normotensive controls.Supp.Table4.xlsxSupplementary Table 4. Gene ontology analysis for increased abundant cfRNA in early-onset preeclampsia and late-onset preeclampsia.Supp.Table5.xlsxSupplementary Table 5. cfRNAs composing the predictive models for early-onset preeclampsia and late-onset preeclampsia at the first and second trimester of pregnancy.Supp.Table6.xlsxSupplementary Table 6. Summary of predictive model performance metrics for early-onset \u00a0preeclampsia and late-onset preeclampsia during the first and second trimesters of pregnancy",
+            "section_image": []
+        }
+    ],
+    "nature_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Early- and late-onset preeclampsia (EOPE and LOPE) pose serious maternal-fetal risks, yet non-invasive early prediction remains challenging. In a prospective cohort of 9,586 pregnancies, we analyze trimester-specific plasma cell-free RNA (cfRNA) profiles from 42 EOPE and 43 LOPE cases versus 131 normotensive controls. Organ-specific transcriptomic shifts distinguish EOPE from LOPE. Predictive models based on cfRNA signatures identify EOPE up to 18.0 weeks before clinical onset in the first-trimester (T1) (AUC\u2009=\u20090.88), and 8.5 weeks in the second trimester (T2) (AUC\u2009=\u20090.89). LOPE is predicted 14.9 weeks in advance using T2 data (AUC\u2009=\u20090.90), while T1 performance is lower (AUC\u2009=\u20090.68). External validation confirms robust EOPE prediction (AUC\u2009=\u20090.87 at T1; 0.81 at T2) and acceptable LOPE performance (AUC\u2009=\u20090.63 at T1; AUC\u2009=\u20090.77 at T2). EOPE models are enriched for decidual transcripts, suggesting early maternal involvement; LOPE models reflect broader tissue contributions. These findings offer a path to early, non-invasive, subtype-specific preeclampsia risk stratification and prevention.",
+            "section_image": []
+        },
+        {
+            "section_name": "Introduction",
+            "section_text": "Maternal and infant mortality during pregnancy and labor are critical indicators of community and national health1,2. Most pregnancy complications arise from disorders that develop during the periconceptional phase, particularly during embryonic implantation and early placentation3.\n\nPreeclampsia\u2014a life-threatening obstetric syndrome\u2014is characterized by new-onset of hypertension after 20 weeks of gestation, accompanied by signs of kidney, liver, or brain damage4. Each year, preeclampsia contributes to 14% of maternal deaths worldwide, leaving a lasting impact on survivors\u2019 health5. It also constitutes a significant public health burden, incurring $1.03 billion in maternal healthcare costs and an additional $1.15 billion for neonatal care in infants born to mothers affected by preeclampsia within the first year after birth in the United States6.\n\nThe heterogeneity of preeclampsia is notable, differentiated by the timing of onset and severity of symptoms. Early-onset preeclampsia (EOPE) arises before 34 weeks of gestation, necessitating emergency delivery to mitigate risks to maternal and fetal health7,8. In contrast, late-onset preeclampsia (LOPE) manifests after 34 weeks and can lead to severe maternal organ damage such as kidney, liver, or brain damage8,9,10,11. Therefore, there is an urgent need for straightforward, non-invasive methods for early diagnosis of preeclampsia in the first trimester to implement preventive strategies effectively12,13,14.\n\nSince the maternal decidua regulates the initial steps of maternal-embryo communication, decidualization resistance (DR)\u2014characterized by defective endometrial cell differentiation\u2014results in abnormal placentation, which has been associated with the etiology of major obstetric syndromes, including preeclampsia15,16,17,18,19, even though symptoms may manifest later in gestation15,16,17,18,19. Recently, we provided an in-depth multi-omics characterization of DR in former EOPE patients, further underscoring the uterine contribution to this pathological condition20.\n\nAnalyzing plasma cell-free RNA (cfRNA) through liquid biopsy (i.e., from a blood sample) has emerged as a promising non-invasive tool for molecular monitoring in pregnancy, offering insights into physiological and pathological events21,22. However, previous cfRNA studies on preeclampsia prediction have faced limitations such as small EOPE sample size23, lack of clear subtype distinction23,24, or sampling at later gestational ages24,25. Our study builds on these foundations and addresses these gaps by including a large, prospectively collected cohort of EOPE cases with strict first-trimester sampling, clearly differentiating EOPE and LOPE, and employing longitudinal sampling. This comprehensive design has allowed us to develop and validate predictive models with improved early and subtype-specific risk stratification.\n\nSpecifically, in this case-control study, we prospectively analyzed the cfRNA profiles in pregnant women across the three trimesters of pregnancy, comparing EOPE and LOPE with normotensive controls. This approach facilitated the characterization of the circulating transcriptome by mapping the tissue origins and transcriptional changes associated with EOPE and LOPE, revealing that both subtypes display distinct transcriptional differences compared to controls. Our research identified cfRNA profiles that exhibited robust predictive performance for EOPE in both the first (averaging 18.0 weeks before diagnosis) and second trimesters (averaging 8.5 weeks prior to clinical onset), as well as for LOPE in the second trimester (14.9 weeks prior to clinical onset). Monitoring cfRNA profiles not only aids in predicting the risk of developing preeclampsia but also allows the differentiation of both subtypes of preeclampsia and the evaluation of different organ damage in affected patients, providing insights into their prognosis.",
+            "section_image": []
+        },
+        {
+            "section_name": "Results",
+            "section_text": "A total of 9586 pregnant women with singleton pregnancies were enrolled in this prospective and longitudinal case-control study in fourteen tertiary hospitals in Spain (ClinicalTrials.gov Identifier: NCT04990141). Blood samples were collected prospectively across all three trimesters and at the time of EOPE or LOPE diagnosis. Each participant was followed until delivery, ensuring the availability of obstetrical outcome and the creation of a curated database with comprehensive clinical data. Uncomplicated pregnancies that progressed to term (>\u200937 weeks) were classified as normotensive controls, while those diagnosed with EOPE or LOPE, were categorized according to current established ACOG4 and FIGO24 clinical guidelines.\n\nOf the 9586 pregnant women enrolled, 7142 were eligible for analysis after excluding participants for selection failure, loss to follow-up, and obstetric complications other than preeclampsia. We included all EOPE cases (n\u2009=\u200942) and randomly selected a subset of LOPE cases (n\u2009=\u200943). The number of LOPE cases was established to match the number of EOPE cases, ensuring that both groups had the same control-to-case ratio of 1:3, which is optimal for model development. Normotensive controls (n\u2009=\u2009131) were randomly selected from the 6,905 uncomplicated pregnancies and matched to both EOPE and LOPE cases for key epidemiological variables including gestational age at sampling, maternal age, parity, BMI and ethnicity (Supplementary Fig.\u00a01a, b, and Supplementary Table\u00a01). Then, a subset of 216 participants composed by preeclampsia cases (EOPE and LOPE) and normotensive controls was selected for total cfRNA sequencing to characterize cfRNA profiles throughout the progression of pregnancy (Fig.\u00a01). For the development of predictive models, the cohort was randomly stratified into a discovery set (70% of patients) and a validation set (30% of patients). The discovery set was used to build the predictive model and the validation set to assess its performance in a hold-out group of samples (Supplementary Fig.\u00a01c).\n\nA total of 9586 pregnant participants were recruited. After excluding participants due to selection failure and loss to follow-up, 8991 remained. Within this cohort, 237 (2,6%) individuals were diagnosed with preeclampsia, including 42 EOPE and 195 LOPE cases, while 1849 (20.6%) individuals had other pregnancy-related pathologies, and 6905 (76,8%) participants had no obstetric complications. For cfRNA analysis, we included all 42 EOPE cases, a subset of 43 LOPE cases and 131 normotensive controls, randomly selected from the matched cohort based on gestational age at sample collection, maternal age, parity, ethnicity, and BMI.\n\nFrom each participant, we collected three peripheral blood samples between 9 and 14 weeks of gestation (T1), 18-28 weeks (T2), and at the time of diagnosis of EOPE and LOPE or after 28 weeks (T3) (Fig.\u00a02). Data on the gestational weeks of blood sample collection are summarized in Supplementary Table\u00a02. Due to clinical emergencies necessitating immediate termination of pregnancy, T3 could not be collected from fourteen EOPE patients and seven LOPE patients.\n\nBar graph illustrating the number of samples collected at each gestational week for the EOPE (a), LOPE (c) and control (e) groups. Color represents the time point of sample collection: T1 (9-14 gestational weeks); T2 (18\u201328 gestational weeks); T3 (at the time of preeclampsia diagnosis or >28 gestational weeks). Density plot showing the relative frequency of preeclampsia diagnosis and delivery across gestational weeks for the EOPE (b), LOPE (d) and control (f) groups.\n\nMaternal characteristics, clinical symptoms, and birth outcomes are summarized in Table\u00a01. There were no significant differences in maternal age, parity, ethnicity, BMI index or smoking habits between patients and controls (p\u2009>\u20090.05). Natural conception rate was statistically lower in EOPE patients compared to controls (p\u2009=\u20090.0003) but did not differ significantly in LOPE (p\u2009=\u20090.105). Aspirin prophylaxis (150\u2009mg) was prescribed to 30 EOPE (71.4%), 23 LOPE cases (53.5%), and 10 normotensive controls (7.6%). EOPE was diagnosed at 30.0\u2009\u00b1\u20093.4 weeks, with severe symptoms in 76.2% of patients; LOPE was diagnosed at 36.5\u2009\u00b1\u20091.8 weeks, with severe symptoms in 41.9% of patients. Severe symptoms were considered the presence of severely elevated blood pressure (systolic \u2265160\u2009mm Hg or diastolic \u2265100\u2009mm Hg), thrombocytopenia, impaired liver function, progressive renal insufficiency, pulmonary edema, or neurological complications such as cerebral or visual disturbances4.\n\nBirth outcomes for EOPE and LOPE included higher rates of small for gestational age, preterm birth, cesarean delivery, and lower fetal weight (p\u2009<\u20090.001). Specifically, preterm deliveries occurred in 87.8% of EOPE patients and in 41.9% of LOPE patients, with cesarean sections required in 69.0% and 44.2% of patients, respectively. In contrast, all deliveries in the control group occurred at term, and only 19.8% involved cesarean sections. Fetal sex did not differ between groups. EOPE patients had significantly higher rates of stillbirth (11.9%) and post-delivery complications (p\u2009<\u20090.001), with 35.2% of mothers and 50.0% of neonates requiring intensive care. In comparison, among patients with LOPE, 18.6% of mothers and 16.3% of newborns required intensive care, whereas no mothers and 0.8% of neonates in the control group needed intensive care.\n\nWe analyzed a total of 29,871 cfRNA transcripts after applying quality filtering and normalization processes. To determine the tissue origins of the identified transcripts, we compared our cfRNA dataset to the Human Protein Atlas database26, focusing on transcripts classified as \u201cenriched\u201d or \u201cenhanced\u201d in specific tissues or organs. In this analysis, we examined tissues and organs that are directly involved in the pathophysiology of preeclampsia and contribute to its clinical manifestations. Our experimental protocol detected over 90% of these classified transcripts for each targeted organ or tissue of interest (Fig.\u00a03a), indicating a robust coverage of tissue-specific cfRNA signatures in our dataset.\n\na Number and proportion of cfRNA transcripts from organs/tissues implicated in preeclampsia, relative to Human Protein Atlas reference. b Box plots show cfRNA abundance scores by tissue of origin at each time point, calculated as the sum of log-transformed CPM-TMM normalised counts. Color indicates group. Horizontal lines represent medians; boxes, 25th\u201375th percentiles; whiskers extend to 1.5x interquartile range. Sample sizes for each time point and group are as follows: T1 (EOPE, n\u2009=\u200941; LOPE, n\u2009=\u200943; control, n\u2009=\u2009129); T2 (EOPE, n\u2009=\u200940; LOPE, n\u2009=\u200941; control, n\u2009=\u2009120); T3 (EOPE, n\u2009=\u200919 vs. control, n\u2009=\u200934; LOPE, n\u2009=\u200924 vs. control, n\u2009=\u200939). P-values were determined by Wilcoxon rank-sum test with two tails. Exact P-values for all comparisons are provided in Supplementary Table\u00a03. *P\u2009<\u20090.05, **P\u2009<\u20090.01, ***P\u2009<\u20090.001, ****P\u2009<\u20090.0001.\n\nWe then calculated the organ/tissue-specific signature score for patients and controls at three time points during pregnancy (T1, T2 and T3) (Fig.\u00a03b and Supplementary Table\u00a03). In EOPE patients, a significant increase in cfRNA transcripts from the liver, kidney, and decidua was identified at T2 (p\u2009<\u20090.01), indicating tissue specific damage approximately eight weeks before diagnosis. At T3, when clinical symptoms appear, EOPE patients displayed a significantly higher signature score (p\u2009<\u20090.0001) for additional organs including brain, lungs, placenta, and lymphoid tissues, signaling widespread organ injury. In contrast in LOPE patients, tissue-specific transcripts suggesting organ damage was only observed at T3 (p\u2009<\u20090.01), with lower levels of significance than those in EOPE.\n\nTo decode cfRNA dynamics throughout pregnancy, we performed a differential abundance analysis at each time point, elucidating molecular changes in the circulating transcriptome associated with disease progression and offering insights into underlying mechanisms. At the time of diagnosis (T3), we identified 24,336 transcripts with significantly altered abundance in EOPE patients compared to controls (FDR\u2009<\u20090.05) (Supplementary Fig.\u00a02a and Supplementary Data File\u00a01). In contrast, LOPE patients exhibited 11,859 differentially abundant transcripts (FDR\u2009<\u20090.05) (Supplementary Fig.\u00a02b and Supplementary Data File\u00a02). Notably, 8,127 cfRNAs showed differential abundance in T2 for EOPE patients (FDR\u2009<\u20090.05), whereas no differentially abundant cfRNAs were detected in T1 for either EOPE or LOPE patients, nor in T2 for LOPE. These findings suggest that transcriptomic alterations emerge as EOPE progresses, while LOPE remains largely unchanged.\n\nGene ontology overrepresentation analysis within the differentially abundant cfRNAs at diagnosis revealed biological processes indicative of fetal and maternal organ-specific damage (FDR\u2009<\u20090.05) (Supplementary Fig.\u00a02c and Supplementary Table\u00a04). Both, EOPE and LOPE patients displayed significant enrichment in key biological processes, including transport across the blood-brain barrier, renal water homeostasis, regulation of blood pressure and cognition, which are hallmark processes of the pathology. Importantly, signatures of fetal tissue damage were identified in both EOPE and LOPE, with a notably greater impact in EOPE patients. Distinct biological processes were associated with either EOPE or LOPE. In EOPE, overrepresentation analysis revealed significantly enriched pathways related to neuronal death, renal filtration, and immune dysfunction \u2500including interleukin-8 production, response to interleukin-4, neutrophil-mediated immunity, and antimicrobial humoral immune response. In contrast, LOPE cfRNA profile showed signatures linked to heart and brain function (FDR\u2009<\u20090.05), suggesting significant damage to these organs.\n\nThus, cfRNA profile analysis at diagnosis (T3) indicates more extensive transcriptomic alterations in EOPE compared to LOPE, highlighting an exacerbated proinflammatory state as a defining feature. These findings underscore the impacts of the disease on multiple organ systems and suggest that cfRNA profiling may provide valuable insights into the molecular distinctions between preeclampsia subtypes. Additionally, the identification of distinct biological processes linked to each preeclampsia subtype emphasizes the need for tailored therapeutic approaches targeting specific dysfunctions observed in EOPE and LOPE.\n\nGiven the evidence that cfRNA profiles reflect molecular changes throughout pregnancy, disruptions in these pathways may help identify pregnancies at risk for EOPE or LOPE. Here, we developed a model for EOPE risk assessment based on plasma cfRNA profiles in the first trimester (T1), approximately 18.0 weeks before clinical onset.\n\nOur optimal predictive model for EOPE utilized 36 cfRNA transcripts (Supplementary Table\u00a05) and was evaluated in a hold-out validation set. The model achieved a sensitivity of 83% and specificity of 90%, with an area under the receiver operator characteristic curve (AUC) of 0.88 (Fig.\u00a04a and Supplementary Table\u00a06). Nearly all samples were correctly classified, with minimal misclassifications observed reinforcing the model\u2019s robustness and indicating no evidence of overfitting (Fig.\u00a04b). Relative contribution of individual cfRNA transcripts to the model\u2019s performance are detailed in Fig.\u00a04c. We further evaluated the same cfRNA signature in an independent external dataset23 (Fig.\u00a04a,b and Supplementary Table\u00a06), confirming consistent performance (sensitivity 78%, specificity 90%; AUC 0.87), despite cross-cohort variability in protocols and data origin.\n\nReceiver operating characteristic (ROC) curves for EOPE (a) and LOPE (d) models across internal validation (validation 1) and external validation23 (validation 2). The X-axis represents the False Negative Rate; the Y-axis, the True Positive Rate. Violin plots showing correctly and misclassified patients and controls based on the classifier score obtained from the predictive model for EOPE (b) and LOPE (e). The X-axis shows the real obstetric outcome; the Y-axis, the predicted outcome. Bar plot illustrating each cfRNAs contribution to EOPE (c) and LOPE (f) models. The X-axis shows the feature importance scores, which quantify the relative contribution of each cfRNA to the model\u2019s predictions, with higher scores indicating features that play a more significant role in discriminating between outcomes. CfRNAs associated with DR are marked with an asterisk. AUC, area under the curve.\n\nFurther analysis of these 36 transcripts revealed that 17 (47.2%) were identified as markers of DR in women with a history of severe preeclampsia, including CBR3, MMP7, MDK, TRIB1, PAEP20. The model also incorporates cfRNA transcripts known to be disrupted in preeclamptic placentas, such as RFLBN27, and CD7428, as well as others associated with fetal growth restriction, such as CCL4L229 and MYL630.\n\nUsing the same computational approach, we developed a predictive model for LOPE in the first trimester (T1), with predictions averaging 24.9 weeks before clinical onset. However, the model\u2019s performance in the validation set was limited, achieving a sensitivity of 72%, specificity of 64%, and an AUC of 0.68 (Fig.\u00a04d and Supplementary Table\u00a06). Consistent with these findings, the model showed similarly limited performance when applied to an independent external cfRNA dataset23 (sensitivity 39%, specificity 58%, AUC 0.63) (Fig.\u00a04d, e and Supplementary Table\u00a06), underscoring the challenges in early LOPE prediction. Misclassified samples are shown in Fig.\u00a04e, and the relative contribution of individual cfRNAs to predictive accuracy detailed in Fig.\u00a04f. While predictive capability was limited, analysis of the selected cfRNAs offers insights into LOPE mechanisms.\n\nFurther exploration revealed that several of these cfRNAs map to protein-coding genes with known roles in cardiovascular, hepatic, and immune functions, including PRR23D1, SnoRD126, CD52, TRDV3. Unlike EOPE, no cfRNA transcripts in this model were associated with decidua, underscoring distinct pathophysiological pathways for EOPE and LOPE.\n\nIn conclusion, our findings demonstrate the effectiveness of cfRNA signatures in predicting EOPE during the first trimester, while LOPE prediction remains challenging, likely reflecting fundamental differences in pathophysiology between EOPE and LOPE.\n\nWe next investigated the potential for early detection of EOPE and LOPE in the second trimester (T2). The most effective predictive model for EOPE was based on 87 cfRNA transcripts (Supplementary Table\u00a05), achieving a sensitivity of 89% and specificity of 86%, with an AUC of 0.89 in the validation set (Fig.\u00a05a and Supplementary Table\u00a06). Misclassified samples are shown in Fig.\u00a05b, and importance scores for each transcript are illustrated in Fig.\u00a05c. This model reliably identifies patients at risk for EOPE between 18 and 28 weeks of gestation, approximately 8.5 weeks before clinical onset. When applied to an independent external cfRNA dataset23, the signature demonstrated good performance (sensitivity 67%, specificity 78%, AUC 0.81), with a moderate reduction likely influenced by the small sample size of EOPE cases (n\u2009=\u20095) (Fig.\u00a05a, b and Supplementary Table\u00a06).\n\nReceiver operating characteristic (ROC) curves for EOPE (a) and LOPE (d) models across internal validation (validation 1) and external validation23 (validation 2). The X-axis represents the False Negative Rate; the Y-axis, the True Positive Rate. Violin plots showing correctly and misclassified patients and controls based on the classifier score obtained from the predictive model for EOPE (b) and LOPE (e). The X-axis shows the real obstetric outcome; the Y-axis, the predicted outcome. Bar plot illustrating each cfRNAs contribution to EOPE (c) and LOPE (f) models. The X-axis shows the feature importance scores, which quantify the relative contribution of each cfRNA to the model\u2019s predictions, with higher scores indicating features that play a more significant role in discriminating between outcomes. cfRNAs associated with DR are marked with an asterisk. AUC, area under the curve.\n\nFurther investigation into the tissue-specific origin of these transcripts revealed that 32 (36.8%) are associated with DR signature previously described in endometrial tissue from women with a history of severe preeclampsia, including CCL20, CXCR4, IGF1, RBP4, SQSTM1, WNT5A20. The persistence of decidual contributions as EOPE approaches underscores the maternal decidua\u2019s role in its pathophysiology. The model also includes inflammatory mediators such as SQSTM1, IL1B, CCL20, FASLG and TREM1, as well as transcripts encoding T cell receptors (e.g. TRAV21, TRBV27, TRBV5-7). Additionally, it incorporates anti-inflammatory mediators like ALOX5AP, an immunosuppressive gene linked to recurrent miscarriage31, and IL19. Transcripts such as RBP4, which directly influences blood pressure regulation32, NRBF2 involved in autophagy and liver protection33, and WNT5A, a key regulator of placental growth34, further support the model\u2019s clinical relevance.\n\nThe top-performing predictive model for LOPE at T2 included 92 cfRNAs (Supplementary Table\u00a05), achieving a sensitivity of 88%, specificity of 92%, and an AUC of 0.90 in the validation cohort (Fig.\u00a04d and Supplementary Table\u00a06). An analysis of misclassified samples is shown in Fig.\u00a05e, with the contributions of individual cfRNAs to predictive accuracy detailed in Fig.\u00a05f. Further validation using an independent external dataset23, performance was lower (sensitivity 60%, specificity 92%, AUC 77%) (Fig.\u00a05d, e and Supplementary Table\u00a06), likely due to differences in sample timing. While all samples were annotated as collected after 23 weeks, some were obtained near symptom onset or during the third trimester, and metadata limitations precludes precise identification of those cases.\n\nPathway enrichment analysis revealed that this model included cfRNAs related to immune function, such as CFHR1 and CFHR3, involved in complement activation, and immunoglobulin transcripts (e.g., IGKV3D-20, IGKV3D-11, IGHV5-10-1, IGHV3-69-1), and CXCR5, linked to B-cell migration35. Additionally, the model incorporates a cfRNA corresponding to HISLA, highly expressed in the liver36, and LINC0141937. Notably, most predictive cfRNAs were classified as non-coding RNAs or pseudogenes with no annotated function. In contrast to the EOPE model, this LOPE model includes only two cfRNAs related to DR, HES4 and SPEF1.",
+            "section_image": [
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+            ]
+        },
+        {
+            "section_name": "Discussion",
+            "section_text": "Previous efforts to develop screening tests for preeclampsia have primarily focused on circulating biomarkers related to placental dysfunction, such as sFLT1 and PlGF38. These tests have been validated for use starting at 23 weeks of gestation, with their strongest predictive accuracy typically observed within two weeks of symptom onset. Consequently, they are recommended for patients with suspected preeclampsia39,40. While these tests are particularly useful for short-term prediction, placental dysfunction-based tests are also utilized as early as the first trimester. They are often combined with maternal epidemiological factors and ultrasound or Doppler parameters. However, they face significant limitations in their effectiveness and application41,42,43,44. In settings where guidelines from the National Institute for Health and Care Excellence (NICE) and the ACOG are applied, screening primarily relies on pregnancy-related factors and maternal characteristics. While this approach minimizes additional costs, it has low sensitivity (<\u200941%)45,46.\n\nPredictive models based on cfRNAs from liquid biopsy, grounded in biological plausibility and applicable early in pregnancy, offering potential improvements for the clinical management of preeclampsia22,23,24,25, yet they have not been clinically applied. Building on this foundation, we prospectively collected blood samples from 9586 pregnant women across three gestational trimesters (9\u201342 weeks). Then, we selected a subset of 216 participants composed by preeclampsia cases and normotensive controls to generate a comprehensive longitudinal dataset of cfRNA profiles related to EOPE or LOPE progression. The performance metrics demonstrate substantial advancements in leveraging cfRNA signatures for early detection of EOPE in both the first and second trimesters, as well as LOPE in the second trimester.\n\nOur study stands out from previous research by addressing several key limitations in the field. First, we report the largest prospective cohort of EOPE cases with first-trimester sampling strictly between 9 and 14 weeks of gestation. This early and consistent inclusion window allowed us to capture cfRNA signatures an average of 18 weeks before clinical onset. Second, our carefully curated dataset enabled a clear distinction between EOPE and LOPE, classified according to established clinical guidelines. Unlike many previous studies that analyze preeclampsia as a single entity or rely on later gestational time points, our approach allows for a more precise molecular characterization of disease subtypes. This also suggests that cfRNA reflects a time-specific pathological status rather than a fixed disease signature. Third, the longitudinal design with multiple sampling points across gestation provided a dynamic view of disease progression, from preclinical stages to diagnosis.\n\nThe clinical implications of early risk stratification warrant consideration. While low-dose aspirin remains the primary intervention and is already recommended for many at-risk patients, earlier and more precise identification of individuals at high risk for preeclampsia allows for tailored clinical management strategies47. A shared approach to surveillance\u2014including frequent blood pressure monitoring, renal and liver function assessment, and fetal growth evaluations\u2014has been recommended to mitigate complications in high-risk pregnancies. Furthermore, structured lifestyle interventions, such as calcium and vitamin D supplementation, aerobic exercise, and improved sleep hygiene, may complement pharmacological strategies. A cfRNA-based screening tool offers potential advantages over existing multimarker approaches, which require strict quality control and trained operators, potentially reducing costs and improving accessibility48.\n\nIn addition, our analysis highlighted the tissue-specific origins of the detected cfRNAs, offering further insight into the pathophysiology of both subtypes of preeclampsia. For EOPE patients, early signs of tissue distress were observed in the liver, kidney, and decidua at T2, suggesting that these organs may be affected up to eight weeks before clinical diagnosis. By the time of the clinical onset (T3), cfRNA levels associated with critical organs such as the placenta, heart, brain and lungs showed marked elevation in EOPE, indicating widespread organ involvement likely due to apoptotic processes releasing cfRNA into circulation. In LOPE patients, although cfRNA levels also increased by T3, levels were lower compared to EOPE. Furthermore, differential abundance analysis at diagnosis revealed distinct transcriptomic profile in EOPE, with more pronounced cfRNA changes than in LOPE reflecting potential differences in severity and inflammatory response between both preeclampsia subtypes.\n\nThese distinctions between the subtypes extended to the biological roles of cfRNAs included in the predictive models. In models predicting EOPE, a substantial proportion of cfRNA transcripts were associated with genes involved in decidualization and DR, along with some placental-related transcripts. In contrast, cfRNA transcripts associated with LOPE prediction reflecting broader systemic contributions including placental malfunction. This molecular characterization provides opportunities for the development of targeted interventions. For instance, transcriptomic profiling, such as that presented in this study, could facilitate in silico drug repurposing by identifying dysregulated pathways as potential therapeutic targets49,50. Experimental approaches using siRNA or mRNA-based interventions to modulate key regulators of preeclampsia pathogenesis are already being explored51, highlighting the translational potential of cfRNA-driven insights. Furthermore, the progression of cfRNA changes throughout pregnancy could also play a pivotal role in the development of novel therapies. By tracking how cfRNA levels shift in response to disease onset and progression, new therapeutic windows can be explored and more effective treatment targets identified. This approach could pave the way for the development of interventions that could not only prevent the disease but also modify its course, thereby improving maternal and fetal outcomes.\n\nWhile external validation is crucial to confirm the diagnostic performance of our models, we have already conducted validation using an independent external dataset, which supported the relevance of the predictive signature across datasets for both EOPE and LOPE. We acknowledge, however, that the case\u2013control design may limit generalizability compared to case-cohort studies. To address this, a large-scale external validation is currently underway (ClinicalTrials.gov Identifier: NCT06716242), as part of the iPregnostic study, which will assess the performance of these models across a wider range of clinical backgrounds, thereby enhancing their applicability to diverse patient populations.\n\nOverall, by analyzing circulating RNAs from a single blood sample at T1 or T2, our approach provides a reliable, standardized diagnostic measure that minimizes subjective interpretation and reduces variability in clinical decision-making. This streamlined strategy simplifies risk stratification, improving both the accuracy and efficiency of preeclampsia screening and facilitating personalized patient monitoring.",
+            "section_image": []
+        },
+        {
+            "section_name": "Methods",
+            "section_text": "This prospective, multicenter case-control study was conducted between September 2021 and June 2024 in fourteen hospitals across Spain (ClinicalTrials.gov Identifier: NCT04990141) in compliance with all relevant ethical regulations. Given the incidence rate of preeclampsia, the cohort size was designed to capture a minimum of 30 patients of EOPE over the course of the study. Approval was obtained from the following Clinical Research Ethics Committees in Spain: Comit\u00e9 de \u00c9tica de la Investigaci\u00f3n con medicamentos del Hospital General Universitario de Castell\u00f3n (Castell\u00f3n); CEIm - Hospital Universitario y Polit\u00e9cnico La Fe (Valencia); CEIm Hospital General de Alicante (Alicante); CEIm Hospital Virgen de la Arrixaca (Murcia); CEI Hospital Universitario Sta. M\u00aa del Rosell (Cartagena); CEIm de la Gerencia de Atenci\u00f3n Integrada de Albacete (Albacete); CEIm Hospital Puerta del Hierro de Majadahonda (Madrid); Comisi\u00f3n de Investigaci\u00f3n del Hospital de Torrej\u00f3n (Madrid); CEIc Arag\u00f3n (Zaragoza); CEIm de Euskadi (Bilbao); CEIm \u00c1rea de Salud Valladolid Oeste (Valladolid); CEI Provincial de C\u00f3rdoba (C\u00f3rdoba); CEIm Complejo Hospitalario Universitario de Canarias (Tenerife); and CEIm del Hospital Universitario de Gran Canaria Dr. Negr\u00edn (Las Palmas). Written informed consent was collected from all participants prior to blood collection and sample anonymization. A total of 9,586 pregnant women were enrolled based on the following criteria: signed informed consent, age over 18, singleton pregnancy, and first blood sample collection within 9\u201314 gestational weeks. Each participant provided 20\u2009mL of peripheral blood in the three trimesters of pregnancy, coinciding with routine clinical follow-up: (T1) 9\u201314 weeks, (T2) 18\u201328 weeks, and (T3)\u2009>\u200928 weeks or at the time of preeclampsia diagnosis. Gestational age was confirmed via ultrasound during the first trimester. Clinical data for each participant were recorded in an electronic data capture system. All blood samples were processed to isolate plasma and stored at \u221280\u2009\u00b0C until pregnancy outcomes were available. Preeclampsia patients were diagnosed following ACOG4 and FIGO52 guidelines, as per the clinical protocol of each hospital involved.\n\nTo develop predictive models for EOPE and LOPE, a subset of participants was selected from the cohort. All EOPE patients (n\u2009=\u200942), a randomly selected subset of LOPE patients (n\u2009=\u200943) and a subset of normotensive pregnant women with uncomplicated pregnancies were included as controls (n\u2009=\u2009131). Control participants were randomly selected from the 6905 uncomplicated pregnancies and matched to both EOPE and LOPE cases for key clinical variables including gestational age at sampling, maternal age, parity, BMI and ethnicity. Participants in the control group were selected based on matching gestational age at the time of blood collection, maternal age, and parity, utilizing Euclidean distance for optimal pairing. Patients and controls were randomly stratified following a 70:30 proportion into two sets: discovery and validation. Sample sizes for the EOPE, LOPE, and control groups in each set are detailed in Supplementary Table\u00a06. The discovery set was used for feature selection, model training, and optimization, with model performance assessed by leave-one-out cross-validation. For feature selection, a 1:2 case-to-control ratio was used, as it is optimal for identifying distinct patterns between the groups. For model training, the case-to-control ratio was increased to 1:3 to ensure a larger sample size, which supports better learning of the patterns by the model and improves predictive accuracy. The optimal model from this process was then applied to the validation set to assess the predictive performance, yielding metrics based on an unexposed sample set. The bioinformatic workflow is detailed in Supplementary Fig.\u00a03.\n\nPeripheral blood samples (20\u2009mL) were collected in Streck Cell-Free DNA BCT tubes (Illumina, 15073345), stored, shipped at room temperature, and processed within seven days to obtain the plasma fraction. All blood samples were centrifuged for 15\u2009min at 1600 x g and 4\u2009\u00b0C. Plasma was transferred to a new collection tube and stored at -80\u2009\u00b0C until use.\n\nPlasma supernatant samples (n\u2009=\u2009548) from the study patients (n\u2009=\u2009216) were centrifuged for 10\u2009min at 13,000 x g. Following the manufacturer\u2019s protocol, cfRNA from 2\u2009mL of plasma was isolated using MiRNeasy Serum/Plasma Advanced Kit (Qiagen, 217204). According to the manufacturer\u2019s protocol, cDNA libraries from total cfRNA samples were prepared using Illumina RNA Prep with Enrichment (L) Tagmentation (Illumina, 20040537). cDNA libraries were quantified using an Agilent D1000 ScreenTape in a 4200 TapeStation system (Agilent Technologies Inc, 5067-5582). Libraries were normalized to 10\u2009nM and pooled in equal volumes. The pool concentration was quantified by qPCR using the KAPA Library Quantification Kit (Roche, 7960336001) and an Agilent D1000 ScreenTape in a 4200 TapeStation system (Agilent Technologies Inc, 5067-5582). The mean value was used to establish pool concentration, which was then sequenced in a NextSeq 500/550 High Output kit with 2.5 cartridges of 150 cycles (Illumina, 20024907).\n\nRaw reads were aligned to the human reference genome (GRCh38 Gencode v38 Primary Assembly) using STAR (2.7.10a). The SAM/BAM files were further processed using SAMtools (v.1.6). Only reads with mapping quality more significant than 90% were maintained (MAPQ score obtained from the alignment). The duplicated reads were removed with Picard MarkDuplicates (v.2.27.4). The mapping and the quantification of the reads were done using featureCounts (v.2.0.1). Read statistics were estimated using FastQC (v.0.11.9) and RseqQC (v.5.0.1) and summarized using MultiQC (v.1.13).\n\nThree key quality parameters related to the sequencing process were estimated for each analyzed sample: RNA degradation, DNA contamination, and rRNA fraction as previously defined21,53 (Supplementary Fig.\u00a04a-c). Samples were retained for further analysis if they met the established cut-off values for each parameter: RNA degradation (cut-off: 40%), DNA contamination (cut-off ratio: 3), and rRNA fraction (cut-off: 15%). Principal Component Analysis (PCA) was used as an additional quality control measure (Supplementary Fig.\u00a04d, e). Samples deviating by more than 3 standard deviations from the mean of the first and second components for each dataset were excluded from the analysis. In total, 12 samples were removed\u20142 due to a high rRNA fraction and 10 due to PCA-based exclusion.\n\nCfRNAs were filtered based on their detection value, and only cfRNAs with levels over more than 0.5 counts per million reads (CPMs) in \u226570% of discovery samples after removing outlier samples were kept. Discovery set CPMs were normalized using the \u201cdeseq median ratio normalization\u201d with pydeseq2 (v0.4.1). The validation set were then normalized with the same algorithm using size factors from discovery set as described in MLSeq package54,55. Batch effect and other possible confounding factors were assessed using PCA, hierarchical clustering with Spearman correlation as a distance metric, and variance component analysis. Finally, the normalized counts of each sample of discovery and validation sets were re-scaled to 0-1 range with a min-max scaling process.\n\nCfRNAs differentially abundant between EOPE or LOPE patients and controls at each time point (T1, T2, T3) were identified using the limma-Voom method from the Bioconductor package limma (v3.60.5). For the T3 samples, comparisons only included patients whose samples were collected at the time of EOPE or LOPE diagnosis and gestationally matched control samples collected during routine medical appointments. Genes with False Discovery Rate (FDR) less or equal to 0.05 were considered statistically significant.\n\nGene Ontology (GO) analyses were performed to identify biological processes using the enrichGO function from the clusterProfiler R package (v4.2.2). The input consisted of cfRNAs that were differentially abundant between EOPE and controls, as well as LOPE and controls (FDR\u2009<\u20090.05). The p-value adjustment method used was FDR, with a significance threshold set at 0.05 (FDR\u2009<\u20090.05).\n\nGene sets for each tissue of interest \u2500those directly involved in the pathophysiology of preeclampsia\u2500 were derived from the Human Protein Atlas database26, which includes gene expression data across tissues, focusing specifically on transcripts classified as either \u201cenriched\u201d or \u201cenhanced\u201d within those tissues, but only if they were additionally categorized as \u201cdetected in single\u201d to ensure higher tissue specificity. The signature score in our dataset was calculated by summing the log-transformed, normalized counts of each gene in the set. For the T3 samples, comparisons included only those patients whose samples were collected at the time of EOPE or LOPE diagnosis and gestationally matched control samples collected during routine medical appointments, to avoid potential bias. Differences between groups were assessed using the Wilcoxon rank-sum test.\n\nOur study cohort was divided into discovery and validation sets to develop and evaluate the predictive models, following best practices to prevent overfitting in artificial intelligence. Using stratified sampling based on obstetric outcomes (patient/control groups) and the scikit-learn library (v1.5.1) in Python, 70% of participants were allocated to the discovery set.\n\nFor feature selection, a 1:2 case-to-control ratio was used, as it is optimal for identifying distinct patterns between the groups. The Lasso regression model was used to select the more relevant cfRNAs to discriminate between patients and controls. The discovery dataset was used with a lasso regression algorithm (v1.5.2, sklearn.linear_model.Lasso) with a penalty term (alpha) of 0.5 and the case condition as a dependent part and the cfRNA abundance levels as the independent components, resulting in a regression formula that assigns a coefficient to each cfRNA variable, indicating the correlation between the condition and each variable. The number of cfRNAs selected was determined by a minimum coefficient threshold, which determined whether a cfRNA was relevant or not. Different minimum coefficient thresholds, ranging from 0 to the maximum coefficient in increments of 0.05, were tested to determine the optimal set of cfRNAs. The F1-score was calculated for each set of cfRNAs using the strategy of leave-one-out cross-validation, and the set that yield the highest F1-score metric was selected. Lasso regression was chosen over other feature selection methods due to the relatively small sample size, which can lead to model overfitting. The penalty term of the model helps to counteract overfitting by shrinking and selecting features with less importance56.\n\nFor the development of the optimal predictor, the discovery set was used, with cfRNA selection performed using the lasso regression method as previously described. Six different algorithms were tested with Python (v3.10.6): Support Vector Machine (v1.5.2, sklearn.svm.SVC), Elastic Net Linear Regression (v1.5.2, sklearn.linear_model.ElastcNet), Lasso Linear Regression (v1.5.2, sklearn.linear_model.Lasso), Random Forest (v1.5.2, sklearn.ensemblel.RandomForestClassifier), XGBoost (v1.7.6 xgboost. XGBClassifier) and TabPFN (v0.1.10 tabpfn.TabPFNClassifier). Each algorithm was trained with the best parameters calculated with a grid search applied with a cross-fold strategy. The evaluation of the predictive capacity of each model was done with a leave-one-out cross-validation with the discovery samples. The algorithm providing the best F1-score was selected for each group of samples: EOPE in the first trimester (EOPE T1), in the second trimester (EOPE T2), LOPE in the first trimester (LOPE T1) and LOPE in the second trimester (LOPE T2). The resulting chosen algorithms were TabPFN for EOPE (T1 and T2) and Lasso Linear Regression for LOPE (T1 and T2).\n\nFor each model (EOPE T1, LOPE T1, EOPE T2, LOPE T2), the ML algorithm showing the highest F1-score and its best parameters was trained with the discovery dataset, which was based on a 1:3 case-to-control ratio. To evaluate the predictive capacity with the discovery data, a strategy of leave-one-out was performed. The selected algorithm was trained N number of times. In each iteration, one sample was isolated, and the rest were used to fit the model. The fitted model was used to predict the label of the isolated sample, and the result of the prediction was added to a pool of predicted labels that were used to calculate the discovery leave-one-out metrics. Finally, the algorithm was fitted with all the discovery samples, and the obtained trained model was used to predict the labels in the validation dataset and evaluate the performance with never seen samples.\n\nWe evaluated the predictive performance of each model (EOPE T1, LOPE T1, EOPE T2, LOPE T2) using three approaches: (1) leave-one-out cross-validation on the discovery dataset; (2) predictions on the hold-out validation dataset using the final model (validation 1); and (3) external validation of the predictive cfRNA signature using an independent dataset23 (Gene Expression Omnibus: GSE192902), which includes cfRNA profiles of EOPE and LOPE collected during pregnancy (n\u2009=\u2009190) (validation 2). For external validation, we retuned the model architecture to account for technical differences in cfRNA processing between datasets. Since the external cohort did not distinguish between EOPE and LOPE, we constructed separate balanced case\u2013control subsets for each subtype. All available PE cases were included, and controls were selected using an agnostic downsampling approach based on cfRNA profiles and gestational age (T1 or T2). Within each timepoint, the largest available subset of controls was retained using a reproducible selection criterion. Model performance was assessed using leave-one-out cross-validation. Performance across the three validations was assessed with key metrics, including accuracy, sensitivity, specificity, AUC, and F1-score.\n\nFurther information on research design is available in the\u00a0Nature Portfolio Reporting Summary linked to this article.",
+            "section_image": []
+        },
+        {
+            "section_name": "Data availability",
+            "section_text": "Data supporting the findings described in this manuscript are available in the article and in the Supplementary Information, or as Source Data available from the corresponding authors upon reasonable request and under controlled access. Source Data contain individual-level results derived from human samples; access is restricted to comply with data privacy laws and the ethical approvals governing these samples. The cell-free RNA-sequencing data are available under controlled access to comply with data privacy laws and the ethical approvals governing these samples. Access can be granted upon reasonable request, subject to approval by the Institutional Review Board of the Spanish hospitals involved and execution of a Data Transfer and Use Agreement. Inquiries for data usage can be directed to C.S. (carlos.simon@uv.es) or T.G. (tgarrido@fundacioncarlossimon.com), and requests will be reviewed within 30 days.",
+            "section_image": []
+        },
+        {
+            "section_name": "Code availability",
+            "section_text": "The custom code used to perform the analysis presented here is available on GitHub under the repository name ipremom-cfrna-preeclampsia-predictor [https://github.com/marinaigual/ipremom-cfrna-preeclampsia-predictor/tree/main].",
+            "section_image": []
+        },
+        {
+            "section_name": "References",
+            "section_text": "Organization WH. 2018 Global Reference List of 100 Core Health Indicators (plus health-related SDGs). (WHO, 2018).\n\nSay, L. et al. Global causes of maternal death: a WHO systematic analysis. Lancet Glob. Health 2, e323\u2013e333 (2014).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMoreno, I. et al. The human periconceptional maternal-embryonic space in health and disease. Physiol. Rev. 103, 1965\u20132038 (2023).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nACOG Practice Bulletin No 202 Summary: gestational hypertension and preeclampsia. Obstet. Gynecol. 133, 1 (2019).\n\n\n                    Google Scholar\u00a0\n                \n\nHinkle, S. N. et al. Pregnancy complications and long-term mortality in a diverse cohort. Circulation 147, 1014\u20131025 (2023).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nStevens, W. et al. Short-term costs of preeclampsia to the United States health care system. Am. J. Obstet. Gynecol. 217, 237\u2013248.e16 (2017).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLisonkova, S. & Joseph, K. S. Incidence of preeclampsia: risk factors and outcomes associated with early- versus late-onset disease. Am. J. Obstet. Gynecol. 209, 544.e1\u2013544.e12 (2013).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLisonkova, S. et al. Maternal morbidity associated with early-onset and late-onset preeclampsia. Obstet. Gynecol. 124, 771\u2013781 (2014).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nde Havenon, A. et al. Association of preeclampsia with incident stroke in later life among women in the Framingham Heart Study. JAMA Netw. Open 4, e215077 (2021).\n\nArticle\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nConti-Ramsden, F. I. et al. Pregnancy-related acute kidney injury in preeclampsia: risk factors and renal outcomes. Hypertension 74, 1144\u20131151 (2019).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLisonkova, S. et al. Incidence and risk factors for severe preeclampsia, hemolysis, elevated liver enzymes, and low platelet count syndrome, and eclampsia at preterm and term gestation: a population-based study. Am. J. Obstet. Gynecol. 225, 538.e1\u2013538.e19 (2021).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nRolnik, D. L. et al. Aspirin versus placebo in pregnancies at high risk for preterm preeclampsia. N. Engl. J. Med. 377, 613\u2013622 (2017).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDavidson, K. W. et al. Aspirin use to prevent preeclampsia and related morbidity and mortality: US preventive services task force recommendation statement. JAMA 326, 1186\u20131191 (2021).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBibbins-Domingo, K. et al. Screening for preeclampsia: US preventive services task force recommendation statement. JAMA 317, 1661\u20131667 (2017).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nGarrido-Gomez, T. et al. Defective decidualization during and after severe preeclampsia reveals a possible maternal contribution to the etiology. Proc. Natl. Acad. Sci. USA 114, E8468\u2013E8477 (2017).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nGarrido-Gomez, T. et al. Disrupted PGR-B and ESR1 signaling underlies defective decidualization linked to severe preeclampsia. Elife 10, 28 (2021).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nGarrido-G\u00f3mez, T., Castillo-Marco, N., Cordero, T. & Sim\u00f3n, C. Decidualization resistance in the origin of preeclampsia. Am. J. Obstet. Gynecol. 226, S886\u2013S894 (2022). 02.\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nNg S. W. et al Endometrial Decidualization: The Primary Driver of Pregnancy Health. Int. J. Mol. Sci. 21, 4092 (2020).\n\nWoods, L. et al. Decidualisation and placentation defects are a major cause of age-related reproductive decline. Nat. Commun. 8, 352 (2017).\n\nArticle\u00a0\n    ADS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMu\u00f1oz-Blat, I. et al. Multi-omics-based mapping of decidualization resistance in patients with a history of severe preeclampsia. Nat Med. 31, 502\u2013513 (2025).\n\nMoufarrej, M. N., Wong, R. J., Shaw, G. M., Stevenson, D. K. & Quake, S. R. Investigating pregnancy and its complications using circulating cell-free RNA in women\u2019s blood during gestation. Front. Pediatr. 8, 605219 (2020).\n\nArticle\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nRasmussen, M. et al. RNA profiles reveal signatures of future health and disease in pregnancy. Nature 601, 422\u2013427 (2022).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMoufarrej, M. N. et al. Early prediction of preeclampsia in pregnancy with cell-free RNA. Nature 602, 689\u2013694 (2022).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nElovitz, M. A. et al. Molecular subtyping of hypertensive disorders of pregnancy. Nat. Commun. 16, 2948 (2025).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMunchel S. et al. Circulating transcripts in maternal blood reflect a molecular signature of early-onset preeclampsia. Sci. Transl. Med. 12, eaaz0131 (2020).\n\nUhl\u00e9n, M. et al. Proteomics. Tissue-based map of the human proteome. Science 347, 1260419 (2015).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nNevalainen, J., Skarp, S., Savolainen, E. R., Ryyn\u00e4nen, M. & J\u00e4rvenp\u00e4\u00e4, J. Intrauterine growth restriction and placental gene expression in severe preeclampsia, comparing early-onset and late-onset forms. J. Perinat. Med. 45, 869\u2013877 (2017).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nPrzybyl, L. et al. CD74-downregulation of placental macrophage-trophoblastic interactions in preeclampsia. Circ. Res. 119, 55\u201368 (2016).\n\nArticle\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMedina-Bastidas D. et al. Placental microarray profiling reveals common mrna and lncrna expression patterns in preeclampsia and intrauterine growth restriction. Int. J. Mol. Sci. 21, 3597 (2020).\n\nTimofeeva A. V. et al. miRNAs and their gene targets-A clue to differentiate pregnancies with small for gestational age newborns, intrauterine growth restriction, and preeclampsia. Diagnostics. 11, 729 (2021).\n\nWang, F. et al. Single-cell Immune Landscape of Human Recurrent Miscarriage. Genomics Proteom. Bioinforma. 19, 208\u2013222 (2021).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKraus, B. J. et al. Novel role for retinol-binding protein 4 in the regulation of blood pressure. FASEB J. 29, 3133\u20133140 (2015).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLu, J. et al. NRBF2 regulates autophagy and prevents liver injury by modulating Atg14L-linked phosphatidylinositol-3 kinase III activity. Nat. Commun. 5, 3920 (2014).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMeinhardt, G. et al. Wingless ligand 5a is a critical regulator of placental growth and survival. Sci. Rep. 6, 28127 (2016).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nStelzer, G. et al. The GeneCards Suite: from gene data mining to disease genome sequence analyses. Curr. Protoc. Bioinforma. 54, 1.30.1\u20131.30.33 (2016).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nFagerberg, L. et al. Analysis of the human tissue-specific expression by genome-wide integration of transcriptomics and antibody-based proteomics. Mol. Cell Proteom. 13, 397\u2013406 (2014).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDang, H. et al. LINC01419 promotes cell proliferation and metastasis in hepatocellular carcinoma by enhancing NDRG1 promoter activity. Cell Oncol. 43, 931\u2013947 (2020).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nZeisler, H. et al. Predictive Value of the sFlt-1:PlGF Ratio in Women with Suspected Preeclampsia. N. Engl. J. Med. 374, 13\u201322 (2016).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nHund, M. et al. Multicenter prospective clinical study to evaluate the prediction of short-term outcome in pregnant women with suspected preeclampsia (PROGNOSIS): study protocol. BMC Pregnancy Childbirth 14, 324 (2014).\n\nArticle\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nThadhani, R. et al. Circulating angiogenic factor levels in hypertensive disorders of pregnancy. NEJM Evid. 1, EVIDoa2200161 (2022).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nChaemsaithong, P., Sahota, D. S. & Poon, L. C. First trimester preeclampsia screening and prediction. Am. J. Obstet. Gynecol. 226, S1071\u2013S1097.e2 (2022).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nRana, S., Lemoine, E., Granger, J. P. & Karumanchi, S. A. Preeclampsia: pathophysiology, challenges, and perspectives. Circ. Res 124, 1094\u20131112 (2019).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nAgrawal, S., Cerdeira, A. S., Redman, C. & Vatish, M. Meta-Analysis and Systematic Review to Assess the Role of Soluble FMS-Like Tyrosine Kinase-1 and Placenta Growth Factor Ratio in Prediction of Preeclampsia: The SaPPPhirE Study. Hypertension 71, 306\u2013316 (2018).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMacDonald, T. M., Walker, S. P., Hannan, N. J., Tong, S. & Kaitu\u2019u-Lino, T. J. Clinical tools and biomarkers to predict preeclampsia. EBioMedicine 75, 103780 (2022).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nACOG Committee Opinion No 743: Low-dose aspirin use during pregnancy. Obstet. Gynecol. 132, e44\u2013e52 (2018).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nVisintin, C. et al. Management of hypertensive disorders during pregnancy: summary of NICE guidance. BMJ 341, c2207 (2010).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nRoberts, J. M. et al. Care plan for individuals at risk for preeclampsia: shared approach to education, strategies for prevention, surveillance, and follow-up. Am. J. Obstet. Gynecol. 229, 193\u2013213 (2023).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nCuenca-G\u00f3mez, D. et al. Performance of first-trimester combined screening for preterm pre-eclampsia: findings from cohort of 10 110 pregnancies in Spain. Ultrasound Obstet. Gynecol. 62, 522\u2013530 (2023).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nTejera E., P\u00e9rez-Castillo Y., Chamorro A., Cabrera-Andrade A. & Sanchez M. E. A Multi-Objective Approach for Drug Repurposing in Preeclampsia. Molecules. 26, 777 (2021).\n\nArdissino, M. et al. Proteome- and transcriptome-wide genetic analysis identifies biological pathways and candidate drug targets for preeclampsia. Circ. Genom. Precis Med. 17, e004755 (2024).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDong, J. et al. Therapeutic effect of E-Lip-siRNA-sFlt1 on pre-eclampsia: targeted gene silencing and improved pregnancy outcomes. Nanomedicine 19, 1615\u20131627 (2024).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nPoon, L. C. et al. The International Federation of Gynecology and Obstetrics (FIGO) initiative on pre-eclampsia: a pragmatic guide for first-trimester screening and prevention. Int. J. Gynaecol. Obstet. 145, 1\u201333 (2019).\n\nArticle\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nTong, Y. K. & Lo, Y. M. Diagnostic developments involving cell-free (circulating) nucleic acids. Clin. Chim. Acta 363, 187\u2013196 (2006).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nGoksuluk, D. et al. MLSeq: Machine learning interface for RNA-sequencing data. Comput Methods Prog. Biomed. 175, 223\u2013231 (2019).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLove, M. I., Huber, W. & Anders, S. Moderated estimation of fold change and dispersion for RNA-seq data with DESeq2. Genome Biol. 15, 550 (2014).\n\nArticle\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nJi Hyung Lee, Z. S. & Zhan, G. On LASSO for predictive regression. J. Econ. 229, 322\u2013349 (2022).\n\nArticle\u00a0\n    MathSciNet\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDownload references",
+            "section_image": []
+        },
+        {
+            "section_name": "Acknowledgements",
+            "section_text": "We are especially grateful to Roberto Romero for reviewing the manuscript and providing valuable feedback. We thank D. Valbuena and C. G\u00f3mez for their input during the preliminary study design. We are grateful to D. Blesa, J. Jimenez-Almazan, and A. Amadoz for their support in protocol set-up. We also thank M.C. Carbajo and C. Montagud for their assistance with the experimental analyses. We also acknowledge the PREMOM Consortium and all clinical collaborators involved in patient recruitment, clinical data and sample collection at participating centers. Most importantly, we are especially grateful to all the participants in the PREMOM study for their generous contribution to this research.",
+            "section_image": []
+        },
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+            "section_name": "Author information",
+            "section_text": "Carlos Simon Foundation, Valencia, Spain\n\nNerea Castillo-Marco,\u00a0Teresa Cordero,\u00a0Irene Mu\u00f1oz-Blat,\u00a0Sheila Ortega-Sanch\u00eds,\u00a0Petr Volkov,\u00a0Carlos Sim\u00f3n\u00a0&\u00a0Tamara Garrido-G\u00f3mez\n\nR&D Department, iPremom Pregnancy healthcare Diagnostics, Valencia, Spain\n\nNerea Castillo-Marco,\u00a0Teresa Cordero,\u00a0Marina Igual,\u00a0Carla G\u00f3mez-\u00c1lvarez,\u00a0Neus Bernat-Gonz\u00e1lez,\u00a0\u00c1ngela Gaspar-Dom\u00e9nech,\u00a0\u00c9rika Ortiz-Domingo,\u00a0Alba Vives,\u00a0Carlos Sim\u00f3n\u00a0&\u00a0Tamara Garrido-G\u00f3mez\n\nDepartment of Obstetrics, University Hospital La Fe, Valencia, Spain\n\nRogelio Monfort-Ortiz,\u00a0Alfredo Perales-Mar\u00edn,\u00a0Beatriz Marcos-Puig,\u00a0S. Florez-Perez,\u00a0M. Montesinos-Albert,\u00a0M. Nieto-Tous,\u00a0A. Orive-Boluda\u00a0&\u00a0E. Satorres-P\u00e9rez\n\nFetal Medicine Unit Murcia, IMIB Arrixaca, Murcia, Spain\n\nJuan Luis Delgado,\u00a0Laura Hernandez-Hernandez,\u00a0Esther Canovas,\u00a0JL Delgado-Gonzalvez,\u00a0P. Diaz-Lozano,\u00a0A. Jimenez-Mendez,\u00a0Y. Mico,\u00a0A. Salinas\u00a0&\u00a0E. Sanchez-Martinez\n\nObstetrics and Gynecology Department, Hospital Universitario de Torrej\u00f3n, Madrid, Spain\n\nMaria del Mar Gil,\u00a0Bel\u00e9n Santacruz,\u00a0S. Alonso-Men\u00e9ndez,\u00a0MC Casanova,\u00a0D. Cuenca-G\u00f3mez,\u00a0E. Ferrer\u00a0&\u00a0A. Martin-Arias\n\nObstetrics and Gynecology Department, Hospital Universitario La Paz, Madrid, Spain\n\nMaria del Mar Gil\n\nSchool of Medicine, Universidad Francisco de Vitoria, Madrid, Spain\n\nMaria del Mar Gil,\u00a0Bel\u00e9n Santacruz,\u00a0S. Alonso-Men\u00e9ndez,\u00a0MC Casanova,\u00a0D. Cuenca-G\u00f3mez,\u00a0E. Ferrer\u00a0&\u00a0A. Martin-Arias\n\nDepartment of Obstetrics and Gynecology, University of La Laguna, Tenerife, Spain\n\nNieves Luisa Gonzalez-Gonzalez\n\nDepartment of Obstetrics and Gynecology, Hospital Universitario de Canarias, Tenerife, Spain\n\nWalter Plasencia,\u00a0M. Hern\u00e1ndez-Su\u00e1rez\u00a0&\u00a0E. Padr\u00f3n-P\u00e9rez\n\nDepartment of Pediatrics, Obstetrics, and Gynecology, University of Valencia, Valencia, Spain\n\nAlfredo Perales-Mar\u00edn\u00a0&\u00a0Carlos Sim\u00f3n\n\nObstetrics and Gynecology Department, Dr. Balmis General University Hospital, Alicante, Spain\n\nAna Mar\u00eda Palacios-Marqu\u00e9s,\u00a0P. Baviera-Royo,\u00a0J. Franc\u00e9s-Ferr\u00e9,\u00a0V Garc\u00eda-Sousa\u00a0&\u00a0E. P\u00e9rez-Pascual\n\nAlicante Institute for Health and Biomedical Research (ISABIAL), Alicante, Spain\n\nAna Mar\u00eda Palacios-Marqu\u00e9s\n\nDepartment of Gynecology, Miguel Hern\u00e1ndez University, Alicante, Spain\n\nAna Mar\u00eda Palacios-Marqu\u00e9s\n\nObstetrics and Gynecology Service, BioCruces Health Research Institute, Hospital Universitario Cruces (Basque Country University), Biscay, Spain\n\n\u00cd\u00f1igo Melchor,\u00a0A. Aiartzaguena,\u00a0MJ Barbaz\u00e1n,\u00a0J. Burgos,\u00a0A. Del Campo,\u00a0E. Gibbone,\u00a0H. Goiti,\u00a0A. Meabe,\u00a0JC Melchor,\u00a0V Recio\u00a0&\u00a0L. Rodr\u00edguez\n\nDepartment of Obstetrics and Gynecology, Complejo Hospitalario Universitario Insular, Materno Infantil, Las Palmas, Spain\n\nAlicia Martin-Martinez,\u00a0Taysa Benitez-Delgado\u00a0&\u00a0S. De Leon-Socorro\n\nDepartment of Obstetrics and Gynecology, Beth Israel Deaconess Medical Center, Harvard Medical School, Boston, MA, USA\n\nCarlos Sim\u00f3n\n\nINCLIVA Health Research Institute, Valencia, Spain\n\nCarlos Sim\u00f3n\u00a0&\u00a0Tamara Garrido-G\u00f3mez\n\nDepartment of Obstetrics and Gynecology, University Hospital Complex of Albacete, Albacete, Spain\n\nA. Amezcua,\u00a0A. Gomez\u00a0&\u00a0E. Gonzalez\n\nDepartment of Obstetrics and Gynecology, University General Hospital, Castell\u00f3n, Spain\n\nC. Andrada-Ripolles,\u00a0R. Batalla-Urrea,\u00a0CR Cabrera-Leon,\u00a0A. Lozano-Moreno,\u00a0C. Reula-Blasco,\u00a0L. Rubert\u00a0&\u00a0E. Villar-Graullera\n\nDepartment of Obstetrics and Gynecology, Rio Hortega Hospital, Valladolid, Spain\n\nEM Arias-Vald\u00e9s,\u00a0AM Arnal-Burr\u00f3,\u00a0RM Lobo-Valent\u00edn,\u00a0MJ Mac\u00edas-Alonso,\u00a0EM Mart\u00edn-Medrano\u00a0&\u00a0A. Moreno-Reviriego\n\nInstituto de Investigaci\u00f3n Sanitaria de Arag\u00f3n (IISA), Hospital Cl\u00ednico Universitario Lozano Blesa, Zaragoza, Spain\n\nM. Bond\u00eda,\u00a0M. Fabre,\u00a0D. Oros,\u00a0C. Paules\u00a0&\u00a0S. Ruiz-Martinez\n\nDepartment of Obstetrics and Gynecology, University Hospital Miguel Servet, Zaragoza, Spain\n\nJM Campillos-Maza,\u00a0C. De Bonrostro-Torralba,\u00a0SE Gregorio-Gonz\u00e1lez,\u00a0R. Herrero-Serrano,\u00a0A. Lasierra-Beamonte\u00a0&\u00a0AC Ruiz-Pe\u00f1a\n\nDepartment of Obstetrics and Gynecology, Santa Lucia Hospital, Cartagena, Murcia, Spain\n\nO. Garc\u00eda-Izquierdo,\u00a0MA Jodar-Perez,\u00a0A. L\u00f3pez-Soto,\u00a0JP Mart\u00ednez-Cend\u00e1n\u00a0&\u00a0I. Martinez-Rivero\n\nDepartment of Clinical Biochemistry, University Hospital Miguel Servet, Zaragoza, Spain\n\nMM Larrea-Ort\u00edz Quintana\n\nDepartments of Obstetrics and Gynecology. Hospital Universitario Reina Sof\u00eda, C\u00f3rdoba, Spain\n\nSM Pe\u00f1a-Lobo\u00a0&\u00a0MI Romero\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nC.S., and T.G.-G. conceptualized the study. R.M.-O., J.L.D., L.H.-H., E.C., M.M.G., B.S., N.L.G.-G., W.P., A.P.-M., B.M.-P., A.M.P.-M., I.M., A.M.-M., T.B.-D. and all PREMOM consortium members recruited patients, collected samples, and contributed clinical data to the central research database. C.G.-\u00c1., \u00c9.O.-D., and A.V. were responsible for study monitoring and data entry into the central research database. N.C.-M., T.C., I.M.-B., N.B.-G., \u00c1.G.-D., and S.O.-S. conducted the laboratory experiments. N.C.-M., M.I., and P.V. performed the bioinformatic analyses. N.C.-M., C.S., and T.G.-G. wrote the original draft of the manuscript. C.S. and T.G.-G. supervised the work and reviewed and edited the final version of the paper. All authors have substantively revised the paper and approved the submitted version.\n\nCorrespondence to\n                Carlos Sim\u00f3n or Tamara Garrido-G\u00f3mez.",
+            "section_image": []
+        },
+        {
+            "section_name": "Ethics declarations",
+            "section_text": "N.C-M., M.I., T.G-G., C.S. are inventors on a patent application (EP24383276.3) covering methods for determining the risk of preeclampsia. N.C-M., T.C., M.I., C.G-A., N.B-G., A.G-D., E.O-D., A.V., T.G.-G. are employees of iPremom Pregnancy Healthcare Diagnostics. C.S. is a founder of iPremom Pregnancy Healthcare Diagnostics. The remaining authors declare no conflict of interest.",
+            "section_image": []
+        },
+        {
+            "section_name": "Peer review",
+            "section_text": "Nature Communications thanks the anonymous reviewers for their contribution to the peer review of this work. A peer review file is available.",
+            "section_image": []
+        },
+        {
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+            "section_image": []
+        },
+        {
+            "section_name": "About this article",
+            "section_text": "Castillo-Marco, N., Cordero, T., Igual, M. et al. Maternal plasma cell-free RNA as a predictor of early and late-onset preeclampsia throughout pregnancy.\n                    Nat Commun 16, 9208 (2025). https://doi.org/10.1038/s41467-025-64215-2\n\nDownload citation\n\nReceived: 17 April 2025\n\nAccepted: 09 September 2025\n\nPublished: 20 October 2025\n\nVersion of record: 20 October 2025\n\nDOI: https://doi.org/10.1038/s41467-025-64215-2\n\nAnyone you share the following link with will be able to read this content:\n\nSorry, a shareable link is not currently available for this article.\n\n\n\n\n                            Provided by the Springer Nature SharedIt content-sharing initiative\n                        ",
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11b9e66bad4ba115da6cbbbd336e319b922ab42a87300eaec1f724b205793811/metadata.json

@@ -0,0 +1,133 @@
+{
+    "title": "An efficient multi-gram access in a two-step synthesis to soluble, nine-atomic, silylated silicon clusters",
+    "pre_title": "An Efficient Multi-Gram Access in a Two-step Synthesis to Soluble Nine-atomic Silylated Silicon Clusters",
+    "journal": "Nature Communications",
+    "published": "23 December 2024",
+    "supplementary_0": [
+        {
+            "label": "Supplementary Information",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-024-55211-z/MediaObjects/41467_2024_55211_MOESM1_ESM.pdf"
+        },
+        {
+            "label": "Transparent Peer Review file",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-024-55211-z/MediaObjects/41467_2024_55211_MOESM2_ESM.pdf"
+        }
+    ],
+    "supplementary_1": NaN,
+    "supplementary_2": NaN,
+    "source_data": [
+        "http://www.ccdc.cam.ac.uk/data_request/cif"
+    ],
+    "code": [],
+    "subject": [
+        "Synthetic chemistry methodology",
+        "Organic\u2013inorganic nanostructures",
+        "Synthesis and processing"
+    ],
+    "license": "http://creativecommons.org/licenses/by/4.0/",
+    "preprint_pdf": "https://www.researchsquare.com/article/rs-4073358/v1.pdf?c=1735045538000",
+    "research_square_link": "https://www.researchsquare.com//article/rs-4073358/v1",
+    "nature_pdf": "https://www.nature.com/articles/s41467-024-55211-z.pdf",
+    "preprint_posted": "28 Mar, 2024",
+    "research_square_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Silicon is by far the most important semiconducting material. However, solution-based synthetic approaches for unsaturated silicon-rich molecules require less efficient multi-step syntheses. We report on a straightforward access to soluble, polyhedral Si9 clusters from the binary phase K12Si17, which contains both [Si4]4- and [Si9]4- clusters. [Si4]4- ions, characterised by a high charge per atom ratio, behave as strong reducing agents, preventing [Si9]4- from directed reactions. By the here reported separation of [Si4]4-, Si9 clusters are isolated as monoprotonated [Si9H]3- ions on a multi-gram scale and further crystallised as their 2.2.2 Cryptate salt. 20 grams of the product can be obtained through this two-step procedure - a new starting point for silicon Zintl chemistry such as the first isolation and structural characterisation of a trisilylated [MeHyp3Si9]- cluster.Physical sciences/Chemistry/Inorganic chemistry/Organometallic chemistryPhysical sciences/Chemistry/Chemical synthesis",
+            "section_image": []
+        },
+        {
+            "section_name": "Additional Declarations",
+            "section_text": "There is NO Competing Interest.",
+            "section_image": []
+        },
+        {
+            "section_name": "Supplementary Files",
+            "section_text": "NCOMMS2414778SupportingInformation.pdfAn Efficient Multi-Gram Access in a Two-step Synthesis to Soluble Nine-atomic Silylated Silicon ClustersNCOMMS24147781.cifCrystal structure 1NCOMMS24147782a.cifCrystal structure 2a",
+            "section_image": []
+        }
+    ],
+    "nature_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Silicon is by far the most important semiconducting material. However, solution-based synthetic approaches for unsaturated silicon-rich molecules require less efficient multi-step syntheses. We report on a straightforward access to soluble, polyhedral Si9 clusters from the binary phase K12Si17, which contains both [Si4]4\u2212 and [Si9]4\u2212 clusters. [Si4]4\u2212 ions, characterised by a high charge per atom ratio, behave as strong reducing agents, preventing [Si9]4\u2212 from directed reactions. By the here reported separation of [Si4]4\u2212 by means of fractional crystallisation, Si9 clusters of the precursor phase K12Si17 are isolated as monoprotonated [Si9H]3\u2212 ions on a multi-gram scale and further crystallised as their 2.2.2-Cryptate salt. 20 grams of the product can be obtained through this two-step procedure - a new starting point for silicon Zintl chemistry, such as the isolation and structural characterisation of a trisilylated [MeHyp3Si9]\u2212 cluster.",
+            "section_image": []
+        },
+        {
+            "section_name": "Introduction",
+            "section_text": "With the progressing technologisation of our society and the accompanying miniaturisation of electronic devices, physicists and chemists face new challenges. Silicon stands out as the most important semiconducting material by far. However, traditional manufacturing methods, such as lithography and etching of crystalline silicon (top-down) or Chemical Vapour Deposition (CVD) of volatile silanes for producing nanostructured components, are reaching their limits. Nevertheless, not only manufacturing these materials requires different approaches. Bulk materials and semiconducting materials in the nanometre range significantly differ in their optical and electronic properties (quantum confinement). Molecular precursors could provide an answer to new manufacturing methods and the necessity for targeted investigations of quantum confinement effects in low-dimensional materials (quantum dots, wires and wells). Alongside the targeted synthesis of silicon nanoparticles, defined molecular (silicon) clusters are also considered model systems for studying physical and chemical processes in nanomaterials.\n\nThe targeted synthesis of saturated cage oligosilanes1,2, unsaturated siliconoids3,4,5 and Zintl clusters6,7,8 has been intensively studied in the past decades. In 1970, West et al. achieved the preparation of a cage oligosilane under reductive conditions starting from chlorosilane precursors for the first time9. Such Wurtz-type couplings or metathesis reactions also provide access to paradigmatic clusters like silaprismanes10,11,12, -cubanes13,14,15,16, and -tetrahedranes17,18 (Fig.\u00a01; II), primarily impressive by their structural beauty. Following West\u2019s initial hints towards the synthesis of a permethylated sila-adamantane19, Marschner et al. established the synthetic pathway to the sila-adamantane derivative\u00a0I (Fig.\u00a01), representing a molecular fragment of the diamond structure of elemental silicon. Via a simple and elegant cascade of silyl abstraction and silylation steps, coupled with subsequent Lewis acid mediated isomerisation, this molecule was obtained in a stepwise synthesis from readily available TMS4Si20. Later, targeted functionalised sila-diamondoid derivatives were reported as well21. Apart from the synthesis of perchlorocyclohexasilane, the disproportionation of the versatile precursor Si2Cl6 also enables the synthesis of an endohedral, chloride-decorated silafullerane (Fig.\u00a01; III)22,23,24. In addition to the described saturated silicon clusters, Breher, Scheschkewitz, and Lips report on unsaturated so-called siliconoid clusters, a term introduced by Scheschkewitz11. Silapropellane IV (Fig.\u00a01) is obtained via the co-reduction of Mes2SiCl2 and Si2Cl6, exhibiting a biradicaloid character of the transannular interaction between both bridgeheads25. The structurally related,\u00a0bridged silapropellane V (Fig.\u00a01)26\u00a0can be derived from an aromatic dismutational isomer of hexasilabenzene in a thermal or photochemical rearrangement and serves as a starting point for a rich cluster functionalisation and expansion chemistry27,28,29,30. Furthermore, the suitability of amido ligands31,32 has been demonstrated in stabilising six-atomic silicon clusters (Fig.\u00a01; VI), accessible via both the reductive coupling of corresponding bromosilane precursors and the thermal transformation of a zwitterionic tetrasilane33.\n\nExamples I\u2013III represent saturated, IV\u2013VI siliconoid and VII and VIII Zintl-type clusters. Silicon is depicted as blue, SiMe2 units as grey and Si-SiCl3 units as red circles. TMS Trimethylsilyl, Dis TMS2HC, Mes 2,4,6-Trimethylphenyl, Tip 2,4,6-Tri-iso-propylphenyl, Dipp 2,6-Di-iso-propylphenyl, MeHyp TMS3Si, Cy Cyclohexyl.\n\nWhile all discussed routes require multi-step syntheses to build up molecules with multiple Si\u2013Si bonds, an alternative method involves the direct formation of bare silicon clusters in a one-step synthesis by the solid-state reaction of silicon with alkali metals. This approach has yielded considerable success in the case of heavier Ge9 clusters. For instance, the solid-state phase M4Ge9 (M\u2009=\u2009Na\u2013Cs)34 can easily be obtained and readily dissolves in various polar solvents. In recent years, a rich chemistry has been established around the nine-atomic [Ge9]4\u2212 cluster anion such as (organo)functionalisation35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50, metalation43,51,52,53,54,55,56,57,58, and cluster growth59,60,61,62,63,64,65. In contrast to the heavier tetrel elements (Ge-Pb), [Si9]4\u2212 cannot be selectively obtained in a solid-state reaction. Instead, only phases with the composition M12Si17 (equivalent to {(M+)12([Si4]4\u2212)2([Si9]4\u2212); M\u2009=\u2009Na\u2013Cs) are accessible, which\u00a0also contain four-atomic [Si4]4\u2212 clusters in addition to the desired nine-atomic clusters66. Due to the highly reductive character of these tetrahedral ions, direct reactions of K12Si17 with electrophilic reagents like chlorosilanes are not feasible. As a result, silicon-based Zintl cluster chemistry\u00a0has lagged behind the heavier homologues up to now and is limited to reactions and studies in liquid ammonia. Apart from bare anions [Si9]x\u2212 (x\u2009=\u20092\u20134)67,68,69 and protonated ions like [Si4H]3\u221270 and [Si9Hn](4-n)\u2212 (n\u2009=\u20091, 2)71,72,73 there are only six examples of metalated silicon-based Zintl ions, such as [PhZnSi9]3\u221274, [{Ni(CO)2}2(\u03bc-Si9)2]8\u221275, [NHCDippCu(\u03b74-Si9)H]2\u221276, and [(NHCtBuAu)6(\u03b72-Si4)]2\u221277, as well as [(MesCu)2Si4]4\u2212 (Fig.\u00a01; VII)78 and [NHCDippCu(\u03b74-Si9)]3\u221279. Both the removal of the highly reactive four-atomic silicon clusters and the avoidance of liquid ammonia as a reaction medium are crucial for further developing this kind of chemistry and overcoming synthetic limitations.\n\nIn a first step, we recently made the nine-atomic [Si9]4\u2212 clusters available for reactions in organic solvents by dissolving K12Si17 in ammonia with 2.2.2-cryptand and subsequent solvent removal. Starting from this so-called activated precursor phase, the extraction of bis-protonated [Si9H2]2\u2212 clusters in pyridine and the transformation into disubstituted dianions of the form [2R2Si9]2\u2212 (Fig.\u00a01; XIII; 2R\u2009=\u2009MeHyp, tBu2HSi, Cy3Sn) in thf was achieved72,80,81. However, the four-atomic clusters continue interfering with the respective electrophilic reagents, causing limited functional group tolerance, poor product purity and low yields.\n\nIn this work, we report on wet chemical access to a synthetic K4Si9 analogue via separation of four- and nine-atomic clusters in\u00a0liquid ammonia through fractional crystallisation. Obtaining such a precursor compound represents a key step in the still largely unexplored chemistry of nine-atomic silicon clusters and allows for the selective synthesis of trisilylated [K(2.2.2-crypt)][(R3Si)3Si9] cluster salts.",
+            "section_image": [
+                "https:////media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41467-024-55211-z/MediaObjects/41467_2024_55211_Fig1_HTML.png"
+            ]
+        },
+        {
+            "section_name": "Results",
+            "section_text": "Our previous work shows that the solid-state phase K12Si17 can be converted into an activated form, accessible for follow-up reactions like silylation. This conversion is done by dissolving K12Si17 in liquid ammonia with 2.2.2-cryptand as\u00a0a sequestering agent and subsequent solvent removal80,81. Nevertheless, interfering four-atomic clusters might still\u00a0be present in this activated phase.\n\nIn order to separate [Si4]4\u2212 and [Si9]4\u2212,\u00a0we exploit their different solubilities in liquid ammonia. Keeping the ammonia extract of K12Si17 for ~12\u2009h at \u221240\u2009\u00b0C, we observe the formation of a bright red solid under a reddish-brown solution (Fig.\u00a02a). After filtration and\u00a0solvent removal,\u00a0an orange, coarse solid\u00a0(Fig. 2b) was isolated\u00a0from the filtrate. In contrast, the former red filtration residue changed into a grey, finepowder (Fig.\u00a02c). Surprisingly, the Raman measurements of the filtrate and filtration residue after solvent removal (Fig.\u00a03a, b) show a clear separation of the four- and nine-atomic cluster species. For the residue, the most intense resonances at 477\u2009cm\u22121, 287\u2009cm\u22121, and 272\u2009cm\u22121 can be assigned by comparison with the solid-state phase K4Si4 (Fig.\u00a03c), which contains exclusively four-atomic [Si4]4\u2212 clusters. The slight shift in the resonances is due to the non-identical chemical environment within the crystalline solid and the amorphous filtration residue. In contrast, the Raman spectrum of the filtrate does not show any Si4 band, as can be detected in K4Si4 and K12Si17 (Fig.\u00a03d). The resonances at 294\u2009cm\u22121 and 384\u2009cm\u22121 agree with the Raman data already described by Schnering for Cs4Si9,\u00a0which was obtained by the thermal decomposition of Cs4Si482. The third resonance at 248\u2009cm\u22121 indicates a further mode due to the different symmetry with respect to the C4v symmetric [Si9]4\u2212 ion.\n\na Ammonia solution of K12Si17 and 2.2.2-cryptand after storage at \u221240\u2009\u00b0C for 12\u2009h; b K1-x[K(2.2.2-crypt)]2+x[Si9] (x\u2009=\u20090.2) obtained from the filtrate after solvent removal; c Highly reactive filtration residue after solvent removal.\n\na Filtrate, b filtration residue, c K4Si4, and d K12Si17.\n\nAlthough we can clearly demonstrate that four- and nine-atomic clusters are separated by this procedure, the exact chemical composition of the dried filtrate cannot be conclusively determined with respect to the number of sequestered cations. We chose the minimum amount of expensive 2.2.2-cryptand, and elemental analysis of the solid shows a composition corresponding to K1-x[K(2.2.2-crypt)]2+x[Si9] (x\u2009=\u20090.2). The exact 2.2.2-cryptand content in this intermediate after filtration may vary around an ideal composition of K1[K(2.2.2-crypt)]2[Si9], which, however, had no impact on the follow-up chemistry.\n\nSingle crystals as orange blocks suitable for SC-XRD were obtained by vapour diffusion of Et2O into an ammonia solution of the filtrate by adding additional 2.2.2-cryptand to sequester all cations. The structure determination results in the composition of [K(2.2.2-crypt)]3[Si9H]\u00b78.5 NH3 (1). The crystal structure analysis unambiguously shows the formation of a threefold negatively charged cluster. The exceptionally good data quality allows for further structure refinement and the localisation of a hydrogen atom at the cluster from the difference Fourier map and a free refinement of the position of the H atom. The asymmetric unit contains a monoprotonated, threefold negatively charged [Si9H]3\u2212 cluster, three [K(2.2.2-crypt)]+ counter ions and 8.5 equivalents of co-crystallised ammonia. The co-crystallised ammonia primarily occupies the voids between the [K(2.2.2-crypt)]+ units and the cluster. This results in a particular thermal and mechanical sensitivity of the crystals. The refinement shows the presence of an orientationally disordered Cs symmetric [Si9H]3\u2212 cluster (for details, see the Supplementary Discussion). For the main orientation \u03b1 (Fig.\u00a04), the refinement allows for the localisation of the proton H1A at the Si1A position with a bond length of 1.55(3)\u2009\u00c5, which is in the range of typical Si\u2013H bond distances. The cluster framework shows the expected involvement of the substituted Si1A position of the open square plane. Thus, the Si1A-Si2B (2.347(3)\u2009\u00c5) and Si1A-Si4 (2.322(2)\u2009\u00c5) distances are significantly shortened compared to the Si2B-Si3B (2.580(2)\u2009\u00c5) and Si3B-Si4 (2.532(2)\u2009\u00c5) distances of the open square plane. The ratio of the square diagonals (Si2B-Si4/Si1A-Si3B) of 1.20 clearly shows the deviation from the ideal C4v symmetry of the parent [Si9]4\u2212 ion69. The structural characteristic of shorter Si-Si bonds at cluster atoms with ligands supports the existence of an H atom at Si1A and agrees with findings for the solvate [K(DB-18-crown-6)][K(2.2.2-crypt)]2[Si9H]\u00b7NH371,73.\n\na Front view; b top view. Anisotropic displacement ellipsoids of silicon (blue) are drawn at 50% probability. The hydrogen atom (red) is displayed as\u00a0a sphere of an arbitrary radius. Silicon and hydrogen atoms of minor disorder components are omitted for clarity. Selected bond length (\u00c5): Si1A-H1A: 1.55(3); Si1A-Si2B: 2.347(3); Si1A-Si3B: 3.121(4); Si1A-Si4: 2.322(2); Si1A-Si5: 2.4244(10); Si1A-Si6: 2.4342(9); Si2B-Si3B: 2.580(2); Si2B-Si4: 3.755(3); Si2B-Si6: 2.5193(12); Si2B-Si7: 2.4655(12); Si3B-Si4: 2.532(2); Si3B-Si7: 2.4553(9); Si3B-Si8: 2.4325(9); Si4-Si5: 2.4905(7); Si4-Si8: 2.4268(7); Si5-Si9: 2.4474(8); Si6-Si9: 2.4326(8); Si7-Si9: 2.4348(8); Si8-Si9: 2.4539(7); Si2B-Si4/Si1A-Si3B: 1.20.\n\nThe crystallographic data are supported by mass spectra of acetonitrile (MeCN) solutions of the filtration residue showing Si9 species (Fig.\u00a05), confirming the presence of nine-atomic clusters in the dried filtration product. Additionally, 1H NMR (Fig.\u00a06) of K1-x[K(2.2.2-crypt)]2+x[Si9] in DMF-d7 verifies the existence of monoprotonated cluster species. The prominent signal in the high-field region at \u22121.80\u2009ppm aligns with the spectral range reported for [Si9H2]2\u221272. The characteristic satellite pattern emerges from scalar coupling to all nine cluster atoms. This pattern displays the superposition of all possible isotopologues caused by the low natural abundance of NMR active 29Si (Natural abundance\u2009=\u20094.7%) in the cluster framework. Consequently, the intense main singlet (indicated in grey) results from all non-NMR active isotopologues ([28/30Si9H]3\u2212). While the first set of satellites (indicated in red) is due to a doublet splitting of the isotopologues [28/30Si829Si1H]3\u2212, the second\u00a0set is due to a triplet splitting (indicated in blue) of the isotopologues [28/30Si729Si2H]3\u2212. The satellite signals of higher isotopologues are not detectable due to the low natural abundance of 29Si. A full overview of the statistical intensity distribution for the superposition of all isotopologues is given in the Supplementary Information (Supplementary Fig.\u00a017 and Supplementary Table\u00a07) and in accordance with previous work72. The exceptionally small coupling constant of J(1H, 29Si)\u2009=\u200919.5\u2009Hz and the interaction of the proton with all nine silicon atoms of the cluster framework paints the picture of a highly dynamic system at room temperature. At \u221250\u2009\u00b0C, however, a doublet with a significantly increased coupling of 152\u2009Hz is observed (see Supplementary Fig.\u00a018), falling within the typical range of localised 1J(1H, 29Si) couplings. Thus, proton migration becomes slow on the 1H NMR timescale at the transition from the high- to the low-temperature limit of proton migration, allowing for direct detection of a localised Si\u2013H unit. This spectroscopic behaviour perfectly aligns with previously reported data in liquid ammonia71. Similar ligand migrations have also been described for [Sn9R3]3\u2212 (R3\u2009=\u2009H83, SnCy384) at room temperature.\n\na {[K(2.2.2-crypt)][Si9]\u2009+\u20092H}\u2212 (m/z\u2009=\u2009670.37); b {[K(2.2.2 crypt)][Si9]\u2009+\u20092H\u2009+\u2009mecn}\u2212 (m/z\u2009=\u2009711.42).\n\nMain resonance of non-coupled isotopologues [28/30Si929Si0H]3\u2212 is indicated in grey, doublet splitting of [28/30Si829Si1H]3\u2212 in red and visible part of triplet splitting of [28/30Si729Si2H]3\u2212 in blue. (400\u2009MHz, DMF-d7, 300\u2009K).\n\nIn order to clarify the origin of the cluster attached proton, we repeated the whole synthetic protocol of separation of [Si4]4\u2212 and [Si9]4\u2212 in ND3 instead of NH3 as solvent. After this, a signal at \u22121.62\u2009ppm for [Si9D]3\u2212 can only be detected in the 2H NMR (Supplementary Fig.\u00a019). This shows that the proton of [Si9H]3\u2212 originates from ammonia.\n\nThe access to isolated Si9 clusters on a multi-gram scale, in the absence of highly reductive [Si4]4\u2212 clusters, provides promising and well-defined conditions for follow-up reactions of nine-atomic silicon clusters. Silylation reactions of K1-x[K(2.2.2-crypt)]2+x[Si9] in tetrahydrofuran (thf) lead to the isolation and the structural characterisation of trisilylated cluster salts [K(2.2.2-crypt)][(R3Si)3Si9] (2a\u20132d; Fig.\u00a07) in good yields as orange-brown solids. All compounds were characterised by NMR and ESI-MS analyses. Yellow block-shaped single crystals of [K(2.2.2-crypt)][MeHyp3Si9]\u00b7thf were grown from a thf solution at \u221232\u2009\u00b0C over two weeks. The crystal structure of the molecular anion in 2a is depicted in Fig.\u00a08. 2a crystallises in the monoclinic space group P21/n (14) (a\u2009=\u200915.0913(4)\u2009\u00c5, b\u2009=\u200924.7859(6)\u2009\u00c5, c\u2009=\u200923.9571(6)\u2009\u00c5, \u03b1\u2009=\u200990\u00b0, \u03b2\u2009=\u200990.959(2)\u00b0, \u03b3\u2009=\u200990\u00b0, V\u2009=\u20098959.9(4)\u2009\u00c53) with one trisilylated [MeHyp3Si9]\u2212 cluster anion, one disordered [K(2.2.2-crypt)]+ unit and one disordered thf molecule in the asymmetric unit (for more details see Supplementary Discussion). Analogously to the homologous germanium cluster85, the present silicon cluster can also be described as a D3h symmetric threefold capped trigonal prism. The attachment of a further hypersilyl group to the C2v symmetric dianion [MeHyp2Si9]2\u221281 leads to a closure of the planar square plane Si1-Si4-Si8-Si5 by shortening of the Si1-Si8 bond from 3.770(7)\u2009\u00c5 to 3.2565(10)\u2009\u00c5. At the same time, the remaining prism edges (Si2-Si9 and Si3-Si7) are elongated by 0.526\u2009\u00c5 and 0.430\u2009\u00c5, respectively. The attachment of the third silyl substituent at the Si9 cluster induces the same geometric changes that have been described for the homologous [MeHypnGe9](4-n)\u2212 (Supplementary Table\u00a06)41,85 and [MeHypnSn9](4-n)\u2212 clusters (n\u2009=\u20092, 3)86,87. As expected, the cluster framework undergoes a significant contraction from tin and germanium to silicon. Similar to the homologous germanium cluster [MeHyp3Ge9]\u221247, the UV-VIS spectra of 2a and 2d in thf (Supplementary Figs.\u00a033 and 34) exhibit intense, overlapping signals below 400\u2009nm. The attachment of the electron-withdrawing silyl ligand tBu2FSi in 2d results in a hypsochromic shift compared to 2a.\n\nSilicon is depicted as blue circles. RHyp\u2009=\u2009(R3Si)3Si.\n\nAnisotropic displacement ellipsoids of silicon (blue) are drawn at 50% probability. Carbon (grey) is displayed as spheres of an arbitrary radius and hydrogen atoms are omitted for clarity.\n\nAs expected from the crystal structure and analogously to [MeHyp3Ge9]\u221285, 2a also\u00a0behaves D3h symmetric on NMR time scale in thf-d8 at room temperature. Hence, the three hypersilyl groups collapse to two 29Si resonances at \u2212130.03\u2009ppm and \u22128.71\u2009ppm. These signals can be attributed to the exo-bonded silicon atoms (SiTMS3) and the TMS groups, respectively. Further, in the high field\u00a0region at \u2212175.3\u2009ppm, the three capping positions show one signal, while the six equivalent prism positions exhibit a strongly shielded signal at \u2212360.8\u2009ppm. The NMR data are consistent with the data described in our previous studies81. The remaining derivatives 2b\u2013d exhibit similar behaviour, with the cap and prism signals falling within the characteristic range of \u2212160\u2009ppm and \u2212350\u2009ppm. The high quality of the data enables the determination of the 1J(29Si, 29Si) homonuclear couplings between the cap and prism atoms (Table\u00a01). The coupling constants of the sterically demanding hypersilyl groups (40.1\u2009Hz for 2a and 42.7\u2009Hz for\u00a02b) are significantly higher than those of the sterically less demanding silyl groups in 2c (24.4\u2009Hz) and 2d (23.2\u2009Hz). These couplings differ from localised Si\u2013Si bonds as in cyclic oligosilanes (1J(29Si, 29Si)\u2009\u2248\u200950\u201370\u2009Hz)88 and may indicate possible dynamic processes in the cluster framework, which have not yet been described in homologous silylated clusters. The access to NMR active cluster frameworks could reveal processes that have remained hidden from us so far.\n\nThe presence of strongly reductive [Si4]4\u2212 clusters in the solid-state phase K12Si17 limits the directed conversion of nine-atomic [Si9]4\u2212 silicon clusters. However, in this work, we have shown that the separation of both cluster species is easily possible on a multi-gram scale in liquid ammonia and provides valuable synthetic access to [Si9H]3\u2212 ions.\n\n[Si9H]3\u2212 shows a pronounced tautomerisation tendency, in which the proton rapidly migrates over the entire nine-atomic cluster framework. In addition, those monoprotonated silicon clusters in the form of the crude product K1-x[K(2.2.2-crypt)]2+x[Si9] represent a synthetic equivalent to [Si9]4\u2212 ions that are still not accessible in an isolated form via a solid-state approach. Thus, the trisilylated cluster salts [K(2.2.2-crypt)][(R3Si)3Si9] (2a\u2013d) are obtained in good yields and high purity by direct silylation of K1-x[K(2.2.2-crypt)2+x[Si9H] with the corresponding chlorosilanes. The spectroscopic behaviour and the crystallographic characterisation of 2a prove the strong similarities between silicon- and germanium-based Zintl clusters. With the present work, we were able to close a significant gap in the chemistry of group 14 Zintl ions. Studies on the further reactivity of the obtained trisilylated monoanions are underway.",
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+            "section_name": "Methods",
+            "section_text": "All reactions and manipulations were performed in oven dried glassware under a purified argon atmosphere using standard Schlenk and glove box techniques unless otherwise mentioned. NMR solvents were purchased from Sigma\u2013Aldrich and stored over molecular sieve (3\u2009\u00c5) for at least one day. Dichloromethane, Tetrahydrofuran (THF), and pentane were dried by using a solvent purificator (MBraun MB-SPS) and stored over molecular sieve (3\u2009\u00c5). Ammonia was liquified in a dry ice/iPrOH bath and dried over sodium metal for one night prior to use. ND3 was prepared from D2O and Mg3N2. Triethylene glycol bis(p-toluenesulfonate) was prepared by a modified literature procedure89.\n\nA mixture of potassium (1.49\u2009g, 38.0\u2009mmol, 12.0 eq.) and silicon (1.51\u2009g, 53.9\u2009mmol, 17.0 eq.) was sealed in a tantalum ampule and heated up to 800\u2009\u00b0C with a rate of 2\u2009K/min. After 18\u2009h, the reaction mixture was cooled down to room temperature (1\u2009K/min) yielding K12Si17 (2.91\u2009g, 97%) as a dark grey microcrystalline solid. The analytical data (Supplementary Fig.\u00a09) agree with the literature72.\n\nA mixture of 350\u2009mg potassium (8.95\u2009mmol, 1.00 eq.) and 251\u2009mg silicon (8.95\u2009mmol, 1.00 eq.) was sealed in a tantalum ampule and heated up to 600\u2009\u00b0C with a rate of 2\u2009K/min. After ten hours, the reaction mixture was cooled down to room temperature (1\u2009K/min) yielding K4Si4 (589\u2009mg, 98%) as a dark grey microcrystalline solid. The analytical data (Supplementary Fig.\u00a010) agree with the literature72.\n\n45.1\u2009g triethylen glycol (300\u2009mmol, 1.00 eq.) was dissolved in 300\u2009mL CH2Cl2 under non-inert conditions. After addition of 114\u2009g TsCl (600\u2009mmol, 2.00 eq.), the mixture was cooled to 0\u2009\u00b0C and 135\u2009g powdered KOH (2.40\u2009mol, 8.00 eq.) was carefully added in small portions (Caution: Can cause strong heat evolution). After stirring for three hours at 0\u2009\u00b0C, 300\u2009mL CH2Cl2 and 600\u2009mL ice-water were added. The organic layer was separated and the aqueous phase was extracted with CH2Cl2 (3\u2009\u00d7\u2009200\u2009mL). The combined organic layers were washed with water (2\u2009\u00d7\u2009100\u2009mL), dried over Na2SO4 and rotary evaporated. Triethylene glycol bis(p-toluenesulfonate) (118\u2009g, 258\u2009mmol, 86%) was obtained as a white solid. 1H NMR (400\u2009MHz, CDCl3, 298\u2009K): \u03b4 7.77 (d, J\u2009=\u20098.0\u2009Hz, 4 H), 7.33 (d, J\u2009=\u20098.0\u2009Hz, 4 H), 4.12 (t, J\u2009=\u20094.8\u2009Hz, 4 H), 3.63 (t, J\u2009=\u20094.8\u2009Hz, 4 H), 3.50 (s, 4 H), 2.42 (s, 6 H); 13C{1H} NMR (100\u2009MHz, CDCl3, 298\u2009K): \u03b4 145.0, 133.0, 129.9, 128.0, 70.7, 69.3, 68.8, 21.7. The analytical data agree with the literature89.\n\nA mixture of 31.0\u2009g triethylene glycol bis(p-toluenesulfonate) (67.0\u2009mmol, 2.00 eq.), 62.1\u2009g of Na2CO3 (586\u2009mmol, 17.5 eq.) and 4.89\u2009mL 2,2\u2032-(ethylenedioxy)bis(ethylamine) (33.5\u2009mmol, 1.00 eq.) was refluxed in 1000\u2009mL MeCN for five days under non-inert conditions. After cooling to room temperature, the mixture was filtrated and rotary evaporated. The resulting orange oil was redissolved in 375\u2009mL EtOH and 50.0\u2009mL citric acid (1.8\u2009m), heated to 85\u2009\u00b0C for three hours and filtrated again. After adjusting the pH of the filtrate to 14 with aqueous tetramethylammonium hydroxide solution, the mixture was rotary evaporated. The resulting residue was redissolved with Celite in CH2Cl2 and rotary evaporated again. After Soxhlet extraction with cyclohexane overnight and recrystallisation from CH2Cl2:Et2O (1:4), 2.2.2-cryptand was obtained as a white crystalline solid (5.29\u2009g, 14.1\u2009mmol, 42%). Further purification was achieved via sublimation (0.1\u2009mbar, 130\u2009\u00b0C). The analytical data match with an authentic sample of 2.2.2-cryptand. 1H NMR (400\u2009MHz, CDCl3, 298\u2009K): \u03b4 2.62 (t, 3J\u2009=\u20095.56\u2009Hz, 12H, NCH2CH2), 3.56 (t, 3J\u2009=\u20095.56\u2009Hz, 12H, NCH2CH2), 3.66 (s, 12H, CH2). Elemental Analysis: (calcd., found for C18H36N2O6) C (57.42, 57.52), H (9.64, 9.64), N (7.44, 7.44).\n\nK12Si17 (25.0\u2009g, 26.4\u2009mmol, 1.00 eq) and 2.2.2-cryptand (18.9\u2009g,50.2\u2009mmol, 1.90 eq) were dissolved in 250\u2009mL NH3(l) at \u221278\u2009\u00b0C under inert atmosphere leading to a deep red dispersion. The reaction was stirred for one hour before it was stored at \u221240\u2009\u00b0C for twelve hours. After filtration under continuous cooling with dry ice, the ammonia of the deep red filtrate was evaporated. The resulting red-orange solid was weighted (20.4\u2009g) and used without further purification for silylation experiments. According to the elemental analysis, the solid consist of K1-x[K(2.2.2-crypt)]2+x[Si9H] (x\u2009=\u20090.2). We\u00a0would like to point out that the number of non-sequestered and sequestered potassium ions may not always have the same ratio and the exact composition of the crude product might slightly vary with respected to the number of sequestered cations. The amount of 2.2.2-cryptand was optimised in order to reach the best separation of Si9 and Si4 clusters also considering using the minimum amount of 2.2.2-cryptand to reduce the costs. We found that the follow-up chemistry of the anion [Si9H]3\u2212 is not influenced by the amount of 2.2.2-cryptand. Caution: The grey, dried filtration residue reacts explosively with air and protic solvents. Isolation is strongly discouraged. Even Raman measurements conducted within airtight glass capillaries have sometimes resulted in the detonation of these capillaries. Hence, it is strongly recommended to carefully quench the undried residue with iPrOH at \u221278\u2009\u00b0C overnight! The solid passivates in iPrOH. After one night, a bright red reactive solid may remain in the flask. Do not quench this solid with water or iPrOH at room temperature under any circumstances! Even small amounts of this residue can react explosively.\n\nRed orange block-shaped single crystals (20%) of [K(2.2.2-crypt)]3[Si9H]\u22198.5NH3 (1) were obtained by vapour diffusion of Et2O into an ammonia solution of K1-x[K(2.2.2-crypt)]2+x[Si9H] (1.00 eq.) and cryptand (1.00 eq.) at \u221240\u2009\u00b0C after one week. 1H NMR (400\u2009MHz, DMF-d7, 298\u2009K): \u03b4 \u22121.80 (s, Si\u2013H). ESI-MS (negative mode, 3500\u2009V, 300\u2009\u00b0C): m/z 670.37 ({[K(2.2.2-crypt)][Si9]+2H}\u2212), 711.42 ({[K(2.2.2-crypt)][Si9]+2H+mecn}\u2212); Elemental Analysis (calcd., found for K1-x[K(2.2.2-crypt)]2+x[Si9H]; x\u2009=\u20090.2; C39.6H80.2K3N4.4O13.2Si9): C (39.70, 39.66), H (6.78, 6.74), N (5.47, 5.14).\n\n1.50\u2009g TMS4Si (4.68\u2009mmol, 1.00 eq.) and 551\u2009mg KOtBu (4.91\u2009mmol, 1.05 eq.) were dissolved in 7.50\u2009mL THF and stirred for 5\u2009h at room temperature. The resulting yellowish solution was slowly added to a solution of 442\u2009mg Me2SiHCl (4.68\u2009mmol, 1.00 eq.) in 5.00\u2009mL THF at \u221278\u2009\u00b0C. After complete addition, the reaction mixture was stirred at room temperature overnight before quenched with sat. aqueous NH4Cl solution. The mixture was extracted with Et2O (3\u2009\u00d7\u200925\u2009mL). The combined organic layers were washed with brine and dried over Na2SO4. After filtration rotary\u00a0and evaporation of the solvent, MeHypMe2SiH (1.32\u2009g, 4.34\u2009mmol, 93%) was obtained as colourless solid. 1H NMR (400\u2009MHz, CDCl3, 298\u2009K): \u03b4 4.02 (sept, 3J(1H, 1H)\u2009=\u20094.4\u2009Hz, dsept, 1J(1H, 29Si)\u2009=\u2009177\u2009Hz, 3J(1H, 1H)\u2009=\u20094.4\u2009Hz, 1H, Si\u2013H), 0.26 (d, 3J(1H, 1H)\u2009=\u20094.4\u2009Hz, 6H, SiMe2), 0.21 (s, 27H, MeHyp); 13C{1H} NMR (101\u2009MHz, CDCl3, 298\u2009K): \u03b4 2.63 (MeHyp), \u22121.95 (SiMe2); 29Si{1H} INEPT (79.5\u2009MHz, CDCl3, 298\u2009K): \u03b4 \u22129.42 (TMS), \u221233.51 (SiMe2), \u2212136.59 (TMS3Si).\n\n1.00\u2009g MeHypMe2SiH (3.26\u2009mmol, 1.00 eq.) and 277\u2009mg TCCA (1.19\u2009mmol, 0.37 eq.) were stirred in 2.00\u2009mL CH2Cl2 overnight under formation of a white suspension. After solvent removal under reduced pressure, the resulting white solid was extracted with pentane (3\u2009\u00d7\u200915\u2009mL). The combined solutions were evaporated under reduced pressure, giving MeHypMe2SiCl as colourless solid. 1H NMR (400\u2009MHz, MeCN-d3, 298\u2009K): \u03b4 0.61 (s, 6H, SiMe2), 0.26 (s, 27H, MeHyp). The analytical data agree with the literature90.\n\nK1-x[K(2.2.2-crypt)]2+x[Si9H] (x\u2009=\u20090.2) (1.00 eq.) and chlorosilane (3.10 eq.) were dissolved in thf and stirred at room temperature under formation of a red-brown solution. After filtration and removing of the solvent in vacuo, the resulting solid was washed with pentane. After drying under reduced pressure, the trisilylated cluster salts [K(2.2.2-crypt)][(R3Si)3Si9] (2) were obtained as orange-brown solids.\n\nCrystal preparation was carried out under a continuous flow of cold nitrogen in perfluorinated ether (Galden\u00ae LS 230, Solvay Specialty Polymers Italy SpA). For single-crystal data collection, the crystals were fixed on a glass capillary and positioned in a cold stream (150\u2009K) of dried N2 gas. Single-crystal data collection was performed with a STOE StadiVari diffractometer (Mo K\u03b1 radiation; \u03bb\u2009=\u20090.71072\u2009\u00c5) equipped with a DECTRIS PILATUS 300\u2009K detector.\n\nThe X-Area 1.9 software package (Stoe) was used for data reduction and absorption correction91. Structures were solved by Direct Methods (SHELXS-2014) and refined by full-matrix least-squares calculations against F2 (SHELXL-2014)92,93. The positions of the hydrogen atoms were either refined from the difference Fourier map or calculated and refined using a riding model. Unless otherwise stated, all non-hydrogen atoms were treated with anisotropic displacement parameters. The silicon cluster in compound 1 (CCDC 2338275) shows orientational disorder over three orientations and disorder of non-coordinated ammonia molecules. In compound 2 (CCDC 2232604) the disorder of [K(2.2.2-crypt)]+ and thf has been refined by a split layer refinement. For more details see the Supplementary Information (section Crystallographic Data). The crystal structures have been visualised with CrystalMaker\u00ae 11.1.194 and Diamond 3.295.\n\nThe data were collected at room temperature on a STOE Stadi P diffractometer (Ge(111) monochromator, Cu K\u03b11 radiation, \u03bb\u2009=\u20091.54056\u2009\u00c5) with a DECTRIS MYTHEN 1\u2009K detector in Debye\u2013Scherrer geometry. For the measurements, the samples were sealed in glass capillaries (\u00d8\u2009=\u20090.3\u2009mm). The raw data were processed with WinX-POW96. OriginPro 2023 (OriginLab Corporation) was used for visualisation97.\n\n1H, 2H, 13C, 19F and 29Si NMR spectra were recorded on a Bruker AVIII Ultrashield 400 and AVIII HD 500 Cryo. The signals of the 1H NMR spectra were referenced to the residual proton signal and the 13C-NMR spectra on the 13C signal of the deuterated solvent. 2H (\u03b4 (Me4Si-d12)\u2009=\u20090\u2009ppm), 19F (\u03b4 (CFCl3)\u2009=\u20090\u2009ppm), and 29Si (\u03b4 (Me4Si)\u2009=\u20090\u2009ppm) were referenced to external standards. Chemical shift values are given in \u03b4 values in parts per million (ppm). The coupling constants J are given in Hz. Signal multiplicities are abbreviated as follows: s\u2014singlet, d\u2014doublet, t\u2014triplet, q\u2014quartet, sept\u2014septet, dsept\u2014doublet of septet, b\u2014broad. The spectra were processed and visualised with MestReNova 15.0.098 and OriginPro 2023 (OriginLab Corporation)97.\n\nRaman measurements were performed with a Renishaw inVia Reflex Raman System with a CCD Detector (Renishaw 266n10 detector) and a 785\u2009nm laser of 500\u2009mW max. power (Software WiRE 5.3 Renishaw) in sealed glass capillaries (\u00d8\u2009=\u20090.5\u2009mm)99. The spectra were visualised with OriginPro 2023 (OriginLab Corporation)97.\n\nESI-MS spectra were measured on an HCT instrument (Bruker Inc). The data were processed with Bruker Compass Data Analysis 4.0 SP 5. The dry gas temperature was adjusted to 573\u2009K and the injection speed to 270\u2009\u03bcL/s. Data visualisation of the spectra was carried out with the programs OriginPro 2023 (OriginLab Corporation)97.\n\nUV\u2010VIS spectra were recorded on an Agilent Cary 60 UV\u2010Visible spectrophotometer (Agilent Technologies). The absorption spectra were recorded in 1\u2009mm quartz cuvettes (Hellma Analytics) in thf at room temperature. OriginPro 2023 (OriginLab Corporation) was used for visualisation97.\n\nElemental analyses were performed by the microanalytical laboratory at the Catalysis Research Center (CRC) of the Technical University of Munich\u00a0(TUM). The elements C, H, and N were determined by a combustion analyser (EURO-EA, HEKATech).",
+            "section_image": []
+        },
+        {
+            "section_name": "Data availability",
+            "section_text": "All data generated or analysed during this study are available in this published article, its Supplementary Information files or from the corresponding authors on request. The X-ray crystallographic coordinates for the structures reported in this study have been deposited at the Cambridge Crystallographic Data Centre (CCDC), under the deposition numbers 2338275 (1) and 2232604 (2a). These data can be obtained free of charge from The CCDC via www.ccdc.cam.ac.uk/data_request/cif.",
+            "section_image": []
+        },
+        {
+            "section_name": "References",
+            "section_text": "Sekiguchi, A. & Sakurai, H. Cage and cluster compounds of silicon, germanium, and tin. Adv. Organomet. Chem. 37, 1\u201338 (1995).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLee, V. Y. Organosilicon Compounds: Theory and experiment (Synthesis) Vol. 1 (Academic Press, 2017).\n\nHeider, Y. & Scheschkewitz, D. Molecular silicon clusters. Chem. Rev. 121, 9674\u20139718 (2021).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nHeider, Y. & Scheschkewitz, D. Stable unsaturated silicon clusters (siliconoids). Dalton Trans. 47, 7104\u20137112 (2018).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nSchnepf, A. Metalloid group 14 cluster compounds: an introduction and perspectives to this novel group of cluster compounds. Chem. Soc. Rev. 36, 745\u2013758 (2007).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nScharfe, S., Kraus, F., Stegmaier, S., Schier, A. & F\u00e4ssler, T. F. Zintl ions, cage compounds, and intermetalloid clusters of group 14 and group 15 elements. Angew. Chem. Int. Ed. 50, 3630\u20133670 (2011).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLiu, C. & Sun, Z.-M. Recent advances in structural chemistry of group 14 zintl ions. Coord. Chem. Rev. 382, 32\u201356 (2019).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWilson, R. J., Weinert, B. & Dehnen, S. Recent developments in zintl cluster chemistry. Dalton Trans. 47, 14861\u201314869 (2018).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWest, R. & Indriksons, A. Cyclic polysilanes. V. Tetradecylmethylbicyclo[2.2.2]octasilane, a cage polysilane. J. Am. Chem. Soc. 92, 6704\u20136705 (1970).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nSekiguchi, A., Yatabe, T., Kabuto, C. & Sakurai, H. Chemistry of organosilicon compounds. 303. The missing hexasilaprismane: synthesis, x-ray analysis and photochemical reactions. J. Am. Chem. Soc. 115, 5853\u20135854 (1993).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nAbersfelder, K. et al. Contraction and expansion of the silicon scaffold of stable Si6R6 isomers. J. Am. Chem. Soc. 134, 16008\u201316016 (2012).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLi, Y., Li, J., Zhang, J., Song, H. & Cui, C. Isolation of R6Si6 dianion: a bridged tricyclic isomer of dianionic hexasilabenzene. J. Am. Chem. Soc. 140, 1219\u20131222 (2018).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMatsumoto, H. et al. The first octasilacubane system: synthesis of octakis-(t-butyldimethylsilyl)pentacyclo[4.2.0.02,5.03,8.04,7]octasilane. J. Chem. Soc., Chem. Commun. 1083\u20131084 https://doi.org/10.1039/C39880001083 (1988).\n\nMatsumoto, H., Higuchi, K., Kyushin, S. & Goto, M. Octakis(1,1,2-trimethylpropyl)octasilacubane: synthesis, molecular structure, and unusual properties. Angew. Chem. Int. Ed. 31, 1354\u20131356 (1992).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nSekiguchi, A., Yatabe, T., Kamatani, H., Kabuto, C. & Sakurai, H. Chemistry of organosilicon compounds. 293. Preparation, characterization, and crystal structures of octasilacubanes and octagermacubanes. J. Am. Chem. Soc. 114, 6260\u20136262 (1992).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nFurukawa, K., Fujino, M. & Matsumoto, N. Cubic silicon cluster. Appl. Phys. Lett. 60, 2744\u20132745 (1992).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWiberg, N., Finger, C. M. M. & Polborn, K. Tetrakis(tri-tert-butylsilyl)-tetrahedro-tetrasilane (tBu3Si)4Si4: the first molecular silicon compound with a Si4 tetrahedron. Angew. Chem. Int. Ed. 32, 1054\u20131056 (1993).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nIchinohe, M., Toyoshima, M., Kinjo, R. & Sekiguchi, A. Tetrasilatetrahedranide: a silicon cage anion. J. Am. Chem. Soc. 125, 13328\u201313329 (2003).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWest, R. & Indriksons, A. Cyclic polysilanes. VI. Bicyclic and cage permethylcyclopolysilanes. J. Am. Chem. Soc. 94, 6110\u20136115 (1972).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nFischer, J., Baumgartner, J. & Marschner, C. Synthesis and structure of sila-adamantane. Science 310, 825\u2013825 (2005).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nSiu, T. C. et al. Site-selective functionalization of sila-adamantane and its ensuing optical effects. Angew. Chem. Int. Ed. 61, e202206877 (2022).\n\nTillmann, J. et al. One-step synthesis of a [20]silafullerane with an endohedral chloride ion. Angew. Chem. Int. Ed. 54, 5429\u20135433 (2015).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBamberg, M. et al. [Cl@Si20H20]\u2212: parent siladodecahedrane with endohedral chloride ion. J. Am. Chem. Soc. 143, 10865\u201310871 (2021).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBamberg, M. et al. Regioselective derivatization of silylated [20]silafulleranes. J. Am. Chem. Soc. 145, 11440\u201311448 (2023).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nNied, D., K\u00f6ppe, R., Klopper, W., Schn\u00f6ckel, H. & Breher, F. Synthesis of a pentasilapropellane. Exploring the nature of a stretched silicon\u2013silicon bond in a nonclassical molecule. J. Am. Chem. Soc. 132, 10264\u201310265 (2010).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nAbersfelder, K., White, A. J. P., Berger, R. J. F., Rzepa, H. S. & Scheschkewitz, D. A stable derivative of the global minimum on the Si6H6 potential energy surface. Angew. Chem. Int. Ed. 50, 7936\u20137939 (2011).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLeszczy\u0144ska, K. I. et al. Atomically precise expansion of unsaturated silicon clusters. Angew. Chem. Int. Ed. 58, 5124\u20135128 (2019).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWillmes, P. et al. Isolation and versatile derivatization of an unsaturated anionic silicon cluster (siliconoid). Angew. Chem. Int. Ed. 55, 2907\u20132910 (2016).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nHeider, Y., Willmes, P., Huch, V., Zimmer, M. & Scheschkewitz, D. Boron and phosphorus containing heterosiliconoids: stable p- and n-doped unsaturated silicon clusters. J. Am. Chem. Soc. 141, 19498\u201319504 (2019).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nPoitiers, N. E., Giarrana, L., Huch, V., Zimmer, M. & Scheschkewitz, D. Exohedral functionalization vs. core expansion of siliconoids with group 9 metals: catalytic activity in alkene isomerization. Chem. Sci. 11, 7782\u20137788 (2020).\n\nArticle\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nHelmer, J., Hepp, A., Berger, R. J. F. & Lips, F. Synthesis and functionalization of the six-vertex anionic amido-substituted silicon cluster [Si6{N(SiMe3)Ph}5]\u2212. Dalton Trans. 52, 14949\u201314955 (2023).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKeuter, J., Hepp, A., Daniliuc, C. G., Feldt, M. & Lips, F. Cycloadditions with a stable charge-separated cyclobutadiene-type amido-substituted silicon ring compound. Angew. Chem. Int. Ed. 60, 21761\u201321766 (2021).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKeuter, J. et al. A highly unsaturated six-vertex amido-substituted silicon cluster. Chem. Sci. 11, 5895\u20135901 (2020).\n\nArticle\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nVon Schnering, H. G. et al. Binary alkali metal compounds with the zintl anions [Ge9]4\u2212 and [Sn9]4\u2212. Z. Anorg. Allg. Chem. 623, 1037\u20131039 (1997).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBenda, C. B., Wang, J.-Q., Wahl, B. & F\u00e4ssler, T. F. Syntheses and 1H NMR spectra of substituted zintl ions [Ge9Rn](4\u2013n)\u2212: crystal structures of [Ge9R]3\u2212 (R = 2,4,6-Me3C6H2, CHCH2) and indication of tris-vinylated clusters. Eur. J. Inorg. Chem. 2011, 4262\u20134269 (2011).\n\nBentlohner, M. M., Klein, W., Fard, Z. H., Jantke, L.-A. & F\u00e4ssler, T. F. Linking deltahedral zintl clusters with conjugated organic building blocks: synthesis and characterization of the zintl triad [R-Ge9-CH=CH-CH=CH-Ge9-R]4\u2212. Angew. Chem. Int. Ed. 54, 3748\u20133753 (2015).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nHull, M. W. & Sevov, S. C. Functionalization of nine-atom deltahedral zintl ions with organic substituents: detailed studies of the reactions. J. Am. Chem. Soc. 131, 9026\u20139037 (2009).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nFrischhut, S., Bentlohner, M. M., Klein, W. & F\u00e4ssler, T. F. Synthesis of zintl triads comprising extended conjugated \u03c0-electronic systems: [RGe9\u2013CH\u2550CH\u2013CH\u2550CH\u2013Ge9R]4\u2013 (R = \u2212CH\u2550CH2, \u2212C(CH3)\u2550CH\u2013CH\u2550N(CH2)2NH2. Inorg. Chem. 56, 10691\u201310698 (2017).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBenda, C. B., He, H., Klein, W., Somer, M. & F\u00e4ssler, T. F. Bisvinylated [R\u2013Ge9\u2013Ge9\u2013R]4\u2013 cluster dimers. Z. Anorg. Allg. Chem. 641, 1080\u20131086 (2015).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nHull, M. W. & Sevov, S. C. Addition of alkenes to deltahedral zintl clusters by reaction with alkynes: synthesis and structure of [Fc-CH=CH-Ge9-CH=CH-Fc]2\u2212, an organo-zintl\u2013organometallic anion. Angew. Chem. Int. Ed. 46, 6695\u20136698 (2007).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKysliak, O. & Schnepf, A. {Ge9[Si(SiMe3)3]2}2\u2212: a starting point for mixed substituted metalloid germanium clusters. Dalton Trans. 45, 2404\u20132408 (2016).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMayer, K., Schiegerl, L. J., Kratky, T., G\u00fcnther, S. & F\u00e4ssler, T. F. Targeted attachment of functional groups at Ge9 clusters via silylation reactions. Chem. Commun. 53, 11798\u201311801 (2017).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nSchiegerl, L. J., Geitner, F. S., Fischer, C., Klein, W. & F\u00e4ssler, T. F. Functionalization of [Ge9] with small silanes:[Ge9(SiR3)3]\u2013 (R = iBu, iPr, Et) and the structures of (CuNHCDipp)[Ge9{Si(iBu)3}3], (K-18c6)Au[Ge9{Si(iBu)3}3]2, and (K-18c6)2[Ge9{Si(iBu)3}2]. Z. Anorg. Allg. Chem. 642, 1419\u20131426 (2016).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKysliak, O., Kunz, T. & Schnepf, A. Metalloid Ge9R3\u2013 clusters with various silyl substituents: from shielded to open cluster cores. Eur. J. Inorg. Chem. 2017, 805\u2013810 (2017).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKysliak, O., Schrenk, C. & Schnepf, A. {Ge9[Si(SiMe3)2(SiPh3)]3}\u2212: ligand modification in metalloid germanium cluster chemistry. Inorg. Chem. 54, 7083\u20137088 (2015).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKysliak, O., Schrenk, C. & Schnepf, A. {[Si(SiMe3)3]2Ge9-SiMe2-(C6H4)-SiMe2-Ge9[Si(SiMe3)3]2K}\u2212: the connection of metalloid clusters via an organic linker. Inorg. Chem. 56, 9693\u20139697 (2017).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nFrischhut, S., Machado De Carvalho, J. G., Karttunen, A. J. & F\u00e4ssler, T. F. On the affinity between fullerenes and deltahedral zintl ions: a UV/Vis spectroscopic investigation. Z. Anorg. Allg. Chem. 644, 1337\u20131343 (2018).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLi, F. & Sevov, S. C. Synthesis, structures, and solution dynamics of tetrasubstituted nine-atom germanium deltahedral clusters. J. Am. Chem. Soc. 136, 12056\u201312063 (2014).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nFrischhut, S. & F\u00e4ssler, T. F. Synthesis of low-oxidation-state germanium clusters comprising a functional anchor group\u2014synthesis and characterization of [(Ge0)5(Ge-R)3(Ge-(CH2)n-CH=CH2)] with R = Si(SiMe3)3. Dalton Trans. 47, 3223\u20133226 (2018).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nFrischhut, S., Klein, W., Drees, M. & F\u00e4ssler, T. F. Acylation of homoatomic Ge9 cages and subsequent decarbonylation. Chem. Eur. J. 24, 9009\u20139014 (2018).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nFrischhut, S. et al. Capping nido-nonagermanide clusters with M-PPh3 and dynamics in solution: synthesis and structure of closo-[(Me3Si)3Si]3Et[Ge9M](PPh3) (M = Ni, Pt). Organometallics 37, 4560\u20134567 (2018).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nHenke, F., Schenk, C. & Schnepf, A. [Si(SiMe3)3]3Ge9M(CO)3\u2212 (M = Cr, Mo, W): coordination chemistry with metalloid clusters. Dalton Trans. 40, 6704\u20136710 (2011).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nSchenk, C. & Schnepf, A. {Ge9R3Cr(CO)5}\u2212 and {Ge9R3Cr(CO)3}\u2212: a metalloid cluster (Ge9R3\u2212) as a flexible ligand in coordination chemistry [R = Si(SiMe3)3]. Chem. Commun. 3208\u20133210 https://doi.org/10.1039/B901870K (2009).\n\nLi, F., Mu\u00f1oz-Castro, A. & Sevov, S. C. [(Me3Si)Si]3EtGe9Pd(PPh3), a pentafunctionalized deltahedral zintl cluster: synthesis, structure, and solution dynamics. Angew. Chem. Int. Ed. 55, 8630\u20138633 (2016).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWilleit, N. S., Klein, W., Coburger, P., Fritz-Langhals, E. & F\u00e4ssler, T. F. Functionalised [Ge9Ni] clusters as homogeneous single-site catalysts for olefin isomerisation reactions. ChemCatChem 16, e202301200 (2024).\n\nSchiegerl, L. J. et al. Silylated Ge9 clusters as new ligands for cyclic (alkyl)amino and mesoionic carbene copper complexes. Inorg. Chem. 58, 3256\u20133264 (2019).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nGienger, C., Schynowski, L., Schaefer, J., Schrenk, C. & Schnepf, A. New intermetalloid Ge9-clusters with copper and gold: filling vacancies in the cluster chemistry of [Ge9(Hyp)3]\u2212 (Hyp=Si(SiMe3)3. Eur. J. Inorg. Chem. 26, e202200738 (2023).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMayer, K., Schiegerl, L. J. & F\u00e4ssler, T. F. On the reactivity of silylated Ge9 clusters: synthesis and characterization of [ZnCp*(Ge9{Si(SiMe3)3}3)], [CuPiPr3(Ge9{Si(SiMe3)3}3)], and [(CuPiPr3)4{Ge9(SiPh3)2}2]. Chem. Eur. J. 22, 18794\u201318800 (2016).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nUgrinov, A. & Sevov, S. C. [Ge9Ge9Ge9]6-: a linear trimer of 27 germanium atoms. J. Am. Chem. Soc. 124, 10990\u201310991 (2002).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nNienhaus, A., Hoffmann, S. D. & F\u00e4ssler, T. F. First synthesis of group-14 polyanions by extraction of a binary alloy with dmf and a novel conformation of the (Ge9\u2212Ge9)6\u2212 dimer: crystal structures of [K6(Ge9\u2212Ge9)](dmf)12, [Rb6(Ge9\u2212Ge9)](dmf)12 and [K2.5Cs3.5(Ge9\u2212Ge9)](dmf)12. Z. Anorg. Allg. Chem. 632, 1752\u20131758 (2006).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nHauptmann, R. & F\u00e4ssler, T. F. Low dimensional arrangements of the zintl ion [Ge9-Ge9]6- and chemical bonding in [Ge6]2-, [Ge9-Ge9]6-, and 1\u221e{[Ge9]}2-. Z. Anorg. Allg. Chem. 629, 2266\u20132273 (2003).\n\nYong, L., Hoffmann, S. D. & F\u00e4ssler, T. F. The controlled oxidative coupling of Ge94\u2212 zintl anions to a linear trimer [Ge9=Ge9=Ge9]6\u2212. Z. Anorg. Allg. Chem. 631, 1149\u20131153 (2005).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nXu, L. & Sevov, S. C. Oxidative coupling of deltahedral [Ge9]4- zintl ions. J. Am. Chem. Soc. 121, 9245\u20139246 (1999).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nScharfe, S. & F\u00e4ssler, T. F. Synthesis of (Ge9\u2013Ge9)6\u2013 dimeric zintl ions in liquid ammonia solutions of K4Ge9: low-dimensional coordination networks in the crystal structure of the ammoniates Kn[K([2.2.2]crypt)]6\u2013n[Ge9\u2013Ge9](NH3)m (n = 2, 3, and 4). Z. Anorg. Allg. Chem. 637, 901\u2013906 (2011).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nUgrinov, A. & Sevov, S. C. Synthesis of a chain of nine-atom germanium clusters accompanied with dimerization of the sequestering agent. Comptes Rendus Chim. 8, 1878\u20131882 (2005).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nHoch, C., Wendorff, M. & R\u00f6hr, C. Synthesis and crystal structure of the tetrelides A12M17 (A=Na, K, Rb, Cs; M=Si, Ge, Sn) and A4Pb9 (A=K, Rb). J. Alloys Compd. 361, 206\u2013221 (2003).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nGoicoechea, J. M. & Sevov, S. C. Ligand-free deltahedral clusters of silicon in solution: synthesis, structure, and electrochemistry of Si92-. Inorg. Chem. 44, 2654\u20132658 (2005).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nGoicoechea, J. M. & Sevov, S. C. Naked deltahedral silicon clusters in solution: synthesis and characterization of Si93- and Si52-. J. Am. Chem. Soc. 126, 6860\u20136861 (2004).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBenda, C. B., Henneberger, T., Klein, W. & F\u00e4ssler, T. F. [Si4]4\u2013 and [Si9]4\u2013 clusters crystallized from liquid ammonia solution\u2014synthesis and characterization of K8[Si4][Si9]\u00b7(NH3)14.6. Z. Anorg. Allg. Chem. 643, 146\u2013148 (2017).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nHastreiter, F. et al. Elusive zintl ions [\u03bc-HSi4]3\u2212 and [Si5]2\u2212 in liquid ammonia: protonation states, sites, and bonding situation evaluated by NMR and theory. Angew. Chem. Int. Ed. 58, 3133\u20133137 (2019).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLorenz, C. et al. The structure of [HSi9]3\u2212 in the solid state and its unexpected highly dynamic behavior in solution. Angew. Chem. Int. Ed. 57, 12956\u201312960 (2018).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nSchiegerl, L. J. et al. Charged Si9 clusters in neat solids and the detection of [H2Si9]2\u2212 in solution: a combined NMR, Raman, mass spectrometric, and quantum chemical investigation. Angew. Chem. Int. Ed. 57, 12950\u201312955 (2018).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nHenneberger, T., Klein, W. & F\u00e4ssler, T. F. Silicon containing nine atom clusters from liquid ammonia solution: crystal structures of the first protonated clusters [HSi9]3\u2013 and [H2{Si/Ge}9]2\u2013. Z. Anorg. Allg. Chem. 644, 1018\u20131027 (2018).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nGoicoechea, J. M. & Sevov, S. C. Organozinc derivatives of deltahedral zintl ions: synthesis and characterization of closo-[E9Zn(C6H5)]3- (E = Si, Ge, Sn, Pb). Organometallics 25, 4530\u20134536 (2006).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nJoseph, S. et al. Chemistry with bare silicon clusters in solution: a transition-metal complex of a polysilicide anion. Angew. Chem. Int. Ed. 48, 8770\u20138772 (2009).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nStreitferdt, V. et al. NMR-spectroscopic detection of an elusive protonated and coinage metalated silicide [NHCDippCu(\u03b74-Si9)H]2\u2212 in solution. Eur. J. Chem. 2021, 3684\u20133690 (2021).\n\n\n                    Google Scholar\u00a0\n                \n\nTiefenthaler, S. M. et al. On the reactivity of NHCtBuAuCl towards Rb6Cs6Si17: the first gold-silicon cluster [(NHCtBuAu)6(\u03b72-Si4)]Cl2\u00b77NH3 and an imide capped gold triangle (NHCtBuAu)3NHCl. Z. Anorg. Allg. Chem. 646, 1595\u20131602 (2020).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWaibel, M., Kraus, F., Scharfe, S., Wahl, B. & F\u00e4ssler, T. F. [(MesCu)2(\u03b73-Si4)]4\u2212: a mesitylcopper-stabilized tetrasilicide tetraanion. Angew. Chem. Int. Ed. 49, 6611\u20136615 (2010).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nGeitner, F. S. & F\u00e4ssler, T. F. Low oxidation state silicon clusters\u2014synthesis and structure of [NHCDippCu(\u03b74-Si9)]3\u2212. Chem. Commun. 53, 12974\u201312977 (2017).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nSchiegerl, L. J., Karttunen, A. J., Klein, W. & F\u00e4ssler, T. F. Anionic siliconoids from zintl phases: R3Si9\u2212 with six and R2Si92\u2212 with seven unsubstituted exposed silicon cluster stoms (R=Si(tBu)2H. Chem. Eur. J. 24, 19171\u201319174 (2018).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nSchiegerl, L. J., Karttunen, A. J., Klein, W. & F\u00e4ssler, T. F. Silicon clusters with six and seven unsubstituted vertices via a two-step reaction from elemental silicon. Chem. Sci. 10, 9130\u20139139 (2019).\n\nArticle\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nvon Schnering, H. G. et al. Das clusteranion Si94\u2212. Angew. Chem. 110, 2507\u20132509 (1998).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKocak, F. S. et al. Surprising acid/base and ion-sequestration chemistry of Sn94\u2013: HSn93\u2013, Ni@HSn93\u2013, and the Sn93\u2013 ion revisited. J. Am. Chem. Soc. 134, 9733\u20139740 https://doi.org/10.1039/B905239A (2012).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKocak, F. S., Zavalij, P. Y., Lam, Y.-F. & Eichhorn, B. W. Substituent-dependent exchange mechanisms in highly fluxional RSn93\u2212 anions. Chem. Commun. 4197\u20134199 (2009).\n\nLi, F. & Sevov, S. C. Rational synthesis of [Ge9{Si(SiMe3)3}3]\u2212 from its parent zintl ion Ge94\u2013. Inorg. Chem. 51, 2706\u20132708 (2012).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nSchrenk, C., Winter, F., P\u00f6ttgen, R. & Schnepf, A. {Sn9[Si(SiMe3)3]2}2-: a metalloid tin cluster compound with a Sn9 core of oxidation state zero. Inorg. Chem. 51, 8583\u20138588 (2012).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nSchrenk, C., Neumaier, M. & Schnepf, A. {Sn9[Si(SiMe3)3]3}\u2212 and {Sn8Si[Si(SiMe3)3]3}\u2212: variations of the E9 cage of metalloid group 14 clusters. Inorg. Chem. 51, 3989\u20133995 (2012).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nJenkner, P. K., Spielberger, A., Eibl, M. & Hengge, E. 29Si NMR spektroskopie von cyclopentasilanen. Spectrochim. Acta A 49, 161\u2013165 (1993).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBonger, K. M. et al. Synthesis and evaluation of homo-bivalent GnRHR ligands. Bioorg. Med. Chem. 15, 4841\u20134856 (2007).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDerouiche, Y. & Lickiss, P. D. Preparation and reactions of tris(trimethylsilyl)silyl silicon derivatives and related tetrasilylsilanes. J. Organomet. Chem. 407, 41\u201349 (1991).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nX-Area, version 1.90. Stoe & Cie GmbH (2020).\n\nSheldrick, G. M. Crystal structure refinement with SHELXL. Acta Crystallogr. Sect. C 71, 3\u20138 (2015).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nH\u00fcbschle, C. B., Sheldrick, G. M. & Dittrich, B. ShelXle: a qt graphical user interface for SHELXL. J. Appl. Crystallogr. 44, 1281\u20131284 (2011).\n\nArticle\u00a0\n    ADS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nCrystalMaker\u00ae Version 11.1.1. CrystalMaker Software Ltd (www.crystalmaker.com).\n\nDiamond Version 3.2k. Crystal Impact GbR (2014).\n\nWinXPOW, version 3.0.2.1. STOE & Cie GmbH (2011).\n\nOriginPro, Version 2023. OriginLab Corporation.\n\nMestreNova, version 15.0.0. Mestrelab Research (2023).\n\nRenishaw, WiRE. inVia Reflex Raman.\n\nDownload references",
+            "section_image": []
+        },
+        {
+            "section_name": "Acknowledgements",
+            "section_text": "This work was co-funded by the Wacker Institute of Silicon Chemistry (Wacker Chemie AG) and the Technical University of Munich\u00a0(TUM). The authors thank Ulrike Ammari and Petra Ankenbauer for the execution of the elemental analyses. They further thank B.Sc. Vivienne Wolde and B.Sc. Thanh N. Tr\u00e2n for their assistance in the synthesis of 2.2.2-cryptand.",
+            "section_image": []
+        },
+        {
+            "section_name": "Funding",
+            "section_text": "Open Access funding enabled and organized by Projekt DEAL.",
+            "section_image": []
+        },
+        {
+            "section_name": "Author information",
+            "section_text": "Department of Chemistry, TUM School of Natural Sciences, Technical University of Munich (TUM), Lichtenbergstra\u00dfe 4, D-85748, Garching, Germany\n\nKevin M. Frankiewicz,\u00a0Nicole S. Willeit,\u00a0Viktor Hlukhyy\u00a0&\u00a0Thomas F. F\u00e4ssler\n\nWacker Institute of Silicon Chemistry, Technical University of Munich (TUM), Lichtenbergstra\u00dfe 4, D-85748, Garching, Germany\n\nKevin M. Frankiewicz,\u00a0Nicole S. Willeit\u00a0&\u00a0Thomas F. F\u00e4ssler\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nK.M.F. conceived and performed the syntheses of cluster compounds and collected the single-crystal X-ray data of 1 and 2a, solved and refined the structure of 1 and 2a, performed the ESI-MS and NMR measurements and prepared samples for further analyses. N.S.W. performed the Raman measurements. V.H. reviewed the structural refinement of 2a. T.F.F. supervised the work. K.M.F. wrote the paper. K.M.F. and N.S.W. conceived and performed the synthesis of 2.2.2-cryptand. All authors approved the submission of the manuscript.\n\nCorrespondence to\n                Thomas F. F\u00e4ssler.",
+            "section_image": []
+        },
+        {
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+            "section_text": "Nature Communications thanks the anonymous reviewer(s) for their contribution to the peer review of this work. A peer review file is available.",
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+            "section_image": []
+        },
+        {
+            "section_name": "About this article",
+            "section_text": "Frankiewicz, K.M., Willeit, N.S., Hlukhyy, V. et al. An efficient multi-gram access in a two-step synthesis to soluble, nine-atomic, silylated silicon clusters.\n                    Nat Commun 15, 10715 (2024). https://doi.org/10.1038/s41467-024-55211-z\n\nDownload citation\n\nReceived: 11 March 2024\n\nAccepted: 04 December 2024\n\nPublished: 23 December 2024\n\nVersion of record: 23 December 2024\n\nDOI: https://doi.org/10.1038/s41467-024-55211-z\n\nAnyone you share the following link with will be able to read this content:\n\nSorry, a shareable link is not currently available for this article.\n\n\n\n\n                            Provided by the Springer Nature SharedIt content-sharing initiative\n                        ",
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19a49b5392b6ecc9b2b1cb7e9c4673f0cfa1d11b956f8b9bd67664c341dc49f0/metadata.json

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+{
+    "title": "Experimental determination of giant polarization in wurtzite III-nitride semiconductors",
+    "pre_title": "Experimental Determination of Giant Polarization in Wurtzite III-Nitride Semiconductors",
+    "journal": "Nature Communications",
+    "published": "24 April 2025",
+    "supplementary_0": [
+        {
+            "label": "Supplementary Information",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-58975-0/MediaObjects/41467_2025_58975_MOESM1_ESM.pdf"
+        },
+        {
+            "label": "Transparent Peer Review file",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-58975-0/MediaObjects/41467_2025_58975_MOESM2_ESM.pdf"
+        }
+    ],
+    "supplementary_1": [
+        {
+            "label": "Source data",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-58975-0/MediaObjects/41467_2025_58975_MOESM3_ESM.xlsx"
+        }
+    ],
+    "supplementary_2": NaN,
+    "source_data": [
+        "/articles/s41467-025-58975-0#Sec13"
+    ],
+    "code": [],
+    "subject": [
+        "Ferroelectrics and multiferroics",
+        "Semiconductors"
+    ],
+    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
+    "preprint_pdf": "https://www.researchsquare.com/article/rs-5438804/v1.pdf?c=1745579149000",
+    "research_square_link": "https://www.researchsquare.com//article/rs-5438804/v1",
+    "nature_pdf": "https://www.nature.com/articles/s41467-025-58975-0.pdf",
+    "preprint_posted": "24 Nov, 2024",
+    "research_square_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Polarization engineering has revolutionized the photonic and electronic landscape of III-nitride semiconductors over the past decades. However, recent revelations of giant ferroelectric polarization in wurtzite III-nitrides challenge the long-standing paradigms. Here, we experimentally elucidate the polarization, including its magnitude and orientation, and its relationship to lattice polarity in III-nitrides. Those experimentally determined polarizations exceeding 1 C/m2 with an upward orientation in metal-polar wurtzite nitride compounds align with recent theoretical predictions. This unified framework redefines the polarization landscape in contemporary GaN heterostructures, quantum structures, and ferroelectric heterostructures. Furthermore, we predict significant tunability and a dramatic increase in sheet electron concentration in ferroelectric ScAlN/GaN heterostructures, heralding advancements in high-power, high-frequency, and reconfigurable transistors, and non-volatile memories. This work bridges the critical gap in the understanding of polarization in both conventional and ferroelectric wurtzite nitrides, offering fundamental insights and paving the way for next-generation photonic, electronic, and acoustic devices.Physical sciences/Physics/Condensed-matter physics/SemiconductorsPhysical sciences/Materials science/Condensed-matter physics/SemiconductorsPhysical sciences/Physics/Condensed-matter physics/Ferroelectrics and multiferroicsPhysical sciences/Materials science/Condensed-matter physics/Ferroelectrics and multiferroics",
+            "section_image": []
+        },
+        {
+            "section_name": "Additional Declarations",
+            "section_text": "There is NO Competing Interest.",
+            "section_image": []
+        },
+        {
+            "section_name": "Supplementary Files",
+            "section_text": "SIIIINpolarization.pdf",
+            "section_image": []
+        }
+    ],
+    "nature_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Polarization engineering has revolutionized the photonic and electronic landscape of III-nitride semiconductors over the past decades. However, recent revelations of giant ferroelectric polarization in wurtzite III-nitrides challenge the long-standing paradigms. Here, we experimentally elucidate the polarization, including its magnitude and orientation, and its relationship to lattice polarity in III-nitrides. Those experimentally determined polarizations exceeding 1 C/m2 with an upward orientation in metal-polar wurtzite nitride compounds align with recent theoretical predictions. To reconcile these findings, a unified polarization framework is established based on the centrosymmetric layered-hexagonal reference structure. This unified framework redefines the polarization landscape in contemporary GaN heterostructures, quantum structures, and ferroelectric heterostructures. Furthermore, we predict significant tunability and a dramatic increase in sheet carrier concentration in ferroelectric ScAlN/GaN heterostructures, heralding advancements in high-power, high-frequency, and reconfigurable transistors, and non-volatile memories. This work bridges the critical gap in the understanding of polarization in both conventional and ferroelectric wurtzite nitrides, offering fundamental insights and paving the way for next-generation photonic, electronic, and acoustic devices.",
+            "section_image": []
+        },
+        {
+            "section_name": "Introduction",
+            "section_text": "III-nitride semiconductors, characterized by their non-centrosymmetric wurtzite (WZ, P63mc) structure, inherently exhibit nonvanishing spontaneous polarization and piezoelectric polarization1,2. The pronounced polarization discontinuities at the III-nitride heterointerfaces result in the formation of bound sheet charges. These charges generate an internal polarization field, leading to phenomena such as the formation of two-dimensional electron or hole gases (2DEG or 2DHG)3,4,5, polarization-induced doping6, quantum-confined Stark effect7, etc. in III-nitride heterostructures. Over the past decades, polarization engineering has remarkably boosted the photonic and electronic ecosystem of III-nitrides8,9,10. However, recent discoveries of wurtzite nitride ferroelectrics, such as scandium aluminum nitride (ScAlN)11,12,13,14,15, which exhibit a giant spontaneous polarization compared to traditional expectations3,16, challenge the well-established paradigms. Therefore, refining and unifying the cognition of polarization within the III-nitride semiconductor family is crucial to ensuring continued progress in material and device development.\n\nExperimentally determining the polarization of a solid, particularly the spontaneous polarization, faces significant challenges. In crystalline solids, people generally measure the changes in polarization rather than the absolute values17. Consequently, theoretically predicted spontaneous polarizations are often relied upon to simulate and interpret the experiments. Within the framework of the Modern Theory of Polarization (MTP), the spontaneous polarization of a crystal is defined as the difference in the formal polarization between the material of interest and a reference structure: \\({{{{\\boldsymbol{P}}}}}_{{{{\\rm{SP}}}}}^{{{\\mathrm{int}}},{{{\\rm{ref}}}}}={{{{\\boldsymbol{P}}}}}_{{{{\\rm{f}}}}}^{{{\\mathrm{int}}}}-{{{{\\boldsymbol{P}}}}}_{{{{\\rm{f}}}}}^{{{{\\rm{ref}}}}}\\), where \\({{{{\\boldsymbol{P}}}}}_{{{{\\rm{f}}}}}^{{{\\mathrm{int}}}}\\) and \\({{{{\\boldsymbol{P}}}}}_{{{{\\rm{f}}}}}^{{{{\\rm{ref}}}}}\\) are the formal polarization of the material and its reference structure, respectively, \\({{{{\\boldsymbol{P}}}}}_{{{{\\rm{SP}}}}}^{{{\\mathrm{int}}},{{{\\rm{ref}}}}}\\) is the spontaneous polarization of the material relative to the reference structure17,18,19,20. Normally, the reference structure should have vanished formal polarization. The reference structure for wurtzite crystals can be either a zinc-blende (ZB, \\({{\\mbox{F}}}\\bar{4}3{\\mbox{m}}\\)) or a h-BN like layered-hexagonal (LH, P63/mmc) structure, as shown in Fig.\u00a01a and detailed in Supplementary Note\u00a01. The polarization properties of WZ III-nitrides were firstly investigated by Bernardini et al. in 1997 using the MTP framework, with ZB serving as the reference structure1. Their predictions, with polarization values below 0.1\u2009C/m2, have been extensively used to predict the net polarization bound charge at GaN-based heterointerfaces. In 2016, Dreyer et al. revised the polarization constants within WZ III-nitrides using a LH reference structure21, predicting giant spontaneous polarizations exceeding 1\u2009C/m2\u2014more than an order of magnitude larger than the initial ones with the ZB reference structure. This divergence garnered attention following the report of ferroelectric polarization switching in ScAlN films by Fichtner et al. in 2019, where remnant polarizations over 1\u2009C/m2 were measured11,22,23,24. Nevertheless, the polarization values and their orientations in III-nitride semiconductors are still open questions, in particular, convincing experimental evidences remain elusive.\n\na Crystal structures of III-nitrides, including WZ, ZB, and LH configurations (top), and atomic schematics illustrating the adiabatic and gap-preserving displacement between WZ and its ZB and LH reference structures along the c-axis (bottom). b Electron localization function (ELF) of WZ AlN projected along the \\([11\\bar{2}0]\\) zone-axis, showing both the ionic (Pion) and electronic (Pel) contributions to polarization. c Diagram of the local polarization measurement method based on a simulated ABF-STEM image of WZ AlN. Atomic displacement (\u0394r) and lattice constants (a and c) are measurable. The inset shows a quadrilateral prism representing the unit cell with volume of \u03a9. d\u2013k ABF-STEM images of WZ M-polar (d) AlN, (e) GaN, (f) InN, and (g) ScAlN, and N-polar (h) AlN, (i) GaN, (j) InN, and (k) ScAlN, each overlaid with vector map of the measured local polarization.\n\nIn this work, we establish a unified perspective on the polarization of III-nitride semiconductors through systematic experimental examinations. The inherent correlation between the spontaneous polarization and lattice polarity are determined via comprehensive local and macroscopic polarization characterizations. These experimental findings corroborate that the understanding of the spontaneous polarization, ferroelectric polarization, and lattice polarity in WZ III-nitride family can be much more accurately unified by referencing the LH structure, rather than the long-standing ZB reference structure. Accordingly, the polarization landscape in the advanced AlGaN/GaN and ferroelectric ScAlN/GaN heterostructures has been reevaluated using the newly unified polarization framework. This approach not only reconciles the existing experimental observations, but also predicts significant tunability and a dramatic increase of sheet carrier concentration in the ferroelectric ScAlN/GaN heterostructures, providing new insights into the development of high-performance electronic and ferroelectric devices.",
+            "section_image": [
+                "https:////media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41467-025-58975-0/MediaObjects/41467_2025_58975_Fig1_HTML.png"
+            ]
+        },
+        {
+            "section_name": "Results",
+            "section_text": "As illustrated in the top panel of Fig.\u00a01a, III-nitride semiconductors exhibit a wurtzite ground state structure, featuring with an in-plane lattice a for the basal hexagon, an out-of-plane lattice c for the hexagonal prism, and an internal parameter u, which is defined as the ratio of the metal-nitrogen (M-N) bond length along the c-axis to the lattice constant c. Wurtzite is a non-centrosymmetric structure where metal and nitrogen atoms occupy two separate atomic planes. A sublattice displacement, \\(d=\\frac{1}{2}-u\\), represents the smallest interplanar spacing between the metal and nitrogen atomic planes in unit of c. The lack of spatial inversion symmetry results in a non-zero spontaneous polarization along the c-axis. Two opposite crystallographic lattice polarities exist along this axis, defined as M-polarity and N-polarity, corresponding to the [0001] and \\(\\left[000\\bar{1}\\right]\\) directions, respectively3. In the M-polarity configuration, metal atoms are positioned above the nearest nitrogen atom plane, resulting in d\u2009>\u20090 (Fig.\u00a01a), whereas in the N-polar one, the order is reversed. Although spontaneous polarization plays a crucial role in the development of III-nitride semiconductors, direct polarization measurements have been experimentally challenging. Therefore, the reported values of polarization are basically theoretically predicted ones1,2,21,25. The MTP modeling is usually used for such theoretical prediction17,20,26, where it suggests that both ionic and electronic contributions to polarization can be calculated from the atomic displacement (\u0394r) using the Born effective charges (Z *) (Fig.\u00a01c and Supplementary Note\u00a02). In this approach, \u0394r is the atomic displacement of a crystal compared to its centrosymmetric structure. The bottom panel of Fig.\u00a01a shows the atomic chains for the WZ phase and the corresponding ZB and LH reference structures along their polar axes, specifically the \\(\\left\\langle 0001\\right\\rangle\\), \\(\\left\\langle 111\\right\\rangle\\), and \\(\\left\\langle 0001\\right\\rangle\\) axes, respectively. Obviously, the centrosymmetric reference structure for WZ is the LH phase, where both metal and nitrogen atoms share the same atomic plane. Moreover, an adiabatic, gap-preserving atomic displacement path can only be established between the WZ and LH reference structure for III-nitrides.\n\nIn the WZ structures, as shown in Figs.\u00a01a, c, the smallest atomic plane spacing along the c-axis is the atomic displacement used for polarization calculation, i.e., \u0394r = dc. This displacement is possible to be directly measured using atomically resolved scanning transmission electron microscope (STEM) by identifying the positions of metal and nitrogen atom columns27,28. Furthermore, for III-nitride semiconductors, \u0394r determines the polarization orientation21,25,28: positive (d\u2009>\u20090) and negative (d\u2009<\u20090) \u0394r correspond to upward and downward polarizations, which can be defined as +P and \u2212P, respectively, as indicated in Fig.\u00a01a. Therefore, local polarization measurements utilizing STEM provide a direct and accurate way for determining the intrinsic polarization at the unit cell scale. While STEM has been widely used to investigate microstructure and lattice polarity in III-nitrides15,29, its application for local polarization measurements remains limited.\n\nIn this work, we conducted comprehensive local polarization measurements on III-nitrides, including M-polar and N-polar AlN, GaN, InN, and ScAlN by using annular bright field STEM (ABF-STEM). Figure\u00a01d\u2013g displays ABF-STEM images of M-polar AlN, GaN, and InN films, respectively, which were grown on sapphire substrates. The lattice parameters of these films, measured by X-ray diffraction (XRD), are consistent with previous theoretical and experimental reports, showing negligible strain (Fig.\u00a0S4 and Table SII). The spatial positions of atom columns were determined by using a two-dimensional Gaussian fitting process on the ABF-STEM images, enabling precise measurement of \u0394r across the entire image (Fig.\u00a0S6). Polarization was then quantified using Born effective charges derived from the density-functional theories (DFT) (Supplementary Note\u00a02 and Table SII). Vector maps of the calculated polarization per unit cell were superposed on the corresponding ABF-STEM images (Fig.\u00a01d\u2013g). The measured average polarization for M-polar AlN, GaN, and InN is +1.37\u2009\u00b1\u20090.11, +1.29\u2009\u00b1\u20090.11, and +1.04\u2009\u00b1\u20090.15\u2009C/m2, respectively, all exhibiting upward-orientated spontaneous polarization. The error bar arises from the measurement uncertainty resulting from the atomic position fitting process.\n\nWe further conducted local polarization measurements on a M-polar ScAlN layer which was grown on GaN/sapphire template by molecular beam epitaxy (MBE)30. The ScAlN has a monocrystalline wurtzite structure with 18% Sc content, which is nearly\u00a0lattice-matched to the underlying GaN, minimizing strain effect on the polarization measurements16,31,32. More details can be found in the Methods and Supplementary Fig.\u00a0S5. Figure\u00a01g shows the ABF-STEM image of the ScAlN, overlaid with the measured polarization vector map. We obtained an average polarization of +1.38\u2009\u00b1\u20090.17\u2009C/m2. To further validate the accuracy and reliability of this approach and obtain a systematic understanding of polarization in WZ III-nitrides, the same measurements were performed on the N-polar counterparts of these materials. As illustrated in Fig.\u00a01h\u2013k, the measured average polarization for N-polar AlN, GaN, InN, and ScAlN is \u22121.34\u2009\u00b1\u20090.20, \u22121.28\u2009\u00b1\u20090.24, \u22121.09\u2009\u00b1\u20090.26, and \u22121.38\u2009\u00b1\u20090.21\u2009C/m2, respectively, all showing downward-orientated spontaneous polarization.\n\nSince ScAlN is a ferroelectric material, we then conducted macroscopic electrical measurements on the MBE-grown ferroelectric ScAlN/GaN heterostructure to determine its polarization value. Figure\u00a02a shows the high angle annular dark field (HAADF) STEM image captured from the ScAlN/GaN sample, exhibiting atomically sharp interface. Lithographically patterned circular Ti/Au pads served as top electrodes, while the n+-GaN layer functioned as the bottom electrode, with voltages applied from the top electrode, as schematically shown in the inset of Fig.\u00a02b. Figure\u00a02b shows a typical polarization versus electric field (P-E) hysteresis loop measured from the ferroelectric ScAlN/GaN heterostructure, yielding a remanent polarization of approximately 1.48\u2009C/m2, consistent with the locally measured polarization value of 1.38\u2009C/m2. The slightly higher remanent polarization is attributed to overestimation due to electric leakage at high voltage. This issue can be partially mitigated by using positive-up-negative-down (PUND) measurements (Fig.\u00a0S7). The remanent polarization obtained from PUND analysis using a triangular pulse sequence is 1.11\u2009C/m2.\n\na HAADF-STEM image of the as-grown ScAlN/GaN heterostructure, exhibiting an atomically sharp interface. b Typical P-E hysteresis loop recorded from a ScAlN capacitor at 1\u2009kHz without subtracting electric leakage. The inset shows a schematic of the ScAlN metal-ferroelectric-semiconductor (MFS) capacitor structure. c, d ABF-STEM images of ScAlN, captured from (c) positively and (d) negatively biased MFS capacitors, as indicated in (b). The superimposed metal (pink) and nitrogen (blue) atoms highlight the atomic stacking sequence, revealing N- and M-polar lattices in (c) and (d), respectively. e Monopolar measurements executed on ScAlN MFS capacitors with opposite initial polarization states: (i, ii) fresh M-polar ScAlN, exhibiting upward spontaneous polarization, and (iii, iv) switched N-polar ScAlN, presenting downward spontaneous polarization. The insets depict the applied voltage pulses and the evolution of polarization orientation under an external electric field, with arrows in the ScAlN/GaN heterostructures indicating the polarization orientation.\n\nThe ferroelectric nature of ScAlN also enables local polarization measurement in III-nitrides after reversing the lattice polarity, which was previously unattainable. Figure\u00a02c, d shows ABF-STEM images captured from two ScAlN devices with opposite polarization states, corresponding to the positive and negative biases indicated in Fig.\u00a02b. By comparing the stacking order of metal (Sc/Al) and nitrogen atoms in these ABF images with the atomic model in Fig.\u00a01a, the lattice polarity was confirmed as N-polarity for positively-biased state (Fig.\u00a02c) and M-polarity for negatively-biased one (Fig.\u00a02d). The measured average polarizations are \u22121.34\u2009\u00b1\u20090.14 and +1.43\u2009\u00b1\u20090.11\u2009C/m2, respectively. The excellent agreement of these STEM quantified and electrically measured polarization magnitudes for as-deposited and lattice-reversed ScAlN films unambiguously identifies that this material possesses a polarization over 1\u2009C/m2. Notably, recent studies have demonstrated ferroelectric polarization switching in sputter-deposited AlN films33,34, showing a remanent polarization of 1.5\u2009C/m2, which aligns well with the polarization values obtained for AlN in Fig.\u00a01. Given that conventional III-nitrides and ferroelectric III-nitrides share identical crystal symmetry, as well as comparable Born effective charges and atomic displacements (Table SII), we can infer, based on the MTP, that the polarization landscape of the WZ III-nitride family should be similar. In other words, conventional III-nitrides possess strong polarization effects akin to those observed in ferroelectric nitrides. Thus far, both local and macroscopic polarization measurements corroborate that WZ III-nitrides exhibit spontaneous polarization values exceeding 1\u2009C/m2.\n\nSubsequently, we examined the intrinsic orientation of the spontaneous polarization in WZ III-nitrides, an ongoing topic of debate, through macroscopic electrical measurements. The wake-up-free nature and highly controllable, uniform lattice polarity of MBE-grown monocrystalline ferroelectric ScAlN allowed us to perform monopolar measurements on fresh devices without pre-cycling treatments. This is essential for examining intrinsic polarization orientation. In ferroelectrics, once the orientation of the spontaneous polarization is reversed by an external electric field, the redistribution of the polarization-compensated charges gives rise to an instantaneous current flow known as \u201cdisplacement current\u201d35,36. Displacement current, therefore, serves as an indicator of changes in polarization orientation. For monopolar measurements, a single positive or negative triangular pulse exceeding the coercive field was applied to the top electrodes of fresh ScAlN capacitors. The corresponding current density versus electric field (J-E) curves are plotted in Fig.\u00a02e. A distinct displacement current is observed following the application of a positive pulse bias on a fresh M-polar ScAlN capacitor, while no displacement current is detected after executing a negative pulse bias, as displayed in the top panel of Fig.\u00a02e. This behavior indicates that the orientation of the spontaneous polarization in M-polar ScAlN can be inverted by a downward external electric field (towards the ScAlN/GaN interface), but not by an upward one (towards the ScAlN surface), as depicted in the insets of Fig.\u00a02e(i, ii).\n\nThe same measurements were conducted on N-polar ScAlN/GaN capacitors, shown in the bottom panel of Fig.\u00a02e. Those N-polar ScAlN/GaN capacitors were obtained by converting the original M-polar to N-polar lattice via applying positive voltage pulses (Fig.\u00a02c). In contrast to the M-polar capacitors, the N-polar ones exhibited negligible response to a positive voltage pulse, while a definite displacement current was generated under a negative pulse. This phenomenon suggests that it is an upward external electric filed\u2014rather than a downward one\u2014that induces inversion of the spontaneous polarization orientation in N-polar ScAlN, as illustrated in the insets of Fig.\u00a02e(iii, iv). According to the theory of dielectric polarization, the spontaneous polarization of a ferroelectric aligns with the external electric field after polarization reversing17,36,37. Based on this, above monopolar analyses suggest that M-polar ScAlN exhibits an upward spontaneous polarization, while N-polar ScAlN has a downward one. These findings, when combined with the local polarization measurements shown in Fig.\u00a01, provide unambiguous experimental confirmation that M-polar III-nitrides possess an upward spontaneous polarization (+P), while N-polar III-nitrides exhibit a downward one (\u2212P).\n\nThe spontaneous polarization of wurtzite ScAlN with Sc content in a range of 0 to 0.375 was calculated by using first-principles DFT (Fig.\u00a0S3a). See Supplementary Note\u00a01 for details. The theoretically predicted spontaneous polarizations align well with both local and macroscopic measurements, as well as the experimentally reported remanent polarization for ScAlN, in terms of both magnitude and evolution trend (Fig.\u00a0S3b). Table\u00a01 lists our results alongside previously reported experimental measurements34,38,39,40 and theoretical calculations1,16,21,25,41 of spontaneous polarizations in III-nitride semiconductors. Notably, while the experimentally determined local and macroscopic polarizations in our data are well consistent, they show significant discrepancies when compared to the widely adopted polarization values for III-nitride semiconductors over the past two decades, which were obtained using ZB reference structure1,16,21,38. These discrepancies are evident in two key aspects: (i) the experimentally determined spontaneous polarization values are an order of magnitude higher than the theoretical predictions using ZB reference structure; (ii) for the same lattice polarity, such as M-polar AlN, our experimental findings indicate an orientation that is exactly opposite to the previous theoretical predictions.\n\nThe reason for the significant discrepancy lies in the reference structure used when calculating the polarization within the MTP framework (Supplementary Note\u00a01)17,26. In the MTP modeling, polarization is a periodic multiple-valued lattice, where only the polarization differences between two states, such as the material of interest and the reference, taken from the same branch, are uniquely defined17,18,20,21. The multivalued formal polarizations for WZ, ZB, and LH III-nitrides within the MTP modeling are illustrated in Fig.\u00a03a. The spontaneous polarization relative to the ZB (\\({P}_{{{{\\rm{SP}}}}}^{{{{\\rm{WZ}}}},{{{\\rm{ZB}}}}}\\)) and LH (\\({P}_{{{{\\rm{SP}}}}}^{{{{\\rm{WZ}}}},{{{\\rm{LH}}}}}\\)) references can be calculated by taking the difference in formal polarization from the same branch17,19,20,26. Obviously, both magnitude and orientation of the polarization are strongly linked to the reference structure. For example, as shown in Fig.\u00a03b and Table\u00a01, M-polar AlN has a spontaneous polarization of \u22120.090\u2009C/m2 when referenced to the ZB structure, whereas a spontaneous polarization of +1.351\u2009C/m2 is obtained using the LH reference structure. The latter one agrees well with our experimentally measured polarization of +1.37\u2009C/m2.\n\na Multivalued formal polarization Pf, predicted by the MTP modeling as a function of the atomic displacement d. Each black dashed line represents a branch of multivalued function, while the difference between two branches is the modulo of the polarization quantum Pq. The blue, brown, and red spots correspond to the Pf values for a WZ structure and its ZB and LH reference structures, respectively. b Formal polarization of WZ, ZB and LH III-nitrides (AlN, GaN, InN and ScAlN) with M-polar lattice (d\u2009>\u20090) taking from the \u201c0\u201d branch in (a). Black arrows represent spontaneous polarizations of WZ III-nitrides relative to the ZB and LH reference structures, showing downward and upward orientations, respectively.\n\nThere is no inherent issue with utilizing either the ZB or LH reference structure to define the spontaneous polarization in WZ crystals. Nevertheless, when using the spontaneous polarization to evaluate the polarization difference at a WZ heterointerface, such as an AlN/GaN (\\(\\Delta {P}_{\\inf }^{{{{\\rm{AlN}}}}/{{{\\rm{GaN}}}}}={P}_{{{{\\rm{f}}}}}^{{{{\\rm{AlN}}}}}-{P}_{{{{\\rm{f}}}}}^{{{{\\rm{GaN}}}}}\\)), a correction term accounting for the polarization difference between the corresponding reference structures (\\(\\Delta {P}_{{{{\\rm{corr}}}}}^{{{{\\rm{AlN}}}}/{{{\\rm{GaN}}}},{{{\\rm{ref}}}}}={P}_{{{{\\rm{f}}}}}^{{{{\\rm{AlN}}}},{{{\\rm{ref}}}}}-{P}_{{{{\\rm{f}}}}}^{{{{\\rm{GaN}}}},{{{\\rm{ref}}}}}\\)) must be incorporated21,25, as shown in Fig.\u00a03b and Supplementary Note\u00a01. For the AlN/GaN heterostructure, the correction term for ZB reference structure is clearly nonzero: \\(\\Delta {P}_{{{{\\rm{corr}}}}}^{{{{\\rm{AlN}}}}/{{{\\rm{GaN}}}},{{{\\rm{ZB}}}}}=\\frac{e\\sqrt{3}}{2}\\left(\\frac{1}{{a}_{{{{\\rm{AlN}}}}}^{2}}-\\frac{1}{{a}_{{{{\\rm{GaN}}}}}^{2}}\\right)\\), where e is the electronic charge, \\({a}_{{{{\\rm{AlN}}}}}\\) and \\({a}_{{{{\\rm{GaN}}}}}\\) are the in-plane lattice constant of WZ AlN and GaN, respectively. In contrast, the correction term for LH reference structures (\\(\\Delta {P}_{{{{\\rm{corr}}}}}^{{{{\\rm{AlN}}}}/{{{\\rm{GaN}}}},{{{\\rm{LH}}}}}\\)) is just zero because all LH reference structures exhibit vanished formal polarization. Therefore, the spontaneous polarization of WZ III-nitrides determined by using the LH reference structure can be directly used to calculate the polarization difference at heterointerfaces without requiring a correction term. Moreover, spontaneous polarizations derived using the ZB reference are not possible for understanding the reversible giant polarization of wurtzite ferroelectrics (Fig.\u00a02 and Supplementary Note\u00a01). It is thus clear that the discrepancies between theoretically predicted and experimentally determined spontaneous polarization are fairly addressed by using the LH reference structure.\n\nThe above findings contribute to a refined understanding of polarization in GaN-based heterostructures, where strain induced piezoelectric polarization should also be considered. WZ III-nitrides are typically hetero-grown on substrates along the polar c-axis. Consequently, an in-plane biaxial strain (\\({\\varepsilon }_{1}\\), where \\({\\varepsilon }_{1}=\\frac{a-{a}_{0}}{{a}_{0}}\\), with \\({a}_{0}\\) and \\(a\\) being the in-plane lattice constants for the relaxed and strained layers, respectively) is present in the top layer, leading to a strain induced piezoelectric polarization (\\({P}_{{{{\\rm{PE}}}}}\\))3. \\({P}_{{{{\\rm{PE}}}}}\\) is defined as the formal polarization difference between the strained and relaxed structure. It can be expressed in terms of the in-plane biaxial strain (\\({\\varepsilon }_{1}\\)), piezoelectric coefficients (\\({e}_{31}\\), \\({e}_{33}\\)), and elastic constants (\\({C}_{13}\\), \\({C}_{31}\\))3,16,21,42,43,44. See details in Supplementary Note\u00a01.\n\nWe use a state-of-the-art M-polar AlGaN/GaN high electron mobility transistor (HEMT) structure as an example to assess the spontaneous, piezoelectric, total polarization, as well as the interface polarization difference (\\(\\Delta {P}_{\\inf }\\)). Calculation details are discussed in Supplementary Note\u00a03. To quantitively compare the difference arising from the divergent reference structures, we set the Al composition to 0.3 (Al0.3Ga0.7N), a commonly used barrier in AlGaN/GaN HEMT structures10. The biaxial strain effect in Al0.3Ga0.7N is evaluated by considering two extreme cases: fully relaxed (\\({\\varepsilon }_{1}=0\\)) and fully strained (\\({\\varepsilon }_{1}=0.0073\\)) one. The left panel of Fig.\u00a04a(i-iii) presents the polarization schematic in M-polar AlGaN/GaN heterostructures derived using the LH reference, exhibiting a significant difference compared to the conventional understanding based on the ZB reference, as shown in Fig.\u00a04a(iv-vi).\n\na Spontaneous polarization, piezoelectric polarization, interface polarization difference, and sheet carriers in (i, iv) relaxed, (ii, v) tensile-strained, and (iii, vi) compressive-strained AlGaN/GaN heterostructures. The schematics in (i-iii) and (iv-vi) are drawn with the LH and ZB reference structures, respectively. Black arrows indicate the polarization orientation. b\u2013d Polarization charge distribution and corresponding band diagrams for (b) M-polar AlGaN/GaN, (c) M-polar GaN/AlGaN, and (d) N-polar GaN/AlGaN heterostructures, illustrating the formation of 2DEG or 2DHG at the interface.\n\nFor fully relaxed AlGaN/GaN heterostructures, a positive \\({\\Delta P}_{\\inf }^{{{{\\rm{AlGaN}}}}/{{{\\rm{GaN}}}},{{{\\rm{LH}}}}}\\) (+0.012\u2009C/m2) is obtained, suggesting a negative net polarization charge at the interface. Therefore, as shown in Fig.\u00a04a(i), the fully relaxed AlGaN/GaN interface tends to attract free holes, rather than electrons, to compensate the negative net polarization charge. However, the fully relaxed structure is a hypothetical scenario, as strain is typically present in real systems. For fully strained AlGaN/GaN heterostructures, a negative \\({\\Delta P}_{\\inf }^{{{{\\rm{AlGaN}}}}/{{{\\rm{GaN}}}},{{{\\rm{LH}}}}}\\) (\u22120.021\u2009C/m2) is obtained, which is comparable with \\({\\Delta P}_{\\inf }^{{{{\\rm{AlGaN}}}}/{{{\\rm{GaN}}}},{{{\\rm{ZB}}}}}\\) (\u22120.030\u2009C/m2). The similarity between these two values results from the cancelation of the correction terms, which has been discussed in detail by Dreyer et al.21. As shown in Fig.\u00a04a(ii), the negative polarization difference leads to a positive net polarization charge, which tends to accumulate free electrons at the tensile strained AlGaN/GaN heterointerface. This phenomenon underlies the formation of 2DEG in AlGaN/GaN HEMTs.\n\nThe polarization discontinuities at other M-polar and N-polar AlGaN/GaN heterostructures can be deduced using the same method. Figure\u00a04a presents the polarization schematics for several representative heterostructures. Based on this understanding, the polarization charge distribution and band profiles for three typical III-nitride heterostructures, including M-polar AlGaN/GaN, M-polar GaN/AlGaN, and N-polar GaN/AlGaN, are redrawn in Fig.\u00a04b\u2013d. These heterostructures have attracted tremendous attention in high-frequency and high-power electronics due to their potential to form high-mobility 2DEG or 2DHG. Although there are no significant differences in band profiles between the two reference structures, the refined polarization distribution and formation mechanisms provide a deeper and more solid foundation for the understanding and engineering of polarization in advanced nitride heterostructures. A comprehensive comparison of our predictions with previously reported experimental results and theoretical studies for AlGaN/GaN HEMT structures is provided in Fig.\u00a0S9 and further discussed in Supplementary Note\u00a03. Referring to the pioneering explanation of III-nitride polarization and 2DEG/2DHG formation, this new understanding aligns well with existing experimental observations. Furthermore, by comparing the fully relaxed and strained AlGaN/GaN heterostructures within the unified polarization framework, we conclude that: (i) piezoelectric polarization is oriented opposite to spontaneous polarization under tensile strain while in the same orientation under compressive strain; and (ii) piezoelectric polarization plays a crucial role in the formation of 2DEG or 2DHG at the interface.\n\nWe then turn to ScAlN/GaN heterostructures, which are more attractive since ScAlN has a ferroelectric polarization, and the strain in ScAlN can be tuned from tensile to compressive through modifying the Sc content and the orientation of the piezoelectric polarization can thus be manipulated as well11,12,13,16,31,45. Figure\u00a05a illustrates the polarization schematics of ferroelectric ScAlN/GaN heterostructures, where the ScAlN layer is in M- (left panel) and N-polarity (right panel), while the underlying GaN layer remains M-polarity in both cases. In Fig.\u00a05a, the evolution of the in-plane lattice parameter a can be divided into three regimes with increasing Sc content from top to bottom: \\({a}_{{{{\\rm{ScAlN}}}}} \\, < \\, {a}_{{{{\\rm{GaN}}}}}\\) (panel i, tensile strain), \\({a}_{{{{\\rm{ScAlN}}}}}={a}_{{{{\\rm{GaN}}}}}\\) (panel ii, fully relaxed), and \\({a}_{{{{\\rm{ScAlN}}}}} \\, > \\, {a}_{{{{\\rm{GaN}}}}}\\) (panel iii and iv, compressive strain). The spontaneous and piezoelectric polarizations, as well as the polarization differences, are indicated with black arrows in Fig.\u00a05a. The net polarization charge at the ScAlN/GaN interface is plotted in Fig.\u00a05b (solid curve), with the corresponding maximum sheet carrier concentration indicated on the right axis. Further details are provided in Supplementary Note\u00a03.\n\na Spontaneous polarization, piezoelectric polarization, interface polarization difference, and sheet carriers in as-grown M-polar (left) and polarization switched N-polar (right) ferroelectric ScAlN/GaN heterostructures with varying Sc content. The strain transitions in ScAlN undergo three regimes along with Sc content increasing: (i) tensile strain, (ii) fully relaxed, and (iii, iv) compressive strain. Black arrows indicate the polarization orientation. b Net polarization charge and corresponding maximum sheet carrier density of ScAlN/GaN heterostructures as a function of Sc content. The red and blue curves represent sheet charge density before and after polarization switching, respectively. While solid and dashed curves correspond to the values calculated using LH and ZB reference structures, respectively. c Schematic of a ScAlN/GaN Fe-HEMT with opposite polarization orientations for ScAlN (left) and its typical transfer characteristic curves (right), showing counterclockwise ID\u2013VGS hysteresis loops with tunable Vth.\n\nAs shown in Fig.\u00a05a, the initial tensile strain in the ScAlN layer gradually evolves into compressive strain with increasing Sc content, leading to a reversed orientation of the piezoelectric polarization. Consequently, the sheet carriers at the heterointerface transform from 2DEG to 2DHG (Fig.\u00a05a, b). As the Sc content increases from 0 to 0.25, the positive polarization bound charge initially rises slightly and then lowers down to zero, followed by a gradual increase in negative polarization bound charge. This evolution trend reflects the trade-off between spontaneous and piezoelectric polarizations. For comparison, the net polarization charge calculated using ZB reference structure is plotted as a blue dashed line in Fig.\u00a05b, revealing a larger transition point at the Sc content of 0.4.\n\nThe polarization bound charge in the switched ScAlN/GaN heterostructure is\u00a0also plotted in Fig.\u00a05b (red curve). In this scenario, the top ScAlN layer exhibits N-polar lattice while the underlying GaN remains M-polar one, forming a head-to-head polarization domain wall at the ScAlN/GaN interface, as illustrated in the right panel of Fig.\u00a05a. This configuration results in a significant increase in positive polarization sheet charge, at least 30 times higher than typically observed, which is completely contradict to the predictions by using ZB reference structure, indicated with red dashed curve in Fig.\u00a05b. In idealized configurations, assuming sharp, clean polarization reversal interfaces without dead layer, dangling bonds, defects, alloy composition fluctuations, or charge compensation, this high positive polarization charge leads to pronounced downward band bending (Fig.\u00a0S10). This facilitates the formation of 2DEG with ultra-high sheet carrier densities exceeding 1 \u00d7 1015\u2009cm\u22122 in the polarization switched ScAlN/GaN heterostructures. Such high carrier density has never been observed at any semiconductor heterointerfaces. This unprecedented phenomenon reveals a significant potential for advancing high-frequency and high-power electronic applications.\n\nFurthermore, since ScAlN is a ferroelectric semiconductor, the threshold voltage (Vth) of ScAlN/GaN ferroelectric HEMTs (Fe-HEMTs) can be tuned by ferroelectric polarization through either the quantity or sign of the polarization bound charge, resulting in a counterclockwise ID\u2013VGS hysteresis loop, as shown in Fig.\u00a05c. The initial net polarization charge at the ScAlN/GaN interface determines the highest Vth, while the giant positive polarization charge induced by ferroelectric switching governs the lowest Vth. Therefore, Vth can be precisely modulated by controlling the ferroelectric switching process. Additionally, a steep-slope ID\u2013VGS curve with a reduced subthreshold swing is likely observed during backward (positive-to-negative) sweeps, benefiting from the negative capacitance effect caused by ferroelectric switching46,47. It should be noted that the substantial positive polarization charge induced by polarization reversal at the interface can significantly enhance vertical conductivity. This enhancement contributes to the low-resistance state observed in ferroelectric ScAlN/GaN memristors48,49. Such a phenomenon could also facilitate the formation of low-resistance drain and source Ohmic contacts in ScAlN/GaN Fe-HEMTs and photodetectors.",
+            "section_image": [
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+            ]
+        },
+        {
+            "section_name": "Discussion",
+            "section_text": "Although the above analyses are promising, experimental demonstration and precise determination of the electron density and mobility of the 2DEG formed at the ferroelectric switched ScAlN/GaN interface remain significant challenges. The primary difficulty lies in the presence of ferroelectric dead layers, as well as dangling bonds, defects, and roughness at the polarization reversal interface in practical ferroelectric heterostructures15,29,50. In contrast, polarization modeling normally assumes an idealized polarization reversal interface. Those undesirables in practical systems significantly suppress the modulation capability of ferroelectric polarization on the ScAlN/GaN interface carriers, for instance, through mitigated field effects and partial charge compensation50, as discussed in detail in Supplementary Note\u00a03. Nevertheless, the increased vertical conductivity48,49 and the negatively shifted pinch-off voltage (Supplementary Note\u00a03) or Vth51 observed in ferroelectric ScAlN/GaN heterostructures after polarization reversal confirm the enhancement of interfacial carrier concentration. These experimental observations suggest that the potential applications of the extreme sheet charges predicted in Fig.\u00a05b are already emerging. We believe that ongoing advancements in ferroelectric nitride technologies, such as mitigating or eliminating dead layers, achieving sharp switching, and creating clean polarization-reversal interfaces, will gradually bring experimental results closer to the theoretical predictions presented here.\n\nIn summary, the magnitude and orientation of polarization in wurtzite III-nitrides have been identified through quantitative local polarization analysis at the unit cell scale as well as macroscopic electrical measurements. Giant upward (downward) spontaneous polarizations exceeding 1\u2009C/m2 have been experimentally determined in as-grown M-polar (N-polar) wurtzite III-nitride films, including conventional AlN, GaN, and InN, as well as the emerging ferroelectric ScAlN. These findings align well with theoretical predictions based on the centrosymmetric LH reference structure, establishing a unified perspective on the polarization of III-nitride semiconductors with strong support from both theoretical and experimental evidence. Furthermore, the polarization landscape and band profile in the cutting-edge AlGaN/GaN and ferroelectric ScAlN/GaN heterostructures have been reevaluated within this unified polarization framework. The potential for achieving 2DEG with ultra-high sheet carrier densities in ferroelectric ScAlN/GaN heterostructures has been highlighted. The proposed and validated new understanding not only bridges the knowledge gap in polarization engineering when integrating ferroelectric nitrides with contemporary GaN device architectures, but also remains consistent with existing experimental observations. This work provides essential insights into the understanding and modulation of polarization in III-nitride heterostructures, setting the stage for the development of advanced photonic, electronic, optoelectronic, and acoustic devices by incorporating ferroelectricity into the III-nitride ecosystem.",
+            "section_image": []
+        },
+        {
+            "section_name": "Methods",
+            "section_text": "M-polar InN and ScAlN films were grown on commercial GaN/sapphire templates, while N-polar AlN, GaN, InN, and ScAlN films were grown on C-face 4H-SiC substrates utilizing an SVTA MBE system. M-polar GaN and AlN films were prepared using metal organic chemical vapor deposition (MOCVD) on sapphire substrates. The MBE system was equipped with a Veeco Unibulb radio frequency (RF) N-plasma source, dual-filament Knudsen cells for the Al (purity 99.99995%), Ga (purity 99.99999%), and In (purity 99.99999%) sources, and a high-temperature Knudsen cell for the Sc source (purity 99.999%). The epitaxy conditions for MBE-grown AlN, GaN, and InN films have been previously reported52,53,54. For ScAlN growth, an N2 (purity 99.9999%) gas flow rate of 1 sccm with an RF power of 400\u2009W was maintained throughout the growth process, corresponding to a deposition rate of 300\u2009nm/h for GaN under slightly Ga-rich conditions. The GaN/sapphire template was degassed at 300\u2009\u00b0C for 1\u2009h in the MBE preparation chamber, followed by outgassing at 750\u2009\u00b0C for 10\u2009min in the growth chamber prior to deposition. A 100-nm-thick Si-doped n+-GaN (with an electron concentration of 5 \u00d7 1019\u2009cm-3) was first grown, followed by the deposition of an 80-nm-thick ScAlN under N-rich growth conditions. In order to match the underlying GaN lattice, the Sc content was controlled to be about 18%, confirmed utilizing X-ray photoelectron spectroscopy (XPS) and electron dispersive spectroscopy (EDS) in STEM. For standard metal/ScAlN/GaN capacitor fabrication, 50/100\u2009nm thick Ti/Au circular pads with a diameter of 20\u2013100 \u03bcm were lithographically patterned on the ScAlN surface as top electrodes, with the n+-GaN layer serving as the bottom electrode.\n\nThe surface morphology of ScAlN was characterized using a Dimension ICON atomic force microscope (AFM). XRD analysis was performed with a Philips PANalytical X\u2019pert high-resolution XRD system equipped with a 1.54\u2009\u00c5 Cu \u039a\u03b11 X-ray source. Ferroelectric measurements were conducted with a Radiant Premier II Ferroelectric Tester. The P-E hysteresis loop was measured using a triangular wave with a frequency of 1\u2009kHz. The sample lamellae used for STEM measurements were prepared with a ThermoFisher Helios G4 UX focused ion beam (FIB). HAADF- and ABF-STEM images were captured using a JEM-ARM300F2 aberration-corrected STEM at an acceleration voltage of 300\u2009kV, with pixel integration times ranging from 0.5 to 2 \u03bcs.\n\nSee details in\u00a0Supplementary Information.",
+            "section_image": []
+        },
+        {
+            "section_name": "Data availability",
+            "section_text": "All data in this work are available within the main text and Supplementary Information files, as well as available from the corresponding author. Source data are provided in this paper.\u00a0Source data are provided with this paper.",
+            "section_image": []
+        },
+        {
+            "section_name": "References",
+            "section_text": "Fiorentini, V., Vanderbilt, D. & Bernardini, F. Spontaneous polarization and piezoelectric constants of III-V nitrides. Phys. Rev. B. 56, R10024\u2013R10027 (1997).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nFiorentini, V., Vanderbilt, D. & Bernardini, F. Accurate calculation of polarization-related quantities in semiconductors. Phys. Rev. B. 63, 193201 (2001).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nAmbacher, O. et al. Two-dimensional electron gases induced by spontaneous and piezoelectric polarization charges in N- and Ga-face AlGaN/GaN heterostructures. J. Appl. Phys. 85, 3222\u20133233 (1999).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nChaudhuri, R. et al. A polarization-induced 2D hole gas in undoped gallium nitride quantum wells. Science 365, 1454\u20131457 (2019).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nvan Deurzen, L. et al. Using both faces of polar semiconductor wafers for functional devices. Nature 634, 334\u2013340 (2024).\n\nSimon, J., Protasenko, V., Lian, C., Xing, H. & Jena, D. Polarization-induced hole doping in wide\u2013band-gap uniaxial semiconductor heterostructures. Science 327, 60\u201364 (2010).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nTakeuchi, T. et al. Quantum-confined Stark effect due to piezoelectric fields in gainn strained quantum wells. Jpn. J. Appl. Phys. 36, L382\u2013L385 (1997).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nNakamura, S. Nobel lecture: background story of the invention of efficient blue InGaN light emitting diodes. Rev. Mod. Phys. 87, 1139\u20131151 (2015).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nAmano, H. Nobel lecture: growth of GaN on sapphire via low-temperature deposited buffer layer and realization of p-type GaN by Mg doping followed by low-energy electron beam irradiation. Rev. Mod. Phys. 87, 1133\u20131138 (2015).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nAmano, H. et al. The 2018 GaN power electronics roadmap. J. Phys. D: Appl. Phys. 51, 163001 (2018).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nFichtner, S., Wolff, N., Lofink, F., Kienle, L. & Wagner, B. AlScN: A III-V semiconductor based ferroelectric. J. Appl. Phys. 125, 114103 (2019).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWang, P. et al. Fully epitaxial ferroelectric ScAlN grown by molecular beam epitaxy. Appl. Phys. Lett. 118, 223504 (2021).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWolff, N. et al. Demonstration and STEM analysis of ferroelectric switching in MOCVD-grown single crystalline Al0.85Sc0.15N. Adv. Phys. Res. 3, 2300113 (2024).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nHeron, J. & Mi, Z. Emerging Ferroelectric Materials and Devices (Elsevier, 2023).\n\nSch\u00f6nweger, G. et al. From fully strained to relaxed: epitaxial ferroelectric Al1-xScxN for III-N technology. Adv. Funct. Mater. 32, 2109632 (2022).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nAmbacher, O. et al. Wurtzite ScAlN, InAlN, and GaAlN crystals, a comparison of structural, elastic, dielectric, and piezoelectric properties. J. Appl. Phys. 130, 45102 (2021).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nResta, R. & Vanderbilt, D. In: Ascheron, C. E. $ Skolaut, W., editor. Physics of Ferroelectrics: A Modern Perspective 31\u201368 (Springer Berlin Heidelberg, 2007).\n\nResta, R. Theory of the electric polarization in crystals. Ferroelectrics 136, 51\u201355 (1992).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nResta, R. Modern theory of polarization in ferroelectrics. Ferroelectrics 151, 49\u201358 (1994).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nSpaldin, N. A. A beginner\u2019s guide to the modern theory of polarization. J. Solid State Chem. 195, 2\u201310 (2012).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDreyer, C. E., Janotti, A., Van de Walle, C. G. & Vanderbilt, D. Correct implementation of polarization constants in wurtzite materials and impact on III-nitrides. Phys. Rev. X. 6, 21038 (2016).\n\n\n                    Google Scholar\u00a0\n                \n\nYassine, M. et al. Modeling of polarization reversal-induced interface sheet charge in wurtzite-type AlScN/GaN heterostructures. J. Appl. Phys. 135, 155702 (2024).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWang, D., Wang, D., Yang, S. & Mi, Z. Rethinking polarization in wurtzite semiconductors. Appl. Phys. Lett. 124, 263502 (2024).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nFichtner, S., Yassine, M., Van de Walle, C. G. & Ambacher, O. Clarification of the spontaneous polarization direction in crystals with wurtzite structure. Appl. Phys. Lett. 125, 40501 (2024).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBenbedra, A., Meskine, S., Boukortt, A., Abbassa, H. & Abbes, E. H. Polarization properties of wurtzite III-nitride alloys using the hexagonal reference structure. ECS J. Solid State Sci. Technol. 12, 103008 (2023).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKing-Smith, R. D. & Vanderbilt, D. Electric polarization as a bulk quantity and its relation to surface charge. Phys. Rev. B. 48, 4442\u20134455 (1993).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nCalderon, S., Funni, S. D. & Dickey, E. C. Accuracy of local polarization measurements by scanning transmission electron microscopy. Microsc. Microanal. 28, 2047\u20132058 (2022).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nCalderon, S. et al. Atomic-scale polarization switching in wurtzite ferroelectrics. Science 380, 1034\u20131038 (2023).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWolff, N. et al. Atomic scale confirmation of ferroelectric polarization inversion in wurtzite-type AlScN. J. Appl. Phys. 129, 34103 (2021).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nYe, H. et al. ScAlInN/GaN heterostructures grown by molecular beam epitaxy. Appl. Phys. Lett. 125, 122105 (2024).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nZhang, S., Fu, W. Y., Holec, D., Humphreys, C. J. & Moram, M. A. Elastic constants and critical thicknesses of ScGaN and ScAlN. J. Appl. Phys. 114, 243516 (2013).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMotoki, K. et al. Improved crystallographic order of ScAlN/GaN heterostructures grown at low temperatures under metal rich surface conditions. J. Appl. Phys. 135, 135105 (2024).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nZhu, W. et al. Strongly temperature dependent ferroelectric switching in AlN, Al1-xScxN, and Al1-xBxN thin films. Appl. Phys. Lett. 119, 62901 (2021).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nHasegawa, K., Shimizu, T., Ohsawa, T., Sakaguchi, I. & Ohashi, N. Full polarization reversal at room temperature in unsubstituted AlN. Appl. Phys. Lett. 123, 192903 (2023).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDevonshire, A. F. Theory of ferroelectrics. Adv. Phys. 3, 85\u2013130 (1954).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nRabe, K. M., Ahn, C. H. & Triscone, J. Physics of fErroelectrics: A Modern Perspective Vol. 105 (Springer Science & Business Media, 2007).\n\nRabe, K. M., Dawber, M., Lichtensteiger, C., Ahn, C. H. & Triscone, J. in Physics of Ferroelectrics: A Modern Perspective 1\u201330 (Springer Berlin Heidelberg, 2007).\n\nBrandt, O. et al. Direct experimental determination of the spontaneous polarization of GaN. Phys. Rev. B. 86, 81302 (2012).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWang, P. et al. Dawn of nitride ferroelectric semiconductors: from materials to devices. Semicond. Sci. Technol. 38, 43002 (2023).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKim, K., Karpov, I., Olsson, R. H. & Jariwala, D. Wurtzite and fluorite ferroelectric materials for electronic memory. Nat. Nanotechnol. 18, 422\u2013441 (2023).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWang, H., Adamski, N., Mu, S. & Van de Walle, C. G. Piezoelectric effect and polarization switching in Al1-xScxN. J. Appl. Phys. 130, 104101 (2021).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMartin, R. M. Piezoelectricity. Phys. Rev. B. 5, 1607\u20131613 (1972).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLax, M. & Nelson, D. F. Linear elasticity and piezoelectricity in pyroelectrics. Phys. Rev. B. 13, 1785\u20131796 (1976).\n\nArticle\u00a0\n    ADS\u00a0\n    MathSciNet\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nVanderbilt, D. Berry-phase theory of proper piezoelectric response. J. Phys. Chem. Solids 61, 147\u2013151 (2000).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nUrban, D. F., Ambacher, O. & Els\u00e4sser, C. First-principles calculation of electroacoustic properties of wurtzite (Al,Sc)N. Phys. Rev. B. 103, 115204 (2021).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWang, D. et al. Fully epitaxial, monolithic ScAlN/AlGaN/GaN ferroelectric HEMT. Appl. Phys. Lett. 122, 90601 (2023).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\n\u00cd\u00f1iguez, J., Zubko, P., Luk Yanchuk, I. & Cano, A. Ferroelectric negative capacitance. Nat. Rev. Mater. 4, 243\u2013256 (2019).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWang, R. et al. Composition-graded nitride ferroelectrics based multi-level non-volatile memory for neuromorphic computing. Adv. Mater. 37, e2414805 (2024).\n\nWang, D. et al. Ultrathin nitride ferroic memory with large ON/OFF ratios for analog in-memory computing. Adv. Mater. 35, 2210628 (2023).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWang, D. et al. Electric-field-induced domain walls in wurtzite ferroelectrics. Nature https://www.nature.com/articles/s41586-025-08812-7 (2025).\n\nWang, D. et al. An epitaxial ferroelectric ScAlN/GaN heterostructure memory. Adv. Electron. Mater. 8, 2200005 (2022).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWang, P. et al. Interfacial modulated lattice-polarity-controlled epitaxy of iii-nitride heterostructures on Si(111). Acs Appl. Mater. Interfaces 14, 15747\u201315755 (2022).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nHu, M. et al. Heteroepitaxy of N-polar AlN on C-face 4H-SiC: structural and optical properties. Apl. Mater. 11, 121111 (2023).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWang, T. et al. High-mobility two-dimensional electron gas at InGaN/InN heterointerface grown by molecular beam epitaxy. Adv. Sci. 5, 1800844 (2018).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDownload references",
+            "section_image": []
+        },
+        {
+            "section_name": "Acknowledgements",
+            "section_text": "This work was supported by the National Key Research and Development Program of China (No. 2023YFB3610400 to P.W.), the National Natural Science Foundation of China (NSFC) (No. 62321004 to X.W.; 62374002 to P.W.; 62304008 to R.W.; 62374010 to T.W.; 12304218 to W.T.), the Natural Science Foundation of Beijing Municipality (No. Z230024 to P.W.), the Research Fund of Suzhou Laboratory (No. SK-1202-2024-012 to P.W.), the China Postdoctoral Science Foundation (No. 2023T160016 to R.W.), Shanghai Pujiang Program (No. 23PJ1402200 to C.D.), and the State Key Laboratory of Artificial Microstructure and Mesoscopic Physics at Peking University.",
+            "section_image": []
+        },
+        {
+            "section_name": "Author information",
+            "section_text": "State Key Laboratory for Mesoscopic Physics and Frontiers Science Center for Nano-Optoelectronics, School of Physics, Peking University, 100871, Beijing, China\n\nHaotian Ye,\u00a0Ping Wang,\u00a0Rui Wang,\u00a0Jinlin Wang,\u00a0Xifan Xu,\u00a0Ran Feng,\u00a0Tao Wang,\u00a0Fang Liu,\u00a0Bowen Sheng,\u00a0Wenjie Ma,\u00a0Bingxuan An,\u00a0Hongjian Li,\u00a0Zhaoying Chen,\u00a0Weikun Ge,\u00a0Bo Shen\u00a0&\u00a0Xinqiang Wang\n\nElectron Microscopy Laboratory, School of Physics, Peking University, 100871, Beijing, China\n\nTao Wang\n\nKey Laboratory of Polar Materials and Devices (MOE), School of Physics and Electronic Science, East China Normal University, 200241, Shanghai, China\n\nWen-Yi Tong\u00a0&\u00a0Chun-Gang Duan\n\nShanghai Center of Brain-Inspired Intelligent Materials and Devices, East China Normal University, 200241, Shanghai, China\n\nChun-Gang Duan\n\nPeking University Yangtze Delta Institute of Optoelectronics, 226010, Nantong, Jiangsu, China\n\nBo Shen\u00a0&\u00a0Xinqiang Wang\n\nCollaborative Innovation Center of Quantum Matter, 100871, Beijing, China\n\nBo Shen\u00a0&\u00a0Xinqiang Wang\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nH.Y., P.W., and X.W. conceived the original concept and initiated the project. H.Y., P.W., R.F., and B.A. conducted the material growth and performed the AFM, XRD and XPS analyses. R.W. was responsible for the device fabrication and electrical measurements. J.W., X.X., and T.W. conducted the STEM measurements, with H.Y., P.W., J.W., X.X., and T.W. analyzing the STEM data. X.X. and H.Y. carried out the local polarization measurements. W.T. and C.D. performed the DFT calculations. H.Y., P.W., W.T., F.L., B. Sheng, W.M., H.L., Z.C., W.G., B. Shen, and X.W. contributed to the polarization analysis. H.Y., P.W., and X.W. drafted the manuscript, with all authors contributing to the discussions of the results and providing feedback on the manuscript at all stages. P.W. and X.W. supervised the research.\n\nCorrespondence to\n                Ping Wang, Tao Wang or Xinqiang Wang.",
+            "section_image": []
+        },
+        {
+            "section_name": "Ethics declarations",
+            "section_text": "The authors declare no competing interests.",
+            "section_image": []
+        },
+        {
+            "section_name": "Peer review",
+            "section_text": "Nature Communications thanks the anonymous, reviewer(s) for their contribution to the peer review of this work. A peer review file is available.",
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+            "section_image": []
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+            "section_text": "Open Access  This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article\u2019s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article\u2019s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.\n\nReprints and permissions",
+            "section_image": []
+        },
+        {
+            "section_name": "About this article",
+            "section_text": "Ye, H., Wang, P., Wang, R. et al. Experimental determination of giant polarization in wurtzite III-nitride semiconductors.\n                    Nat Commun 16, 3863 (2025). https://doi.org/10.1038/s41467-025-58975-0\n\nDownload citation\n\nReceived: 12 November 2024\n\nAccepted: 08 April 2025\n\nPublished: 24 April 2025\n\nVersion of record: 24 April 2025\n\nDOI: https://doi.org/10.1038/s41467-025-58975-0\n\nAnyone you share the following link with will be able to read this content:\n\nSorry, a shareable link is not currently available for this article.\n\n\n\n\n                            Provided by the Springer Nature SharedIt content-sharing initiative\n                        ",
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+    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
+    "preprint_pdf": "https://www.researchsquare.com/article/rs-4950329/v1.pdf?c=1745924945000",
+    "research_square_link": "https://www.researchsquare.com//article/rs-4950329/v1",
+    "nature_pdf": "https://www.nature.com/articles/s41467-025-58867-3.pdf",
+    "preprint_posted": "14 Oct, 2024",
+    "research_square_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Relativistic collisionless shocks1, which are ubiquitous in the cosmos, play a significant role in various astrophysical phenomena such as gamma-ray bursts2\u20134, PeVatrons5\u20137, and shock breakouts accompanying a supernova explosion8. To unravel these processes happening at enormous spatial and energy scales, the most convenient and feasible approach so far \u2013 laser \u2013 has been long sought to access such extreme conditions in an ultrafast and volume-efficient manner9\u201313. Yet observing a relativistic collisionless shock in a laboratory has remained out of reach. Here, we demonstrate that sub-relativistic collisionless shocks with velocities\u2009~\u20090.03c of astrophysical significance can be produced and characterized in a laboratory using a table-top femtosecond \u201claser engine\u201d. We attribute the shock formation to a rapidly growing Weibel instability in a carefully adjusted low-density preplasma environment, which resembles the interstellar media near an astrophysical central engine. Owing to this Weibel instability, a magnetic field as high as ~\u20095000 T is developed within 2.7 ps, leading to the formation of a collisionless shock and shock breakout is finally observed at the preplasma edge. Our results not only pave the way for further exploration of astrophysics related to relativistic collisionless shocks but also enable a new regime of ultrahigh magnetic field physics on a tabletop scheme14.Physical sciences/Physics/Plasma physics/Astrophysical plasmasPhysical sciences/Physics/Astronomy and astrophysics/Laboratory astrophysics",
+            "section_image": []
+        },
+        {
+            "section_name": "Additional Declarations",
+            "section_text": "There is NO Competing Interest.",
+            "section_image": []
+        },
+        {
+            "section_name": "Supplementary Files",
+            "section_text": "SupplementaryInformations.docx",
+            "section_image": []
+        }
+    ],
+    "nature_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Relativistic collisionless shocks, which are ubiquitous in the cosmos, play a significant role in various astrophysical phenomena such as gamma-ray bursts, PeVatrons, and supernova shock breakouts. Here we present a demonstration using a compact femtosecond laser system to generate sub-relativistic collisionless shocks (0.03c) under astrophysically relevant conditions. We attribute the shock formation to a rapidly growing Weibel instability in a precisely tuning low-density preplasma environment, which resembles the interstellar media near an astrophysical central engine. Owing to this Weibel instability, a 5000 Tesla magnetic field is developed within 2.7\u2009ps, leading to the collisionless shock formation and subsequent breakout at the preplasma boundaries. This platform enables direct investigation of astrophysics related to relativistic collisionless shocks. The achieved parameters bridge the gap between astrophysical observations and controlled laboratory experiments, offering unprecedented opportunities to validate cosmic shock models.",
+            "section_image": []
+        },
+        {
+            "section_name": "Introduction",
+            "section_text": "In astrophysics, relativistic collisionless shocks can happen in the expansion of intense plasmas into interstellar or intergalactic media1,2,3,4. Examples of such phenomena include the shocks observed in gamma-ray bursts, supernova explosions, and pulsar wind nebulae2,5,6. The formation of collisionless shocks could depend on a turbulent magnetic field induced by Weibel instability which can generate a magnetic field from unmagnetized plasmas7,8,9. When the plasmas are highly anisotropic, Weibel instability occurs, and the enhanced magnetic field could divert the trajectory of the charged particles, thereby converting the plasma into isotropic10,11. In this process requiring enormous energy, black holes, and supernova explosions function as the central engine for driving the collisionless shocks12. Consequently, various phenomena such as PeVatrons13 and their relevant energetic radiations from synchrotron radiation or inverse Compton scattering14,15 are observed. The high energy gamma ray from these PeVatrons also serves as an important tool for positioning these central engines such as those discovered by HESS and LHAASO telescopes16,17.\n\nRecent exploration of astrophysics has seen a new trend in the laboratories. During recent decades, a succession of experiments has been conducted to investigate the Weibel instability-mediated collisionless shocks by utilizing large laser facilities of OMEGA18,19, and NIF7. With driving energy in the range of about kilojoule, the characteristic expanding plasma plumes have showcased velocities up to ~106\u2009m/s and temperatures around 1\u2009keV, demonstrating a platform for studying extraordinary phenomena in astrophysics. Meanwhile, in contrast to experimental approaches that aimed at stimulating intense filamentary magnetic fields by counter-streaming two laser-produced plasma plumes, a theoretical prototype design utilizing a laser piston-driven scheme to induce forward near-relativistic collisionless shocks has been proposed20,21. However, this kind of forward-propagating relativistic collisionless shock experiment does not seem realizable very shortly.\n\nFor collisionless shocks to form, the mean free path li of the ion7\n\nshould be greater than the length of the interacting region Lint, where vi is the ion velocity, ni is the density, Ai is the atomic number of the ion, qi is the charge state of the ion and ln\u03bb is the coulomb logarithm. In Weibel instability, due to energy conservation, the amplification of the magnetic field is accompanied by the deceleration of the charged particles. As a result, ions that drives the instability will be scattered and trapped in the interaction region by the magnetic field, decelerating without collisions. This will result in the pile-up of the charged ions and the formation of a collisionless shock. For a typical interaction region of ~100\u2009\u03bcm, a magnetic field >1000\u2009T is needed. Nevertheless, since the growth rate of the Weibel instability is proportional to the anisotropic parameter and the shock formation time is \u03c4shock\u2009~\u2009(\u03b2d\u03c9p)\u22121\u2009~\u2009(\u03b3F)\u22121, which is approximately an e-folding time of the ion Weibel instability, where \u03b2d is the normalized velocity of the accelerated ions, \u03c9p is ion plasma frequency and \u03b3F is the growth rate of the Weibel instability. The formation length of the shock wave can be greatly reduced if a highly directional ion beam with low energy divergence is used for driving the instability. Unlike picosecond or nanosecond laser pulses for producing collisionless shocks, compressing the pulse duration to femtosecond provides unprecedented intensity for creating extreme plasma environments that are naturally collisionless. Particularly, the interaction scale of ~100\u2009\u03bcm allows for a forward propagating collisionless shock by using merely a tabletop 10-mJ-level femtosecond laser beam.",
+            "section_image": []
+        },
+        {
+            "section_name": "Results",
+            "section_text": "Our design draws on the idea of a laser engine. Specifically, energetic expanding plasmas are induced in the laser-plasma interaction which then leads to collisionless shocks, analogous to the black hole engine. As shown in Fig.\u00a01a, a customized laser pulse is used. The highly controllable laser beams are analogous to those applied in inertial confinement fusion experiments whose temporal profiles could tune between a high-foot and low-foot pulse mode (Methods), allowing for precise density control of the preplasmas.\n\na The experimental setup: By illuminating a customized laser pulse (which can be tuned between the low-foot and high-foot modes by the two Pockels cells in the regeneration cavity) onto a solid target, sub-relativistic collisionless shocks are driven in the vicinity of the target. The magnetic field and the plasma density are monitored by the Faraday rotation method and the interferometry. OAP, off axis parabola. GL, Glan polarizer. CCD, Charge-Coupled Device. BS, Beam Splitter b A characteristic filamentary magnetic structure observed in front of the target and the formation of a collisionless shock c Five consecutive frames of the experimental result at preplasma density ~ 0.1nc are displayed, which shows the temporal evolution of the magnetic field after the action of the laser engine. A shock breakout is observed at a time delay of ~ 4\u2009ps.\n\nThe first-stage ignitor (leakage pulses from the regeneration cavity) is employed to generate an expanding plasma within a nanosecond time scale. This highly reproducible plasma with a background magnetic field of ~ 10\u2009T is homogeneous. As shown in Fig.\u00a01b, the electromagnetic energy of the main laser beam functions as a Laser engine, which drives the expanding energetic plasma out of the target as well as the subsequent collisionless shock22.\n\nAs demonstrated in Fig.\u00a01c, the experiment reveals a Weibel instability-mediated collisionless shock with a velocity of ~ 0.03c at preplasma density ~ 0.1nc(To see the shock is collisionless, for ions with a velocity ~ 0.03c, the Al+8-Al+8 collision mean free path is \\({\\lambda }_{A{l}^{+8}-A{l}^{+8}}\\)\u2009~\u200930\u2009m), almost on par with the expanding plasmas at the boundary of an exploding supernova23,24. With a velocity of ~10000\u2009km/s, we can study the shocks relevant to the youngest supernova remnant (SNRs) (~ 100year) in the laboratory, such as the SNR G1.9\u2009+\u20090.3 which25 has a shock velocity of ~ 13000\u2009km/s. The magnetic field peaks at ~ 2.7\u2009ps and lasts for about 5\u2009ps, and the formation time of the shock \\({\\tau }_{{shock}}\\)\u2009~\u2009\\({({\\beta }_{d}{\\omega }_{p})}^{-1} \\sim \\,{({\\gamma }_{F})}^{-1}\\) is estimated to be ~1\u2009ps and can be clearly seen in the density profile measured in experiment. The topological structures of the magnetic field experienced an abrupt change after a time delay of ~ 4\u2009ps, indicating the breakout of the shock wave.\n\nWe note in Fig.\u00a01c that for time delays smaller than 2\u2009ps, magnetic tube structures emerge through Weibel instability self-organization. Soon later, at time delays of ~ 2.7\u2009ps, the magnetic filaments demonstrate a curved structure, which is regarded as a precursor for the nonlinear stage of the collisionless shock. The energy spectrum of the magnetic field is displayed in Fig. 2a, b. Filamentary peaks are apparent in the figures as indicated by the blue shaded area which is indicative of the Weibel instability. From time delays ~ 2.7\u2009ps to ~ 4.0\u2009ps, the scaling law of the magnetic energy spectrum evolves from \\({k}_{s}^{-8/3}\\) to \\({k}_{s}^{-2}\\), suggesting the magnetic energy cascade during the interaction.\n\nThe magnetic energy spectrum Fs at time delays (a) blue: 1.3\u2009ps and yellow: 2.7\u2009ps, (b) dark blue: 4.0\u2009ps and orange: 5.3\u2009ps. The dashed lines shows a fit to the scaling law of the magnetic energy spectrum. The blue-shaded area in both figures represents the range of the most unstable scale; Particle-in-cell simulation of the time evolution of the magnetic field space distribution at (c) 2.7\u2009ps and (d) 4.0\u2009ps; The density of the preplasma are ~ 0.1\\({n}_{c}\\).\n\nFor shock formation, the time required can be expressed26 as \u03c4shock\u2009=\u2009n\u03c4i\u2009+\u2009\u03c4e, where \u03c4e and \u03c4i are the saturation times of electron and ion Weibel instability respectively, and n accounts for the time needed for the current filaments to merge. However, for our specific experiment conditions, a revision of the equation is required20. Since the expanding plasma is ion-dominated, electron Weibel instability can be neglected, as is the time needed for the merging of the current filaments. Thus, as the initial filament distance is already near its maximum, only \u03c4i is taken into consideration for the shock formation. In fact, an e-folding time of the ion Weibel instability is needed for the shock to form, which is \u03c4shock\u2009~\u2009(\u03b3F)\u22121\u2009~\u2009(\u03b2d\u03c9p)\u22121\u2009~\u20091\u2009ps and is consistent with our experimental observation (See Supplementary Fig.\u00a01). In the later stage of nonlinear ion Weibel instability, the deceleration of ions and the pile-up of ions at the front of the expanding plasma contribute to the formation of the collisionless shock27. A \\({k}_{s}^{-8/3}\\) law of plasma spectrum at scales smaller than the ion gyroradius can be induced due to structure formations28 and turbulent motion of electrons, since electron gyroradius is ~ 1\u03bcm. Electrons can be heated during the interaction, leading to a change in the scaling law from \\({k}_{s}^{-8/3}\\) to \\({k}_{s}^{-2}\\), which implies that magnetic field is dominant in the collisionless shock29.\n\nUnder our experimental conditions, the steady shock velocity is ~ 0.03c and the maximum plasma expanding velocity observed in the experiment is ~ 0.07c before shock formation. The peak magnetic field estimated from the experiment is ~ 5000\u2009T. After the formation of the shock wave, by assuming an effective degree of ionization Z\u2009=\u20098 for the aluminum target, the gyroradius of the accelerated Al+8 ions in the target can be calculated to be \\({\\widetilde{R}}_{g}={p}_{i}/{q}_{i}B\\)\u2009~\u200935\u03bcm, which is comparable to the filament distance \u03bbF\u2009=\u200931\u2009\u03bcm. Since the particles are all ionized, the influence of neutral particles, which could potentially have a cooling effect, can be neglected. Based on the magnetic bouncing mechanism, the maximum magnetic field is determined by Bsat\u2009~\u2009\\({\\gamma }_{F}^{2}{m}_{i}c/{q}_{i}v{k}_{{sat}}\\). Where \u03b3F is the growth rate of the instability and qi is the charge of the ion, v is the shock velocity, ksat\u2009=\u20092\u03c0/\u03bbsat is the saturation wave vector, this gives a maximum magnetic field of ~ 4000\u2009T. It indicates that the Weibel instability-induced magnetic field is already saturated which takes ~ 2-3 e-folding time of the instability. The magnetic field energy density reaches ~14% of equipartition with the plasma kinetic energy density (ek =(B2/8\u03c0)/(nimiv2/2)\u2009~\u20090.14, where ni is the density of the ions), which indicates that a magnetized collisionless shock is induced.\n\nThe plasma dynamics and the formation of the collisionless shocks are investigated using Particle-in-cell (PIC, EPOCH)30 (See in Supplementary\u00a0Information 3). Our simulation results feature a laser-heated electron expanding time of about 100\u2009fs, after when the ions are drawn out of the target by the sheath field. Since the sheath field is perpendicular to the surface of the target, ions can be accelerated to velocities as high as ~ 0.07c. This acceleration leads to the occurrence of Weibel instability within 1\u2009ps, as well as the formation and amplification of a filamentary magnetic field. Turbulent magnetic islands are then created, as demonstrated in the temporal dynamics of the magnetic fields in Fig.\u00a02c, d. A peak magnetic field as high as ~ 5000\u2009T is approached in the simulation and is consistent with our experimental results (Fig.\u00a03a).\n\na The time evolution of the maximum magnetic field in front of the target at different time delays. The solid lines show the experimental results, whereas the dashed lines display our simulation results. As indicated by the legend, the curves with different colors correspond to pre-plasma densities of 0.4nc, 0.2nc, and 0.1nc respectively. The error bar represents the standard deviation of multiple shots. b The leading-edge position of the expanding plasma; The red solid line presents the experimental results measured when the preplasma density is ~ 0.2nc. The blue line presents the front of the expanding plasma when the density of the preplasma is ~ 0.1nc. The yellow dashed line is a linear fit of the leading edge of the expanding plasma when the preplasma density is ~ 0.1nc; the equation for the fitted curve is kt3/5, where k\u2009=\u200927 is used; The yellow-shaded area delineates the shock wave impact region associated with the fitted curve; The error bar represents the standard deviation of multiple shots; (c) PIC simulation results of the time evolution of the density of the plasma along the line y\u2009=\u20090. The horizontal solid red line indicates the position of shock formation; The vertical dashed yellow line indicates the time of shock breakout; The dashed white curve shows the fitted curve with a function R(t) = 27t3/5. d The catastrophe model: density of the plasma at shock front.\n\nAfter the shock formation, the otherwise hardly accessible dynamics of the collisionless shock wave become detectable by pump-probe recording of its propagation processes. We have tracked the leading-edge position of the expanding plasma by monitoring the plasma density and the magnetic field (Fig.\u00a01c). The leading-edge position can be fitted by a function of R(t)=27t3/5, t in ps and R in \u03bcm, which describes well the experimental results, as shown in Fig.\u00a03b. We note that this function is slightly different from a 2/5 power law that is expected with a spherical shock. This discrepancy could arise from the finite size of the laser focus spot which leads to an ellipsoidal expanding wavefront rather than strictly spherical. By comparing Fig.\u00a03a and b, we observe that an increase in magnetic field energy is accompanied by a decrease in shock velocity. Some portion of the ion energy is lost during shock formation due to the driving of the return current and the amplification of the magnetic field. This results in a magnetic field-dominated collisionless shock that resembles what happens in a supernova remnant25. The fitting function for the shock front is consistent with our PIC simulations and follows a curve R(t) ~ 27t3/5. Meanwhile, the density jump npk/nbg measured in the experiment is ~ 5 as shown in Supplementary Fig.\u00a01, where npk and nbg is the peak plasma density and background plasma density measured in the experiment respectively. Since for a strong shock30 the density jump is determined by npk/nbg\u2009~\u2009(\u03b3g\u2009+\u20091)/(\u03b3g\u22121), this gives an adiabatic index \u03b3g\u2009~\u20091.5. The adiabatic index indicates the distribution of energy among different degrees of freedom, which implies that the magnetic field is crucial to the formation of the density jump, and the eventual collisionless shock mediated by Weibel instability.\n\nThe shock wave observed in experiment resembles that observed in the supernova remnant, such as SNRs G1.9\u2009+\u20090.3 like SNRs. Though the total scale of the shock wave is ~70\u2009\u03bcm, the radius\u2014time relation for our experiment and SNRs G1.9\u2009+\u20090.3 like SNRs are both approximately R(t) ~ t0.6 which can be seen as the selfsimilar solution of a central engine-driven spherical collisionless shock. The characteristic dimensionless parameters in our experiment, such as the Sonic Mach number(vsh/cs) and the Alfven Mach number(vsh/va) are 40 and 300 respectively. Meanwhile, for the dimensionless magnetic energy (magnetization), ek =(B2/8\u03c0)/(nimiv2/2)\u2009~\u20090.14, which is comparable with that observed in the SNRs G1.9\u2009+\u20090.3 like SNRs. Thus our experimental results can be used for the probe of the dynamics related to the SNRs G1.9\u2009+\u20090.3 like SNRs. A comparison between plasma parameters in our experiments and SNRs G1.9\u2009+\u20090.3 type young supernova remnant is listed in Table\u00a01.\n\nIn the cosmos, a shock breakout is initiated when the shock reaches the edge of a star31,32, such as that during a supernova explosion. Interestingly, our experiment observations have shown a resemblance to the collisionless shock breakout: the shock structure experienced a catastrophic breakdown at about 4.0\u2009ps after the illumination of the pump pulse. Meanwhile, the magnetic field also vanishes in accompany with the shocks (Fig.\u00a01c) and this may indicate a release of electromagnetic energy. The sudden disappearance of the magnetic field will cause the accumulated high-density shock front to explode. The Weibel-mediated collisionless shock breakout is reproduced in a laboratory. Since the trapped ions can expand almost isotropically inside the intense magnetic field, the duration of the shock breakout can be roughly estimated by the ions\u2019 expanding velocities. Specifically, the steady shock velocity of ~0.03c in our experiment suggests that approximately 1\u2009ps is required for the plasma to expand to a density of <0.01nc, where the plasma\u2019s volume has increased by six-fold (plasma radius raised by ~10\u2009\u03bcm) and the shock breakout has stopped.\n\nThe experimental results are supported by our PIC simulations. Figure\u00a03c shows the density profile of the plasma density at different time delays. It shows that the Al+8 ions continue to expand after 4\u2009ps at an almost constant velocity, which is consistent with our basic estimation of the shock breakout time and is a hallmark of the breakout of a shock wave. This ultrafast release of energetic ions from the target surface, as revealed by the shock breakout process, has important implications not only for astrophysics but also for multiple plasma and radiation phenomena. Specifically, the detachment of the ions in the acceleration process directly indicates the basic mechanisms behind the laser-driven ion acceleration, which has yearned for further explorations.\n\nGiven the complexity of the breakout process, a simple catastrophe model is developed to show the basic working principles33. By assuming a Gaussian curve of the shock front density,\n\nwe assume that the width of the shock, \u03c3(t), expands with a small velocity and is on the order of the ion skin depth before reaching the edge of the preplasma, and we take n0 to be a constant. The shock front expands with the fitted curve 27t3/5 before breakout and the expanding velocity of the width of the shock front \u03c3(t) is set to ~0.03c while reaching the plasma edge. As shown in Fig.\u00a03d the plasmas show an abrupt decrease in density which eventually leads to the disappearance of the shock. To compare with shock breakouts observed in astrophysics, we have listed several characteristic duration times of the shock breakouts34 in Table\u00a02. Besides the catastrophic disappearance of the shock front observed in the experiment, an electromagnetic pulse with a duration of ~1\u2009ps, which indicates the occurrence of the breakout, should be detectable in the experiment and this calls for further exploration.\n\nGiven the complexity of the interaction between the intense laser pulse and the plasma, a proper preplasma density that depends on the laser\u2019s contrast ratio is decisive for the shock formation. This is because high preplasma densities will prohibit the ion dynamics as electron Weibel instabilities will dominate the plasma expansion. In our experiment, this specific threshold for the collisionless shock formation is below 0.1nc, corresponding to high contrast (or the low-foot mode) of the laser conditions (see Methods). Otherwise, at high preplasma densities of ~ 0.4nc or ~ 0.2nc, filamentary magnetic tubes are formed at the boundary of the preplasma region, and no shock waves are visible.\n\nTo qualitatively characterize the underlying interaction processes, we now examine other two particular cases of preplasma densities of 0.4nc, and 0.2nc\u2014each representative of the Weibel instability in the unsaturated and saturated regime. Figure\u00a04 compares the spatiotemporal evolution of the magnetic fields at the target front in these two scenarios, respectively. At the preplasma density of ~ 0.4nc, it is clear a concentration of the filamentary structures appears in the middle of the plasma region with three recognizable magnetic filaments. The physical origin of these ion Weibel instability-related filaments is seeded by electron Weibel instabilities. Since ions cannot undergo adequate acceleration for preplasma densities of 0.4nc, the expanding hot electrons from the target surface account primarily for the filamentary structures, which are then amplified by the insufficient accelerated ion beams. To account for this process, a hot electron expanding model is developed in Supplementary\u00a0Information 2 (A sketch map of the model is shown in Supplementary Fig.\u00a02, and the calculated anisotropic parameter is shown in Supplementary Fig.\u00a03.).\n\nSpatiotemporal evolution of the magnetic field in front of the target when the preplasma density npre is (a) npre\u2009=\u20090.4nc; (b) npre\u2009=\u20090.2nc, \u03c4d is the time delay; The target surface is located at x\u2009=\u20090 which is indicated by an arrow in each picture.\n\nWith declining preplasma density, the peak sheath field gradually migrates from the preplasma boundary to the target surface. The ions thus can gain greater energy, leading to a nearly saturated magnetic field induced by the ion Weibel instability at the preplasma density of ~0.2nc (Fig.\u00a03b). The gyroradius of an Al+8 ion in the magnetic field can be estimated as \\({\\widetilde{R}}_{g} \\sim 100\\mu m\\). The filament distance, dF, as determined by the experiment is ~15\u2009\u03bcm, indicating that the Weibel instability is nearly at the saturation point.\n\nIn comparison with the higher preplasma density situation, a major difference between 0.2nc and 0.4nc is the trajectory of the Al+8 ions. For the preplasma density of ~ 0.2 nc, the deflection angle \u03b8 of Al+8 ions in the magnetic field can be calculated as,\n\nwhich indicates that the Al+8 ions can propagate somewhat freely in the magnetic field. The expanding ions hence can be regarded as a Weibel instability-mediated rarefactive wave. Near the boundary of the preplasma, the magnetic field structures stop moving, as being frozen because the return currents cannot be supported outside of the preplasma region.\n\nFigure\u00a03a presents the temporal evolution of the peak magnetic field for three different preplasma densities. Notably, for preplasma density ~ 0.1nc, the magnetic field increases to its maximum value of B\u2009~\u20095000\u2009T at around 2.7\u2009ps. It suggests that the growth rate \\({\\gamma }_{F}\\) of the magnetic field is approximately three times greater than in the case of a low-foot laser and is estimated to be ~ 1\u2009\u00d7\u20091012 s\u22121, which is compatible with our estimation of the growth rate of the Weibel instability: \u03b3F\u2009~\u2009\u03b2d\u03c9p.",
+            "section_image": [
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+            ]
+        },
+        {
+            "section_name": "Discussion",
+            "section_text": "We have obtained the unambiguous experimental evidence of sub-relativistic collisionless shock driven by a table-top femtosecond laser using a concept which we termed laser engine. In this concept, a carefully adjusted laser temporal profile is used to create a low-density isotropic preplasma and the ensuing ion acceleration by the second femtosecond main laser pulse. Afterward, a strong flow of highly directional ion beams develops, which in turn drives a rapidly growing Weibel magnetic field and leads to the formation of a collisionless shock wave. Much different from the amplification of the Weibel magnetic fields observed in ref. 18, a real Weibel instability mediated forward propagating collisionless shock with subrelativistic velocity is observed in the experiment. When the shock propagates out of the plasma region, collisionless shock breakout is observed in the experiment. Importantly, our experimental results identify the Weibel instability as an efficient mechanism for escalating the magnetic field and could provide an essential boost in the formation of relativistic collisionless shocks in the universe. Meanwhile, femtosecond laser beams can provide far larger energy densities and, concomitantly, significantly reduced time and space scales required for studying the laser-plasma interactions. As a general application, we anticipate the use of femtosecond laser systems for studying collisionless shock formation, propagation, and breakout, as an alternative to large laser facilities that are beyond the reach of common researchers. This simple scheme, conducted with only a mJ-level laser system, is flexible and can, in principle, be extended to much higher laser energies to escalate the collisionless shock velocity beyond our current observations. Looking ahead, since vshock\\(\\,\\propto \\,\\)E for a spherical shock, relativistic collisionless shock mediated with a turbulent magnetic field as high as 105 \u2013 106 T with picosecond-scale duration can be induced with currently available petawatt-level femtosecond laser facilities35. With this high magnetic field, the atomic properties and the behaviors of matter will be changed fundamentally. Extreme physics resembling that observed on the surface of neutron stars and similar compact objects can be explored36.",
+            "section_image": []
+        },
+        {
+            "section_name": "Methods",
+            "section_text": "A laser system with 30-fs pulse width and central wavelength of ~800\u2009nm is used in the experiment. The laser beam is split into two parts with a beam splitter, the laser beam with about ~ 90% of the total energy is named the pump pulse. This beam with ~ 4-mJ energy was focused at 90\u00b0 with an off-axis parabola mirror onto the surface of fused quartz that is coated with ~30\u2009\u03bcm thick aluminum film. The peak intensity of the laser beam is ~ 1\u2009\u00d7\u20091017\u2009W\u2009cm\u20132. Another beam with ~10% of the total energy is frequency doubled to 400\u2009nm to be used as a probe beam. The off-axis parabola and the targets were held in a vacuum chamber with ambient air pressure ~10\u22123\u2009Pa. The relative time delay of the main beam and the probe beam is controlled by an electric stepper motor.\n\nThe laser temporal contrast is defined as the ratio of the peak intensity of the main pulse to the prepulse intensity. The temporal contrast can be controlled by the relative time delays between different Pockels cells in the Chirped Pulse Amplification system (CPA system). The laser consists of a Ti:sa oscillator, a repetition amplifier, and a single-pass amplifier. The repetition rate of the oscillator is 80\u2009MHz, i.e., the time interval between two neighboring oscillator pulses is 12.5\u2009ns. The cavity length of the regeneration amplifier is 3\u2009m, which corresponds to a round-trip time of 10\u2009ns. A schematic drawing of a time series of laser pulses is shown in Fig.\u00a05. As the extinction ratio of the Pockels cell is ~1000:1, when the selected oscillator pulses (PC I in Fig.\u00a05) enter the regeneration cavity, leakage pulses are accompanying with the selected ones. When the cavity is dumped at a second Pockel cell, the leakage pulses are output with the selected pulses (PC II in Fig.\u00a05) which affects the contrast in nanoseconds. And the contrast can be controlled by the switching time of the second Pockel cell.\n\nThe temporal separation between consecutive seed pulses is 12.5 ns. Within the regeneration cavity (Regen), the round-trip time is 10 ns. When the selected seed pulses are injected into the regeneration cavity (via Pockels cell I), they are accompanied by leakage pulses. The\u00a0contrast of the amplified laser pulse can be controlled by\u00a0the switching time\u00a0of the second Pockels cell (Pockels cell II).\n\nThe prepulse approaches the target ~2.8\u2009ns before the main pulse, and a preplasma is induced. Due to the long-time delay between the main pulse and the prepulse, when the main pulse illuminates on the target the preplasma density distribution is almost homogeneous in front of the target. The density of the preplasma is determined by the intensity of the prepulse, thus the temporal contrast of the laser beam can be easily monitored by the density of the preplasma at the zero delay.\n\nTo diagnose the plasma density in front of the target, complex laser interferometry is used in the experiment37. The interference fringes are used to reconstruct the phase changes due to the presence of plasma in front of the target. This phase change can then be used for the extraction of the density distribution of the plasma.\n\nThe magnetic field is measured by the classical Faraday rotation method. To overcome the difficulties meeting in two-channel Faraday rotation experiments, we follow a method developed in ref. 37, in which only one CCD camera is needed, thus overcoming the difficulties of perfectly matching two images from different CCD channels. Glan-type polarizing prisms are used in the experiment to measure the rotation of the polarization plane of the probe beam transmitted through the plasma region. By comparing this rotation angle with the background polarization state of the probe beam the magnetic field can be extracted.\n\nPrecise control of the time delay between the main pulse and the prepulse, as well as adjustment of the prepulse intensity, can be used for the regulation of the preplasma density situated ahead of the target. This control facilitates achieving a preplasma density on the order of near critical density, such as ~0.1nc. In the target normal sheath acceleration mechanism (TNSA), ~ MeV level proton beams (vi\u2009~\u20091\u2009\u00d7\u2009107\u2009m/s) can be easily induced with a millijoule level femtosecond laser system as it is demonstrated in ref. 22. When the accelerated ion beams penetrate into the preplasma in front of the target, the mean free path of the ion beam is ~30\u2009m which ensures that the ion plasma interaction is collisionless and can be used for the study of the collisionless shocks.\n\nWhile hot electrons are stimulated by the ultrashort laser beam expanding out of the target an electrostatic sheath field is formed at the boundary of the target which can accelerate the charged ions. However, if the density of the preplasma is very high, this acceleration field can be shielded by the preplasma, which can lead to low efficiency in the acceleration of ion beams. There must be some critical density ncrt, below which the ion beams can be efficiently accelerated. Based on a model developed in ref. 38, in TNSA the energy gained by an ion beam in a plasma with two electron temperatures Th and Tc can be written as Eion\u2009~\u2009Ze(nhTh + ncTc)/(nh + nc). The kinetic energy of the accelerated ions in our experiment is ~ MeV. The growth rate \u03b3F of the ion Weibel instability is \u03b3F\u2009~\u2009\u03b2i\u03c9i. Based on PIC simulations, the maximum ion velocity can reach ~ 0.07c which is consistent with the experiment. The growth rate of the Weibel instability decreases exponentially with increasing preplasma density because the sheath field also decreases exponentially with preplasma density. As shown in the article, just like in high harmonic generation, a \u201cphase transition-like\u201d behavior should be observed, and this transition has been observed in the experiment.",
+            "section_image": [
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+            ]
+        },
+        {
+            "section_name": "Data availability",
+            "section_text": "The data supporting the findings in this study are available within the article and its Supplementary Information/Source Data file. All other relevant data are available from the corresponding author upon request.\u00a0Source data are provided with this paper.",
+            "section_image": []
+        },
+        {
+            "section_name": "Code availability",
+            "section_text": "The EPOCH code used in this study is publicly available for download from https://github.com/Warwick-Plasma/epoch.",
+            "section_image": []
+        },
+        {
+            "section_name": "References",
+            "section_text": "Pelletier, G., Bykov, A., Ellison, D. & Lemoine, M. Towards understanding the physics of collisionless relativistic shocks. Space Sci. Rev. 207, 319\u2013360 (2017).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMedvedev, M. V. & Loeb, A. Generation of magnetic fields in the relativistic shock of gamma-ray burst sources. Astrophys. J. 526, 697 (1999).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nSilva, L. O. et al. Interpenetrating plasma shells: near-equipartition magnetic field generation and nonthermal particle acceleration. Astrophys. J. 596, L121 (2003).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nPiran, T. The physics of gamma-ray bursts. Rev. Mod. Phys. 76, 1143 (2005).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBamba, A., Yamazaki, R., Ueno, M. & Koyama, K. Small-scale structure of the SN 1006 shock with Chandra observations. Astrophys. J. 589, 827\u2013837 (2003).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDiego, F. T. Ed. Modelling Pulsar Wind Nebulae (Springer International Publishing AG, (2017).\n\nFiuza, F. et al. Electron acceleration in laboratory-produced turbulent collisionless shocks. Nat. Phys. 16, 916\u2013920 (2020).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMatsumoto, Y., Amano, T., Kato, T. N. & Hoshino, M. Stochastic electron acceleration during spontaneous turbulent reconnection in a strong shock wave. Science 347, 974\u2013978 (2015).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nRuyer, C. et al. Growth of concomitant laser-driven collisionless and resistive electron filamentation instabilities over large spatiotemporal scales. Nat. Phys. 16, 983\u2013988 (2020).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWeibel, E. Spontaneously growing transverse waves in a plasma due to an anisotropic velocity distribution. Phys. Rev. Lett. 2, 83 (1959).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDavidson, R. C., Hammer, D. A., Haber, I. & Wagner, C. E. Nonlinear development of electromagnetic instabilities in anisotropic plasmas. Phys. Fluids 15, 317\u2013333 (1972).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nM\u00e9sz\u00e1ros, P. Gamma-ray bursts: accumulating afterglow implications, progenitor clues, and prospects. Science 291, 79\u201384 (2001).\n\nArticle\u00a0\n    ADS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWilhelmi, E. D. O. et al. The hunt for PeVatrons as the origin of the most energetic photons observed in the Galaxy. Nat. Astron. 8, 425\u2013431 (2024).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDiesing, R. & Caprioli, D. Spectrum of electrons accelerated in supernova remnants. Phys. Rev. Lett. 123, 071101 (2019).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nAharonian, F. The very-high-energy gamma-ray sky. Science 315, 70\u201372 (2007).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nHESS Collaboration. Acceleration of Petaelectronvolt protons in the Galactic Centre. Nature 531, 476\u2013479 (2016).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nCao, Z. et al. Ultrahigh-energy photons up to 1.4 petaelectronvolts from 12 \u03b3-ray Galactic sources. Nature 594, 33\u201336 (2021).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nHuntington, C. M. et al. Observation of magnetic field generation via the Weibel instability in interpenetrating plasma flows. Nat. Phys. 11, 173\u2013176 (2015).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nManuel, M. E. et al. Experimental evidence of early-time saturation of the ion-Weibel instability in counterstreaming plasmas of CH, Al, and Cu. Phys. Rev. E 106, 055205 (2022).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nFiuza, F., Fonseca, R. A., Tonge, J., Mori, W. B. & Silva, L. O. Weibel-instability-mediated collisionless shocks in the laboratory with ultraintense lasers. Phys. Rev. Lett. 108, 235004 (2012).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nRuyer, C., Gremillet, L. & Bonnaud, G. Weibel-mediated collisionless shocks in laser-irradiated dense plasmas: Prevailing role of the electrons in generating the field fluctuations. Phys. Plasmas 22, 082107 (2015).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nHou, B. et al. MeV proton beams generated by 3 mJ ultrafast laser pulses at 0.5\u2009kHz. Appl. Phys. Lett. 95, 101503 (2009).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nFransson, C. et al. Emission lines due to ionizing radiation from a compact object in the remnant of Supernova 1987A. Science 383, 898\u2013903 (2024).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nChen, P. et al. A 12.4 day periodicity in a close binary system after a supernova. Nature 625, 253\u2013258 (2024).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nReynolds, S. P. et al. The youngest galactic supernova remnant: G1.9\u2009+\u20090.3. Astrophys. J. 680, L44 (2008).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nNovo, A. S., Bret, A., Fonseca, R. A. & Silva, L. O. Shock formation in electron\u2013ion plasmas: mechanism and timing. Astrophys. J. Lett. 803, L29 (2015).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nZhou, S. Y. et al. Self-organized kilotesla magnetic-tube array in an expanding spherical plasma irradiated by kHz femtosecond laser pulses. Phys. Rev. Lett. 121, 255002 (2018).\n\nArticle\u00a0\n    ADS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nZhou, M., Liu, Z. & Loureiro, N. F. Spectrum of kinetic-Alfv\u00e9n-wave turbulence: intermittency or tearing mediation? Mon. Not. R. Astron. Soc. 524, 5468\u20135476 (2023).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nChatterjee, G. et al. Magnetic turbulence in a table-top laser-plasma relevant to astrophysical scenarios. Nat. Commun. 8, 15970 (2017).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nArber, T. D. et al. Contemporary particle-in-cell approach to laser-plasma modelling. Plasma Phys. Contr. F. 57, 113001 (2015).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBlandford, R. D., McKee, C. F. Fluid dynamics of relativistic blast waves. Phys. Fluids 19: 1130\u20131138 (1976).\n\nGarnavich, P. M. et al. Shock breakout and early light curves of type II-P supernovae observed with Kepler. Astrophys. J. 820, 23 (2016).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nArnold, V. I. Catastrophe Theory (Springer-Verlag Berlin, 1986).\n\nBayless, A. J. et al. Supernova shock breakout/emergence detection predictions for a wide-field X-ray survey. Astrophys. J. 931, 15 (2022).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMourou, G. Nobel Lecture: Extreme light physics and application. Rev. Mod. Phys. 91, 030501 (2019).\n\nArticle\u00a0\n    ADS\u00a0\n    MathSciNet\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBeskin, V. S. et al. Ed. The Strongest Magnetic Fields In The Universe (Springer Science+Business Media New York, (2016).\n\nKalal, M., Nugent, K. A. & Luther-Davies, B. Phase-amplitude imaging: its application to fully automated analysis of magnetic field measurements in laser-produced plasmas. Appl. Opt. 26, 1674\u20131679 (1987).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nPassoni, M., Tikhonchuk, V. T., Lontano, M. & Bychenkov, V. Y. Charge separation effects in solid targets and ion acceleration with a two-temperature electron distribution. Phys. Rev. E 69, 026411 (2004).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDownload references",
+            "section_image": []
+        },
+        {
+            "section_name": "Acknowledgements",
+            "section_text": "Y.T. acknowledge the support of the National Natural Science Foundation of China under grant numbers 12388102, 12325409, U2267204 and Shanghai Pilot Program for Basic Research, Chinese Academy of Sciences, Shanghai Branch. Y.B. acknowledge the support of the National Natural Science Foundation of China under grant numbers 12474350, the Youth Innovation Promotion Association of Chinese Academy of Sciences, CAS Project for Young Scientists in Basic Research under grant number YSBR-060, the Natural Science Foundation of Shanghai, China under grant number 24ZR1493000 and Strategic Priority Research Program of Chinese Academy of Sciences under grant number XDB0890203.",
+            "section_image": []
+        },
+        {
+            "section_name": "Author information",
+            "section_text": "State Key Laboratory of Ultra-intense Laser Science and Technology, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai, 201800, China\n\nYafeng Bai,\u00a0Dongdong Zhang,\u00a0Yushan Zeng,\u00a0Jiakang Mao,\u00a0Liwei Song,\u00a0Ye Tian\u00a0&\u00a0Ruxin Li\n\nCenter of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing, 100049, China\n\nYafeng Bai,\u00a0Yushan Zeng,\u00a0Jiakang Mao,\u00a0Liwei Song,\u00a0Ye Tian\u00a0&\u00a0Ruxin Li\n\nZhangjiang Laboratory, Shanghai, 201210, China\n\nRuxin Li\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nY.T. and R.L. conceived and supervised the project. Y.B., J.M. conducted the experimental measurements. Y.B. and Y.T. developed the theory. Y.B. and D.Z. performed the data analyses. Y.T., Y.B., D.Z. and Y.Z. wrote the manuscript. All authors reviewed and discussed the manuscript and made substantial contribution to it.\n\nCorrespondence to\n                Ye Tian or Ruxin Li.",
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+            "section_name": "About this article",
+            "section_text": "Bai, Y., Zhang, D., Zeng, Y. et al. Observation of sub-relativistic collisionless shock generation and breakout dynamics.\n                    Nat Commun 16, 3770 (2025). https://doi.org/10.1038/s41467-025-58867-3\n\nDownload citation\n\nReceived: 24 September 2024\n\nAccepted: 31 March 2025\n\nPublished: 28 April 2025\n\nVersion of record: 28 April 2025\n\nDOI: https://doi.org/10.1038/s41467-025-58867-3\n\nAnyone you share the following link with will be able to read this content:\n\nSorry, a shareable link is not currently available for this article.\n\n\n\n\n                            Provided by the Springer Nature SharedIt content-sharing initiative\n                        ",
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1aa501c9b53d916be7200fed7b878d3f8603c3870d4edc7d60ebed9d2f6d916e/metadata.json

@@ -0,0 +1,137 @@
+{
+    "title": "Electric transmission value and its drivers in United States power markets",
+    "pre_title": "Electric transmission value and its drivers in United States power markets",
+    "journal": "Nature Communications",
+    "published": "28 August 2025",
+    "supplementary_0": [
+        {
+            "label": "Supplementary Information",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-63143-5/MediaObjects/41467_2025_63143_MOESM1_ESM.pdf"
+        },
+        {
+            "label": "Reporting Summary",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-63143-5/MediaObjects/41467_2025_63143_MOESM2_ESM.pdf"
+        },
+        {
+            "label": "Transparent Peer Review file",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-63143-5/MediaObjects/41467_2025_63143_MOESM3_ESM.pdf"
+        }
+    ],
+    "supplementary_1": NaN,
+    "supplementary_2": NaN,
+    "source_data": [],
+    "code": [],
+    "subject": [
+        "Energy economics",
+        "Energy policy",
+        "Energy supply and demand",
+        "Social sciences"
+    ],
+    "license": "http://creativecommons.org/licenses/by/4.0/",
+    "preprint_pdf": "https://www.researchsquare.com/article/rs-3957695/v1.pdf?c=1756465774000",
+    "research_square_link": "https://www.researchsquare.com//article/rs-3957695/v1",
+    "nature_pdf": "https://www.nature.com/articles/s41467-025-63143-5.pdf",
+    "preprint_posted": "28 Mar, 2024",
+    "research_square_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Electric transmission infrastructure serves a critical role during extreme weather and supply disruptions and can enable low-cost, low-carbon electricity systems. This paper contributes to a more complete understanding of transmission\u2019s value, cost-effectiveness, and market barriers. By studying wholesale energy market prices in the United States during 2012-2022, we find that additional transfer capacity between regions was especially valuable (median of $116M/GW-year) and directionally balanced. Transmission\u2019s market value was highly influenced by a small fraction of time: 5% of hours typically capture at least 45% of value. These peak periods were driven primarily by unforeseen changes in conditions within one day of operations. Transmission infrastructure cost estimates were less than market values for most studied locations, including all links crossing regional seams where value-to-cost ratios were frequently above 4, suggesting barriers to the development of valuable infrastructure. These results complement forward-looking modeling studies and aid efforts to improve modeling practices.Scientific community and society/Energy and society/Energy economicsScientific community and society/Energy and society/Energy policyScientific community and society/Energy and society/Energy supply and demand",
+            "section_image": []
+        },
+        {
+            "section_name": "Additional Declarations",
+            "section_text": "There is NO Competing Interest.",
+            "section_image": []
+        },
+        {
+            "section_name": "Supplementary Files",
+            "section_text": "SupplementalInformation.pdf",
+            "section_image": []
+        }
+    ],
+    "nature_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Electric transmission infrastructure plays a vital role during extreme weather and supply disruptions and can enable low-cost electricity systems. This paper contributes to a more complete understanding of the value and cost-effectiveness of transmission, as well as barriers to its development. By studying wholesale energy market prices in the United States between 2012 and 2022, we find that additional transfer capacity between regions would have been especially valuable, with a median value of $116 million per GW per year. This capacity would often have provided balanced benefits to each region. The market value of transmission was highly influenced by a small fraction of time: 5% of hours typically captured at least 45% of the total value. These peak periods were primarily driven by unforeseen changes in conditions within one day of operations. Annualized transmission infrastructure cost estimates were lower than the average market value for most locations, including all links crossing regional seams, where the value-to-cost ratio was often greater than 4. This suggests that there are barriers to developing valuable grid infrastructure. These results complement forward-looking modeling studies and support efforts to improve modeling practices.",
+            "section_image": []
+        },
+        {
+            "section_name": "Introduction",
+            "section_text": "Recent events have put electric transmission in the spotlight. In the United States, extreme winter storms have caused electric system outages, leading to discussion of transmission as a possible solution1,2. In Europe\u2019s 2021\u20132022 energy crisis, existing well-connected electricity networks increased supply security3, yet the value of more cross-border transmission capacity was also apparent4. Looking beyond individual events, discussion around transmission development has also been elevated by industry trends during the 2010s and early 2020s, including generation fleets shifting away from coal and nuclear toward gas, wind, and solar, record infrastructure investments by China\u2019s State Grid5, and continued siting challenges such as local opposition6,7 and complex permitting8. In the US, a slowdown in construction of new high-voltage lines9 suggests there may be pent-up demand for transmission, while transmission also serves an increasing role in accessing generation resources in new locations. Transmission is also considered a key enabler of a low-cost and low-carbon electricity system10,11,12,13. Motivated by this confluence of factors, improving transmission planning processes and expanding transmission is a focus of regulators14, legislators3,15,16,17, and private sector analyses4,18,19.\n\nTransmission development in the United States typically occurs through one of three channels: centrally planned through a regional system operator (most common), independently constructed by a merchant transmission developer (rare), or generator interconnection processes (frequent, mostly incremental upgrades). In the latter channel, development is narrow in scope, including only those upgrades required to maintain grid safety, reliability, and often deliverability after adding specific new resources. In the first two channels, development decisions come down to a cost/benefit trade-off, though system operators and merchants may assess different sets of costs and benefits. Traditionally in centralized planning processes a need for transmission is established to either ensure reliability or satisfy public policy directives. Economically driven transmission projects have also been pursued and are typically evaluated on their ability to reduce production costs of the system. However, modeled production cost benefits alone rarely outweigh transmission costs20. In recognition of the many ways transmission can be beneficial, including lower generation capital costs, reduced pollution, risk mitigation, and reducing unserved demand, in addition to traditional production cost savings21, some system planners have moved to a multi-value study framework22.\n\nTo account for system changes expected during a transmission asset\u2019s lifetime, cost/benefit analyses are typically performed by simulating the electricity system under assumptions about future system conditions. A weakness of such models is that often they do not replicate real-world conditions that affect the benefits of transmission, conditions such as forecast errors, extreme weather, and infrastructure outages18,19,23,24. Because transmission infrastructure takes many years to plan and build and, by nature, affects multiple locations, the impacts of misestimating transmission value during the planning phase could be long lasting and widespread.\n\nThe purpose of this paper is to provide insight into transmission value by offering a direct contrast to forward-looking modeling. We use observed wholesale market prices, along with load and renewable data, to assess where, when, and why transmission is valuable, focusing on 70 location pairs across the contiguous US from 2012 through 2022. We also conduct a scoping-level analysis to compare historical energy market values of transmission to the costs of transmission infrastructure projects while accounting for market depth, i.e., the extent to which prices would change as a result of new capacity. These comparisons contextualize the empirical value estimates and highlight where market barriers including, but not limited to, current planning processes are greatest.\n\nSpecifically, we analyze locational marginal prices (LMPs) that measure the marginal cost of serving the next increment of demand at a specified pricing node and reflect the sum of three components: system-wide marginal energy cost, marginal cost of losses, and marginal cost of congestion. LMPs are defined by the seven independent system operators (ISOs) and regional transmission organizations (RTOs) in the US (i.e., CAISO, ERCOT, ISO-NE, MISO, PJM, and SPP) at over 80,000 nodes, typically for both a forward day-ahead market and a spot real-time market. Concurrent price differences between market nodes indicate network congestion and reflect challenges due to actual generator and infrastructure outages. Market prices serve as an investment signal to market actors and are a rich data source that have been used by researchers to advance our understanding of the value of renewable energy25,26, efficient levels of subsides for energy efficiency27, and the impact of specific transmission investments that are already online28,29,30, for example.\n\nWhile our approach is not meant to replace models, it is intended to help identify key mechanisms that may lead to biased model estimates of transmission value. Future efforts could use these insights to improve transmission planning processes. There are several categories of societal benefits that transmission may provide, including resource adequacy, resilience, risk mitigation, and reductions in emissions, market power, capital costs and production costs21. These concepts are priced into wholesale electricity markets to varying degrees, and similarly reflected in market values of transmission. Centralized system planners, however, separately quantify each benefit they consider and typically use production cost savings as the main economic benefit. We do not offer a one-to-one comparison between transmission\u2019s market value and each of its modeled benefit types, instead using market value as an aggregate signal. Empirical prices precisely reflect actual system conditions and market participant behavior as they occurred in the past, providing insights that cannot be gained from system models.\n\nPrior to this work, studies of transmission value using historical market price data focused on select severe weather1,2 or geopolitical4 events, the specific benefits of increased competition31,32, measuring the impact of a specific transmission investment that is already online28,29,30, or congestion on existing lines within a limited footprint (ISO/RTO annual reports, such as33,34,35). The authors of this paper have previously employed a subset of the methods used here and published the findings in refs. 36,37,38. This paper contributes to a more complete understanding of transmission\u2019s value, cost-effectiveness, and market barriers and aids efforts to improve modeling practices by identifying key patterns and value drivers for use in model validation.",
+            "section_image": []
+        },
+        {
+            "section_name": "Results",
+            "section_text": "The transmission value analyzed in this section is a pairwise quantity between two wholesale market pricing nodes (i.e., a \u201clink\u201d) defined as the mean absolute locational marginal price difference between the nodes over time (in units $/MWh). It represents the marginal energy value of spatial price arbitrage within a specific market interval. A link is uniquely defined by two pricing nodes; it does not correspond to a specific transmission line, and there may be zero, one, or multiple existing transmission paths between a link\u2019s nodes. This paper primarily focuses on the real-time market, because we are most interested in transmission\u2019s ultimate value to the system and real-time prices reflect physically binding dispatch decisions under the actual operating conditions of the system. Further, only real-time prices exist for all 70 links depicted in Fig.\u00a01, though day-ahead prices, derived from a forward financial market, exist for many of the links. We will later offer a comparison to value based on prices from the day-ahead timeframe. The marginal value is useful as it can be directly compared to market prices, but it can also be converted to an equivalent total value per link, such as millions $/GW. Total value metrics are useful when compared to transmission costs. When considering total value metrics, it is important to also consider market saturation effects (e.g., in each hour, is the full GW of transmission capacity needed, or would prices converge with less capacity?).\n\na Map of mean marginal transmission market values for all 70 analyzed links over the entire study period (real-time market). The line segments depict which pairs of wholesale market pricing nodes are analyzed and do not portray existing transmission lines. b Distribution of mean marginal transmission market values (real-time market) across the set of 70 analyzed links. Each point represents one link, and there are the following number of links in each category: cross-interconnect: 9, interregional: 31, within-region: 30. The horizontal lines on each box plot show, from low to high, the smallest data point lying within 1.5x the inter-quartile range (IQR) from the 25th percentile, the 25th percentile, the 50th percentile (median), the 75th percentile, and the largest data point lying within 1.5x the IQR from the 75th percentile.\n\nSeventy hypothetical transmission links between major market regions in the contiguous U.S. are considered; 30 links are contained within a balancing authority (\u201cwithin-region\u201d), 31 links are interregional within the same interconnection (\u201cinterregional\u201d) and 9 links span an interconnection seam (\u201ccross-interconnect\u201d). In the contiguous U.S. there are three interconnections \u2013 the Western Interconnection, the Eastern Interconnection, and the Electric Reliability Council of Texas (ERCOT) \u2013 that operate almost independently with separate frequency synchronization and limited cross-interconnect transfer capacity. Each line segment in Fig.\u00a01a and each point in Fig.\u00a01b show the marginal transmission market value for an individual link, averaged over the study period. Relatively high value links are found within and between many regions.\n\nGenerally, links crossing market seams have greater potential to arbitrage high and low prices: The market value for the median cross-interconnect and interregional links are $30/MWh and $15/MWh, respectively, compared to $8/MWh for a within-region link. For context, if the marginal value of $15/MWh was maintained for the entire capacity of a 1\u2009GW line, the line\u2019s market value would be $131 million per year \\(\\left(\\frac{{{{\\rm{\\$}}}}15}{{{{\\rm{MWh}}}}}*\\frac{1000{{{\\rm{MW}}}}}{1{{{\\rm{GW}}}}}*\\,\\frac{8760{{{\\rm{h}}}}}{{{{\\rm{year}}}}}\\right)\\). Note that market saturation effects will be quantified and discussed later. Interregional and cross-interconnect links may have higher value due to more diversity of weather, load profiles, and generator resources than is found within regions and due to a historical focus by transmission system operators on development within their own geographic footprint39.\n\nLinks connecting ERCOT to any of its neighbors (SPP, MISO, non-ISO West) register the highest values, driven by exceptionally high values since 2018. Links bridging the western and eastern interconnections (i.e., between the West and SPP or MISO) and connecting NYISO and ISO-NE are also among the most valuable. ERCOT, SPP, and NYISO contain the highest value within-region links. Not all links have substantial value, however. For example, the average hourly price difference between ISO-NE\u2019s Massachusetts and Maine hubs is just $2/MWh, consistent with ISO-NE\u2019s statement that \u201ctransmission system upgrades have nearly eliminated congestion costs in the New England energy market\u201d40.\n\nPersistent pricing gradients often underlie this value, but do not fully capture it since the lower-priced location of the pair can alternate over time. The transmission value suggested by differences in annual average prices is typically only 18\u201345% of the value suggested by our methodology based on hourly differences in real-time prices for cross-interconnect links, 26\u201361% for interregional links and 35\u201381% for within-region links. Similarly, only considering the value in one direction (e.g., when the price on side A of the link is higher than on side B) captures just 59\u201367%, 63\u201380% and 67\u201390% of the value for cross-interconnect, interregional and within-region links, respectively. All ranges reported in this paragraph reflect the 25th-75th percentiles of the studied transmission links. As shown in Fig.\u00a02a, cross-interconnect and interregional links tend to be fairly balanced in terms of which direction power flow would be valuable over time. Figure\u00a02b shows an example of a balanced link in a specific year. Studying directionality has important implications for concerns over winners and losers in transmission planning41,42. Balanced directional value could suggest comparable benefits from transmission development for multiple parties.\n\na Consistency of high-low price direction (real-time market). Each point represents one link, and there are the following number of links in each category: cross-interconnect: 9, interregional: 31, within-region: 30. The horizontal lines on each box plot show, from low to high, the smallest data point lying within 1.5x the inter-quartile range (IQR) from the 25th percentile, the 25th percentile, the 50th percentile (median), the 75th percentile, and the largest data point lying within 1.5x the IQR from the 75th percentile. Supplementary Fig.\u00a01 provides analogous information for the day-ahead market. b Example of a link-year with balanced value of power flow in each direction. The graph shows the distribution of marginal transmission market value (real-time market) across the months of 2022 and by which location had the higher price in any particular hour, for the link between southern Texas and Louisiana. For this example, the maximum share of value in a single direction \u2013 the metric used in (a) \u2013 is 0.54.\n\nThe market value of transmission varies over the course of years, but also between the day-ahead and real-time markets and from hour to hour. The bars in Fig.\u00a03 show the trend in transmission value for each year 2012\u20132022. In 2022, large locational price differences were a broad phenomenon across most of the U.S., resulting in the highest median (left) and mean (right) transmission value of any calendar year since at least 2012, the earliest year in-scope of this study. The increase in transmission value across so many locations is suggestive of a cause that is national in scope, such as overall increased energy prices (see the lines in Fig.\u00a03). In contrast, high mean values without corresponding high median values, such as in 2018 and 2021, indicate events that drove extremely high transmission value in isolated regions. In 2021, for example, winter storm Uri drove high values for interregional transmission into SPP and ERCOT but had less impact on other regions of the U.S. This pattern underscores the importance of considering a long time horizon when analyzing transmission investments, which have lifespans of 50-80 years, while also considering possible value drivers that derive from national, regional, and local conditions.\n\nNote that the set of links in the early years is smaller due to data constraints, as explained in the Methods. Supplementary Fig.\u00a02 provides analogous information for the day-ahead market.\n\nFocusing on shorter, operational time scales, a typical link had a transmission value 30% greater in the real-time market than in the day-ahead market. While electricity prices are positively correlated with transmission market value across years, the same is not true when looking at day-ahead and real-time markets: Real-time transmission value is greater than day-ahead value on average (Fig.\u00a04, left panel) and for the vast majority of links each year (Fig.\u00a04, center panel), yet average electricity prices are lower in the real-time market (Fig.\u00a04, left panel). It is the magnitude, not frequency, of the change in transmission value between markets that primarily drives greater real-time value: Our analysis finds that a link\u2019s market value is approximately equally likely to increase or decrease from the day-ahead to the real-time market for any given hour (Fig.\u00a04, center panel), but the mean increase is far greater than the mean decrease (Fig.\u00a04, right panel). Because an increase in transmission value often coincides with a price increase at one or both nodes, this finding is consistent with the real-time nodal price(s) being on more inelastic portions of the supply curve(s) when transmission value increased relative to day-ahead than when it decreased. Transmission value is also more volatile in the real-time market, with a standard deviation of $42/MWh compared with $16/MWh in the day-ahead market for a typical link.\n\nExcludes links connected to the non-ISO West where there is not a day-ahead market. The set of links in the early years is smaller due to data constraints. Left: Average in the real-time market relative to average in the day-ahead market for (1) transmission market value and (2) wholesale electricity prices. Center: Prevalence of greater real-time transmission value in terms of (1) the share of links where annual real-time value was greater than day-ahead and (2) the share of hours across all links in which real-time value was greater than day-ahead. Right: Magnitude of the average hourly difference between day-ahead and real-time transmission value presented separately for hours in which (1) real-time value was greater than day-ahead value and (2) day-ahead value was greater than real-time value.\n\nGiven the volatility of congestion, aggregating to calendar year intervals offers an incomplete view of how a link\u2019s value potential is distributed over time. Instead, we consider how the value is distributed within the entire study horizon. This perspective is presented in Fig.\u00a05 and reveals that, for real-time markets, at least 45% of total value is accounted for by only 10% of hours for all links and by just 5% of hours for the majority of links. Narrowing further, the top 1% of hours by real-time market value typically account for 20\u201330% of a link\u2019s potential, but it can reach over 50% in some cases. Transmission value in day-ahead markets is not only lower than in real-time markets, as discussed earlier, but also more dispersed. Figure\u00a05 shows that a smaller share of total day-ahead market value is concentrated in the hours with the highest day-ahead value as compared to real-time. Still, transmission value in day-ahead markets is not distributed evenly across all hours and the majority of day-ahead transmission value is usually found in just 10% of hours. Since transmission\u2019s marginal market value is heavily influenced by a relatively small collection of key hours with exceptionally large price differences, capturing the tails of market outcomes is important for transmission planners aiming to estimate the value of a transmission line.\n\nSample sizes: RT market: 70, DA market: 57. The horizontal lines on each box plot show, from low to high, the smallest data point lying within 1.5x the inter-quartile range (IQR) from the 25th percentile, the 25th percentile, the 50th percentile (median), the 75th percentile, and the largest data point lying within 1.5x the IQR from the 75th percentile.\n\nTo explore conditions during times of high transmission value and therefore assess potential drivers of these large geographic price spreads, in this section, we focus on the hours where the real-time transmission value is in the 95th percentile or above for each link and refer to these 5% of hours as the peak value hours. Due to net load data availability and the absence of a day-ahead market in the non-ISO West, this section focuses on the 52 studied links within or between ISO or RTO regions, excluding those in the non-ISO West and Southeast.\n\nUnforeseen intraday variance, high net load, cold weather, or high renewable power generation conditions are present in over 75% of the hours with peak transmission value. This is not simply because these four conditions are pervasive and present most of the time. Rather, these conditions disproportionately coincide with the peak value hours.\n\nUnforeseen intraday variance is identified by a large change in the LMPs between the day-ahead and real-time markets on either side of the link (see Methods for a precise definition). Such a change between markets reflects sizeable forecast errors in the day-ahead timeframe, for example, errors in estimated supply, demand, weather, or infrastructure outages, and limited flexibility to adapt to unexpected operational circumstances. These large price changes are a price increase 64% of the time and a price decrease the other 36% of the time. Of the transmission value resulting from peak value hours, 74% overlaps with a detected unforeseen event, as shown in Fig.\u00a06a (i.e., the entire blue bar covers 74% of the left gray bar). Remarkably, 43% of all hours with an unforeseen intraday variance detected are in the 5% of hours with greatest transmission value. Figure\u00a06b(i) shows how the distribution of hours with an unforeseen intraday variance are skewed toward the times of highest transmission value. This result directionally supports the simulation-based conclusion in ref. 18 that the benefits of adding transmission depend on the uncertainty between day-ahead scheduling and real-time operations. Unforeseen intraday variances sometimes occur during times of high net load, high renewable power generation and/or cold weather: Of the peak transmission value coinciding with large day-ahead to real-time price differences, 43% overlaps with one or more of these conditions, as shown by the lighter blue labeled segments in Fig.\u00a06a.\n\nAggregate results for all 52 studied links within or between ISO or RTO regions, excluding those in the non-ISO West and Southeast. a Contribution of key system conditions to transmission market value during peak value hours (top 5%). This figure should be read from left to right. When multiple conditions are present at the same time, the associated value appears in the first (i.e., leftmost) applicable column and is identified by lighter segments and \u201c& [overlapping condition]\u201d labels. b Distributions of hours relative to transmission value when a key condition is present (blue) compared to when it is not (orange). The local peaks in the left half of each distribution represent a mass of hours each with $0 transmission value and therefore the same value rank for each link.\n\nCold weather\u2014defined here as the coldest 5% of days in each location \u2013 overlaps with 25% of the value resulting from the peak hours (Fig.\u00a06a). Often this value overlaps with unexpected events, net load, or both, but cold weather is the only studied driver present for 5% of the peak transmission value (dark orange segment). High net load \u2013 defined here as the 5% of hours in each location with the highest net load \u2013 is rarely the only studied condition affecting a peak value hour (dark yellow segment; 2% of peak value). However, it is still an important factor because 20% of the value resulting from the peak value hours comes from times of high net load (Fig.\u00a06a). High net load is the result of high electricity demand and/or low variable renewable energy generation. The distributions of high net load and cold weather periods in Fig.\u00a06b(ii,iii) show a clear skew toward the highest value hours, though to a lesser degree than was observed for unforeseen intraday variance. While a disproportionate amount (13%) of cold weather and high net load hours coincide with the peak value hours, it is still much more common for a period with one of these conditions to pass without encountering a peak transmission value. Thus, peak value periods are difficult to predict, even if you are expecting very cold weather or high net load.\n\nWhile high levels of renewable generation make a period less likely to have high net load, it can still be a driver of peak transmission value due to geographically varying renewable penetration rates and weather patterns. Focusing on the 5% of hours with greatest combined wind and solar generation in each region, Fig.\u00a06b(iv) shows that hours with high renewable generation coincide more often with high transmission value than low value, but they do not have the same presence in the very highest transmission value hours as the other conditions discussed so far. Still, high renewable generation impacts a portion of peak transmission value which unforeseen intraday variance, high net load, and cold weather do not (green segment in Fig.\u00a06a; 2% of peak value).\n\nSupplementary Table\u00a01 details the prevalence of each condition discussed here and its relationship with the top 1%, 5%, and 10% value hours. Further, the Supplementary Information includes analysis on the roles of hot weather and designated storms or grid reliability events on peak transmission value, which were found to be nearly subsumed under the four conditions analyzed here.\n\nThe conditions analyzed above do not affect all links equally. Some conditions are more relevant for interregional links or within region links and others have an outsized impact on certain regions of the country. Figure\u00a07 shows the distribution of links in terms of the share of peak value with each condition. In general, interregional and cross-interconnect links see a greater share of peak transmission value explained by these conditions. This is consistent with greater weather differences across longer distances and our use of regional-level load and renewable generation totals; local condition differences that are not investigated here may have more impact on within-region links. Unforeseen intraday variation is a key condition for all studied links, but especially for interregional links. Interregional transfer quantities are often scheduled several hours or more in advance, with less flexibility to adjust compared to within-region flows. These results point to the lack of interregional operational flexibility within 24\u2009h of operation as a driver of transmission value. The two links with the greatest share of peak value during cold weather are SPP South\u2009<\u2009>ERCOT West and MISO\u2009<\u2009>\u2009ERCOT, but all ISO/RTOs other than CAISO are connected to at least one link where cold weather is present for at least 35% of peak value. High renewable generation rarely coexists with peak transmission value for some links, but for some regional and interregional links, particularly those within or between MISO and SPP, there is considerable overlap.\n\nEach point represents one of the 52 studied links (3 cross-interconnect, 19 interregional, 30 within-region) within or between ISO or RTO regions, excluding those in the non-ISO West and Southeast. The three cross-interconnect links are between ERCOT and either SPP or MISO. The horizontal lines on each box plot show, from low to high, the smallest data point lying within 1.5x the inter-quartile range (IQR) from the 25th percentile, the 25th percentile, the 50th percentile (median), the 75th percentile, and the largest data point lying within 1.5x the IQR from the 75th percentile.\n\nCase studies investigating differences in the conditions affecting transmission value for two links in more detail are provided in the Supplementary Information, including in Supplementary Figs.\u00a03 and 4.\n\nThis analysis has so far focused on transmission\u2019s marginal market value, which is defined precisely by market-clearing prices. If one is instead interested in the energy market value of a finite, larger transmission capacity addition, under the counterfactual that the line existed during 2012\u20132022, there are several factors to consider in addition to the observed marginal market value. One such factor is market depth; each increment of transmission capacity has the ability to reduce the price difference across its span, leading to an average value for the line that is less than the marginal value without it. The impact of market depth is accounted for in the following analysis through the use of statistically-based rolling supply curves and assumes a static market. That is, it does not account for generator entry and exit29,30, demand changes, shifts in market power31,32,43, or other dynamic effects that transmission expansion may create.\n\nHere, we summarize the analytical approach that is detailed in the Methods section. First, we infer supply curves from the data by fitting a non-decreasing third-degree polynomial to the relationship between regional net load and market price at each node for every bi-monthly period during the study horizon, similar to ref. 44. Second, we screen the fitted supply curves to identify which models represent the data sufficiently well and which models produce large-magnitude residuals for a substantial share of the hours. Models that fail to pass the screening are not used to estimate transmission value. Third, the supply curve models and hourly data are analyzed for each link to establish hourly transmission value estimates. In most hours, both (net load, price) observations are near their respective supply curves and the difference between these two supply curves forms a transmission demand curve. The area under this transmission demand curve, yet above the horizonal axis, between zero and the additional transmission capacity is the transmission value estimate (see Fig.\u00a08). When an observation is not near the supply curve or the corresponding supply curve did not pass screening, we use alternative approaches that lead to lower and higher value estimates. Finally, hourly values are summed over the study horizon.\n\nLeft and center panels: Each black point is an hourly observation from the half-month period that starts on the listed date. The red curve is the supply curve fitted to these points, and the blue curve is the red curve shifted to pass through the hour currently being analyzed. Right panel: The blue curves in the left and center panels combine to the transmission demand curve shown here. The area under the curve is the transmission value for the specified hour. In the upper example, transmission value declines slowly and the value is close to the marginal value. In the bottom example, transmission value declines quickly and prices converge before 1\u2009GW of capacity is fully utilized. Supplementary Fig.\u00a09 offers three more detailed illustrations of the same methodology.\n\nApplying this approach, we estimate the transmission value accounting for market depth of a 1\u2009GW increase in transmission capacity individually for each of the 40 interregional and cross-interconnect links in this study. Unlike the directly observable marginal transmission value metric, this value is an estimate for a hypothetical situation. 1\u2009GW of transmission capacity represents a relatively small addition for some links, such as those between PJM and MISO North where there is already 21.7\u2009GW of transfer capacity, and a substantial increase in other regions, such as between PJM and New York and between New York and New England where it represents a 50% increase20. We find values typically 72% to 93% (25th percentile of lower estimate to 75th percentile of higher estimate) of the marginal market value, as shown in Fig.\u00a09. Based on these findings, we conclude that, at a realistic line size of 1\u2009GW, saturation effects are not dominant and instead represent a discount to marginal transmission value that is occasionally moderate but typically modest. Supplementary Fig.\u00a05 presents results for a more aggressive test of market depth that assumes the market size (as defined by net demand) is 50% smaller than the market used here. In that case, transmission value accounting for market depth of a 1\u2009GW capacity increase is typically 59% to 87%2 of the marginal market value.\n\nGray and white bands are used to improve readability; they do not communicate information about the results.\n\nTo better contextualize our market value estimates, we compiled data on the costs to construct individual transmission projects across different regions of the United States. In total, the 26 recent and proposed transmission lines we evaluated correspond to over 87\u2009GW of potential transfer capability (details for each individual line are provided in Table\u00a01) and can be loosely matched, on a regional basis, to a subset of the transmission link values we estimate. Such value-to-cost comparisons should not be used to assess the full cost and value of any individual, specific transmission investment. However, the value-to-cost ratios we present in Fig.\u00a010 do provide some indication of the net economic value of transmission development, focusing here solely on energy market value and excluding other possible benefits of transmission investment.\n\nSee Table\u00a01 for details on the project cost data. See Supplementary Figs.\u00a06 and 7 for versions of this figure comparing multiple value and cost assumptions. a Value-to-cost ratios where the value is the midpoint of the value estimate range in (b) and the cost estimate assumes 60-year depreciation. The horizontal dashed line at 1 represents the break-even ratio. b Range of market value (real-time) estimates accounting for market depth and annualized project cost estimates.\n\nFigure\u00a010 shows the value estimate accounting for market depth and the cost of geographically similar transmission projects for the 26 projects (22 unique links). The figure breaks out our results for the three types of links we study: cross-interconnect, interregional, and within-region transmission lines. Figure\u00a010b shows the range of cost and value estimates in units of $/MW-yr and shows variation both across the types of links as well as within a given link. Across all 26 projects studied, only 3 projects had cost ranges that exceeded the value estimate range. Figure\u00a010a converts the absolute cost and value estimates into a value-to-cost ratio. We find that all cross-interconnect projects have value-to-cost ratios that exceed 4, suggesting that energy market value alone could motivate transmission development to link these areas. All these lines are in fact being privately proposed by merchant developers. The failure and challenge of developing some of these lines imply non-economic constraints. For instance, merchant developers often must seek customers to subscribe to their proposed lines, but those customers can be utilities that might own and operate their own transmission lines and thus not want to participate in such a competitive development process. For interregional lines within a common interconnection, value-to-cost ratios are smaller (median value of 1.6) with all of the ten lines having value-cost ratios > 1. Within-region lines have the lowest value-to-cost ratios with four of the eleven lines assessed having value-to-cost ratios <1 and the seven others > 1. Supplementary Figs.\u00a06 and 7 present results for sensitivity cases under different depreciation rates and where the value estimate range is based on a market size (as defined by net demand) that is 50% smaller than the market used here.\n\nProjects that have higher investment costs compared to historical market value may still have merit, especially if grid conditions are anticipated to change in ways that increase value over time. Additionally, energy arbitrage value is only one of many potential benefits of transmission: other drivers like renewable integration, electric reliability/resiliency, and avoided capacity investments may motivate investment and are not fully captured by wholesale energy prices. Furthermore, several of the lines we analyze came into service during the time period of market value estimation. Figure\u00a010a shows that these lines tend to have lower value-to-cost ratios, especially for within-region projects. Such results imply that while market value still exists for those links, some of the market value may already have been absorbed by the completed transmission line.",
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+            ]
+        },
+        {
+            "section_name": "Discussion",
+            "section_text": "For transmission, the number of merchant projects that have been built in a decentralized manner to capture the value of spatial arbitrage in U.S. electricity markets is small. For instance, in PJM, the largest electricity market in the U.S., only 1% of its total transmission capacity is made up by merchant lines45,46. This could be because all lines that would be valuable to the system are built centrally through regulated ISO, RTO, or utility planning processes. Alternatively, it could be because of barriers to capturing the value provided to the system and/or to financing and constructing the project. These results suggest the latter: that there is valuable transmission infrastructure not being built in a centralized or decentralized fashion.\n\nWe find that transmission links often have substantial economic value in their ability to increase energy trade and, in turn, reduce congestion. Interregional links (those crossing market or grid seams) are especially valuable and see fairly balanced trade in each direction, emphasizing the broad value of such investments and the importance of interregional planning that jointly accounts for benefits to multiple regions. Further, our scoping-level comparison of transmission infrastructure costs to historical energy market values finds greater value than cost for majority of links, including all cross-interconnect links. At the same time, the limited actual investment in interregional transmission over the last decades suggests that barriers are effectively preventing development of otherwise valuable infrastructure.\n\nMany types of barriers prevent an efficient buildout of transmission. For example, Joskow and Tirole47, discuss how deviations away from perfectly competitive markets can interfere with efficient buildout of merchant transmission. Pfeifenberger et al.19 add discussion on barriers presented by limited, localized transmission planning and the challenge of expanding both the size of the planning region and the types of benefits assessed during planning processes. FERC8 focuses on barriers related to (1) regulatory review, including navigation of processes across different states, (2) limits to the locations at which transmission can be built, and (3) the length of time for new transmission to progress from plan to operation, which can take over a decade. The high value of transmission found in our work serves to highlight the cost of these barriers, that is, the potential net value is equal to missed savings. Each of the above citations discuss possible solutions to and implications of these barriers, including institutional reforms to planning, permitting, and cost allocation procedures.\n\nOur findings also have implications for modelers, investors, planners, and policymakers and may serve to motivate and guide change to the processes through which transmission value is estimated. We find that the market value of transmission is highly influenced by the small fraction of time during which transmission is extremely valuable. In this sense, transmission can be thought of as having insurance value. Peak transmission value periods are primarily driven by events that are unforeseen or mis-forecast ~12\u201336\u2009h before the operating window. Secondary causes include high net load, cold weather, and/or high levels of wind and solar generation. Unforeseen intraday variance can occur due to demand and generation forecast errors, or unexpected outages of generators or transmission infrastructure. For modelers, improving the representation of these four drivers in planning scenarios may help improve performance. There is a wide variety of strategies for assessing these conditions in models. For example, models could benchmark simulated transmission market values against empirical market outcomes both in terms of their average magnitude and distribution of values over time. Additional research is warranted to help refine the types of conditions that have driven high transmission market value in the past, compare the results of the empirical analysis in this paper with power-sector planning models, and to identify the highest priority areas for improvement.\n\nFor investors, historical pricing patterns can help identify areas where additional transmission investment may be warranted. Historical data should be paired with modeling simulations to properly judge cost-value tradeoffs over the expected 30+ year life of new infrastructure. However, many of the conditions that drove past transmission value are likely to persist for years to come, e.g., the benefits of weather, load, and generation diversity across large geographic regions. Historical patterns of transmission value can therefore be a useful complement to model results. For example, both forward looking and historical analysis were used by the United States Department of Energy (DOE) to develop a preliminary list of National Interest Electric Transmission Corridors20,48. These corridors are important because they allow transmission developers access to federal financing and permitting tools. The corridors reflect the key high-level findings in this paper, in that 8 of the 10 corridors are interregional, with 3 of those designed to facilitate trade across interconnections, and further, many of the corridors address high value links identified here.\n\nFor planners and policymakers, several important implications derive from our results beyond the aforementioned model improvements that will have derivative value to planners. First, and most simply, they suggest that barriers have been thwarting otherwise valuable transmission investment and thereby provide a signal to policymakers and planners that more effort is needed to identify and mitigate those barriers. Second, the results highlight where additional planning and policy effort may bear the most fruit. In the United States, recently finalized federal regulations have focused on generator interconnection to local transmission networks and within-region transmission planning (refs. 49,50). As has been noted by others (e.g., ref. 51), and as supported by our analysis, a critical next step is to address barriers to interregional and cross-interconnection transmission. Finally, among these barriers has been the perception that such investments primarily benefit consumers in one region at the expense of consumers in the other. On the contrary, the results presented here indicate that in many cases the benefits are bi-directional, and even more balanced for cross-interconnection and interregional lines. Such a finding should further motivate planners and policymakers to overcome the hurdles to new transmission investment.",
+            "section_image": []
+        },
+        {
+            "section_name": "Methods",
+            "section_text": "In electricity markets that employ spatially-differentiated marginal pricing (i.e., locational and, to some extent, zonal pricing), prices signal where investment is needed in the system. High prices incentivize the deployment of lower-cost generation resources and energy efficiency measures. Large variations in prices over time at the same node provide incentives for demand response and energy storage investments. Concurrent price differences between nodes indicate network congestion and signal that additional transmission capacity would be valuable. A price difference between two nodes could be caused by congestion exclusively on a line directly connecting them, but it typically is the result of simultaneous limits on multiple pieces of transmission infrastructure. These market signals of transmission value are the focus of this paper. While markets with a single market clearing price (e.g., Germany) provide location-agnostic signals for some of these investment types and indicators of transmission value may be visible to system operators (e.g., as shadow prices in optimal dispatch models), the presence of market-facing signals reflecting the value of specific transmission capacity is unique to markets with spatially-differentiated marginal pricing (e.g., the liberalized electricity markets in the U.S.: CAISO, ERCOT, ISO-NE, MISO, NYISO, PJM, SPP)52.\n\nThis study utilizes wholesale locational marginal price differences as a market signal for the value of additional transmission between two locations. The following equation defines the transmission market value quantity used throughout the paper,\n\nEquation\u00a01: Definition of the mean marginal transmission market value between two nodes from time t\u2009=\u20091 to time t\u2009=\u2009n.\n\nwhere \\(n\\) is the number of hours under consideration, the market price at node \\(X\\) during hour \\(h\\) is denoted \\({{{\\rm{pric}}}}{{{{\\rm{e}}}}}_{h}^{X}\\), and \\(\\left|\\cdot \\right|\\) is the absolute value operator. The marginal transmission market value at a fixed time (i.e., \\(\\left|{{{\\rm{pric}}}}{{{{\\rm{e}}}}}_{h}^{A}-{{{\\rm{pric}}}}{{{{\\rm{e}}}}}_{h}^{B}\\right|\\)) is sometimes referred to as the locational spot price of transmission53.\n\nThese are real economic signals, but they are distinct from other measures of transmission\u2019s economic impact to the system and should be interpreted with care. One interpretation is that the mean marginal day-ahead transmission market value between nodes A and B is equivalent to the average hourly payment from holding two financial transmission right (FTR) options of equal size over the entire study period: one from A to B and one from B to A. FTR options are financial instruments that pay the LMP difference between two nodes if that difference is positive28. Another interpretation is that, if a link were an existing transmission line, the average congestion (i.e., shadow) price of the line\u2019s transmission constraint would equal the link\u2019s mean marginal transmission market value.\n\nIf a new transmission line were to have been built by 2012 between two nodes linked in this study (hypothetically), the mean marginal transmission market value multiplied by the number of hours is the marginal impact of the line on the total cost of energy bought by loads. The total change in energy costs for a static market is\u00a0at most\u00a0the line\u2019s marginal impact multiplied by its rated capacity for several reasons, including: (1) The transmission market value is marginal. That is, the absolute nodal price difference with the line is typically less than the price difference without the line and so, while the first unit of incremental transmission reduces costs at the rate of the transmission market value, the line as a whole impacts energy costs at a lower rate due to saturation effects. This is addressed in the next section. (2) The line may not be fully utilized even when there is congestion due to security constraints and power flow dynamics. The latter refers to the fact that the path of power flow on alternating current (AC) networks cannot be arbitrarily prescribed, because the electricity flows across transmission facilities according to Kirchoff\u2019s Laws based on the power consumption of loads and the voltage magnitude and real power injection established by generators. While direct current (DC) lines offer greater control over power flows, the surrounding AC system dynamics could still limit utilization. (3) Transmission expansion can further lower energy costs by increasing supply-side competition, reducing the ability of generators to exert market power31,32,43. On the other hand, while the marginal market value reflects elements of transmission\u2019s system value (e.g., savings to electricity production costs and the costs of ensuring reliability) it does not fully capture all benefits (e.g., impacts on generation capacity sharing, reduction in unpriced or mispriced emissions) and it includes generator rents, a reduction in which is not necessarily a net economic benefit but rather a redistribution. Further, there are dynamic impacts of transmission expansion on generator entry and30 found that \u201cignoring this dynamic effect (\u2026) would substantially understate the benefits of transmission investments.\u201d Therefore, a link\u2019s empirical marginal market value cannot be treated as a direct measure of, or strict upper or lower bound on, the total economic impact of expanded transmission capacity along the link. Still, we contend that market outcomes are a meaningful tool for measuring transmission value because concurrent price differences between market nodes indicate network congestion and serve as an investment signal to market actors and because empirical prices precisely reflect actual system conditions and market participant behavior.\n\nIn our empirical analysis, the prices used are the observed market prices as established by the corresponding Independent System Operator (ISO), Regional Transmission Operator (RTO), or energy imbalance market. Real-time prices (averaged within each hour) are used as the default, since they most closely reflect the actual operating conditions of the system. Day-ahead prices are also used selectively as a point of comparison, and values based on day-ahead prices are clearly labeled as such. All results dependent on day-ahead prices exclude links connected to the non-ISO West, as the Western Energy Imbalance Market did not operate a day-ahead market over this period.\n\nThe locational spot price of transmission is the value of the first increment of additional transmission capacity. As more energy is transferred, the prices on either side of the link will begin to converge and may equalize, if there is sufficient transfer capacity. In this paper, we estimate the effect of such price convergence and the depth of markets on transmission value for each link individually. That is, we only consider the change in prices for two nodes at a time, and we assume each link is the only transfer capacity addition when analyzing it. We do not consider a case where the capacities of all, or a group of several, analyzed links are expanded simultaneously.\n\nTo account for the impact of market depth on transmission value, we first computed supply curve functions representing the relationship between regional net load and market price at each node over each bi-monthly (i.e., 1st\u201315th and 16th-end of month) period during the study horizon. Robust polynomial regression with shape constraints was used to find the best-fit cubic function that is non-decreasing on its domain, where best-fit is defined according to the Huber loss54. Each function\u2019s domain was defined as the range of net load values during the period extended in both directions by 10% of this range to allow for some extrapolation without encountering negative slopes. Huber loss uses the squared loss for samples with smaller residuals and the absolute loss for samples with larger residuals, making the model robust to outliers without ignoring their effect. The choice of period length and polynomial order was informed by ref. 44. Our Python implementation of this method was based on ref. 55. Demand is modeled as perfectly inelastic, because demand responsiveness is already reflected in the observations and therefore captured as a supply resource in the fitted supply curves.\n\nSecond, we screened the fitted supply curves to identify which models represent the data sufficiently well and which models produce large-magnitude residuals for a substantial share of the hours. Algorithm 2 in the Supplementary Information details this screening procedure. To summarize Supplementary Algorithm 2, we define an adaptive tolerance level for residuals in each bi-monthly period and a model passes the screening if at least two-thirds of the hours during the period are within the tolerance level. The tolerance level is always at least $25/MWh and can be greater during periods of high price volatility, as determined by the median absolute deviation from the median price. Models that fail to pass the screening, such as the one depicted in Supplementary Fig.\u00a08, are not used to estimate transmission value. For the 5256 total node-period supply curve models computed for the comparison of transmission value to cost, 99.8% passed the screening and at most 2 failed per node.\n\nThird, the supply curve models and hourly data are analyzed for each link to establish hourly transmission value estimates. Here, we will describe the general methodology. In the Supplementary Information, Algorithm 1 details the complete procedure and Fig.\u00a09 visualizes this methodology with several examples. For most link-hours \u2013 those with a model that passed the screening and a residual magnitude within the tolerance level described above on both ends of the link\u2014a single value estimate is found. It is rare that the (net load, price) observation for an hour falls directly on the supply curve, since the model represents the best fit over ~360 observations. The true market might behave similarly to the model at the observed net load or to the model at the observed price. So, the value estimate assumes prices at each node change at rates determined by the shape of each demand curve at the midpoint between these two points, i.e., the observed net load and the net load that the model predicts would produce the observed price. The difference between these two supply curve translations (e.g., the yellow curves in the left and center panels of Supplementary Fig.\u00a09a,b) forms a transmission demand curve, and the area under this transmission demand curve yet above the horizonal axis between zero and the additional transmission capacity is the transmission value estimate. (This area is shaded in the right panels Supplementary Fig.\u00a09a,b). If a node-hour has a successfully screened model but a large residual, we use two approaches to produce two estimates (see Supplementary Fig.\u00a09c). The first approach simply uses a vertical translation of the supply curve; it assumes prices change as the model predicts around the observed net load. The second approach is more complex and assumes prices will change quickly with small changes in net load due to transmission. How quickly prices change is node-specific and determined using the steepest slopes found across all of the node\u2019s fitted models (excluding those that failed screening) on their observed net load domains, as detailed in Supplementary Algorithm 3. These are the steepest slopes across 264 models, for a node whose study period is 2012\u20132022. Finally, when a node-hour corresponds to a model that failed screening, we use only the latter, \u201csteepest slope,\u201d method. This should produce a conservative value estimate in most hours because, typically, most hours in a 15-day period are on a relatively flat portion of the supply curve. Finally, any link-hours where prices are at or above the price cap for each node are treated as supply-constrained and assumed to have no trade on additional transmission capacity. Hourly value estimates for each link are aggregated into a lower estimate that is the sum of all singular hourly estimates plus the lower estimate when there are two estimates and a higher estimate that is the sum of all singular hourly estimates plus the higher estimate when there are two estimates.\n\nWe analyze several environmental and market conditions that affect transmission value. Each of these conditions is defined based on a combination of measurements and criteria, as defined in Table\u00a02. The unforeseen intraday variation criteria were designed to reflect large day-ahead-real-time price spreads while capturing a similar amount of time as the high net load, cold weather, and high renewable generation drivers. If a condition is present at one or both of a link\u2019s terminal nodes at a given time, we consider the condition to be present for the link.\n\nA survey of large transmission project costs was taken from refs. 56, 57. See Table\u00a01 for details of the projects and corresponding cost estimates. These sources provide both a total cost estimate for construction of the lines (converted to 2022 dollars with the Bureau of Economic Analysis price deflators) as well as the total transfer capacity of the lines (in MW). However, they ignore operational costs for managing transmission lines. We apply the below equation to convert these capital cost estimates to annualized values to facilitate comparison to our transmission market value estimates.\n\nWhere\n\nC = capital cost of transmission investment ($2022)\n\nr = real interest rate (%)\n\nn = transmission asset lifetime (years)\n\nK = incremental capacity of transmission infrastructure (MW)\n\nSimilar to ref. 56, we assume either a 60- or 30-year transmission line lifetime and a 4.44% real interest rate based on a 55/45 debt to equity ratio, 3.6% debt cost, 11.3% ROE, 26% tax rate, and 2% inflation rate. There is uncertainty in the transmission costs identified here, especially for projects that have only been proposed and not completed, as they may incur cost overruns, not represent the full all-in project cost, or not reflect differences in construction schedules.\n\nFinally, we select a specific link from our market value analysis to correspond, as best as possible, with the geographic scope of the actual transmission line path. To perform this linkage, we compare the key market hubs used in our market value analysis to the planned electric linkages created by our actual transmission projects. This process is typically straightforward for cross-interconnect and interregional lines, where transmission projects will explicitly state their plan to electrically link two distinct market regions, oftentimes with HVDC transmission technology. This process is less straightforward for within-region lines, where the inherent nature of the AC connection makes it more difficult to assess transfer capability of new lines.\n\nEach pair of nodes analyzed is referred to as a link. 70 hypothetical transmission links are considered; 30 links are contained within a balancing authority (\u201cwithin-region\u201d) and 40 links are interregional. Over 75% of pricing nodes at which links terminate are hub, zonal, or aggregate nodes that reflect the price signal for a group of buses in the same geographic area. Each of the remaining nodes is either a load, generator, tie generator, interface, or external node. The non-ISO Southeast nodes are of the latter two types as reported by MISO and PJM. Prices in the non-ISO West are Western Energy Imbalance Market prices reported by CAISO. Links between pairs of these nodes were established based on geographic relevance (e.g., a direct link between Arizona and Massachusetts was not included). Note that markets occasionally change their price node definitions over time. When the 2022 node does not exist for a given year, the geographically closest node of a similar type in the same balancing authority is used, if one exists. There are six nodes that experience a definition update during the study period.\n\nThe study period is 2012\u20132022 with the following exceptions: links involving SPP are 2015\u20132022 and the Pacific Northwest (PNW) link is also 2015\u20132022. All links have hourly real-time price data available for at least 90% of hours in each studied year and over 99% of studied link-years have at least 98% of data available.\n\nFurther information on research design is available in the\u00a0Nature Portfolio Reporting Summary linked to this article.",
+            "section_image": []
+        },
+        {
+            "section_name": "Data availability",
+            "section_text": "We purchased data on market prices, load, renewable generation and weather from a commercial vendor; the product is called Velocity Suite, by Hitachi. This information is also publicly available.",
+            "section_image": []
+        },
+        {
+            "section_name": "References",
+            "section_text": "Goggin, M. \u201cTransmission Makes The Power System Resilient to Extreme Weather,\u201d Grid Strategies, LLC; American Council on Renewable Energy, Jul. 2021. [Online]. Available: https://gridprogress.files.wordpress.com/2021/11/transmission-makes-the-power-system-resilient-to-extreme-weather.pdf.\n\nGoggin, M. & Zimmerman, Z. \u201cThe Value of Transmission During Winter Storm Elliott,\u201d Grid Strategies, LLC; American Council on Renewable Energy, Feb. 2023. [Online]. Available: https://acore.org/wp-content/uploads/2023/02/The-Value-of-Transmission-During-Winter-Storm-Elliott-ACORE.pdf.\n\n\u201cGrids, the missing link - An EU Action Plan for Grids.\u201d Nov. 28, 2023. Accessed: Jan. 25, 2024. [Online]. Available: https://eur-lex.europa.eu/legal-content/EN/TXT/?uri=COM%3A2023%3A757%3AFIN&qid=1701167355682.\n\nDimopoulos, G., Heussaff, C. & Zachmann, G. \u201cThe massive value of European Union cross-border electricity transmission,\u201d Bruegel. Accessed: Jan. 25, 2024. [Online]. Available: https://www.bruegel.org/analysis/massive-value-european-union-cross-border-electricity-transmission.\n\n\u201cChina\u2019s State Grid to Keep Spending High to Match Renewables,\u201d Bloomberg.com, Jan. 14, 2024. Accessed: Jan. 26, 2024. [Online]. Available: https://www.bloomberg.com/news/articles/2024-01-15/china-s-state-grid-to-keep-spending-high-to-match-renewables.\n\nCohen, J., Moeltner, K., Reichl, J. & Schmidthaler, M. An empirical analysis of local opposition to new transmission lines across the EU-27. Energy J. 37, 59\u201382 (2016).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKamp, J. \u201cMaine Voters Reject $950 Million Power Line for Hydro Imports; Backers of project claim ballot vote was unconstitutional, and the builder plans a legal challenge,\u201d Wall Street Journal (Online), New York, N.Y., Nov, (2021). [Online]. Available: https://www.proquest.com/newspapers/maine-voters-reject-950-million-power-line-hydro/docview/2592305953/se-2?accountid=14496.\n\nStaff of the Federal Energy Regulatory Commission, \u201cReport on Barriers And Opportunities For High Voltage Transmission: A Report To The Committees on Appropriations of Both Houses of Congress Pursuant to the 2020 Further Consolidated Appropriations Act,\u201d Jun. 2020. [Online]. Available: https://www.congress.gov/116/meeting/house/111020/documents/HHRG-116-II06-20200922-SD003.pdf.\n\nCaspary, J., Goggin, M., Gramlich, R., & Selker, J. \u201cFewer New Miles: The US Transmission Grid in the 2010s,\u201d Grid Strategies, LLC. [Online]. Available: https://gridprogress.files.wordpress.com/2022/08/grid-strategies_fewer-new-miles.pdf.\n\nInternational Energy Agency. Electricity Grids and Secure Energy Transitions: Enhancing the Foundations of Resilient, Sustainable and Affordable Power Systems (OECD, 2023). https://doi.org/10.1787/455dd4fb-en.\n\nCole, W. et al. How much might it cost to decarbonize the power sector? It depends on the metric. Energy 276, 127608 (2023). https://doi.org/10.1016/j.energy.2023.127608.\n\nBrown, P. R. & Botterud, A. The value of inter-regional coordination and transmission in decarbonizing the US electricity system. Joule 5, 115\u2013134 (2021).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nAccelerating Decarbonization in the United States: Technology, Policy, and Societal Dimensions (Washington, D.C., National Academies Press, 2023). https://doi.org/10.17226/25931.\n\nFederal Energy Regulatory Commission, \u201cBuilding for the Future Through Electric Regional Transmission Planning and Cost Allocation and Generator Interconnection.\u201d Apr, (2022). [Online]. Available: https://www.ferc.gov/media/rm21-17-000.\n\nPatrick, T. McHenry, Fiscal Responsibility Act of 2023. (2023). [Online]. Available: https://www.congress.gov/bill/118th-congress/house-bill/3746/summary/00.\n\nPeters S. & Hickenlooper, J. Building Integrated Grids With Inter-Regional Energy Supply (BIG WIRES) Act. [Online]. Available: https://www.hickenlooper.senate.gov/wp-content/uploads/2023/09/PAT23814.pdf.\n\nRegulation (EU) 2018/1999 of 11 December 2018 on the Governance of the Energy Union and Climate Action. (2018). https://doi.org/10.5040/9781782258674.\n\nVan Horn, K., Pfeifenberger, J. & Ruiz, P. \u201cThe value of diversifying uncertain renewable generation through the transmission system,\u201d Boston University Institute for Sustainable Energy, Sep. (2020). [Online]. Available: https://hdl.handle.net/2144/41451.\n\nPfeifenberger, J. et al. Transmission Planning for the 21st Century: Proven Practices that Increase Value and Reduce Costs. Brattle Group, Oct. (2021). [Online]. Available: https://www.brattle.com/wp-content/uploads/2021/10/2021-10-12-Brattle-GridStrategies-Transmission-Planning-Report_v2.pdf.\n\nUnited States Department of Energy. National Transmission Needs Study, Oct. (2023). [Online]. Available: https://www.energy.gov/sites/default/files/2023-12/National%20Transmission%20Needs%20Study%20-%20Final_2023.12.1.pdf.\n\nStenclik, D. & Deyoe, R. Multi-value transmission planning for a clean energy future. Energy Systems Integration Group, Reston, VA, Jun. (2022). [Online]. Available: https://www.esig.energy/multi-value-transmission-planning-report.\n\nMISO (Midcontinent Independent System Operator). LRTP Tranche 1 Portfolio Detailed Business Case, presented at the LRTP Workshop, Mar. (2022). [Online]. Available: https://cdn.misoenergy.org/20220329%20LRTP%20Workshop%20Item%2002%20Detailed%20Business%20Case623671.pdf.\n\nPfeifenberger, J., Chang, J., & Sheilendranath, A. Toward more effective transmission planning: addressing the costs and risks of an insufficiently flexible electricity grid. WIRES, Apr. 2015. Accessed: Jan. 12, 2024. [Online]. Available: https://www.brattle.com/insights-events/publications/toward-more-effective-transmission-planning-addressing-the-costs-and-risks-of-an-insufficiently-flexible-electricity-grid/.\n\nHaugen, M. et al. Power market models for the clean energy transition: state-of-the-art and future research needs. Appl. Energy 357, 122495 (2024).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nHirth, L. The market value of variable renewables: the effect of solar wind power variability on their relative price. Energy Econ. 38, 218\u2013236 (2013).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMillstein, D. et al. Solar and wind grid system value in the United States: the effect of transmission congestion, generation profiles, and curtailment. Joule 5, 1749\u20131775 (2021).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nCallaway, D. S., Fowlie, M. & McCormick, G. Location, location, location: the variable value of renewable energy and demand-side efficiency resources. J. Assoc. Environ. Resour. Econ. 5, 39\u201375 (2018).\n\n\n                    Google Scholar\u00a0\n                \n\nDoshi, G. & Du, X. iaodong Transmission integration and the market for congestion revenue rights. Energy J. 42, 247\u2013281 (2021).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLaRiviere, J. & Lyu, X. Transmission constraints, intermittent renewables and welfare. J. Environ. Econ. Manag. 112, 102618 (2022).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nGonzales, L. E., Ito, K. & Reguant, M. The dynamic impact of market integration: evidence from renewable energy expansion in Chile. Natl. Bur. Econ. Res. 30016 https://doi.org/10.3386/w30016 (2022).\n\nWolak, F. A. Measuring the competitiveness benefits of a transmission investment policy: the case of the Alberta electricity market. Energy Policy 85, 426\u2013444 (2015).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWoerman, M. Market size and market power: evidence from the Texas electricity market. (2023). [Online]. Available: https://drive.google.com/file/d/1ZnxPR14WoXYoUDB4HplsFlM5-YkXlvRj/view.\n\n\u201c2022 Annual Report On Market Issues & Performance,\u201d California ISO, Jul. (2023). [Online]. Available: http://www.caiso.com/Documents/2022-Annual-Report-on-Market-Issues-and-Performance-Jul-11-2023.pdf.\n\n\u201c2022 State of the Market Report for PJM. Volume 2: Detailed Analysis,\u201d Monitoring Analytics, LLC, Mar. (2023). [Online]. Available: https://www.monitoringanalytics.com/reports/PJM_State_of_the_Market/2022/2022-som-pjm-vol2.pdf.\n\n\u201cState of the Market 2022,\u201d Southwest Power Pool Market Monitoring Unit, May (2023). [Online]. Available: https://www.spp.org/documents/69330/2022%20annual%20state%20of%20the%20market%20report.pdf.\n\nMillstein, D. et al. Empirical Estimates of Transmission Value using Locational Marginal Prices. Aug. 2022, Accessed: Oct. (2024). [Online]. Available: https://escholarship.org/uc/item/5s42s6t7.\n\nMillstein, D., Wiser, R. H., Jeong, S., Kemp, J. M. The Latest Market Data Show that the Potential Savings of New Electric Transmission was Higher Last Year than at Any Point in the Last Decade. Feb. 2023, Accessed: Oct. (2024). [Online]. Available: https://escholarship.org/uc/item/4sq3x22k.\n\nMillstein, D., Kemp, J. M., Gorman, W., Wiser, R. Transmission value in 2023: Market data shows the value of transmission remained high in certain locations despite overall low wholesale electricity prices. Jul. (2024), Accessed: Oct. 10, 2024. [Online]. Available: https://escholarship.org/uc/item/7rp5t6q6.\n\nJoskow, P. L. Facilitating transmission expansion to support efficient decarbonization of the electricity sector. Econ. Energy Environ. Policy 10, https://doi.org/10.5547/2160-5890.10.2.pjos (2021).\n\n\u201cTransmission,\u201d ISO New England. Accessed: Oct. 04, 2024. [Online]. Available: https://www.iso-ne.com/about/key-stats/transmission.\n\nDavis, L. W., Hausman, C. & Rose, N. L. Transmission impossible? Prospects for Decarbonizing the US Grid. Natl. Bur. Econ. Res. 31377 https://doi.org/10.3386/w31377 (2023).\n\nHausman, C. Power flows: transmission lines and corporate profits. Natl. Bur. Econ. Res. 32091 (2024). https://doi.org/10.3386/w32091.\n\nRyan, N. The competitive effects of transmission infrastructure in the Indian electricity market. Am. Econ. J. Microecon. 13, 202\u2013242 (2021).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nJenkin, T. J., Larson, A., Ruth, M. F., King, B., & Spitsen, P. The use of statistically based rolling supply curves for electricity market analysis: a preliminary look. Natl. Renew. Energy Lab. (NREL), Golden, CO (United States), NREL/TP-6A20-70954, Mar. (2018). https://doi.org/10.2172/1430827.\n\nRobertson, M. & Palmer, K. Transmission 102: Building New Transmission Lines,\u201d Resources for the Future. Accessed: Oct. 04, 2024. [Online]. Available: https://www.rff.org/publications/explainers/transmission-102-building-new-transmission-lines/.\n\nPJM - Merchant Transmission Facilities. pjm. Accessed: Oct. 04, 2024. [Online]. Available: https://www.pjm.com/markets-and-operations/etools/oasis/merch-trans-facilities.\n\nJoskow, P. & Tirole, J. Merchant transmission investment. J. Ind. Econ. 53, 233\u2013264 (2005).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nU.S. Department of Energy Grid Deployment Office. Initiation of Phase 2 of National Interest Electric Transmission Corridor (NIETC) Designation Process: Preliminary List of Potential NIETCs. May, (2024).\n\nFederal Energy Regulatory Commission. Order No. 1920: Building for the Future Through Electric Regional Transmission Planning and Cost Allocation. (2024). [Online]. Available: https://www.ferc.gov/media/e1-rm21-17-000.\n\nFederal Energy Regulatory Commission, Order No. 2023: Improvements to Generator Interconnection Procedures and Agreements. (2023). [Online]. Available: https://www.ferc.gov/media/order-no-2023.\n\nAlagappan, L., Moore, J., Joseph, B., Mueller, S., & Olson, A. Collaborative enhancements to unlock interregional transmission. NARUC and E3, Jun. 2024. [Online]. Available: https://pubs.naruc.org/pub/BACDBB9D-02BF-0090-0109-B51B36B74439.\n\nStaudt, P. & Oren, S. S. Merchant transmission in single-price electricity markets with cost-based redispatch. Energy Econ. 104, 105610 (2021).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nHogan, W. W. Electricity Market Design: Price Formation,\u201d presented at the International Workshop on Electricity Sector Modernization, Brasilia, Brazil, Sep. 04, 2019. [Online]. Available: https://www.gov.br/mme/pt-br/arquivos/7-hogan-brasilia-price-formation-090419.pdf.\n\nHuber, P. J. Robust estimation of a location parameter. Ann. Math. Stat. 35, 73\u2013101 (1964).\n\nArticle\u00a0\n    MathSciNet\u00a0\n    MATH\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nSchmitz, D. \u201cPolyfit.\u201d Nov. 20, 2021. Accessed: Oct. 17, 2023. [Online]. Available: https://github.com/dschmitz89/Polyfit.\n\nGorman, W., Mills, A., & Wiser, R. Improving estimates of transmission capital costs for utility-scale wind and solar projects to inform renewable energy policy. Energy Policy 135, 110994 (2019). https://doi.org/10.1016/j.enpol.2019.110994.\n\nZimmerman, Z., Goggin, M., Gramlich, R. Transmission Projects Ready to Go,\u201d Grid Strategies for Americans for a Clean Energy Grid, Sep. 2023. Accessed: Jan. 18, (2024). [Online]. Available: https://cleanenergygrid.org/portfolio/transmission-projects-ready-to-go-2023/.\n\nDegree-days - U.S. Energy Information Administration (EIA).\u201d Accessed: Jan. 25, 2024. [Online]. Available: https://www.eia.gov/energyexplained/units-and-calculators/degree-days.php.\n\nDownload references",
+            "section_image": []
+        },
+        {
+            "section_name": "Acknowledgements",
+            "section_text": "This material is based upon work supported by the U.S. Department of Energy\u2019s Office of Energy Efficiency and Renewable Energy (EERE) under Lawrence Berkeley National Laboratory Contract No. DE-AC02-05CH11231. The authors thank Patrick Gilman and Gage Reber of the Wind Energy Technologies Office and Paul Spitsen of the Strategic Analysis Team for supporting this work. The US Government retains, and the publisher, by accepting the article for publication, acknowledges, that the US Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for US Government purposes.",
+            "section_image": []
+        },
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+            "section_name": "Author information",
+            "section_text": "Lawrence Berkeley National Laboratory, Berkeley, CA, USA\n\nJulie Mulvaney Kemp,\u00a0Dev Millstein,\u00a0Will Gorman,\u00a0Seongeun Jeong\u00a0&\u00a0Ryan Wiser\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nJulie Mulvaney Kemp: Methodology, Software, Formal Analysis, Writing \u2013 Original Draft, Review & Editing, Visualization; Dev Millstein: conceptualization, writing - review & editing, funding acquisition, supervision; Will Gorman: data curation, formal analysis, writing - original draft; Seongeun Jeong: data curation, visualization; Ryan Wiser: writing - review & editing, funding acquisition.\n\nCorrespondence to\n                Julie Mulvaney Kemp.",
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+            "section_text": "Nature Communications thanks Audun Botterund, Paul Joskow and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. A peer review file is available.",
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+        {
+            "section_name": "About this article",
+            "section_text": "Kemp, J.M., Millstein, D., Gorman, W. et al. Electric transmission value and its drivers in United States power markets.\n                    Nat Commun 16, 8055 (2025). https://doi.org/10.1038/s41467-025-63143-5\n\nDownload citation\n\nReceived: 19 March 2024\n\nAccepted: 08 August 2025\n\nPublished: 28 August 2025\n\nVersion of record: 28 August 2025\n\nDOI: https://doi.org/10.1038/s41467-025-63143-5\n\nAnyone you share the following link with will be able to read this content:\n\nSorry, a shareable link is not currently available for this article.\n\n\n\n\n                            Provided by the Springer Nature SharedIt content-sharing initiative\n                        ",
+            "section_image": [
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1b241a020ab52e2d1f7b7f61afee2f55b88ee62e2b3e58a8dee0df770f9607af/metadata.json

@@ -0,0 +1,157 @@
+{
+    "title": "Many plants naturalized as aliens abroad have also become more common within their native regions",
+    "pre_title": "Plants that have naturalized as aliens abroad have also become more common at home during the Anthropocene",
+    "journal": "Nature Communications",
+    "published": "05 September 2025",
+    "supplementary_0": [
+        {
+            "label": "Supplementary Information",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-63293-6/MediaObjects/41467_2025_63293_MOESM1_ESM.pdf"
+        },
+        {
+            "label": "Reporting Summary",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-63293-6/MediaObjects/41467_2025_63293_MOESM2_ESM.pdf"
+        },
+        {
+            "label": "Transparent Peer review file",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-63293-6/MediaObjects/41467_2025_63293_MOESM3_ESM.pdf"
+        }
+    ],
+    "supplementary_1": [
+        {
+            "label": "Source data",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-63293-6/MediaObjects/41467_2025_63293_MOESM4_ESM.xlsx"
+        }
+    ],
+    "supplementary_2": NaN,
+    "source_data": [
+        "https://doi.org/10.6084/m9.figshare.25487209",
+        "/articles/s41467-025-63293-6#ref-CR73",
+        "/articles/s41467-025-63293-6#Sec17"
+    ],
+    "code": [
+        "https://doi.org/10.24433/CO.1618280.v1",
+        "https://doi.org/10.6084/m9.figshare.25487209",
+        "/articles/s41467-025-63293-6#ref-CR73"
+    ],
+    "subject": [
+        "Biogeography",
+        "Invasive species",
+        "Macroecology"
+    ],
+    "license": "http://creativecommons.org/licenses/by/4.0/",
+    "preprint_pdf": "https://www.researchsquare.com/article/rs-4177196/v1.pdf?c=1757156746000",
+    "research_square_link": "https://www.researchsquare.com//article/rs-4177196/v1",
+    "nature_pdf": "https://www.nature.com/articles/s41467-025-63293-6.pdf",
+    "preprint_posted": "09 Apr, 2024",
+    "research_square_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Changes in species' native range size and occupancy have been dramatically accelerated by anthropogenic pressures in the last centuries. At the same time humans have introduced thousands of species beyond their historic range limits, and some of these have established self-sustaining populations (i.e. become naturalized). It is known that particularly common plant species have become naturalized, but how dynamics in native distributions relate to global naturalization is unknown. We retrieved data on grid-cell occupancy of native vascular plant species for 10 European regions, for at least two periods, to calculate for each species an occupancy-change index. For nine of the ten regions, we found a significant increase in global naturalization with both the early period occupancy and occupancy-change index. This finding shows that many of the plant species expanding globally as naturalized aliens are also expanding within their native ranges and suggests that the same drivers underlie both processes.Biological sciences/Ecology/Invasive speciesBiological sciences/Ecology/Macroecologydeclining speciesexpanding speciesEuropean native rangeglobal naturalizationnaturalization extent",
+            "section_image": []
+        },
+        {
+            "section_name": "Additional Declarations",
+            "section_text": "There is NO Competing Interest.",
+            "section_image": []
+        },
+        {
+            "section_name": "Supplementary Files",
+            "section_text": "SupplementaryinformationPaudeletal.pdfPlants that have naturalized as aliens abroad have also become more common at home during the Anthropocene",
+            "section_image": []
+        }
+    ],
+    "nature_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Due to anthropogenic pressure some species have declined whereas others have increased within their native ranges. Simultaneously, many species introduced by humans have established self-sustaining populations elsewhere (i.e. have become naturalized aliens). Previous studies have shown that particularly plant species that are common within their native range have become naturalized elsewhere. However, how changes in native distributions correlate with naturalization elsewhere is unknown. We compare data on grid-cell occupancy of native vascular plant species over time for 10 European regions (countries or parts thereof). For nine regions, both early occupancy and occupancy change correlate positively with global naturalization success (quantified as naturalization in any administrative region and as the number of such regions). In other words, many plant species spreading globally as naturalized aliens are also expanding within their native regions. This implies that integrating data on native occupancy dynamics in invasion\u00a0risk assessments might help prevent new invasions.",
+            "section_image": []
+        },
+        {
+            "section_name": "Introduction",
+            "section_text": "Natural processes such as tectonic upheavals and glaciations or evolutionary innovations have driven dynamics in species distributions throughout the history of life1,2. In the last centuries, however, and particularly since the start of the Anthropocene in the mid-20th century3, human pressures, such as land-use change, habitat fragmentation and eutrophication, have accelerated these dynamics dramatically4. In particular, human pressures have caused rapid declines in populations and range sizes of many native species5, resulting in drastic declines in occupancy (i.e., the number of locations of occurrence) in many regions where those species are native e.g.6,7,8. However, while many species are in decline, and c. 25% of assessed animal and plant species are threatened with extinction4, there are also species that benefit from the rapid changes occurring during the Anthropocene and are on the rise9.\n\nData on temporal changes in regional occupancy for large numbers of species are still relatively rare and restricted to European regions. Nevertheless, the few studies that have analyzed such data consistently show that native species with increasing occupancy are typically tall, habitat generalists, classified as competitors in Grime\u2019s CSR-strategy framework, and with high values of the Ellenberg indicator for nitrogen6,10,11,12. This corroborates the idea that these species have benefited from anthropogenic environmental changes, such as atmospheric nitrogen deposition6 and the creation of novel anthropogenic habitats13 within their native ranges.\n\nConcurrent with anthropogenic changes to the environment, humans have intentionally and unintentionally transported many species from their native ranges across major geographical barriers to new regions14. Though most of these introduced alien species have failed to establish self-sustaining populations outside captivity or cultivation, a small percentage have succeeded in becoming naturalized, occasionally in hundreds of regions (e.g., countries, states and provinces) around the globe15,16,17. Among the vascular plants, more than 16,000 species have already become naturalized somewhere on Earth18, provisionally accepted]. Most of these naturalizations happened after the 1950s, i.e., during the Anthropocene19, and predominantly in habitats with high levels of anthropogenic disturbances e.g.20. Previous analyses of the characteristics of naturalized plants or the subset of invasive alien plants (i.e., naturalized plants that have spread rapidly and frequently have ecological and/or socio-economic impacts) have shown that they are typically tall, habitat generalists, classified as competitors in Grime\u2019s CSR-strategy framework, and with high values of the Ellenberg indicator for nitrogen e.g.12,21,22,23,24,25. \u2014 just like the species that are increasing within their native ranges26,27. However, whether species that have increased their occupancy in regions of their native range and species that have become naturalized elsewhere are largely the same species has never been tested explicitly. If this is the case, it would imply that information on native occupancy dynamics could inform invasion\u00a0risk assessments.\n\nUltimately, occupancy dynamics of species, both within and outside their native range, are likely to depend on intrinsic features of the species. Unfortunately, despite the many studies that have measured plant functional traits, for most traits, data are available only for a small proportion of the global flora28. A notable exception is woodiness, which is indicative of both growth form (i.e., woody species are usually shrubs or trees) and habitat affiliation (i.e., woody species typically occur in forests and other closed habitats). On the one hand, the tall stature of woody species allows them to have greater dispersal capacities and a higher competitive dominance, which could facilitate range expansion in both native and non-native regions. However, despite these potential advantages, woody species generally have a lower probability of naturalization than non-woody species29. This may be because woody plants usually are less successful in frequently disturbed habitats, and because they have longer generation times and therefore require more time to become naturalized and to spread after introduction30,31. So, species features, such as woodiness, might mediate the relationship between global naturalization success and occupancy dynamics in the native range.\n\nIt has been suggested that extinction risk of native species and invasion success of alien species might represent two sides of the same coin32. Jeschke and Strayer33 did not find this to be the case for birds and freshwater fish. However, this concept not yet been assessed in plants. The findings that naturalized plants and those spreading in their native range share a common set of traits suggests that it may be the case6,21,22,23,24,25,26,27. Accordingly, numerous studies have shown that common species with large native ranges are more likely to naturalize elsewhere34,35. However, range size is just one dimension of commonness. Other dimensions include habitat breadth and local abundance, as proposed by Rabinowitz36, and occupancy, as recently proposed by Crisfield et al.37. These different dimensions of commonness are frequently positively correlated38,39, and some studies have shown that regional occupancy in the native range correlates positively with naturalization success elsewhere21,22,25. However, in addition to these static measures of commonness, the change in occupancy over time could be considered a further dimension, similar to spread rate, which has been proposed as one of the dimensions of invasiveness for alien species40. If species that increase their occupancy within their native range over time are largely the same species that spread as naturalized aliens elsewhere, this would suggest that similar mechanisms may underlie both processes.\n\nHere, we test the hypothesis that the plant species that have become widely naturalized across the globe are also increasing in occupancy (i.e., in the proportion of grid cells in which they have been recorded) within their native regions. To test this hypothesis, one would ideally have time series data of grid-cell occupancies for the entire native range of the species. However, as such data is not available, we instead retrieve data on grid-cell occupancies of vascular plant species during an early period (i.e., early occupancy) and a later period, each usually covering multiple decades, for 10 regions in Europe (Fig.\u00a01). For each of these 10 native regions, which correspond to countries or parts thereof, we calculate for each native species an occupancy-change index according to Telfer et al.41. This index quantifies the degree to which the change in the proportion of grid cells in which a species has been recorded between the early and later period is higher or lower than expected based on the early\u00a0occupancy41. Consequently, the occupancy-change index is not correlated with early occupancy. We then use hurdle models to analyze how global naturalization success \u2014 a combination of naturalization incidence (i.e. whether or not a species has become naturalized, which is modeled using a Bernoulli distribution) and naturalization extent (i.e. the number of regions where a naturalized species has become naturalized, which is modeled using a zero-truncated negative binomial distribution) \u2014 correlates with occupancy in the early period and the occupancy change within the species\u2019 native regions. Given that the available data for the 10 native regions vary in many aspects (Table\u00a01), the analyses are done for each region separately.\n\nFor these regions, we have information on occupancies of native plant species for an early and a later time period. Polygons were obtained from GADM, the GloNAF database, or were\u00a0created using Google Earth Pro (Data SIO, NOAA, U.S. Navy, NGA, GEBCO; Image Landsat / Copernicus).",
+            "section_image": [
+                "https:////media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41467-025-63293-6/MediaObjects/41467_2025_63293_Fig1_HTML.png"
+            ]
+        },
+        {
+            "section_name": "Results",
+            "section_text": "As we had data on woodiness of all 3920 species in our 10 datasets (see Supplementary Methods for details), we ran hurdle models with and without woodiness of the species as an additional predictor. However, as the results for our two main predictors of interest, occupancy in the early period and occupancy change within the species\u2019 native regions, remained largely the same, we focus here on the models without woodiness. Results for the models with woodiness are provided in Table\u00a0S1 (also see Tables\u00a0S2\u2013S11).\n\nOur hurdle models showed that global naturalization success was associated with occupancy in the early period for all 10 native regions (Table\u00a02 (also see Tables\u00a0S12\u2013S21), Fig.\u00a02). This was true for both the likelihood of being naturalized outside the native range (i.e. for the Bernoulli part of the hurdle model) and for being naturalized in more regions (i.e., for the zero-truncated count part of the hurdle model; Table\u00a02, Fig.\u00a0S1, S2).\n\nThese models combined naturalization incidence (i.e., whether or not a species has become naturalized; Bernoulli distribution) and naturalization extent (i.e., the number of non-native regions where the species has become naturalized; zero-truncated negative binomial distribution). To illustrate how global naturalization success depends on early occupancy in the native region, the data points are colored according to whether they are in the upper, middle or lower third of the early occupancy distribution. Accordingly, the predicted relationships are plotted for early occupancy values set equal to the 5/6th quantile, the median and the 1/6th quantile. Significant relationships between global naturalization success and occupancy change (either for the Bernoulli or zero-truncated count part) are plotted with solid lines, and non-significant relationships are plotted in dashed lines. The regions for which the interaction between early occupancy and occupancy change was significant are marked with an asterisk (*) next to the region names. Source data are provided as a Source Data file.\n\nSpecies with high occupancy-change indices also had a higher likelihood of being naturalized for seven of the 10 native regions and were naturalized in more regions globally for nine of the 10 native regions (Table\u00a02, Fig.\u00a02, Fig.\u00a0S1, S2). The Thi\u00e9rache region was the only region where the occupancy-change index was not significantly associated with any of the two components of global naturalization success (Table\u00a02, Fig.\u00a02j, Fig.\u00a0S1j, S2j). So, overall, our findings indicate that species that have increased in occupancy in their native regions relative to other species with similar early occupancy are also more likely to have become widely naturalized. For three of the 10 native regions (the Czech Republic, the Netherlands and Switzerland), the positive association between global naturalization success (either measured as the likelihood of being naturalized or as being naturalized in more regions) and the occupancy-change index was strongest for species that already had high occupancies in the early period (significant early occupancy \u00d7 occupancy change interactions in Table\u00a02, Fig.\u00a02b, h, i, Fig.\u00a0S1b, h, i, S2h, i). These results thus indicate that recent increases in occupancy within these three native regions are particularly strongly associated with global naturalization success for species that were already common decades ago.",
+            "section_image": [
+                "https:////media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41467-025-63293-6/MediaObjects/41467_2025_63293_Fig2_HTML.png"
+            ]
+        },
+        {
+            "section_name": "Discussion",
+            "section_text": "Our analyses show that global naturalization success is highest not only for species that already had high occupancies in their native European regions decades to centuries ago \u2014when many of them were first introduced to new regions19 \u2014 but also for species that have since then increased in occupancy within their native regions (Table\u00a02). Furthermore, for three of the 10 native regions, the positive association between global naturalization success and the occupancy-change index was particularly pronounced for species that had already a high occupancy in the native region during the early time period (Table\u00a02, Fig.\u00a02b, h, i). Our results thus show that many species that have increased their occupancy within their native regions have also increased their ranges abroad, whereas species that are declining in their native regions are less likely to successfully naturalize elsewhere. This strongly suggests that global naturalization success and the changes of species\u2019 native distributions are driven, at least in part, by similar processes.\n\nSpecies with high occupancies in their native regions decades ago (i.e., in the early period) were more likely to naturalize and to do so in many regions around the globe. This could reflect that such common species were more likely to encountered, transported and introduced elsewhere22,25. It could also reflect that the selective pressures that have made certain species common in their native regions also have preadapted these species for success as invaders. In order to be able to occur at many locations in its native region, a species has to be able to coexist with a variety of biotas and persist in a wide range of climatic and other environmental conditions42. Therefore, species with high occupancies in their native regions are likely to be ecologically versatile, which should also increase the likelihood of naturalization when introduced elsewhere25,43. Furthermore, species that are common in their native regions usually have high dispersal abilities26,44 and are capable of autonomous self-fertilization45, which are characteristics that also facilitate spread within regions where they are not native35,46. For most of the 3920 species in our datasets, information on these traits is not available, so we could not test their importance. However, as woodiness of species is indicative of their growth forms as well as habitat affiliation and is available for all species in our 10 datasets, we ran additional analyses for this variable (see Supplementary Methods for details). While woodiness was not significantly associated with early occupancy in any of the 10 native regions (Table\u00a0S22), it was positively associated with occupancy change in six native regions (Table\u00a0S23). The latter might reflect that many woody species are very long lived and therefore might, in contrast to non-woody species, still occur in grid cells even when the environment is no longer optimal. Inclusion of woodiness in the hurdle models slightly increased the explained variation in global naturalization success (Table\u00a0S24), but did not change the overall conclusions regarding the effects of early occupancy and occupancy change (compare Table\u00a02 and Table\u00a0S1). When woody species did naturalize, they did so in fewer regions than non-woody species, and this was significant for eight of the 10 datasets (Tables\u00a0S1, S2\u2013S11). Similarly, Dong et al.29 recently showed that among introduced plants in China, woody species were less likely to naturalize than non-woody species. Woody species, particularly trees, have longer juvenile periods and/or are probably introduced in lower numbers than non-woody species, and therefore require more time before they spread into multiple regions. Whatever the exact reason, the additional analyses including woodiness indicate that not all of the characteristics associated with species that increase in their native regions are also associated with species that have become widely naturalized globally.\n\nNumerous studies have analyzed how naturalization relates to static measures of commonness in species\u2019 native distributions, such as native range size and grid-cell occupancy e.g.21,34,47. However, we are not aware of any previous study that also considered temporal changes in measures of commonness within native regions. In line with the idea that the drivers of expansion in native regions and naturalization elsewhere should be largely the same, we found that the global naturalization success of species\u2014measured either as naturalization incidence or extent\u2014was positively associated with occupancy change in nine of the 10 native regions for which we had data (Fig.\u00a02). Although these associations were highly significant, and inclusion of occupancy change increased the explained variation in naturalization success (Table\u00a0S24), the standardized effect estimates were always smaller for the occupancy-change index than for occupancy in the early period (Tables\u00a0S12-S21). The association between occupancy-change and global naturalization success, however, may be an underestimate because many species may already have started to change in occupancy within their native regions before the early census periods, most of which were in the second half of the 20th century. Additionally, for species that occurred in almost all grid cells of the early period, an increase in occupancy was hardly possible (Fig.\u00a0S3, Table\u00a0S25). So, although such common species may also be widely naturalized, they would neverthless have low occupancy-change values. This would have weakened the strength of the association between global naturalization success and the occupancy-change index. In addition, it might also have reduced the likelihood of detecting synergistic effects between early occupancy and occupancy change, as was found for the Czech Republic, the Netherlands and Switzerland. Therefore, the associations between global naturalization success and native\u00a0range occupancy change might be even stronger than indicated by our analyses.\n\nSpecies that have been reported previously to increase in occurrence frequencies within their native regions have been found to be adapted to disturbed and anthropogenic habitats48, to be strong competitors and to have a preference for nutrient-rich habitats6,11,27. Similarly, a higher naturalization success has been reported for species that grow in anthropogenic, nutrient-rich and more productive habitats in their native regions24,49. It has also been shown that naturalized and invasive species frequently capitalize more on increases in nutrient availability than less successful alien species50,51. The similar characteristics of species that have become more common in their native regions and those that have successfully naturalized elsewhere strongly suggests that similar processes drive both phenomena. The Thi\u00e9rache region in northern France (Table\u00a02, Fig.\u00a02j, Fig.\u00a0S1j, S2j) was the only region in which the change in occupancy was not significantly associated with global naturalization success. This might reflect that Thi\u00e9rache was the smallest region with the\u00a0fewest number of species, and that the early period was not in the second half of the 20th century, but at the end of the 19th century. Although the latter would better capture the occupancies of species prior to the Great Acceleration (i.e., the period of marked increases in human activity, which started in the mid-20th century), the occupancies in the early period for the Thi\u00e9rache were coarse estimates based on verbal descriptions of the commonness of the species10. Consequently, the data for Thi\u00e9rache were less precise than for the other nine regions, and the analysis had less statistical power because of the fewer number of species.\n\nThe relative consistency between the Bernoulli and zero-truncated count parts of the hurdle models suggests that species with high early occupancies and occupancy-change values were both more likely to naturalize and to do so in many regions. Furthermore, with the exception of Thi\u00e9rache, our results were also consistent across the native regions, despite the large variation in time periods and intervals covered by the datasets (Table\u00a01). This indicates that our results are robust. For Great Britain and Ireland, the original data sources actually provided occupancy data for three different periods (see Supplementary Methods for details). However, irrespective of which period was assigned as an early or later period for calculating the occupancy-change index, the results were largely similar (Tables\u00a0S26, S27, S29, S30). For the Netherlands, we extracted occupancy data using two different years of split. In Fig.\u00a02 and Table\u00a02, we\u00a0present the data for the periods before and after 1990, but if we instead used data for the periods before and after 2000, the results were generally the same (Table\u00a0S32). Furthermore, when we added woodiness and its interactions with early occupancy and occupancy change to the models, the results were, with a few deviations, largely the same (Tables\u00a0S1, S2\u2013S11). The main deviations were for Flanders and Germany, in which the positive main effect of occupancy change on the likelihood of being naturalized was no longer significant, but the interaction between occupancy change and woodiness was significant (Table\u00a0S5, S6). This suggests that for these two native regions the positive effect of occupancy change on the likelihood of naturalization is mainly accounted for by the woody species. Nevertheless, the additional analyses show that the positive associations of global naturalization success with early occupancy and occupancy change in the native regions are robust.\n\nOverall, our analyses show that species with high values of both early occupancy and occupancy change in their native regions are also successful as naturalized species globally. This suggests that data on occupancy and changes therein in the native range could inform invasion\u00a0risk assessments. However, it would ultimately be interesting to unravel which characteristics distinguish the group of widespread and expanding species from other species in the native range. For most traits, data are available for only a small proportion of the global flora28. Indeed, a recent analysis showed that there are only 10 traits with data available for more than 50 percent of naturalized species52. As mentioned above, a notable exception is woodiness, which we therefore also included in an alternative set of hurdle models (Tables\u00a0S1 and S2\u201311). Still, as previous studies found that expanding species are typically strong competitors that take advantage of additional resources, we ran additional analyses using Grime\u2019s CSR strategy53 and Ellenberg environmental indicator\u00a0values54 for the subsets of species for which these data were available (see Supplementary Methods for details). We found that the competitor scores of the species with high values of both early occupancy and occupancy change were significantly higher than those of all other species in nine of the 10 native regions (Fig.\u00a0S4, Table\u00a0S33), whereas the stress-tolerator and ruderal scores were frequently lower (Fig.\u00a0S5, S6, Table\u00a0S33). Furthermore, widespread and expanding species had significantly lower Ellenberg indicator values for light (Fig.\u00a0S7, Table\u00a0S34), and higher Ellenberg indicator values for nutrients (Fig.\u00a0S8, Table\u00a0S34), in all 10 native regions. On the other hand, indicator values for moisture (Fig.\u00a0S9, Table\u00a0S34) and temperature (Fig.\u00a0S10, Table\u00a0S34) differed significantly between the two groups of species only in some of the native regions, and not in a consistent pattern. Overall, these supplementary analyses align with the findings of previous studies that competitively strong species preferring nutrient-rich habitats tend to be widespread and have recently further increased in occurrence frequencies within their native regions6,11,27.\n\nA strength of our study is that we had multiple datasets on temporal changes in the occupancy of native species. However, the data also comes with limitations that should be kept in mind when interpreting the results. First, we only found suitable data for calculating the occupancy-change index for regions in central and north-western Europe. This means that we cannot generalize our findings to species that are native to other continents or to their whole native range. On the other hand, given that Europe is one of the major donors of naturalized plants globally55, the anthropogenic changes that drive the naturalization of European plant species in other continents are likely to similarly affect the occupancy change of native species in these other continents. As many regions around the globe now have plant\u00a0distribution atlas data e.g.56,57, (https://anpsa.org.au/, https://plants.usda.gov/, https://data.canadensys.net/), future reassessments of these distributions will allow for the calculation of occupancy changes in these regions. Second, there might be biases in the recording of different species and in the intensity of recording in different parts of the same region. Moreover, it could be that some species are increasing in part of their native distribution, for example in high-latitude regions, but decreasing in other parts of their native distribution, for example in low-latitude regions. Nevertheless, for species present in multiple datasets, the occupancy-change indices were generally positively correlated between the regions (of the 44 pairwise Pearson correlation coefficients, 41 were significantly positive and only two were significantly negative; Fig.\u00a0S11). This indicates that the species that are increasing or decreasing in one of their native regions usually also do so in the other ones.\n\nRabinowitz36 proposed three dimensions of rarity and commonness \u2014geographic range, habitat specificity and local abundance. Here, we only considered occupancy within native regions, which is arguably only one component of Rabinowitz\u2019s geographic range dimension. However, Crisfield et al.37 recently proposed to add occupancy as another dimension and to remove habitat specificity as a dimension, because the latter is rather a cause of rarity. Native geographic range size is unlikely to have dramatically changed for most species, at least not when quantified as the number of regions (mostly countries) in which a species is native. In our 10 datasets, early occupancy was always positively correlated with native range size (Pearson r\u2009=\u20090.182-0.404, all P\u2009<\u20090.001, Table\u00a0S35). Local abundance, on the other hand, is likely to have changed for many species in the last decades due to anthropogenic environmental change. The local abundance of species is usually positively related to the other measures of a species\u2019 distribution e.g.58,59. Previous studies across various spatial scales and taxonomic groups have also shown that species increasing their occupancy are also very likely to increase in abundance at the sites where they occur60,61. However, quantitative data for changes in local abundances for large numbers of species in areas comparable in size to our 10 datasets are rare. A notable exception is a recent study by Jandt et al. 62, who analyzed data on changes in the local abundances (cover) of plant species in vegetation plots in Germany over the period 1927\u20132020. The change in local abundance was positively correlated with the occupancy-change index that we calculated for the native species in Germany (Pearson r\u2009=\u20090.185, n\u2009=\u20091214, P\u2009<\u20090.001). This suggests that, overall, species that have become more widespread in Germany have also become locally more abundant. Thus, when more such data become available from resurveys of vegetation plots63, it will be worthwhile to look at the interactive effect of changes across different dimensions of commonness in future studies.\n\nIn conclusion, our analyses provide strong evidence that many plant species that are spreading as naturalized aliens around the globe also have high occupancies and/or are increasing in occupancy in their native regions. These findings have several major implications. First, if both phenomena are largely driven by anthropogenic environmental changes and the species\u2019 characteristics that preadapt them to these changes, this could explain why studies that compared widely naturalized aliens with widespread native species did not find differences in e.g., their responses to nutrient addition64, soil heterogeneity65 and competitive abilities66. Second, although the objective of our study was not to build a predictive model of drivers of plant naturalization, our findings suggest that measures of commonness and changes therein in the native regions could provide important insights into the likelihood that these species may naturalize after introduction elsewhere. While national assessment schemes for potential invasion risk, such as the Australian weed\u00a0risk assessment67, consider whether the assessed alien species is known to be naturalized or invasive in other regions, these risk assessment schemes do not yet consider commonness and its dynamics in the species\u2019 native regions. Considering these factors might help policymakers and managers enhance the accuracy and effectiveness of invasion risk assessments, ultimately leading to more informed and proactive conservation strategies.",
+            "section_image": []
+        },
+        {
+            "section_name": "Methods",
+            "section_text": "As a metric of commonness within species\u2019 native regions, we used occupancy (i.e., the proportion of grid cells across a region in which a species has been recorded). To obtain datasets on native species\u2019 occupancies for multiple distinct periods, we searched the scientific literature and online plant atlases and contacted curators of national plant species distribution databases. We found such data for 10 European regions (countries or parts thereof): Austria (number of native species: n\u2009=\u20092419), the Czech Republic (n\u2009=\u20091834), southeastern Denmark (n\u2009=\u2009921), Flanders (including the capital region of Brussels) in Belgium (n\u2009=\u2009861), Germany (n\u2009=\u20091715), Great Britain (including the Isle of Man and the Channel Islands) (n\u2009=\u20091355), Ireland (including the Republic of Ireland and Northern Ireland) (n\u2009=\u2009910), the Netherlands (n\u2009=\u20091115), Switzerland (n\u2009=\u20092307) and the Thi\u00e9rache region in northern France (n\u2009=\u2009775) (Fig.\u00a01, Table\u00a01). Across the\u00a010 regions, there were 3920 unique taxa, with 288 occurring in all 10 regions, 1261 present in only a single region, and the remaining ones shared across combinations of two to nine regions (Table\u00a0S36). Although some are subspecies or varieties, we refer to all taxa as species for simplicity.\n\nFor each native species in the 10 datasets (i.e., native regions), we extracted the number of grid cells where it has been recorded in two or more distinct time periods, where each period usually lasted multiple years or decades (Table\u00a01). Most of the data sources provide data for only two time periods, limiting us to the temporal splits available in the original datasets. However, for Great Britain and Ireland, the data sources provide data for three time periods. In addition, for the Netherlands, we could extract grid-cell numbers from the original data source choosing different years of split. We chose 1990 and 2000, as these years were also used by some of the other datasets. To see how robust the results were with regard to the chosen year of split, we analyzed the data for Great Britain, Ireland and the Netherlands using multiple splits.\n\nThe regions varied in the number of species, the early and later periods, the durations of these periods and the interval between the periods, as well as in the size and total number of grid cells (Table\u00a01). For example, for the Thi\u00e9rache region, which had data on 775 native species and their occurrences in 129 grid cells of 4\u2009\u00d7\u20094\u2009km, the early and later periods were 1880\u20131900 and 1957\u20132005, whereas for Germany, which had data on 1715 native species and their occurrences in 12,024 grid cells of 5\u2032 \u00d7 3\u2032, the early and later periods were 1960\u20131987 and 1997\u20132017. For most of the native regions, the data were actual grid-cell frequency counts, and they covered the entire region. However, for the Thi\u00e9rache region, the grid-cell frequencies for the early period were only coarse estimates based on verbal descriptions of how widespread the species were during that period10. Furthermore, for southeastern Denmark, the data do not cover one contiguous region but 11 subregions that do not all border one another (Fig.\u00a01). The data source for southeastern Denmark7 provides regional abundance data for each of the 11 subregions, where each species\u2019 abundance in a subregion was calculated by dividing the number of grid cells occupied by the species by the total number of grid cells for the subregion. From these data, we back-calculated the numbers of grid cells occupied by a species in each subregion, and then combined them across the 11 subregions to get one single occupancy value. Further details on the data for each of the 10 native regions are provided in the Supplementary Methods.\n\nTo select native plant species for inclusion in the final datasets and to harmonize the taxonomic names, we applied one common workflow to all 10 datasets. First, we excluded species that, according to the original data source, are not native to the respective region. When the native status was not provided or not entirely clear, we checked the native status of the species in the corresponding region in the Plants of the World Online database (POWO; https://powo.science.kew.org/ accessed in April 2023). Second, we harmonized the species names according to the taxonomic backbone of the World Checklist of Vascular Plants (WCVP version 11, which is integrated in POWO). This was done in R version 4.2.368, initially with the TNRS package version 0.3.369, and later, after it became available, the rWCVP package version 1.0.370. Species that did not have exact matching names in WCVP version 11 or that had multiple matching names were checked manually, and corrections were made when necessary. Species that did not match an accepted name were removed from the datasets. If multiple species in the original dataset were assigned to the same accepted name in WCVP, we kept the one that had the largest number of occupied grid cells. We could not merge the grid cell data because most datasets only provide the number of occupied grid cells, and not the identities of the grid cells occupied by each species.\n\nTo calculate an occupancy-change index, defined as the change in the proportion of grid cells between the two time periods covered by the data, relative to the expected change based on the occupancy in the early period (i.e., early occupancy), we followed the method developed by Telfer et al.41. We chose this method because the resulting occupancy-change index corresponds to the residuals of a weighted regression of the logit-transformed occupancy in the later period on the logit-transformed occupancy in the early period. As a consequence, the occupancy-change index is, compared to other change indices, less sensitive to differences in collection effort between the early and later periods. This is because the index does not quantify the absolute change but quantifies how much larger or smaller the magnitude of a species\u2019 occupancy change is relative to species with the same early occupancy. Another advantage is that the occupancy-change index is not correlated with early occupancy, and therefore does not cause multicollinearity issues when both are included in the same statistical model. However, like for any other occupancy-change index, we cannot rule out the possibility that the accuracy of recording certain groups of species might have changed for some regions between the periods.\n\nFollowing the protocol of Telfer et al.41, we first calculated the proportion of occupied grid cells in a native region for each species in each time period as (x\u2009+\u20090.5)/(n\u2009+\u20091), where x is the number of grid cells in which the species has been recorded and n is the total number of grid cells in the respective region. As recommended by Telfer et al.36, we added 0.5 to x and 1 to n to avoid proportion values of zero and one. This was necessary because in the second step, the proportion values were logit transformed, and the logit of zero would be undefined and the logit of one would be infinite. Next, we performed a weighted least-squares linear regression of the logit-transformed proportions of occupied grid cells during the later period as a function of the logit-transformed proportion of occupied grid cells during the early period. The weights were equal to the reciprocal of the variance of the logit-transformed proportions. Data visualization using scatterplots showed that species with low occupancy proportions in the early period deviated from the linear relationship. Therefore, as recommended by Telfer\u00a0et al.41, we excluded species occupying fewer than five grid cells during the early period. The resulting regression plots are shown in Fig.\u00a0S3. The values of the occupancy-change index then correspond to the standardized residuals (i.e., the deviations of the logit-transformed proportions of grid cells occupied by the species in the later period from the regression line). Therefore, for each early occupancy value, we have a more or less symmetrical distribution of negative and positive occupancy-change index values (i.e., standardized residuals; Fig.\u00a0S3). It should be noted that a positive value of the change index does not necessarily mean that the occupancy of a species has increased between the two periods. Instead, it means that the species occupied a higher proportion of grid cells in the later period than expected based on its occupancy in the early period.\n\nTo quantify global naturalization success of each species in the 10 native\u00a0region datasets, we used the Global Naturalized Alien Flora (GloNAF) database. GloNAF is the most comprehensive compendium of lists of naturalized alien vascular plant species for regions around the globe [18, provisionally accepted] and is continuously being updated. We used version 2.0 (extracted in January 2024), with data for 920 non-overlapping regions around the globe, including both mainland regions and islands (Fig.\u00a0S12). GloNAF regions mostly follow geopolitical boundaries, including countries, states, provinces and individual islands. The GloNAF regions range in size from 0.045 to 2336618\u2009km2 (the median size is 34382.71\u2009km2). Global naturalization of a species was quantified as the number of GloNAF regions in which it has naturalized, which is strongly correlated with the cumulative area of these regions15. As the species names in GloNAF version 2.0 follow the WCVP taxonomic backbone, the species names in the native occupancy datasets could be directly matched to the GloNAF database.\n\nBecause the datasets of the 10 regions differed in many aspects (Table\u00a01), we\u00a0analyzed each region separately. The separate analyses also ensure that we only make comparisons of changes in occupancy of species that occurred over the same time-period interval. Global naturalization of a species, quantified as the number of GloNAF regions in which the species is naturalized, was the response variable in our analyses. Because large proportions of the species in the 10 datasets have not naturalized in any region (median proportion: 0.300, range: 0.108\u20130.443), the count data are zero inflated. Therefore, we analyzed global naturalization success as a combination of naturalization incidence (naturalized vs. not naturalized) and naturalization extent (the number of regions where naturalized) using a hurdle model71 with the hurdle function of the pscl package version 1.5.571 in R. The hurdle model consisted of a generalized linear model (GLM) with a Bernoulli distribution with the logit link function for naturalization incidence (comparing the non-zeros to the zeros), and a GLM with a zero-truncated negative binomial distribution with the log link function for naturalization extent. We used a negative binomial distribution for the zero-truncated count part instead of a Poisson distribution to account for overdispersion. All the statistical tests in the hurdle model were two-sided. In both parts of the model, we included occupancy in the early time period (i.e., early occupancy; EO) the occupancy-change index (i.e., OC) and their interaction as predictor variables. Early occupancy and its interaction with the occupancy-change index were included in the model to test whether species that were widespread within the native regions decades ago were more likely to become naturalized elsewhere, and whether this is particularly true when these widespread species have further increased in native\u00a0region occupancy. To illustrate whether the relationship between global naturalization success and occupancy change varied depending on the occupancy in the early period, we fitted the predicted relationship between naturalization success (as a combination of the Bernoulli and zero-truncated count part) and the occupancy-change index for the median value of early occupancy, as well as for the 1/6th quantile (i.e., species that were relatively rare in the early period) and 5/6th quantile (i.e., species that were relatively common in the early period; Fig.\u00a02, Fig.\u00a0S1, S2). To facilitate interpretation and comparison of model estimates across the\u00a010 native regions, early occupancy was scaled to a mean of zero and a standard deviation of one72. This was not necessary for the occupancy-change index because it corresponds to standardized residuals, which are already scaled to a mean of zero and a standard deviation of one.\n\nFurther information on research design is available in the\u00a0Nature Portfolio Reporting Summary linked to this article.",
+            "section_image": []
+        },
+        {
+            "section_name": "Data availability",
+            "section_text": "All the datasets used in this study have been deposited in the Figshare database under the https://doi.org/10.6084/m9.figshare.2548720973.\u00a0Source data are provided with this paper.",
+            "section_image": []
+        },
+        {
+            "section_name": "Code availability",
+            "section_text": "The R code used for the statistical analysis is available in Code Ocean with the identifier https://doi.org/10.24433/CO.1618280.v1 and in the Figshare database under the\u00a0identifier https://doi.org/10.6084/m9.figshare.2548720973.",
+            "section_image": []
+        },
+        {
+            "section_name": "References",
+            "section_text": "Levin, D. A. The Origin, Expansion, and Demise of Plant Species (Oxford University Press, Oxford, 2000).\n\nVermeij, G. J. When biotas meet: understanding biotic interchange. Science 253, 1099\u20131104 (1991).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nSteffen, W. et al. The trajectory of the Anthropocene: the great acceleration.  Anthropocene Rev. 2, 81\u201398 (2015).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nIPBES. Global Assessment Report on Biodiversity and Ecosystem Services of the Intergovernmental Science-Policy Platform on Biodiversity and Ecosystem Services (IPBES Secretariat, 2019).\n\nCeballos, G. et al. Accelerated modern human-induced species losses: Entering the sixth mass extinction. Sci. Adv. 1, e1400253 (2015).\n\nArticle\u00a0\n    ADS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nvan Landuyt, W. et al. Changes in the distribution area of vascular plants in Flanders (northern Belgium): eutrophication as a major driving force. Biodivers. Conserv. 17, 3045\u20133060 (2008).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nNielsen, T. F., Sand-Jensen, K., Dornelas, M. & Bruun, H. H. More is less: net gain in species richness, but biotic homogenization over 140 years. Ecol. Lett. 22, 1650\u20131657 (2019).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nEichenberg, D. et al. Widespread decline in Central European plant diversity across six decades. Glob. Change Biol. 27, 1097\u20131110 (2021).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKress, W. J. & Krupnick, G. A. Lords of the biosphere: plant winners and losers in the Anthropocene. Plants, People, Planet 4, 350\u2013366 (2022).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nVan Calster, H. et al. Unexpectedly high 20th century floristic losses in a rural landscape in northern France. J. Ecol. 96, 927\u2013936 (2008).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nPowney, G. D. et al. A phylogenetically-informed trait-based analysis of range change in the vascular plant flora of Britain. Biodivers. Conserv. 23, 171\u2013185 (2014).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nGuo, W. Y. et al. The role of adaptive strategies in plant naturalization. Ecol. Lett. 21, 1380\u20131389 (2018).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nThomas, C. D. Local diversity stays about the same, regional diversity increases, and global diversity declines. Proc. Natl Acad. Sci. USA 110, 19187\u201319188 (2013).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nHulme, P. E. et al. Grasping at the routes of biological invasions: a framework for integrating pathways into policy. J. Appl. Ecol. 45, 403\u2013414 (2008).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nPy\u0161ek, P. et al. Naturalized alien flora of the world. Preslia 89, 203\u2013274 (2017).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nPy\u0161ek, P. et al. Alien plants in checklists and floras: towards better communication between taxonomists and ecologists. Taxon 53, 131\u2013143 (2004).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nRichardson, D. M. et al. Naturalization and invasion of alien plants: concepts and definitions. Diversity Distrib. 6, 93\u2013107 (2000).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDavis J. S., A. et al. The updated Global Naturalized Alien Flora (GloNAF 2.0) database. Ecology, provisionally accepted.\n\nSeebens, H. et al. No saturation in the accumulation of alien species worldwide. Nat. Commun. 8, 14435 (2017).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nChytr\u00fd, M. et al. European map of alien plant invasions based on the quantitative assessment across habitats. Diversity Distrib. 15, 98\u2013107 (2009).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nPrinzing, A., Durka, W., Klotz, S. & Brandl, R. Which species become aliens? Evolut. Ecol. Res. 4, 385\u2013405 (2002).\n\n\n                    Google Scholar\u00a0\n                \n\nvan Kleunen, M., Johnson, S. D. & Fischer, M. Predicting naturalization of southern African Iridaceae in other regions. J. Appl. Ecol. 44, 594\u2013603 (2007).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nHanspach, J. et al. Correlates of naturalization and occupancy of introduced ornamentals in Germany. Perspect. Plant Ecol. Evol. Syst. 10, 241\u2013250 (2008).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDost\u00e1l, P. et al. Central European plant species from more productive habitats are more invasive at a global scale. Glob. Ecol. Biogeogr. 22, 64\u201372 (2013).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nPy\u0161ek, P. et al. The global invasion success of Central European plants is related to distribution characteristics in their native range and species traits. Diversity Distrib. 15, 891\u2013903 (2009).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBrown, J. H., Stevens, G. C. & Kaufman, D. M. The geographic range: size, shape, boundaries, and internal structure. Annu. Rev. Ecol. Syst. 27, 597\u2013623 (1996).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKlinkovsk\u00e1, K. et al. Dynamics of the Czech flora over the last 60 years: winners, losers and causes of changes. Biol. Conserv. 292, 110502 (2024).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKattge, J. et al. TRY plant trait database\u2013enhanced coverage and open access. Glob. Change Biol. 26, 119\u2013188 (2020).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDong, B. C. et al. Naturalization of introduced plants is driven by life-form-dependent cultivation biases. Diversity Distrib. 30, 55\u201370 (2024).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nPy\u0161ek, P., K\u0159iv\u00e1nek, M. & Jaro\u0161\u00edk, V. Planting intensity, residence time, and species traits determine invasion success of alien woody species. Ecology 90, 2734\u20132744 (2009).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKowarik, I. Time lags in biological invasions with regard to the success and failure of alien species. Plant Invasions: General Aspects and Special Problems 15\u201338 (SPB Academic Publishing, 1995).\n\nvan Kleunen, M. & Richardson, D. M. Invasion biology and conservation biology: time to join forces to explore the links between species traits and extinction risk and invasiveness. Prog. Phys. Geogr. 31, 447\u2013450 (2007).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nJeschke, J. M. & Strayer, D. L. Are threat status and invasion success two sides of the same coin? Ecography 31, 124\u2013130 (2008).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nFristoe, T. S. et al. Evolutionary imbalance, climate and human history jointly shape the global biogeography of alien plants. Nat. Ecol. Evol.7, 1633\u20131644 (2023).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nRazanajatovo, M. et al. Plants capable of selfing are more likely to become naturalized. Nat. Commun. 7, e13313 (2016).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nRabinowitz, D. Seven Forms of Rarity. In The Biological Aspects of Rare Plant Conservation (ed. Synge, H.) (John Wiley & Sons Ltd., 1981).\n\nCrisfield, V. E., Guillaume Blanchet, F., Raudsepp-Hearne, C., & Gravel, D. How and why species are rare: towards an understanding of the ecological causes of rarity. Ecography 2024, e07037 (2024).\n\nFristoe, T. S. et al. Dimensions of invasiveness: Links between local abundance, geographic range size, and habitat breadth in Europe\u2019s alien and native floras. Proc. Natl Acad. Sci. 118, e2021173118 (2021).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBrown, J. H. Macroecology (University of Chicago Press, Chicago, 1995).\n\nCatford, J. A. et al. Disentangling the four demographic dimensions of species invasiveness. J. Ecol. 104, 1745\u20131758 (2016).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nTelfer, M. G., Preston, C. & Rothery, P. A general method for measuring relative change in range size from biological atlas data. Biol. Conserv. 107, 99\u2013109 (2002).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nSlatyer, R. A., Hirst, M. & Sexton, J. P. Niche breadth predicts geographical range size: a general ecological pattern. Ecol. Lett. 16, 1104\u20131114 (2013).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nK\u00fchn, I., Brandenburg, M. & Klotz, S. Why do alien plant species that reproduce in natural habitats occur more frequently? Diversity Distrib. 10, 417\u2013425 (2004).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKunin, W. E. & Gaston, K. J. The biology of rarity: patterns, causes and consequences. Trends Ecol. Evol.8, 298\u2013301 (1993).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nGrossenbacher, D., Briscoe Runquist, R., Goldberg, E. E. & Brandvain, Y. Geographic range size is predicted by plant mating system. Ecol. Lett. 18, 706\u2013713 (2015).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMurray, B. R. & Phillips, M. L. Investment in seed dispersal structures is linked to invasiveness in exotic plant species of south-eastern Australia. Biol. Invasions 12, 2265\u20132275 (2010).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nPy\u0161ek, P. et al. Naturalization of central European plants in North America: species traits, habitats, propagule pressure, residence time. Ecology 96, 762\u2013774 (2015).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nTabarelli, M., Peres, C. A. & Melo, F. P. L. The \u2018few winners and many losers\u2019 paradigm revisited: Emerging prospects for tropical forest biodiversity. Biol. Conserv. 155, 136\u2013140 (2012).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKalusov\u00e1, V. et al. Naturalization of European plants on other continents: The role of donor habitats. Proc. Natl Acad. Sci. 114, 13756\u201313761 (2017).\n\nArticle\u00a0\n    ADS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nChytr\u00fd, M. et al. Habitat invasions by alien plants: a quantitative comparison among Mediterranean, subcontinental and oceanic regions of Europe. J. Appl. Ecol. 45, 448\u2013458 (2008).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDawson, W., Rohr, R. P., van Kleunen, M. & Fischer, M. Alien plant species with a wider global distribution are better able to capitalize on increased resource availability. N. Phytol. 194, 859\u2013867 (2012).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nGreni\u00e9, M. et al. Gaps in global alien plant trait data and how to fill them. https://ecoevorxiv.org/repository/view/7852/ (2024).\n\nGrime, J. P. Vegetation classification by reference to strategies. Nature 250, 26\u201331 (1974).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nEllenberg, H. Indicator values of the vascular plants of central Europe. (1974).\n\nvan Kleunen, M. et al. Global exchange and accumulation of non-native plants. Nature 525, 100\u2013103 (2015).\n\nArticle\u00a0\n    ADS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDauby, G. et al. RAINBIO: a mega-database of tropical African vascular plants distributions. PhytoKeys 74, 1\u201318 (2016).\n\nViers, J. H., Thorne, J. H., & Quinn, J. F. CalJep: a spatial distribution database of CalFlora and Jepson plant species. San Francisco Estuary Watershed Sci. 4, 1\u201327 (2006).\n\nBrown, J. H. & Maurer, B. A. Macroecology: the division of food and space among species on continents. Science 243, 1145\u20131150 (1989).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBrown, J. H. On the relationship between abundance and distribution of species.  Am. Natural. 124, 255\u2013279 (1984).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nThompson, K., Hodgson, J. G. & Gaston, K. J. Abundance\u2013range size relationships in the herbaceous flora of central England. J. Ecol. 86, 439\u2013448 (1998).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLacy, R. C. & Bock, C. E. The correlation between range size and local abundance of some North American birds. Ecology 67, 258\u2013260 (1986).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nJandt, U. et al. More losses than gains during one century of plant biodiversity change in Germany. Nature 611, 512\u2013518 (2022).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKnollov\u00e1, I. et al. ReSurveyEurope: a database of resurveyed vegetation plots in Europe. J. Vegetation Sci. 35, e13235 (2024).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDawson, W., Fischer, M. & van Kleunen, M. Common and rare plant species respond differently to fertilisation and competition, whether they are alien or native. Ecol. Lett. 15, 873\u2013880 (2012).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWei, G. W. & van Kleunen, M. Responses of naturalized alien plants to soil heterogeneity and competition vary with the global naturalization success of the native competitors. J. Ecol. 113, 1532\u20131545 (2025).\n\nZhang, Z. & van Kleunen, M. Common alien plants are more competitive than rare natives but not than common natives. Ecol. Lett. 22, 1378\u20131386 (2019).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nPheloung, P., Williams, P. & Halloy, S. A weed risk assessment model for use as a biosecurity tool evaluating plant introductions. J. Environ. Manag. 57, 239\u2013251 (1999).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nR. Core Team. R: a language and environment for statistical computing. R Foundation for Statistical Computing (Vienna, 2023).\n\nMaitner, B. & Boyle, B. TNRS: taxonomic name resolution service. R package version 03. (2023).\n\nBrown, M. J. M. et al. A companion R package to the world checklist of vascular plants. version 1.0.3. N. Phytol. 240, 1355\u20131365 (2023).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nZeileis, A., Kleiber, C., & Jackman, S. Regression models for count data in R. J. Statist. Softw. 27, 1\u201325 (2008).\n\nSchielzeth, H. Simple means to improve the interpretability of regression coefficients. Methods Ecol. Evol. 1, 103\u2013113 (2010).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nPaudel, R. et al. Datasets for many plants naturalized as aliens abroad have also become more common within their native regions. Figshare. https://doi.org/10.6084/m9.figshare.25487209 (2025).\n\nUniversity of Vienna Institute for Botany Research Group for Plant Biogeography. Floristische Kartierung \u00d6sterreichs - Mapping the Flora of Austria (University of Vienna, 2025).\n\nWild, J. et al. Plant distribution data for the Czech Republic integrated in the Pladias database. Preslia 91, 1\u201324 (2019).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nVan Landuyt, W. et al. Atlas van de Flora van Vlaanderen en het Brussels Gewest (Nationale Plantentuin van Belgi\u00eb, Brussel, 2006).\n\nStroh, P. A. et al. Plant Atlas 2020: Mapping Changes in the Distribution of the British and Irish Flora (Princeton University Press, 2023).\n\nNDFF. NDFF Verspreidingsatlas. URL: http://verspreidingsatlas.nl/ (2015).\n\nFlora, I. The National Data and Information Center on the Swiss Flora. URL: https://www.infoflora.ch/de/ (2021).\n\nDownload references",
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+        },
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+            "section_name": "Acknowledgements",
+            "section_text": "R.P., N.L.K., A.D. and M.v.K. acknowledge funding from the German Research Foundation DFG (grant numbers 264740629 and 432253815 to MvK). R.P. and W.Z. acknowledges support of the International Max Planck Research School for Quantitative Behavior, Ecology and Evolution (IMPRS-QBEE). W.Z. acknowledges the funding from China Scholarship Council (grant no. 202106100035). M.C. and J.D. were supported by the Czech Science Foundation (project no. 19-28491X). K.G. and W.Y.G. acknowledge funding from the Natural Science Foundation of China (grant no. 32301386 to K.G. and 32171588 and 32471676 to W.Y.G.). P.P. and J.P. were supported by EXPRO grant no. 19-28807X (Czech Science Foundation) and, together with J.D., Z.K. and J.W., by long-term research development project RVO 67985939 (Czech Academy of Sciences). F.E. acknowledges funding from the Austrian Science Foundation FWF (Global 458 Plant Invasions, grant no. I 5825-B). H.K. acknowledges funding of research unit FOR2716 DynaCom (379417748) and Biodiversa+ BioMonI (533271599) from the German Research Foundation (DFG). M.W. acknowledges funding from the German Research Foundation (via iDiv, FZT 118, 202548816). We thank Fang-Wei Lin for help with data extraction. This Open Access publication was supported by the Publication Fund of the University of Konstanz.",
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+        },
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+            "section_name": "Funding",
+            "section_text": "Open Access funding enabled and organized by Projekt DEAL.",
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+        },
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+            "section_name": "Author information",
+            "section_text": "Ecology, Department of Biology, University of Konstanz, Konstanz, Germany\n\nRashmi Paudel,\u00a0Trevor S. Fristoe,\u00a0Nicole L. Kinlock,\u00a0Amy J. S. Davis,\u00a0Weihan Zhao\u00a0&\u00a0Mark van Kleunen\n\nInternational Max Planck Research School for Quantitative Behaviour, Ecology and Evolution (IMPRS-QBEE), Max Planck Institute of Animal Behaviour, Konstanz, Germany\n\nRashmi Paudel\u00a0&\u00a0Weihan Zhao\n\nDepartment of Biology, University of Puerto Rico \u2013 Rio Piedras, San Juan, Puerto Rico\n\nTrevor S. Fristoe\n\nBiometry, Methodology and Quality Assurance, Research Institute for Nature and Forest, Brussel, Belgium\n\nHans Van Calster\n\nDepartment of Botany and Zoology, Faculty of Science, Masaryk University, Brno, Czech Republic\n\nMilan Chytr\u00fd\u00a0&\u00a0Ji\u0159\u00ed Danihelka\n\nDepartment of Taxonomy, Institute of Botany, Czech Academy of Sciences, Pr\u016fhonice, Czech Republic\n\nJi\u0159\u00ed Danihelka\u00a0&\u00a0Zden\u011bk Kaplan\n\nEcologie et Dynamique des Syst\u00e8mes anthropis\u00e9s (UMR CNRS 7058 EDYSAN), University of Picardie Jules Verne, Amiens, France\n\nGuillaume Decocq\n\nDepartment of Botany and Biodiversity Research, University of Vienna, Vienna, Austria\n\nLuise Ehrendorfer - Schratt\u00a0&\u00a0Franz Essl\n\nState Key Laboratory of Black Soils Conservation and Utilization, Northeast Institute of Geography and Agroecology, Chinese Academy of Sciences, Changchun, China\n\nKun Guo\n\nZhejiang Tiantong Forest Ecosystem National Observation and Research Station, Institute of Eco-Chongming, Research Center for Global Change and Ecological Forecasting, School of Ecological and Environmental Sciences, East China Normal University, Shanghai, China\n\nWen-Yong Guo\n\nZhejiang Zhoushan Island Ecosystem Observation and Research Station, Zhoushan, China\n\nWen-Yong Guo\n\nState Key Laboratory of Estuarine and Coastal Research, East China Normal University, Shanghai, China\n\nWen-Yong Guo\n\nDepartment of Botany, Faculty of Science, Charles University, Prague, Czech Republic\n\nZden\u011bk Kaplan\n\nDepartment of Agricultural and Environmental Sciences (DiSAA), University of Milan, Milan, Italy\n\nSimon Pierce\n\nDepartment of Geoecology, Institute of Botany, Czech Academy of Sciences, Pr\u016fhonice, Czech Republic\n\nJan Wild\n\nDepartment of Evolution, Ecology and Behaviour, Institute of Infection, Veterinary and Ecological Sciences, University of Liverpool, Liverpool, UK\n\nWayne Dawson\n\nCentre for Invasion Biology, Department of Botany and Zoology, Stellenbosch University, Stellenbosch, South Africa\n\nFranz Essl\n\nBiodiversity, Macroecology and Biogeography, University of G\u00f6ttingen, G\u00f6ttingen, Germany\n\nHolger Kreft\n\nCentre of Biodiversity and Sustainable Land Use (CBL), University of G\u00f6ttingen, G\u00f6ttingen, Germany\n\nHolger Kreft\n\nCampus-Institut Data Science (CIDAS), University of G\u00f6ttingen, G\u00f6ttingen, Germany\n\nHolger Kreft\n\nDepartment of Invasion Ecology, Czech Academy of Sciences, Institute of Botany, Pr\u016fhonice, Czech Republic\n\nJan Pergl\u00a0&\u00a0Petr Py\u0161ek\n\nDepartment of Ecology, Faculty of Science, Charles University, Prague, Czech Republic\n\nPetr Py\u0161ek\n\nGerman Centre for Integrative Biodiversity Research (iDiv) Halle-Jena-Leipzig, Leipzig, Germany\n\nMarten Winter\n\nZhejiang Provincial Key Laboratory of Plant Evolutionary Ecology and Conservation, Taizhou University, Taizhou, China\n\nMark van Kleunen\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nM.v.K. designed research; R.P. performed research; M.v.K & R.P. compiled the data for calculating native range occupancy change; H.V.C., M.C., J.D., G.D., L. E-S., K.G., W.Y. G., Z.K., S.P., J.W., W.D., F.E., H.K., J. P., P.P., M.W. & M.v.K. contributed data; R.P., T.S.F., N.L.K., A.D., W.Z. & M.v.K. prepared the data; R. P. & M.v.K analyzed data; R.P., M.v.K. and T.S.F. wrote the first paper draft and all other coauthors contributed to writing.\n\nCorrespondence to\n                Rashmi Paudel.",
+            "section_image": []
+        },
+        {
+            "section_name": "Ethics declarations",
+            "section_text": "All the authors declare no competing interests.",
+            "section_image": []
+        },
+        {
+            "section_name": "Peer review",
+            "section_text": "Nature Communications thanks Dov Sax and the other anonymous reviewer(s) for their contribution to the peer review of this work. A peer review file is available.",
+            "section_image": []
+        },
+        {
+            "section_name": "Additional information",
+            "section_text": "Publisher\u2019s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.",
+            "section_image": []
+        },
+        {
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+            "section_text": "Paudel, R., Fristoe, T.S., Kinlock, N.L. et al. Many plants naturalized as aliens abroad have also become more common within their native regions.\n                    Nat Commun 16, 8227 (2025). https://doi.org/10.1038/s41467-025-63293-6\n\nDownload citation\n\nReceived: 27 March 2024\n\nAccepted: 15 August 2025\n\nPublished: 05 September 2025\n\nVersion of record: 05 September 2025\n\nDOI: https://doi.org/10.1038/s41467-025-63293-6\n\nAnyone you share the following link with will be able to read this content:\n\nSorry, a shareable link is not currently available for this article.\n\n\n\n\n                            Provided by the Springer Nature SharedIt content-sharing initiative\n                        ",
+            "section_image": [
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20066c606faa29dd51f6e9a6327618fc53895648c109a72437263f3a70cfe9f5/metadata.json

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+{
+    "title": "Influence of individual models and studies on quantitative mitigation findings in the IPCC Sixth Assessment Report",
+    "pre_title": "Influence of individual models and studies on quantitative mitigation findings in the IPCC Sixth Assessment Report",
+    "journal": "Nature Communications",
+    "published": "02 October 2025",
+    "supplementary_0": [
+        {
+            "label": "Supplementary Information",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-64091-w/MediaObjects/41467_2025_64091_MOESM1_ESM.pdf"
+        },
+        {
+            "label": "Description of Addtional Supplementary Files",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-64091-w/MediaObjects/41467_2025_64091_MOESM2_ESM.pdf"
+        },
+        {
+            "label": "Supplementary Data 1-2",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-64091-w/MediaObjects/41467_2025_64091_MOESM3_ESM.zip"
+        },
+        {
+            "label": "Transparent Peer Review file",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-64091-w/MediaObjects/41467_2025_64091_MOESM4_ESM.pdf"
+        }
+    ],
+    "supplementary_1": NaN,
+    "supplementary_2": NaN,
+    "source_data": [
+        "/articles/s41467-025-64091-w#ref-CR3"
+    ],
+    "code": [
+        "/articles/s41467-025-64091-w#ref-CR45"
+    ],
+    "subject": [
+        "Climate-change mitigation",
+        "Climate-change policy",
+        "Research management",
+        "Socioeconomic scenarios"
+    ],
+    "license": "http://creativecommons.org/licenses/by/4.0/",
+    "preprint_pdf": "https://www.researchsquare.com/article/rs-5698716/v1.pdf?c=1759489766000",
+    "research_square_link": "https://www.researchsquare.com//article/rs-5698716/v1",
+    "nature_pdf": "https://www.nature.com/articles/s41467-025-64091-w.pdf",
+    "preprint_posted": "13 Jan, 2025",
+    "research_square_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Quantitative mitigation findings based on emissions scenarios submitted to the Intergovernmental Panel on Climate Change (IPCC) play an authoritative role in climate policy and decision making. We analyse the impact of the uneven representation of models and modelling studies in the IPCC Sixth Assessment Report (AR6) on statistical values that are used to present quantitative mitigation findings. We find that several key AR6 findings are influenced considerably by the model with the most scenarios, including emissions reductions by 2030 and the decline in fossil fuels consistent with 1.5\u00b0C, and we find that the year of net-zero greenhouse gas emissions is influenced considerably by both the model and the study with the most scenarios. We find that weighting by model- or study does not provide a straightforward solution and discuss three issues related to the use of database statistics to present emissions scenarios findings. Based on our findings and informed by the purpose of the IPCC and the kinds of insights that can be obtained from emissions scenarios, we suggest improvements to the current practices used in IPCC assessments.Earth and environmental sciences/Climate sciences/Climate change/Climate-change mitigationEarth and environmental sciences/Environmental social sciences/Climate-change mitigationEarth and environmental sciences/Environmental social sciences/Climate-change policyEarth and environmental sciences/Environmental social sciences/Socioeconomic scenariosScientific community and society/Scientific community/Research management",
+            "section_image": []
+        },
+        {
+            "section_name": "Additional Declarations",
+            "section_text": "There is NO Competing Interest.",
+            "section_image": []
+        },
+        {
+            "section_name": "Supplementary Files",
+            "section_text": "SINCom20241223.pdfSupplementary Information to \u2018Influence of individual models and studies on quantitative mitigation findings in the IPCC Sixth Assessment Report\u2019SupplementaryData1.xlsxSupplementary Dataset 1SupplementaryData2.xlsxSupplementary Dataset 2",
+            "section_image": []
+        }
+    ],
+    "nature_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Quantitative mitigation findings based on emissions scenarios submitted to the Intergovernmental Panel on Climate Change (IPCC) play an authoritative role in climate policy and decision making. We analyse the impact of the uneven representation of models and modelling studies in the IPCC Sixth Assessment Report (AR6) on statistical values that are used to present quantitative mitigation findings. We find that several key AR6 findings are influenced considerably by the model with the most scenarios, including emissions reductions by 2030 and the decline in fossil fuels consistent with 1.5\u2009\u00b0C, and we find that the year of net-zero greenhouse gas emissions is influenced considerably by both the model and the study with the most scenarios. We find that weighting by model- or study does not provide a straightforward solution and discuss three issues related to the use of database statistics to present emissions scenarios findings. Informed by the purpose of the IPCC and the kinds of insights that can be obtained from emissions scenarios, we suggest improvements to the assessment of emissions scenarios.",
+            "section_image": []
+        },
+        {
+            "section_name": "Introduction",
+            "section_text": "Quantitative findings in the Intergovernmental Panel on Climate Change (IPCC) Working Group III (WGIII) reports on climate mitigation rely strongly on scenarios in the IPCC scenarios databases1,2,3,4,5,6. Descriptive database statistics, including median values and interquartile or 5th-95th percentile ranges, are used to report key findings, including emissions reductions over time, the year of net-zero emissions, and the reductions in fossil fuels consistent with different temperature targets2. These findings play authoritative roles and have been used to inform climate negotiations and climate policy at international and national levels7. Increasingly, they are also used by other actors, including local governments, private companies, banks, and financial regulators to inform net-zero strategies8, evaluate alignment with climate targets8, and to assess and disclose climate-related financial risks8,9,10.\n\nThe emissions scenarios in the IPCC scenarios databases are generated almost exclusively by process-based Integrated Assessment Models (IAMs). The collection is based on the voluntary submission of scenarios that have been published in individual modelling studies or in multi-model studies11,12. Because some modelling groups publish and submit more scenarios, the number of scenarios from different models and studies in the database is not even12,13. For this reason, the IPCC scenarios databases are referred to as \u201censembles of opportunity\u201d14. In the Sixth Assessment Report (AR6), the four models with the most scenarios are responsible for two-thirds of the scenarios that passed vetting and received a climate assessment, and the study with the most scenarios is responsible for almost half of the scenarios (Fig.\u20091).\n\na Number of scenarios by model. b Number of scenarios by study. All the scenarios that passed vetting and received a climate assessment are shown (1202 scenarios, out of 2304 submitted global scenarios12). Models are grouped into \u2018model families\u2019 representing potentially several versions of a single model core. The studies cover all scenarios in that study, though often from single papers. Scenario-based mitigation findings in the AR6 WGIII report are based on these scenarios (see \u201cMethods\u201d). Data: IPCC AR6 Scenarios Database3.\n\nBecause scenario outcomes depend on model and study assumptions15,16,17,18, median values and ranges may be sensitive to the sampling of models and studies in the database. Several recent studies have found model differences to be an important driver of scenario outcome variation19,20, and have identified distinct \u2018model fingerprints\u201921. Yet, the impacts of the uneven representation of models and studies on findings presented in the IPCC reports have not yet been quantified. Although it is noted in Chapter 3 of the IPCC WGIII report that uncorrected database statistics may be misleading11, such statistics are still used for headline AR6 findings.\n\nWe first analyse the influence of individual models and studies on database statistics that are used to report key findings in the AR6 WGIII Summary for Policymakers22 (SPM). Secondly, we assess the impact of dominant models on median outcomes in the AR6 scenarios database overall. Third, we compute model- and study-weighted medians and show that the results depend on the choice of weighting, in addition to the representation of models and scenarios. Finally, based on our findings, we discuss more fundamental issues with the use of database statistics to present emissions scenarios findings. Informed by the purpose of the IPCC and of emissions scenarios, we suggest ways forward for the IPCC authors to improve the assessment and communication of emissions scenarios findings.",
+            "section_image": [
+                "https:////media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41467-025-64091-w/MediaObjects/41467_2025_64091_Fig1_HTML.png"
+            ]
+        },
+        {
+            "section_name": "Results",
+            "section_text": "To assess the influence of individual models and studies on key AR6 findings, we calculate the impact on findings reported in the WGIII SPM from removing each model and study one-by-one. WGIII SPM findings are reported using primarily median values, with either interquartile or 5-95th percentile ranges in parenthesis (see e.g., SPM Table SPM.2, or SPM paragraphs C.1.2 or C.3.2 in the AR6 WGIII report). Since the WGIII SPM is focused on scenarios that achieve 1.5\u2009\u00b0C without overshoot (C1 category) and 2\u2009\u00b0C (C3 category), we focus on 1.5\u2009\u00b0C without overshoot and use 2\u2009\u00b0C scenarios as a reference to assess the magnitude of the impacts. We analyse a total of 27 WGIII SPM findings (see Methods for the selection) and measure the impact of each individual model and study in two different ways: First, we measure the impact of removing the individual model and study on the 1.5\u2009\u00b0C median relative to the difference between the 1.5\u2009\u00b0C and 2\u2009\u00b0C medians, and second, we measure how close the 1.5\u2009\u00b0C median is to the individual model and study relative to the median of\u00a0all the other models and studies. The first measure captures the impact of scenario sampling compared to the impact of switching from one climate target (1.5\u2009\u00b0C) to another (2\u2009\u00b0C). The second measure captures the influence of individual models and studies relative to all other models and studies within the same climate category (see Methods for details).\n\nThe impact on median values is substantial for several key AR6 findings (Fig.\u20092, Table\u20091). From removing just one model from the AR6 ensemble, median 2030 greenhouse gas (GHG) reductions in 1.5\u2009\u00b0C scenarios (relative to 2019)\u2014a widely recognised target23 written into the 2022 Sharm el-Sheikh Implementation Plan24\u2014 shifts from 43% to 50%. Median 2030 CO2 reductions shift from 48% to 56%. Median coal and gas reductions in 2050 shift from 95% to 83% and 43% to 29%, respectively. Net-zero GHG year shifts from 2098 to 2086 when removing one model, to 2084 when removing one study, and to after 2100 (the year of net-zero GHG is not specified in these scenarios) when removing several other models and studies.\n\nChanges in median values for a Year of net zero GHG emissions by model, b Year of net zero GHG emissions by study, c GHG emissions in 2030 by model, d Coal in 2050 by model, and e Gas in 2050 by model. Boxes show the minimum and maximum, the interquartile ranges, and the median of each model/study. The number of scenarios from each model/study is shown at the top of each box, and the data points are shown to the left. Models and studies are ordered according to the number of scenarios, with the model/study with the most scenarios furthest to the left. Long, solid horizontal lines show median values when models (orange) and studies (yellow) are removed one-by-one, with letters at the end of each line indicating the model/study that has been removed. Bolded and starred letters show the model/study whose removal leads to the biggest shift in the median value. Dashed grey horizontal lines show ensemble medians. The findings are selected based on a combination of policy relevance and impact (shown in Table\u20091) to illustrate how individual models and studies affect median values (more findings are shown in Supplementary Figs.\u20091\u20133). All variables are from scenarios that limit global warming to 1.5\u2009\u00b0C (>50%) (C1 category). Values above 2100 on the y-axis indicate \u2018after 2100\u2019, which means zero was not reached before 2100 (and may not be reached). The model acronyms are R: REMIND, M: MESSAGE, W: WITCH, I: IMAGE, GC: GCAM, A: AIM, P: POLES, CR: C-ROADS, GE: GEM-E3, CO: COFFEE and the study acronyms are E: ENGAGE, vV: van Vuuren 2021, E33: EMF33, N: NGFS2, C: CD-LINKS, K21: Kikstra 2021, O21: Ou 2021, SSP: SSP, S18: Strefler 2018, S21a: Strefler 2021a, S21b: Strefler 2021b, A: ADVANCE, B21: Baumstark 2021, H18: Holz 2018, K18: Kriegler 2018, So21: Soergel 2021, L21: Luderer 2021, B18: Bertram 2018, F20: Fujimori 2020, G18: Grubler 2018, S21: Schultes 2021. Data: IPCC AR6 Scenarios Database3.\n\nFor most of the assessed WGIII SPM findings, individual models have a much larger impact than individual studies (Table\u00a01, Fig.\u20093 and Supplementary Figs.\u20091\u20133). One exception to this is the net-zero GHG year. For the net-zero GHG year, the ENGAGE study, with 25 of 97 scenarios in the C1 category, has a large influence because many ENGAGE scenarios do not reach net-zero GHG emissions before 2100 by design (Fig.\u20092 and Supplementary Note\u20091). The net-zero GHG year is also sensitive to the removal of models and studies because few scenarios reach net-zero around the median year (2098) (Fig.\u20094). The reason why median values are more sensitive to individual models is partly because the dominant model is responsible for a larger share of the C1 scenarios (41 of 97 scenarios) than the dominant study (25 of 97 scenarios). Models with fewer than 25 scenarios also have a smaller impact (Supplementary Figs.\u20091\u20133). In addition to this, models have a larger impact on median values because some WGIII SPM findings are more model-dependent than they are study-dependent. As seen in the cases of coal, oil, gas, CH4, N2O, and F-Gases, the level of disagreement across models is larger than the level of disagreement across studies (Supplementary Figs.\u20091\u20133). This is consistent with other studies that have found model differences to be larger than other scenarios differences15,18,20,21.\n\na Year of net zero GHG emissions, b Cumulative net-negative CO2 emissions between the year of net zero and 2100, c CO2 emissions in 2030, d GHG emissions in 2030, e CH4 emissions in 2040, f CH4 emissions in 2050, g N2O emissions in 2050, h F-gas emissions in 2050, i Coal in 2050, j Coal without CCS in 2050, k Oil in 2050, l Oil without CCS in 2050, m Gas in 2050. The selection represents the findings that are most impacted according to the \u2018Between\u2019 measure for either models or studies, as shown in Table\u20091. The different years and ranges correspond to what is reported in the SPM: For fossil variables, interquartile ranges are shown; for other variables, 5th-95th percentile ranges are shown. The grey bars show statistics for all scenarios that limit global warming to 1.5\u2009\u00b0C (>50%) (category C1, including only vetted scenarios that received a climate assessment). The other bars show statistics when the model with the most scenarios is removed (orange bars) and when the study with the most scenarios is removed (yellow bars). The blue diamonds show median values of all scenarios that limit global warming to 2\u2009\u00b0C (\u2009>\u200967%) (category C3, including only vetted scenarios that received a climate assessment). The model with the most scenarios is the REMIND model, and the study with the most scenarios is the ENGAGE study for all the findings. \u2018>2100\u2019 means \u2018after 2100\u2019 (the year is not specified for scenario that reach net zero GHG emissions after 2100), \u2018CCS\u2019 stands for Carbon Capture and Storage. Data: IPCC AR6 Scenarios Database3.\n\na Year of net zero GHG emissions by model, b Year of net zero GHG emissions by study, c GHG emissions in 2030 by model, d Coal in 2050 by model, and e Gas in 2050 by model. Dominant model/study scenarios are shown in blue, and all other scenarios are shown in orange/yellow. The findings are selected based on a combination of policy relevance and impact (shown in Table\u20091). All variables are from scenarios that limit global warming to 1.5\u2009\u00b0C (\u2009>\u200950%) (C1 category). The boxes at the top of each histogram show the 5th, 25th, 50th, 75th, and 95th percentiles of all scenarios (in grey), the median of the dominant model/study (in blue), and the median without the dominant model/study (in orange/yellow). \u2018>2100\u2019 means after 2100 (net zero is not reached before 2100 and may not be reached in these scenarios). Data: IPCC AR6 Scenarios Database3.\n\nThe model with the largest impact on most median values is the model with the most scenarios, which, for all the assessed findings, is the REMIND model (Table\u20091). The strong influence on median values for this model is explained in large part due to its substantial share of the 1.5\u2009\u00b0C scenarios in AR6 (41 of 97 scenarios). Because REMIND uses less coal and more oil compared to other models, median coal is higher and median oil is lower when REMIND is removed. And because near-term emissions reductions in REMIND are lower than in\u00a0most other models, median GHG and CO2 reductions in 2030 are higher when REMIND is not included. The model with the second largest impact after REMIND is the model with the second most scenarios, MESSAGE (20 of 97 scenarios). Except for the net-zero GHG year, however, the impact of removing MESSAGE is relatively small (Table\u20091). The magnitude of the shift when removing models depends on both the number of scenarios and the position of those scenarios relative to other scenarios (Fig.\u20094).\n\nThe study with the largest impact on median values is also the study with the most scenarios, ENGAGE18 (Table\u20091). And the study with the largest influence after ENGAGE is also the study with the second most scenarios, van Vuuren 202125,26. This study also happens to contain all the IMAGE scenarios in the C1 category, and removing it is therefore equivalent to removing the IMAGE model. The impact of van Vuuren 2021 on median values is, however, relatively small (Table\u20091).\n\nInterquartile and 5-95th percentile ranges are also influenced by the dominant model and the dominant study, with the interquartile ranges being more sensitive than the 5-95th percentile ranges, and with the dominant model having a larger impact than the dominant study (Fig.\u20093).\n\nThe median values that are least impacted by individual models and studies (relative to the differences in 1.5\u2009\u00b0C and 2\u2009\u00b0C medians) include peak CO2 and GHG emissions years and net-zero CO2 year (Table\u00a01). Because almost all scenarios have the same peak GHG and CO2 year (2020), removing individual models and studies has no impact. For the net-zero CO2 year, inter-model variation is still considerable, but the two models with the most scenarios happen to both be very close to the ensemble median (Supplementary Table\u20091). Therefore, removing these two models has almost no impact on the median in this case. Models that give significantly different net-zero years (such as GCAM, POLES, C-ROADS, and COFFEE) do not have enough scenarios to influence the median net-zero year on their own. This highlights that it is not only the numbers of scenarios that matter, but also their positioning relative to the median.\n\nOverall, the largest influence on the assessed WGIII SPM findings comes from the dominant model (Table\u20091). Compared to the dominant model, the dominant study and other models have much less influence (Supplementary Figs.\u20091\u20133). For 16 of the 27 SPM findings, the reported median is closer to the median of the dominant model than to the median of\u00a0all the other models combined (Table\u20091). For coal reductions, year of net-zero GHG emissions, CH4 and F-gas emissions, the impact from the dominant model on the median is as large as or larger than the distance between reported median values for 1.5\u2009\u00b0C and 2\u2009\u00b0C scenarios. This shows that the uneven representation of models can be as or more important than the climate category for median scenario outcomes.\n\nWe have so far focused on the scenario variables reported in the WGIII SPM. To assess the influence of dominant models on the AR6 scenarios database findings overall, which is relevant for users of the database more broadly7,10,13,27,11, we compute the impact on the median values of all the variables in the database (see \u201cMethods\u201d). In each climate category, we compute the number of variables for which the median (in 2050) is closer to the median of the dominant model than to the median of all the other models combined. We do this for all scenario variables reported by at least two models.\n\nMost median values in the AR6 database are closer to the median of the dominant model than to the median of the other models\u00a0taken together (Fig.\u20095). In scenarios that limit global warming to 1.5\u2009\u00b0C (C1 category), 79% of median values are closer to the median of the dominant model than to the median of all the other models. In scenarios that limit global warming to 2\u2009\u00b0C (C3 category), 64% of median values are closer to the median of the dominant model than to the median of all the other models. Across all climate categories, 67% of median values in the AR6 scenarios database are closer to the median of the dominant model than to the median of all the other models.\n\nThe left column shows the number of variables with median values closer to the dominant model than to the median of all the other models, by climate category and by model (a, c, e). The right column shows the total number of variables across all climate categories with median values closer to the dominant model than to the median of all the other models, by model (b, d, f). Results are shown for all variables (a, b), Tier 1 variables (c, d), and Tier 2 variables (e, f) (see \u201cMethods\u201d). Percentages above bars in (a, c, e) show the proportion of variables in each climate category with median values closer to the dominant model than to the median of all other models. The colours show what model is the dominant model. Percentages above bars in (b, d, f) show the proportion of variables for which the median is closer to the dominant model than to all the other models, by the dominant model. Median values are in 2050. Only variables reported by at least two models in the AR6 Scenarios Database are included (see Methods). Data: IPCC AR6 Scenarios Database3.\n\nWithin each climate category, the dominant model depends on the scenario variable. This is because different models report different scenario variables (Supplementary Fig.\u20094 and Supplementary Data\u20091). In scenarios that limit global warming to 1.5\u2009\u00b0C and 2\u2009\u00b0C, the most common dominant model across variables is REMIND, followed by MESSAGE and IMAGE.\n\nDifferent models dominate across variables in different climate categories (Fig.\u20095). Whereas REMIND is the most common dominant model in the C1, C3, C7, and C8 categories, MESSAGE is the most common dominant model in the C2, C4, C5, and C6 categories. This means that when comparing median outcomes of variables across climate categories\u2014which is often done to show the implications of different climate targets\u2014the differences may in some cases be more reflective of differences in model sampling than of the climate target. For example, comparing the implications of different levels of \u2018overshoot\u2019 (C1 versus C2) may be more about differences in the REMIND and MESSAGE models than about overshoot.\n\nOverall, the models with the most scenarios in the AR6 database have a much larger impact on median values than the models with fewer scenarios. The two models with the most scenarios (47% of all vetted and climate-assessed scenarios), REMIND and MESSAGE, are responsible for 77% of the cases where the median is closer to the dominant model than to the median of all the other models. For 96% of the cases, the responsible model is one of the four models with the most scenarios in the AR6 scenarios database (REMIND, MESSAGE, IMAGE, and WITCH). The distribution of dominant models (Fig.\u20095b) is thus even more uneven than the distribution of scenarios per model (Fig.\u20091a).\n\nThe results are similar if we limit the analysis to include only Tier 1 and Tier 2 variables, which are considered the more important variables (see Methods and Supplementary Data\u20092). All models should submit Tier 1 variables (of which there are 82), suggesting that the uneven submissions across variables should be less common. In the C1 category, 63% of Tier 1 and 73% of Tier 2 variables have median values that are closer to the median of the dominant model than to the median of all the other models (Fig.\u20095). In the C3 category, 48% of Tier 1 and 59% of Tier 2 variables have median values that are closer to the median of the dominant model than to the median of all the other models. Across all climate categories, 47% of Tier 1 variables and 65% of Tier 2 variables have median values that are closer to the median of the dominant model than to the median of all the other models. In most cases, the dominant model is one of the four models with the most (vetted and climate-assessed) scenarios in the AR6 scenarios database. Models other than REMIND, MESSAGE, IMAGE and WITCH are the dominant model in less than 5% of all cases.\n\nWe expect models that report more variables (Supplementary Fig.\u20094) to be the dominant model for more scenario variables. However, models with more scenarios tend to also report more variables, which means that these two effects go in the same direction (Supplementary Fig.\u20095 and Supplementary Data\u00a01). Overall, the number of vetted scenarios per model (Fig.\u20091 and Supplementary Fig.\u20096) is a better predictor of model dominance (Fig.\u20095) than the number of variables reported (Supplementary Fig.\u20094 and Supplementary Note\u20092).\n\nThe median values presented in the AR6 WGIII report are computed by giving each scenario equal weight. A simple way to counteract the uneven number of scenarios from different models and studies is to instead give each model or study equal weight (see Methods for details). For the assessed WGIII SPM findings, the direction of change in median values when each model or each study is given equal weight is usually the same as when the dominant model or study is removed (Fig.\u20096). This is not surprising, given the scenarios from the dominant model and study are given much less weight in model- and study-weighted medians. When each model is given equal weight, median coal reductions in 2050 changes from 95% to 83% in 1.5\u2009\u00b0C scenarios, which is the same as when removing the dominant model, and median gas reductions changes from 43% to 33%, which is close to the change from removing the dominant model (29%). Median GHG reductions in 2030 changes from 43% to 45%, which is less than when removing the dominant model (50%), because the models are evenly distributed on each side of the median for this variable.\n\na Year of net zero GHG emissions by model, b Year of net zero GHG emissions by study, c GHG emissions in 2030 by model, d Coal in 2050 by model, and e Gas in 2050 by model. Boxes show the minimum and maximum, the interquartile ranges, and the median of each model/study. The number of scenarios from each model/study is shown at the top of each box, and the data points are shown to the left. Models and studies are ordered according to the number of scenarios, with the model/study with the most scenarios furthest to the left. Long, solid horizontal lines show median values when models (orange) and studies (yellow) are removed one-by-one, with letters at the end of each line indicating the model/study that has been removed. Bolded and starred letters show the model/study whose removal leads to the biggest shift in the median value. Dashed grey horizontal lines show ensemble medians. Longer dashed horizontal lines show medians weighted by model (orange) and by study (yellow). The findings are selected based on a combination of policy relevance and impact (shown in Table\u20091) to illustrate how individual models and studies affect median values (more findings are shown in Supplementary Figs.\u20091\u20133). All variables are from scenarios that limit global warming to 1.5\u2009\u00b0C (>50%) (C1 category). Values above 2100 on the y-axis indicate \u2018after 2100\u2019, which means zero was not reached before 2100 (and may not be reached). The model acronyms are R: REMIND, M: MESSAGE, W: WITCH, I: IMAGE, GC: GCAM, A: AIM, P: POLES, CR: C-ROADS, GE: GEM-E3, CO: COFFEE and the study acronyms are E: ENGAGE, vV: van Vuuren 2021, E33: EMF33, N: NGFS2, C: CD-LINKS, K21: Kikstra 2021, O21: Ou 2021, SSP: SSP, S18: Strefler 2018, S21a: Strefler 2021a, S21b: Strefler 2021b, A: ADVANCE, B21: Baumstark 2021, H18: Holz 2018, K18: Kriegler 2018, So21: Soergel 2021, L21: Luderer 2021, B18: Bertram 2018, F20: Fujimori 2020, G18: Grubler 2018, S21: Schultes 2021. Data: IPCC AR6 Scenarios Database3.\n\nWeighted medians, however, do not offer a straightforward solution to the problem of model and study representation. There are two reasons for this. First, model- and study-weighted medians often move in opposite directions, leading to large differences for certain key findings (Fig.\u20096 and Supplementary Figs.\u20097\u20139). The median net zero GHG year varies by almost two decades or more, depending on whether you give each scenario equal weight (2098), each study equal weight (2085), or each model equal weight (after 2100). This is partly because the dominant model and the dominant study sit on opposite sides of the median. This shows that the choice of weighting scheme can be a key determinant of median values. But it is not clear what weighting scheme is more appropriate. Scenario outcomes can depend on model or study assumptions, or both, and it is not clear whether it is models or studies (or scenarios) that should be given equal weight in the calculation of database statistics. Second, model- and study-weighted medians may be dependent on what models and studies are included and not included in the AR6 scenarios database. While model- and study-weighted medians are insensitive to the number of scenarios, they are not insensitive to the representation of models and studies. Not all models submitted scenarios to the AR6 database, and of the more than 50 models that submitted scenarios, only 13 models submitted scenarios that passed vetting and received a climate assessment11 (Supplementary Note\u20091 and Supplementary Table\u20092). Furthermore, because not all models report all variables in all climate categories, most findings are based on even fewer than those 13 models (Supplementary Fig.\u200910). Thus, the models that are used to derive AR6 findings represent only a small subset of the models in the scenarios literature.\n\nThe problem of uneven sampling is not unique to the IPCC scenarios database. Unbalanced samples are common in social sciences, and several weighting methods have been developed to deal with this. These methods, however, rely on knowing the target population (see e.g.,28,29.). When the target population is known, weights can be assigned to ensure that the distribution of chosen characteristics in the sample, such as age, gender, education, and geographical location, reflects the target population. For the IPCC scenarios ensemble, however, the target population is unclear. Should it be all plausible scenarios, including ones that have never been modelled, or should it be all scenarios that have been published? And what scenario characteristics should one be ensuring a good representation of? While median fossil fuel reductions depend mostly on model representation, the net-zero year depends on both model and study representation. This suggests that the relevant characteristics depend on the scenario outcome in question.\n\nWeighting methods have also been discussed extensively in relation to physical climate modelling30,31,32,33. Most likely climate outcomes (contingent on forcing levels) are most often computed in structured experiments where each climate model is given equal weight34. In the literature, it has been argued that greater weight should be given to climate models that have been shown to have greater skill and to models that are more independent 31,33. That is, climate models should be weighed based on both performance and model independence, where dependencies may stem from the sharing of ideas for parametrization or simplifications, or from sharing of computer code, which may lead to similar model biases31. Because different climate models have greater skill at simulating different climate outcomes, and because different outcomes depend on different assumptions, both performance and independence depend on the outcome in question33.\n\nDespite valuable suggestions for how to evaluate IAMs35 there are no agreed upon performance metrics for IAMs. While climate model performance is based on comparing model projections with historical observations33, observations that can be used to assess the performance of IAMs are not available in the same way (Supplementary Note\u00a03). And research into IAM dependencies is lacking.\n\nIn lieu of performance and independence metrics, weighting by model might represent an improvement to the current approach of weighting by scenario, as it removes duplication of model outcomes that may result from known model fingerprints. Giving each model equal weight is also the most common approach in climate modelling. But unlike climate model ensembles, where each model is run once for each scenario in a structured experiment34 (such as in Coupled Model Intercomparison Projects (CMIPs)), the IPCC IAM ensembles contain a diversity of different scenarios, run by different sets of models, under different assumptions, to answer different questions. In this case, differences in outcomes do not represent different answers to the same question, which may be interpreted as the uncertainty of the answer, but how the answers change when the questions change. In this case, weighting by model remains an arbitrary approach, which may also remove important variation captured by different studies run by the same model.",
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+            ]
+        },
+        {
+            "section_name": "Discussion",
+            "section_text": "We have shown that several WGIII SPM median values are influenced considerably by the model, and in some cases study, with the most scenarios in the AR6 database. Additionally, we have shown that weighting does not offer a straightforward solution to the uneven representation of models and studies. The median will, in any case, depend on the weighting choice and the representation of models and studies. This brings up more fundamental questions regarding the use of database statistics to present emissions scenarios findings. Informed by the purpose of the IPCC assessment, we discuss three issues and make recommendations based on our findings and the kinds of insights that can be obtained from IAM scenarios.\n\nFirst, median values and percentiles do not convey the level of agreement in findings, which is key to informing confidence and robustness. The IPCC is set up to \u201ctell policymakers what we know and don\u2019t know\u201d and \u201cwhere there is agreement in the scientific community, where there are differences of opinion, and where further research is needed\u201d36. As part of this, assessment findings with stronger agreement and multiple lines of evidence can be assigned a higher degree of confidence37. While interquartile and 5th-95th percentile ranges show the spread in scenario outcomes, they don\u2019t provide information about whether different models and studies agree or disagree. There is relatively low agreement, for example, on the precise reductions of emissions, coal, and gas in specific years, and on the net-zero GHG year. This is because these outcomes clearly depend on choices and assumptions that differ across models and studies (Figs.\u20092, 3 and 5). As our findings show, the reporting of descriptive statistics to the nearest percentage point for emissions reductions, the nearest 5% for coal and gas, and the closest five-year interval for the net-zero year is not robust to the sampling of models and studies. The reporting of median peak CO2 and GHG emissions years is (Table\u20091). If the point is to show differences in implications between different climate targets, robust scenario findings can be defined as those that vary more across climate categories than they do across models and studies20. This robustness could be evaluated, for example, by assessing the sensitivity of outcomes to removing single models and studies or to giving models and studies equal weight, as is done in this paper.\n\nRather than focusing on median values and percentiles, which may not only be sensitive to sampling but can also be misinterpreted as probabilistic confidence intervals, the IPCC could report the full ranges of scenario outcomes and focus more on how outcomes depend on assumptions, including model and study assumptions. Many different strategies are consistent with 1.5\u2009\u00b0C and 2\u2009\u00b0C, and scenario analysis is largely about showing the different implications and trade-offs associated with different choices38. Scenario analysis is less suited to providing precise outcomes for specific variables38. In addition to this, several models and studies fall entirely outside of the interquartile, and in some cases, 5th-95th percentile, ranges that are used to present findings (Supplementary Figs.\u20091\u20133). But given the non-probabilistic nature of the emissions scenario ensemble2 and the role of emissions scenarios in exploring different strategies and trade-offs, these results are no less important. An improved assessment of how scenario outcomes depend on choices and assumptions could be informed by several recent studies that have analysed how the model used, the scenario assumptions, and the climate target affect scenario outcomes19,20,21. A focus on such dependencies could provide policy-relevant insights regarding, for example, how the net-zero emissions year depends on key assumptions, including the climate target definition, which is defined differently in different studies18, and the discount rate, which may be defined differently in different models or studies39.\n\nSecond, the reliance on database statistics to present key scenarios findings give a lot of weight to the subset of scenarios that are submitted to the database, pass vetting, and receive a climate assessment. This comes at the exclusion of findings that are captured by models and studies that are not included in this subset but still contribute to the literature. This is an issue because the IPCC is meant to assess the full scenarios literature, and the scenarios database is meant to aid this assessment, not replace it. With the construction and use of the scenarios database to derive mitigation findings, the IPCC is essentially conducting a meta-analysis of an \u201censemble of opportunity\u201d2 that includes only a subset of the scenarios literature12. But the AR6 is meant to40 \u201ctake all available literature on emissions scenarios fully into account independently of whether underlying emissions scenarios are submitted to the AR6 scenario database\u201d. To serve this goal, the IPCC should assess whether the subset of scenarios used to derive findings gives a good representation of the scenarios literature. Guidelines for the use of database statistics that address the issues of over- and underrepresentation could also be developed. Making this an integral part of the use of the IPCC scenarios database may help reduce biases in key findings that are\u00a0based on the database.\n\nThird, database statistics may not be very meaningful given the varied representation of different research questions and assumptions. According to AR6, \u201cscenarios are neither predictions nor forecasts, but are used to provide a view of the implications of developments and actions\u201d2. These views are provided through specific modelling studies that employ specific models and scenario assumptions to answer specific research questions, such as: What are the cost implications of meeting stringent climate targets without overshoot18? What are the impacts on electrification if renewable energy costs continue to decline?41 How might changes in energy service provision affect global energy demand and supply, and the achievement of climate and development goals42? Although the scenarios database has an advantage in terms of the number of models and studies and therefore diversity of assumptions, this diversity also means that distributions of scenario outcomes are difficult to interpret6 and that database statistics may not be very meaningful2,27. More readily available information on model and scenario assumptions1,13, greater openness and transparency in the curation of the IPCC scenarios database including on vetting12, and more research into the different causes of scenario outcome variability (e.g17.) would enable users to get a better understanding of the representation of key assumptions in the database, which could help them make more meaningful comparisons and draw more relevant insights suited to their needs. But this information does not in itself make the scenarios in the database more comparable43 or statistical values more meaningful. Modelling is for \u201cinsights not numbers\u201d44 and model outcomes carry less meaning when they are not interpreted with respect to the choices and assumptions under which they were generated, and the research questions they were designed to answer. Because of this, the insights that IAM scenarios offer are best understood and appreciated by assessing scenario papers directly.\n\nThe use of scenario database statistics to present key scenario findings, and giving each scenario equal weight, is an easy choice, but it is not a neutral choice as it gives more weight to choices and assumptions embedded in models and studies that have a large number of scenarios in the database. While the uneven representation of studies in the AR6 ensemble might mean that certain questions, and therefore certain answers, are overrepresented, the uneven representation of models might mean that certain mitigation strategies are overrepresented. Our results confirm that different models tend to choose different strategies for reaching the same climate target15,19,20,21 and thus provide different views of the implications of mitigation. REMIND 1.5\u2009\u00b0C scenarios, for example, use less coal and gas, but more oil, and they mitigate more slowly in the beginning, but faster later on, compared to scenarios from other models.\n\nMore research is needed to understand what a representative sample of emissions scenarios might look like and how different models and studies contribute to this. Given that the IPCC scenarios database has a diversity of uses, there might not be a one-size-fits-all method for analysing it, and a transparent discussion of how to leverage it for different purposes, contexts and outputs is important. One way to remedy the uneven representation of models and studies in the database is to use the scenarios literature to better inform and guide the interpretation of different scenario outcomes. Even though the scenarios literature is also prone to an uneven representation of model and study assumptions, the weight given to different insights in the literature does not reflect a simple counting of scenarios and thus does not suffer in the same way.\n\nThe current use of database statistics to present key scenario findings in IPCC reports might mean that targets and decisions are based on findings that are more reflective of idiosyncratic model or study assumptions than of the chosen climate target and the scenarios literature. Moving away from descriptive statistics that are difficult to interpret and sensitive to sampling might be more in line with both the goal of the IPCC, to assess the full scenarios literature, and the purpose of integrated assessment modelling, to provide insights, not numbers.",
+            "section_image": []
+        },
+        {
+            "section_name": "Methods",
+            "section_text": "The statistical values that are reported in the AR6 WGIII report and that are analysed in this paper are based on the subset of global scenarios in the AR6 scenarios database that passed vetting and that received a climate assessment (which means they were categorised into one of the C1-C8 climate categories). A total of 2304 global scenarios were submitted to the AR6 scenarios database. Of these, 1686 passed vetting and 1202 passed vetting and received a climate assessment3.\n\nThe analysis of the influence of individual models and studies on key AR6 findings (Figs.\u20092, 3 and 5) includes scenarios only in the C1 and C3 climate categories, as these categories (1.5\u2009\u00b0C with no or limited overshoot and 2\u2009\u00b0C) are the focus in the WGIII SPM. It includes a select number of scenario variables based on what is reported in the WGIII SPM (see below). The analysis of the impact of dominant models on the AR6 scenarios database overall includes scenarios from all climate categories (C1-C8), and it includes all the scenario variables reported in the database (more detailed information on this is provided further below).\n\nThe AR6 WGIII SPM findings mainly cover scenarios that limit global warming to 1.5\u2009\u00b0C (\u2009>\u200950%) with no or limited overshoot (C1 climate category) and scenarios that limit global warming to 2\u2009\u00b0C (\u2009>\u200967%) (C3 climate category). We analyse 27 global 1.5\u2009\u00b0C scenario (C1 category) variables whose median values are reported in the AR6 WGIII SPM. The list of all the 27 variables and the impacts of removing the models and studies with the largest impact and the models and studies with the most scenarios, is shown in Table\u20091.\n\nThe impacts of removing individual models and studies are measured in two different ways, both shown in Table\u00a01. \u2018Between\u2019 measures the impact relative to the differences between 1.5\u2009\u00b0C and 2\u2009\u00b0C scenarios: it is a unitless measure of the change in median value when an individual model/study is removed relative to the difference between the 1.5\u2009\u00b0C and 2\u2009\u00b0C medians. A value of 100% means that the change in median value is the same as the (absolute) difference between the 1.5\u2009\u00b0C and 2\u2009\u00b0C medians. A value of 0% means that there is no change.\n\nwhere X is an individual model or study. \u2018Within\u2019 measures the impact relative to other models and studies within the same (1.5\u2009\u00b0C) climate category: it is a unitless measure of how close the reported median is to the median of the individual model/study that is removed versus the median of all the other models/studies\u00a0combined. A value of 100% means that the median coincides with the median of the dominant model/study, and a value of 0% means that the ensemble median coincides with the median of all the other models/studies. A value above 50% means that the reported median is closer to the median of the dominant model/study than to the median of all the other models/studies taken together.\n\nwhere X is an individual model or study.\n\nWe use the climate categories as defined in the AR6 WGIII report2. While the analysis of WGIII SPM findings includes scenarios only from the C1 and C3 categories, the analysis of the overall impact of dominant models on the AR6 scenarios database includes scenarios from all (C1\u2013C8) categories.\n\nCategory C1 includes scenarios that limit warming to 1.5\u2009\u00b0C in 2100 with a likelihood of greater than 50% and that reach or exceed warming of 1.5\u2009\u00b0C during the 21st century with a likelihood of 67% or less. These scenarios are referred to in the AR6 report as scenarios that limit warming to 1.5\u2009\u00b0C (\u2009>\u200950%) with no or limited overshoot. Limited overshoot means exceeding 1.5\u2009\u00b0C by up to about 0.1\u2009\u00b0C for up to several decades. Category C3 includes scenarios that limit peak warming to 2\u2009\u00b0C throughout the 21st century with a likelihood of greater than 67%. These scenarios are referred to in the AR6 report as scenarios that limit warming to 2\u00b0C (\u2009>\u200967%).\n\nCategory C2 includes scenarios that limit warming to 1.5\u2009\u00b0C in 2100 with a likelihood of greater than 50% and exceed warming of 1.5\u2009\u00b0C during the 21st century with a likelihood of greater than 67%. These scenarios are referred to in AR6 as scenarios that return warming to 1.5\u2009\u00b0C (\u2009>\u200950%) after a high overshoot. High overshoot refers to temporarily exceeding 1.5\u2009\u00b0C global warming by 0.1\u2009\u00b0C\u20130.3\u2009\u00b0C for up to several decades. Categories C4, C5, C6 and C7 include scenarios that limit warming to 2\u2009\u00b0C, 2.5\u2009\u00b0C, 3\u2009\u00b0C, 4\u2009\u00b0C, respectively, throughout the 21st century with a likelihood of greater than 50%. Category C8 includes scenarios that exceed a warming of 4\u2009\u00b0C during the 21st century with a likelihood of 50% or more.\n\nTo capture core model structure, we group what would generally be considered different versions of the same model (in model documentation and publications) together. For the scenarios that passed vetting and received a climate category, this results in 13 unique models. The list of unique model names and corresponding model versions is provided in Supplementary Table\u20093, together with the model acronyms used in tables and figures.\n\nDue to differences in naming conventions across modelling groups, it is difficult to know how large the differences between different model versions are. Some modelling groups give their model a different name for each modelling study that the model takes part in (e.g., POLES), and other groups do not (e.g., AIM). Some modelling groups use long and detailed model names to distinguish different versions and sub-versions, not only for the core model, but also for sub-models, from each other (e.g., MESSAGE and REMIND, linked to the land use models GLOBIOM and MagPIE).\n\nVisual inspection of box plots (e.g., Figure\u20093 or Supplementary Figs.\u20091\u20133) suggests that the unique model names that we use capture core structural differences: there is a clear correlation between variable values and models.\n\nStudy groupings are based on the \u2018Project_study\u2019 category in the AR6 scenarios database metadata3. \u2018Project_study\u2019 describes the parent project or individual study from which each scenario derives. This category is kept intact, as given in the metadata. This results in a total of 30 studies for the scenarios that passed vetting and received a climate category. The list of studies is provided in Supplementary Table\u20094, together with the acronyms used in tables and figures.\n\nScenarios are first assigned to models and studies from which they derive, according to Supplementary Tables\u20093, 4 (and as explained above). All the scenarios from each model/study are then removed from the ensemble, one-by-one, to calculate the median value without that model/study. The impacts from the models and studies with the largest impact are shown in Table\u00a01, together with the impacts from the models and studies with the most scenarios (when these are different).\n\nThe analysis of the overall impact of dominant models is complicated by the fact that i) each model reports different scenario variables (both from other models and across its own scenarios), and ii) each model has a different number of scenarios in each climate category. What model is the dominant model, therefore, depends on both the scenario category and the scenario variable: the same variable can be dominated by different models in different climate categories, and different variables within the same climate category can be dominated by different models.\n\nTo assess the overall impact of dominant models on the AR6 scenarios database, we compute the impact on each variable in each climate category of the model that (for that variable, in that climate category) has the most scenarios. More specifically, we compute the number of variables for which the median (in 2050) is closer to the median of the dominant model than to the median of all the other models combined, corresponding to a value above 50% for the \u2018Within\u2019 measure (Eq.\u2009(2) above). We do this for all scenario variables reported by at least two models, in each climate category. We exclude variables that are reported by only a single model because the median in this case is closer to the median of the dominant model than to the median of all other model scenarios (of which there are none) by default. Had we also included variables that are reported by only a single model, the percentage of median values that are closer to the median of the dominant model than to the median of all other models would be higher. If there is more than one model that has the most scenarios (for a given variable in a given climate category), we calculate the shift in median value of removing each one at a time and select the model whose removal leads to the greatest shift in the median to be the dominant model.\n\nBecause each climate category contains different scenarios from different models, and because different models report different variables (in different scenarios), the number of variables in each climate category differs (Supplementary Data\u20091). Only a subset of these, again, are reported by more than one model. There are 967 variables reported by at least two models in the C1 category, 978 variables in the C2 category, 1001 variables in the C3 category, 892 variables in the C4 category, 963 variables in the C5 category, 942 variables in the C6 category, 990 variables in the C7 category, and 518 variables in the C8 category. This amounts to a total of 7251 different median values, from at least two models, in the AR6 scenarios database.\n\nAll global scenario data were submitted to the AR6 scenarios database using a common scenario reporting template. In the template, all variables are listed in a common format and assigned a Tier: \u201cTier 1 variables define a core set of information that would enable assessing the scenario in a meaningful way\u201d, \u201cTier 2 variables are important for enabling more specific analyses\u201d40, and remaining variables are not assigned a Tier. In case of constraints for providing scenario data, modelling teams were asked to consider the ranking of importance (Tier 1 and Tier 2).\n\nDifferent Tiers were assigned by different chapters in WGIII. Of the 1871 variables that are listed in the common scenario reporting template, 303 are marked as \u2018core\u2019. Of these core variables, 82 are Tier 1 and 221 are Tier 2. Of these, again, 79 Tier 1 variables and 201 Tier 2 variables are included in the AR6 scenarios database (Supplementary Data\u20092). These are the variables analysed in Fig.\u20095. The AR6 WGIII call for scenarios and templates is available at https://data.ene.iiasa.ac.at/ar6-scenario-submission/#/about.\n\nThe model- and study-weighted medians, shown in Fig.\u20096 and Supplementary Figs.\u20097\u20139, give each model and study equal weight. This is done by weighting each scenario from a model or study according to the inverse of the number of scenarios from that model or study.",
+            "section_image": []
+        },
+        {
+            "section_name": "Data availability",
+            "section_text": "All the data analysed is from the IPCC AR6 Scenarios Database, which is available through the AR6 Scenario Explorer and Database hosted by IIASA3.",
+            "section_image": []
+        },
+        {
+            "section_name": "Code availability",
+            "section_text": "The code used for analysis in this study is available for download45.",
+            "section_image": []
+        },
+        {
+            "section_name": "References",
+            "section_text": "Skea, J., Shukla, P., Al Khourdajie, A. & McCollum, D. Intergovernmental panel on climate change: transparency and integrated assessment modeling. Wiley Interdiscip. Rev. Clim. Change 12, (2021).\n\nIPCC. Climate Change 2022: Mitigation of Climate Change. Contribution of working group III to the sixth assessment report of the intergovernmental panel on climate change. https://doi.org/10.1017/9781009157926 (Cambridge University Press, Cambridge, UK and New York, NY, USA, (2022).\n\nByers, E. et al. AR6 scenarios database. https://doi.org/10.5281/ZENODO.7197970 (2022).\n\nvan Beek, L., Hajer, M., Pelzer, P., van Vuuren, D. & Cassen, C. Anticipating futures through models: the rise of Integrated Assessment Modelling in the climate science-policy interface since 1970. Glob. Environ. Change 65, 102191 (2020).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nIPCC. Global Warming of 1.5\u2009\u00b0C An IPCC Special Report on the Impacts of Global Warming of 1.5\u2009\u00b0C above Pre-Industrial Levels and Related Global Greenhouse Gas Emission Pathways, in the Context of Strengthening the Global Response to the Threat of Climate Change. (2018).\n\nIPCC. Climate Change 2014: Mitigation of Climate Change. Working Group III Contribution to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change. (2014).\n\nAuer, C. et al. Climate change scenario services: from science to facilitating action. One Earth 4, 1074\u20131082 (2021).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nTCFD. Final report: recommendations of the task force on climate-related financial disclosures. https://assets.bbhub.io/company/sites/60/2021/10/FINAL-2017-TCFD-Report.pdf (2017).\n\nNetwork for greening the financial system. NGFS climate scenarios for central banks and supervisors. https://www.ngfs.net/sites/default/files/medias/documents/ngfs_climate_scenarios_for_central_banks_and_supervisors_.pdf.pdf (2022).\n\nChristopher Weber et al. Mitigation scenarios must cater to new users. Nat. Clim. Chang 8, 843\u2013851 (2018).\n\nADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nRiahi, K. et al. Mitigation pathways compatible with long-term goals. in Climate Change 2022: Mitigation of Climate Change. Contribution of Working Group III to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change. (eds. P. R. Shukla, J. Skea & R. Slade) (Cambridge University Press, Cambridge, UK and New York, NY, USA, 2022).\n\nGlen P. P., Alaa Al Khourdajie, Ida Sognnaes. & Benjamin Sanderson. AR6 scenarios database: An assessment of current practices and future recommendations. npj Climate Action 2, https://doi.org/10.1038/s44168-023-00050-9 (2023).\n\nGuivarch, C. et al. Using large ensembles of climate change mitigation scenarios for robust insights. Nat. Clim. Chang 12, 428\u2013435 (2022).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nHuppmann, D., Rogelj, J., Kriegler, E., Krey, V. & Riahi, K. A new scenario resource for integrated 1.5 \u00b0C research. Nat. Clim. Chang 8, 1027\u20131030 (2018).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nSognnaes, I. et al. A multi-model analysis of long-term emissions and warming implications of current mitigation efforts. Nat. Clim. Chang 11, 1055\u20131062 (2021).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKrey, V. et al. Looking under the hood: a comparison of techno-economic assumptions across national and global integrated assessment models. Energy 172, 1254\u20131267 (2019).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nJaxa-Rozen, M. & Trutnevyte, E. Sources of uncertainty in long-term global scenarios of solar photovoltaic technology. Nat. Clim. Chang 11, 266\u2013273 (2021).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nRiahi, K. et al. Cost and attainability of meeting stringent climate targets without overshoot. Nat. Clim. Chang 11, 1063\u20131069 (2021).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nAl Khourdajie, A., Skea, J. & Green, R. Climate ambition, background scenario or the model? Attribution of the variance of energy-related indicators in global scenarios.Energy Clim. Change 5, 10012 (2024).\n\n\n                    Google Scholar\u00a0\n                \n\nDekker, M. M. et al. Spread in climate policy scenarios unravelled. Nature 624, 309\u2013316 (2023).\n\nArticle\u00a0\n    ADS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDekker, M. M. et al. Identifying energy model fingerprints in mitigation scenarios. Nat. Energy 8, 1395\u20131404 (2023).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nIPCC. Summary for Policymakers. In Climate Change 2022: Mitigation of Climate Change. Contribution of Working Group III to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change (eds. Shukla, P. R. et al.) https://doi.org/10.1017/9781009157926.001 (Cambridge University Press, Cambridge, UK and New York, NY, USA, 2022).\n\nUN Environment Programme. Emissions Gap Report 2022: The Closing Window. (2022).\n\nUNFCCC. Sharm el-Sheikh Implementation Plan. https://unfccc.int/sites/default/files/resource/cop27_auv_2_cover%20decision.pdf (2022).\n\nM\u00fcller-Casseres, E., Edelenbosch, O. Y., Szklo, A., Schaeffer, R. & van Vuuren, D. P. Global futures of trade impacting the challenge to decarbonize the international shipping sector. Energy 237, 121547 (2021).\n\nvan Vuuren, D. et al. The 2021 SSP Scenarios of the IMAGE 3.2 Model. http://eartharxiv.org/repository/view/2759/, https://doi.org/10.31223/X5CG92 (2021).\n\nCointe, B., Cassen, C. & Nada\u00ef, A. Organising policy-relevant knowledge for climate action: Integrated assessment modelling, the IPCC, and the emergence of a collective expertise on socioeconomic emission scenarios. Sci. Technol. Stud. 32, 36\u201357 (2019).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nYves Till\u00e9. Balanced Sampling. In International Encyclopedia of Statistical Science (ed. Miodrag Lovric) 81\u201382 (Springer, 2011).\n\nBhattacherjee, A. Social Science Research: Principles, Methods and Practices. (University of Southern Queensland, 219AD).\n\nSanderson, B. M., Knutti, R. & Caldwell, P. Addressing interdependency in a multimodel ensemble by interpolation of model properties. J. Clim. 28, 5150\u20135170 (2015).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nSanderson, B. M., Knutti, R. & Caldwell, P. A representative democracy to reduce interdependency in a multimodel ensemble. J. Clim. 28, 5171\u20135194 (2015).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nSanderson, B. M., Wehner, M. & Knutti, R. Skill and independence weighting for multi-model assessments. Geosci. Model Dev. 10, 2379\u20132395 (2017).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKnutti, R. et al. A climate model projection weighting scheme accounting for performance and interdependence. Geophys Res Lett. 44, 1909\u20131918 (2017).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nIPCC. Climate Change 2021: The Physical Science Basis. Contribution of Working Group I to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change. https://doi.org/10.1017/9781009157896 (Cambridge University Press, Cambridge, 2021).\n\nSchwanitz, V. J. Evaluating integrated assessment models of global climate change. Environ. Model. Softw. 50, 120\u2013131 (2013).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nIPCC. Frequently Asked Questions. https://www.ipcc.ch/help/frequently-asked-questions/ (2025).\n\nMastrandrea, M. D. et al. Guidance note for lead authors of the ipcc fifth assessment report on consistent treatment of uncertainties. Intergovernmental Panel on Climate Change (IPCC) https://www.ipcc.ch/site/assets/uploads/2018/05/uncertainty-guidance-note.pdf (2010).\n\nNakicenovic, N. & Swart, R. IPCC special report on emissions scenarios: a special report of working group iii of the Intergovernmental Panel on Climate Change. Emissions Scenarios (2000).\n\nEmmerling, J. et al. The role of the discount rate for emission pathways and negative emissions. Environ. Res. Lett. 14, 104008 (2019).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nInternational Institute for Applied Systems Analysis (IIASA). Request for emissions scenario data in support of the IPCC\u2019s Sixth Assessment Report. https://data.ece.iiasa.ac.at/ar6-scenario-submission/static/files/global_sectoral/calls/AR6_ScenarioDB_Call_Global-Sectoral_v2_16Jan2020.pdf (2020).\n\nLuderer, G. et al. Impact of declining renewable energy costs on electrification in low-emission scenarios. Nat. Energy 7, 32\u201342 (2022).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nGrubler, A. et al. A low energy demand scenario for meeting the 1.5 \u00b0C target and sustainable development goals without negative emission technologies. Nat. Energy 3, 515 (2018).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nGiarola, S. et al. Challenges in the harmonisation of global integrated assessment models: a comprehensive methodology to reduce model response heterogeneity. Sci. Total Environ. 783, 146861 (2021).\n\nArticle\u00a0\n    PubMed\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nPeace, J. & Weyant, J. P. Insights not numbers: the appropriate use of economic models. (2008).\n\nIda, S. & Glen, P. Peters. MATLAB code for the manuscript \u2018Influence of individual models and studies on quantitative mitigation findings in the IPCC Sixth Assessment Report\u2019. Zenodo https://doi.org/10.5281/zenodo.10975768 (2025).\n\nDownload references",
+            "section_image": []
+        },
+        {
+            "section_name": "Acknowledgements",
+            "section_text": "I.S. and G.P.P. were supported by the European Union\u2019s Horizon Europe research and innovation programme under grant agreement no. 101056306 (IAM COMPACT)\u00a0and\u00a0no.\u00a0101081179 (DIAMOND), by the Norwegian Research Council, Finance Market Fund, project no. 309613 (Using scenarios to assess climate risks in the financial sector, StressTest), and the Norwegian Research Council project no. 334811 (Tracking Risks in Future Emission, Climate and Technological Assumptions, TRIFECTA).",
+            "section_image": []
+        },
+        {
+            "section_name": "Author information",
+            "section_text": "CICERO Center for International Climate Research, Oslo, Norway\n\nIda Sognnaes\u00a0&\u00a0Glen P. Peters\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nI.S. conceived of and designed the analysis and wrote the initial draft. I.S. and G.P.P. interpreted the data and wrote, read, and approved the final article.\n\nCorrespondence to\n                Ida Sognnaes.",
+            "section_image": []
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+            "section_text": "Nature Communications thanks B\u00e9atrice Cointe, Ruben Pr\u00fctz and the other anonymous, reviewer(s) for their contribution to the peer review of this work. A peer review file is available.",
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+            "section_text": "Sognnaes, I., Peters, G.P. Influence of individual models and studies on quantitative mitigation findings in the IPCC Sixth Assessment Report.\n                    Nat Commun 16, 8343 (2025). https://doi.org/10.1038/s41467-025-64091-w\n\nDownload citation\n\nReceived: 23 December 2024\n\nAccepted: 08 September 2025\n\nPublished: 02 October 2025\n\nVersion of record: 02 October 2025\n\nDOI: https://doi.org/10.1038/s41467-025-64091-w\n\nAnyone you share the following link with will be able to read this content:\n\nSorry, a shareable link is not currently available for this article.\n\n\n\n\n                            Provided by the Springer Nature SharedIt content-sharing initiative\n                        ",
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207ec70f665288822320c0b0d0f25d06cc124d0edc8ea9ec03b38b0b65ab8bbd/metadata.json

@@ -0,0 +1,173 @@
+{
+    "title": "Variants in NR6A1 cause a novel oculo vertebral renal syndrome",
+    "pre_title": "Variants in NR6A1 cause a novel oculo-vertebral-renal (OVR) syndrome",
+    "journal": "Nature Communications",
+    "published": "03 July 2025",
+    "supplementary_0": [
+        {
+            "label": "Supplementary Information",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-60574-y/MediaObjects/41467_2025_60574_MOESM1_ESM.pdf"
+        },
+        {
+            "label": "Description of Additional Supplementary Files",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-60574-y/MediaObjects/41467_2025_60574_MOESM2_ESM.pdf"
+        },
+        {
+            "label": "Supplementary Data 1-5",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-60574-y/MediaObjects/41467_2025_60574_MOESM3_ESM.xlsx"
+        },
+        {
+            "label": "Reporting Summary",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-60574-y/MediaObjects/41467_2025_60574_MOESM4_ESM.pdf"
+        },
+        {
+            "label": "Transparent Peer Review file",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-60574-y/MediaObjects/41467_2025_60574_MOESM5_ESM.pdf"
+        }
+    ],
+    "supplementary_1": [
+        {
+            "label": "Source Data",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-60574-y/MediaObjects/41467_2025_60574_MOESM6_ESM.xlsx"
+        }
+    ],
+    "supplementary_2": NaN,
+    "source_data": [
+        "https://sharing.nih.gov/accessing-data/accessing-genomic-data/how-to-request-and-access-datasets-from-dbgap",
+        "/articles/s41467-025-60574-y#Sec26"
+    ],
+    "code": [
+        "https://github.com/davemcg/nr6a1/releases/tag/1.3",
+        "/articles/s41467-025-60574-y#ref-CR58",
+        "https://github.com/NIH-NEI/variant_prioritization/releases/tag/v0.1",
+        "/articles/s41467-025-60574-y#ref-CR59"
+    ],
+    "subject": [
+        "Disease model",
+        "Hereditary eye disease",
+        "Medical genetics"
+    ],
+    "license": "http://creativecommons.org/licenses/by/4.0/",
+    "preprint_pdf": "https://www.researchsquare.com/article/rs-5375105/v1.pdf?c=1751627264000",
+    "research_square_link": "https://www.researchsquare.com//article/rs-5375105/v1",
+    "nature_pdf": "https://www.nature.com/articles/s41467-025-60574-y.pdf",
+    "preprint_posted": "14 Nov, 2024",
+    "research_square_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Colobomatous microphthalmia is a potentially blinding congenital ocular malformation that can present either in isolation or together with other syndromic features. Despite a strong genetic component to disease, many cases lack a molecular diagnosis. We describe a novel autosomal dominant oculo-vertebral-renal (OVR) syndrome in six independent families characterized by colobomatous microphthalmia, missing vertebrae and congenital kidney abnormalities. Genome sequencing identified six rare variants in the orphan nuclear receptor gene NR6A1 in these families. We performed in silico, cellular and zebrafish experiments to demonstrate the NR6A1 variants were pathogenic or likely pathogenic for OVR syndrome. Knockdown of either or both zebrafish paralogs of NR6A1 results in abnormal eye and somite development, which was rescued by wild-type but not variant NR6A1 mRNA. Illustrating the power of genomic ascertainment in medicine, our study establishes NR6A1 as a critical factor in eye and vertebral development and a pleiotropic gene responsible for OVR syndrome.Health sciences/Medical research/Genetics researchBiological sciences/Genetics/Development",
+            "section_image": []
+        },
+        {
+            "section_name": "Additional Declarations",
+            "section_text": "There is NO Competing Interest.",
+            "section_image": []
+        },
+        {
+            "section_name": "Supplementary Files",
+            "section_text": "SupplementalTables.xlsxSupplementary Tables",
+            "section_image": []
+        }
+    ],
+    "nature_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Colobomatous microphthalmia is a potentially blinding congenital ocular malformation that can present either in isolation or together with other syndromic features. Despite a strong genetic component to disease, many cases lack a molecular diagnosis. We describe an autosomal dominant oculo-vertebral-renal (OVR) syndrome in six independent families characterized by colobomatous microphthalmia, missing vertebrae and congenital kidney abnormalities. Genome sequencing identified six rare variants in the orphan nuclear receptor gene NR6A1 in these families. We performed in silico, cellular, and zebrafish experiments to demonstrate the NR6A1 variants were pathogenic or likely pathogenic for OVR syndrome. Knockdown of either or both zebrafish paralogs of NR6A1 results in abnormal eye, kidney, and somite development, which was rescued by wild-type but not variant NR6A1 mRNA. Illustrating the power of genomic ascertainment in medicine, our study establishes NR6A1 as a critical factor in eye, kidney, and vertebral development, and a pleiotropic gene responsible for OVR syndrome.",
+            "section_image": []
+        },
+        {
+            "section_name": "Introduction",
+            "section_text": "Uveal coloboma is a congenital ocular malformation caused by failure of the ventral optic fissure to close during early eye morphogenesis and is usually considered on a phenotypic continuum with microphthalmia and anophthalmia1,2,3,4,5. A rare condition6,7,8,9,10,11, coloboma may nonetheless account for up to 10% of childhood blindness12. Although significant progress has been made in identifying genes associated with syndromic and non-syndromic coloboma, the yield of diagnostic testing remains low, especially for isolated, non-syndromic coloboma, suggesting other genes are yet to be discovered13,14,15. To identify novel coloboma genes, the National Eye Institute has conducted a natural history study since 2006, on the genetics of coloboma that includes systematic deep phenotyping of probands and first-degree family members. We have previously identified a syndrome characterized by missing vertebrae (in the thoracic and/or lumbar spine), congenital kidney abnormalities, and uveal coloboma, inherited in an autosomal dominant fashion with incomplete penetrance and variable expressivity16.\n\nWe identified structural and sequence variants in the transcription factor gene NR6A1 (Nuclear receptor subfamily 6, group A, member 1, OMIM*602778) in three families by genome sequencing (GS). These results were extended via analysis of the Genomics England 100,000 Genomes Project (UK100KGP), where three additional individuals with microphthalmia/anophthalmia/coloboma were identified17.\n\nOriginally termed germ cell nuclear factor (GCNF)/retinoid receptor-related testis-associated receptor (RTR), NR6A1 is an orphan member of the nuclear hormone receptor family of transcription factors, often acting as a transcriptional repressor. NR6A1 is highly expressed in embryonic and other stem cells from various tissues (especially testes) and is repressed upon differentiation. NR6A1 plays an important role in somite and subsequent vertebral development in mice, and in livestock species it is correlated with vertebral number18,19,20,21. To our knowledge, there are no reports on the role of NR6A1 in eye or kidney development.\n\nHere we described an autosomal dominant oculo-vertebral-renal (OVR) syndrome caused by variants in the orphan nuclear receptor gene NR6A1, supporting the pathogenicity of variants through a combination of in silico, in vitro, and in vivo investigations. To our knowledge, this is an undescribed Mendelian trait in humans characterized by missing vertebrae.",
+            "section_image": []
+        },
+        {
+            "section_name": "Results",
+            "section_text": "We identified three rare NR6A1 variants in three families affected by uveal coloboma (COL005, COL034, COL171) with or without microphthalmia, cataract, and missing vertebrae through genome sequencing. In cases where multiple generations are affected, transmission is autosomal dominant with incomplete penetrance and variable expressivity (Fig.\u00a01a). Clinical data for all the participants with a positive molecular result is shown in Table\u00a01. No other candidate pathogenic variants in NR6A1 were identified in the NEI coloboma cohort consisting of a total of 224 probands (66 analyzed by genome sequencing, 57 by exome sequencing, and 101 by amplicon sequencing).\n\na Pedigrees of three families (COL005; COL034; COL171) from the NEI cohort demonstrating coloboma with or without microphthalmia and cataract, missing vertebrae, and congenital renal anomalies. Inheritance is autosomal dominant with incomplete penetrance and variable expressivity. b Linear pigmentary disturbance representing a forme fruste of coloboma (arrow) in COL005.1 (right eye). c Larger chorioretinal coloboma in the left eye of COL005.1 demonstrating a retinal tear in the far periphery (arrowhead). d Iris coloboma of the left eye of COL005.10. e Microphthalmia of the left eye in COL034.1. f Retro-illumination image of the left eye of COL171.1 demonstrating iris coloboma and posterior subcapsular cataract (open arrow). g Spine x-ray of COL005.4 demonstrating 11 thoracic (normal 12) and 4 lumbar (normal 5) vertebrae. h Schematic of NR6A1 variants detected in the NEI and UK Genomics England cohorts. + individual with variant, \u2212 individual without variant. DNA binding domain (DBD) and putative nuclear receptor ligand binding domain (NR-LBD) are noted (Q15406; InterPro).\n\nThe proband of the family (COL005.1) presented at age 14, with bilateral uveal colobomas (Fig.\u00a01b, c). Family history was notable for a younger brother (COL005.4), a second cousin (COL005.10), and a first cousin once removed (COL005.17) with uveal coloboma. The deletion breakpoints were in intron 2 and 6 removing the coding sequence for amino acids (aa) Ile48-Gly275 and likely causing a frameshift (p.Ile48Asnfs*3, Fig.\u00a01h). The status of the heterozygous deletion was determined by breakpoint PCR among family members available, which revealed complete segregation with the missing vertebrae with an estimated LOD score of 3.6 (Fig.\u00a01a, Supplementary Fig.\u00a01). Four family members were also affected by coloboma in addition to missing vertebra, of which one (COL005.17) also had unilateral renal agenesis by report. The proband of the family (COL034.1) presented at age 11 months with bilateral uveal colobomas and microphthalmia OS (Fig.\u00a01e). Prenatal history was remarkable for the inability of an ultrasound at 18 weeks to visualize the left kidney. Systemic testing demonstrated 10 thoracic vertebrae and left renal agenesis. Genome sequencing revealed a heterozygous c.274C>T p.(Arg92Trp) variant in NR6A1, which was found in the affected mother and unaffected grandfather (Fig.\u00a01a, h). The proband of the family (COL171.1) presented at age 36 with bilateral colobomatous microphthalmia affecting the iris, retina/choroid, and optic nerve. Slit lamp exam was notable for bilateral microcornea, bilateral posterior subcapsular and nuclear cataracts, and missing zonules inferiorly OU (Fig.\u00a01f). Genome sequencing revealed a heterozygous c.1306C>T p.(Arg436Cys) variant in the proband which was absent in his unaffected mother (Fig.\u00a01h). Detailed study of the probands and their family members available for evaluation, were described in clinical vignettes in the\u00a0Supplementary Notes. No convincing pathogenic variants in known coloboma genes were identified in any of these subjects.\n\nWe performed an unbiased disease association analysis of rare pLoF variants using the UK100KGP dataset17. After removing variants resulting from calling artifacts or mis-annotation, only three pLoF variants were found in the cohort with approximately 126,700 alleles (Supplementary Data\u00a01, Supplementary Fig.\u00a02). We found three probands, Proband (A1) presented at age 30, with bilateral chorioretinal coloboma (forme fruste OD) and OS coloboma of the optic nerve (Supplementary Fig.\u00a02b). Genome sequencing revealed a heterozygous c.965_980del p.(Ser322Ter), present in both the proband and her unaffected father. Proband (B1) presented at the age of 29, with a severe form of bilateral microphthalmia with a vestigial remnant of eyes, delayed motor development, intellectual disability, abnormal behavior, and schwannoma. This proband carried a heterozygous c.902G>A p.(Trp301Ter) variant. These two nonsense variants are expected to cause loss of protein function either through nonsense-mediated decay or truncation of the putative nuclear receptor ligand binding domain (NR-LBD, Fig.\u00a01h). Proband D (Supplementary Data\u00a01) had a disorder of sex development, carried variant c.288dup p.(Cys96TrpfsTer4), which was absent in either parent. His father was also affected with a disorder of sex development, suggesting that the NR6A1 variant is likely not associated with the condition.\n\nThe UK100KGP MAC cohort, which consists of 215 probands, was queried for rare missense and in-frame insertion/deletion variants. Proband C1, presented at the age of 25 with bilateral microcornea and coloboma affecting the iris, choroid/retina, and optic nerve. One brother had a similar condition by report. Both parents and the two other siblings of the proband had no history of coloboma by report. Genome sequencing revealed a heterozygous variant c.227_229del p.(Ser76del) present in the proband (Fig.\u00a01h, Supplementary Data\u00a01). This variant leads to an in-frame deletion of a serine within the Zn-finger motif. Within the three MAC patients we report, no candidate pathogenic variants were found in the known MAC genes present in the current Genomics England PanelApp (ocular coloboma v1.47, anophthalmia or microphthalmia v1.51, structural eye disease v3.79). Thus, these cases further support that rare variants in NR6A1 can cause MAC with reduced penetrance.\n\nThe NR6A1 amino acid sequence is well-conserved between human, mouse, and zebrafish; specifically, the residues Ser76, Arg92, and Arg436 are conserved across multiple species (Supplementary Fig.\u00a03). To understand the effects, missense variants had on protein stability and function, we created an in-silico model of a complex of NR6A1 with DNA (Supplementary Fig.\u00a04a). The AlphaFold model of NR6A1 is shown by the composition of Zn-finger (residues 60\u2013172) and NR_LBD (residues 246\u2013480) domains shown in orange and green, respectively. The rest of the model shown in gray is predicted as an irregular structure by AlphaFold. In wild-type (WT) NR6A1, a positively charged arginine residue 92 is predicted to interact with negatively charged DNA based on a zinc-finger protein model (Supplementary Fig.\u00a04b). The R92W variant replaces the R92 residue with hydrophobic tryptophan (W), possibly interrupting the electrostatic interaction with DNA. The R436C variant affects the putative nuclear receptor ligand binding domain NR_LBD. In NR6A1, hydrogen atom 1HH2 of arginine R436 closely interacts with the oxygen atom of glutamic acid E388 (Supplementary Fig.\u00a04c). The variant R436C breaks this bond and creates a cysteine residue which could form abnormal disulfide bridges in the variant protein, since residues C443, C391, and C422 are distanced at 8\u201312\u2009\u00c5 from C436 in this variant domain as compared to 14\u201319\u2009\u00c5 (C443\u2013C391), 11.09\u2009\u00c5 (C443\u2013C422) and 4.52\u2009\u00c5 (C91\u2013C422) in the WT protein model.\n\nTo study the functional impact of the missense variants on protein localization in the cell, the R92W and R436C mutations were introduced in WT NR6A1 cDNA fused to a GFP coding sequence. All experiments were performed in context to the NR6A1 isoform NM_033334.4 and repeated at least three times. Transfection efficiencies were between 50-60% for the WT and variant constructs as analyzed by flow-cytometry and Western blotting (Supplementary Figs.\u00a05, 6). The WT-NR6A1 when over-expressed in HEK293 cells was consistently observed to localize in the nucleus (Fig.\u00a02a, b), consistent with a previous report22. The R92W variant, although nuclear, was not uniformly distributed across the nucleus. To study the localization of R92W variant puncta to the nucleolus, we performed immunofluorescence staining of NR6A1 wild-type and mutant isoforms with nucleolar marker FIBRILLARIN. As shown in supplementary Fig.\u00a07, the punctae do not colocalize with FIBRILLARIN staining suggesting that the variant is not mis-localized to the nucleolus. In contrast, the R436C variant localized exclusively in the cytoplasm (Fig.\u00a02a, b). The above-described localization pattern of the WT and variant isoforms was consistent in all transfected cells and across multiple rounds of transfection. Taken together these results suggest that both missense variants likely interfere with NR6A1 function due to improper subcellular localization.\n\nNR6A1 variant localization pattern was studied by overexpression in HEK293 cells and representative high magnification (63X) images are shown from three different trials (a) Scale bar\u2009=\u200910\u2009\u00b5m. Low magnification images (b) scale bar 100\u2009\u00b5m. The localization pattern for the WT and the two variant isoforms was observed to be consistent across three transfection experiments. (Cells counted: WT\u2009=\u2009387, R92W\u2009=\u2009350 and R436C\u2009=\u2009217).\n\nAnalysis of bulk RNA-Seq datasets from ocular and non-ocular tissues demonstrates modest expression of NR6A1 in most tissues and relatively higher levels of expression in embryonic stem cells/induced pluripotent stem cells (compared to adult ocular tissues) and in bone marrow and testis systemically (Fig.\u00a03a, d)23,24. Consistent with this observation, bulk RNA-Seq data from human fetal tissue shows that NR6A1 expression is highest in early stages of development, including the time of optic fissure closure in the first trimester25,26 (Fig.\u00a03b). In the Human Retinal Cell Atlas single nucleus RNA-Seq dataset, NR6A1 is highly expressed in adult horizontal cells and low in microglia and RPE (Supplementary Fig.\u00a08)27. Expression of NR6A1 is strongly correlated (>5 fold enrichment, p\u2009=\u20090.0024) with that of other coloboma-associated genes in fetal ocular tissues (Fig.\u00a03c). This strength of enrichment was not seen in Genotype-Tissue Expression (GTEx) body tissue (p\u2009=\u20090.361) or adult eye tissue (p\u2009=\u20090.451)23,24. We note that several of the highly correlated genes-SALL4 (Duane-Radial Ray Syndrome), PAX2 (Papillorenal syndrome), ACGT1 (Baraitser-Winter Syndrome 2), SALL1 (Townes-Brocks Syndrome 1) can also present with congenital renal anomalies.\n\na Comparative levels of NR6A1 from publicly available bulk human tissue RNA-sequencing (RNA-Seq) datasets accessed on the eyeIntegration website (https://eyeintegration.nei.nih.gov/). On average, expression is higher in embryonic and induced pluripotent stem cells (ESC, iPSC, respectively) than in adult ocular tissues. b Bulk RNA-Seq data in human retinal fetal tissue from two studies suggests NR6A1 expression is highest in early stages of development, including the window of optic fissure closure (lavender box). NR6A1 expression is plotted against the tissue age (days post conception, dpc). A linear regression analysis was added for each paper\u2019s data from the 40 to 80\u2009dpc and 80 to 160\u2009dpc samples. c The density correlation plot (closer to \u22121 and 1 is more negatively or positively correlated, respectively) shows ten notable coloboma associated genes with highly ranked correlations with NR6A1 expression across eyeIntegration curated fetal retina and RPE tissues. This enrichment was not seen in adult tissues. d Among systemic tissues, NR6A1 is expressed most highly in bone marrow and testes. The boxplots display the median, 25th and 75th percentiles, and 1.5 * interquartile range (IQR). Any data outside the 1.5 * IQR are plotted. In panels a and d the number of samples is given above the boxplots.\n\nTo establish plausible causation for NR6A1 variants, we studied the embryonic expression of its orthologs in mouse and zebrafish model systems at developmentally relevant time points. Previous work has demonstrated widespread expression of Nr6a1 in mouse at E8.5 and E9.5 (including the optic vesicle) that becomes nearly undetectable by E12.521. To study expression in the optic cup around the time of optic fissure closure, we used a probe that detects all validated transcripts of mouse Nr6a1 at embryonic day 10.5 (E10.5, early optic cup) and E11.5 (time of optic fissure closure). The manufacturer\u2019s control probe against a bacterial sequence was used for reference (Supplementary Fig.\u00a09). At E10.5, we noted diffuse low-level expression throughout the early optic cup and surrounding tissues that becomes significantly decreased by the time optic fissure closure commences (E11.5) (Supplementary Fig.\u00a09). The level of expression in the optic cup is comparable to that observed in the brain vesicle, but higher than that observed in some areas of the surrounding eye mesenchyme.\n\nIn zebrafish, nr6a1 has two paralogs, nr6a1a and nr6a1b, both of which are maternally expressed28,29. At 11\u2009hpf, when the optic vesicle evaginates, nr6a1a is widely expressed throughout the embryo, especially rostrally, showing less expression towards the posterior embryo axis (Fig.\u00a04a, Supplementary Fig.\u00a010a). Expression of nr6a1a is seen in heart and periocular tissue at 14\u2009hpf (Supplementary Fig.\u00a011); expression in the heart reduced by 16\u2009hpf and is absent by 19\u2009hpf (Fig.\u00a04b, c). At 16\u2009hpf, nr6a1a remains widely expressed, while becoming restricted to the ventral regions of the brain, epiphysis, periocular tissues, heart and in the notochord and neural tube (Fig.\u00a04b); expression in the developing eye is reduced compared to the adjacent developing brain (Supplementary Fig.\u00a010b). Notably, nr6a1a expression is absent from the neural-mesodermal progenitor region in the tail of zebrafish embryos, consistent with its role in the trunk differentiation program21. By 19\u2009hpf the expression appears to decrease overall but remains present in the ventral brain regions, notochord, somites, and the pronephric duct (Fig.\u00a04c). At 24\u2009hpf, expression is prominent in the anterior diencephalon, tegmentum, midbrain, and along most of the length of the embryo in the neural tube; interestingly, expression is nearly absent from the neural retina and retina pigmented epithelia but is prominent in the lens (Fig.\u00a04d\u2013d\u201d). After 26\u2009hpf and up to 72\u2009hpf we observed no detectable nr6a1a expression, consistent with published single-cell mRNA expression during zebrafish development28,29.\n\nnr6a1a is expressed ubiquitously at 11\u2009hours post-fertilization (hpf) (a). By 16\u201319\u2009hpf (b, c) expression is present in multiple structures including the somites (S), neural tube (NT) and notochord (N). At 24\u2009hpf, expression remains in the NT but is decreased in the S and N. Expression in the lens (L) is first noted at 19\u2009hpf and is particularly prominent by 24\u2009hpf (d\u2013d\u201d\u2018\u2019). nr6a1b expression at 11\u2009hpf (e) is in\u00a0anterior trunk, localizing to neural tube and somites from 16\u2009hpf (f) and 19\u2009hpf (g). At 24hpf (h\u2013h\u201d) it remains expressed in the neural tube and somites, with faint expression can be seen in the lens. All embryos are oriented in a lateral view, anterior to the left and dorsal up, except (d\u2019, d\u201d, h\u2019, and h\u201d) shown in dorsal views. Scale bar\u2009=\u2009100\u2009\u00b5m. e-epiphysis, l-lens, p-pronephros, h- heart, n-notochord, s-somite, nt-neural tube, ad-anterior diencephalon, tg-tegmentum.\n\nUnlike nr6a1a, nr6a1b expression at 11\u2009hpf is limited to a patch in the posterior neuroectoderm of the embryo but excluded from the most caudal region (Fig.\u00a04e). At 16\u2009hpf and 19\u2009hpf, nr6a1b expression is prominent in the neural tube, somites, and pronephric duct and, like nr6a1a, is excluded from the neural-mesodermal progenitor region in the tail (Fig.\u00a04f, g). By 24\u2009hpf, expression is decreased in most tissues but remains in the tegmentum, cranial ganglia, neural tube, and somites in the distal region of the trunk (Fig.\u00a04h-h\u201d). By 36\u2009hpf and through 72\u2009hpf, nr6a1b is notably expressed in the developing lens, brain, and cranial ganglions. (Supplementary Fig.\u00a012). At 72\u2009hp we also note faint expression in the retina and in the presumed RPE (Supplementary Fig.\u00a012d, e).\n\nAll MO experiments were carried out following the guidelines set forth for their use in zebrafish30,31,32. These guidelines include: 1) use of two non-overlapping MOs (one translation blocking (TB), one splice blocking (SB)); 2) observation of a consistent phenotype with both TB and SB MOs for each paralog; 3) a correlation between dose of MO and phenotype, with lower concentrations of MO causing a milder phenotype; 4) validation of the efficacy of SB MOs by RT-PCR analysis; 5) lack of a phenotype with injection of a control MO; and; 6) partial rescue of the MO phenotype with co-injection of the corresponding human mRNA.\n\nTo test the functional consequences of nr6a1a and nr6a1b knockdown, we designed TB and SB MOs for each paralog of the gene. The sequence of the TB morpholinos does not overlap with the human mRNA sequence and is therefore unlikely to interfere with mRNA rescue experiments (Supplementary Fig.\u00a013). Morphants were divided into four phenotypes: normal, mild (normal/near normal body axis with microphthalmia), moderate (slightly shortened and mildly curved body axis, microphthalmia\u2009\u00b1\u2009coloboma and heart edema) or severe (significantly shortened and curved body axis, microphthalmia\u2009\u00b1\u2009coloboma, heart edema) (Fig.\u00a05a\u2013d\u2019, Supplementary Figs.\u00a014, 15). Embryos were scored at 72\u2009hpf (after optic fissure closure and initial stages of eye growth are normally completed) to ensure microphthalmia/coloboma represents a true phenotype and not because of developmental delay or undergoing growth compensation.\n\nControls (a, a\u2019) have a straight body axis and the optic fissure (OF) is closed. The nr6a1+nr6a1b morphants that have a mild phenotype (b, b\u2019) have close to a normal body with microphthalmia and heart edema; a moderate phenotype (c, c\u2019) with a slightly bent body axis with smaller eyes, coloboma and a severe heart edema; and severe morphants (d, d\u2019) have a curved body axis with smaller eyes, coloboma and heart edema. The morphant phenotype was rescued when the morpholinos were co-injected along with the human-NR6A1-wild-type mRNA. However, there was no significant rescue in the morphant phenotype when the morpholinos were injected with either R92W or R436C human disease-causing variants (e). Morpholinos were injected at 0.75\u2009ng each (1.5\u2009ng total). Embryos were imaged at 72\u2009hpf. Scale bar\u2009=\u2009100\u2009\u00b5m. Statistical significance was calculated using Chi-square test and Fisher\u2019s test. P value of nr6a1-TB-MO(a\u2009+\u2009b) V hWT-NR6A1 is <0.0001 and between nr6a1-TB-MO(a\u2009+\u2009b) V hR92W and hR436C are 0.0266 and 0.5169 respectively. Source data file has been provided for (e).\n\nKnockdown of nr6a1a (Supplementary Fig.\u00a014e) or nr6a1b (Supplementary Fig.\u00a015e) with either TB-MO or SB-MO resulted in a significant number of moderate and severe phenotypes with few mild phenotypes. Although the effect of TB-MO and SB-MO were similarly potent for nr6a1b knockdown, the SB-MO had a stronger effect than the TB-MO for nr6a1a. SB-MO knockdown of the gene was validated for both paralogs by reverse transcription-PCR experiments (Supplementary Figs.\u00a014f, 15f). MOs can elicit p53-activated cell death and cause non-specific defects33. We therefore tested MOs for both nr6a1 paralogues at all concentrations used with and without co-injection of a p53-MO. The phenotypic spectrum was not affected by co-injection of this p53 MO, suggesting widespread cell death was not the primary cause of our observations (Supplementary Fig.\u00a016).\n\nOverexpression of 100\u2009pg of human NR6A1 mRNA in zebrafish shows no overt phenotype (Supplementary Fig.\u00a017a, b). Co-injection of 2\u2009ng and 1.25\u2009ng of nr6a1a and nr6a1b, TB-MO respectively along with 100\u2009pg of WT human mRNA (hWT-NR6A1), resulted in a rescue, with over 60% embryos exhibiting a normal/control-injected phenotype, thus validating our TB-MO\u2019s (Supplementary Figs.\u00a014g, 15g). In contrast, co-injection with either hR92W or the hR436C missense variants of NR6A1 identified in coloboma patients were significantly less effective in rescuing the zebrafish nr6a1a/b knockdown, indicating that the missense variants are deleterious (Supplementary Figs.\u00a014g, 15g).\n\nTo study the effect of knocking down of both nr6a1a and nr6a1b zebrafish paralogues, we co-injected 0.75\u2009ng of TB-MO for each paralog (1.5\u2009ng total), resulting in a similar spectrum of eye and body axis phenotypes compared to the knockdown of individual paralogues (Fig.\u00a05a\u2013d, a\u2019\u2013d\u2019). At 48\u2009hpf, double morphants exhibited abnormal expression of nphs1/nephrin and nphs2/podocin, both of which are required for the formation, maturation and maintenance of kidneys34,35,36 (Fig.\u00a06a\u2013j). The spectrum of expression patterns included reduced, absent, midline and asymmetric expression of nphs1/2 (Fig.\u00a06d, h) which persisted at 72\u2009hpf (Supplementary Fig.\u00a018).\n\nAt 48\u2009hpf, control embryos demonstrate bilateral expression of nphs1 (nephrin) and nphs2 (podocin) (a, f), markers of kidneys. Knockdown of nr6a1(a\u2009+\u2009b) resulted in a range of abnormal expression patterns including mildly reduced expression (b, g), moderately reduced expression (c, h), unilateral or midline expression (d, i) or absent expression (e, j) of nphs1 and nphs2. Somites (the early precursors of vertebrae) have a sharp, chevron shape with an approximately 90-degree angle in control zebrafish at 24\u2009hpf (k). Knockdown of nr6a1a and nr6a1b resulted in a range of abnormal expression patterns including chevron shapes with obtuse angles (l), as well as mildly rounded (m) or flattened (n) somites. The sclerotome marker pax9 is expressed in a continuous angular pattern in the ventromedial portion of somites along the length of 24\u2009hpf control embryos (o). Double morphant embryos exhibit a spectrum of abnormal patterns of pax9 expression including reduced levels of expression (p), patchy expression extending beyond the caudal tip of the yolk (q) and patchy expression ending near the caudal end of the yolk sac (r). nr6a1(a\u2009+\u2009b) morphants have reduced number of somites (s), statistical significance is calculated using two tailed t-test. Std-MO n\u2009=\u200920 and nr6a1-TB-MO(a\u2009+\u2009b) n\u2009=\u200950. Data is represented as difference between means of nr6a1-TB(a\u2009+\u2009b)\u2013Std-MO\u2009\u00b1\u2009SEM (\u22124.490\u2009\u00b1\u20090.5629). P value is <0.0001. 0.75\u2009ng of each paralogue is used for knock-down. Numbers of each representative pattern are given in each panel. Scale bar\u2009=\u2009100\u2009\u00b5m. Source data file has been provided for (s).\n\nVertebrae develop from the sclerotome of somites during development37,38. At 24\u2009hpf, control embryos have chevron shaped somites, while morphants exhibit a spectrum of abnormal morphologies ranging from blunting of the chevron angle to more severe U-shaped or flattened somites (Fig.\u00a06k-n). Double morphants also exhibit a significantly decreased number of somites, consistent with the missing vertebrae phenotype in several patients (Fig.\u00a01, Fig.\u00a06s). Similarly, the sclerotome marker pax939,40 is expressed in a uniform and regular pattern in the ventromedial region of somites of control embryos at 24\u2009hpf (Fig.\u00a06o). By comparison, double morphants show varying degrees of decreased and/or patchy pax9 expression (Fig.\u00a06p-r). Overall, our results indicate that it is likely that nr6a1a\u2009+\u2009b morphant embryos have defective vertebrae development.\n\nInjection of TB-MO\u2019s, nr6a1(a\u2009+\u2009b), resulted in 16% and 49% embryos having severe and moderate phenotypes respectively; co-injection of 100\u2009pg hWT-NR6A1 mRNA, resulted in >50% embryos having straight body and normal eye, however 19% of these embryos show, heart edema. Breaking down each phenotype separately, we rescued approximately 55% embryos for coloboma, 53% for body axis and 44% for heart edema. Neither the hR92W nor hR436C NR6A1 mRNAs resulted in significant rescue, of any of the described phenotypes, confirming the pathogenicity of these variants (Fig.\u00a05e, Supplementary Data\u00a05). Injection of 0.75\u2009ng of either nr6a1a TB-MO or nr6a1b TB-MO resulted in a significantly milder phenotype, suggesting that co-injection of these had at least an additive phenotypic effect in the combined MO injection experiment (Supplementary Fig.\u00a019).\n\nA prior study reported that both overexpression and loss-of-function of nr6a1 can result in developmental phenotypes in Xenopus laevis41, we also evaluated the effect of injection of human NR6A1 mRNA on zebrafish development. Overexpression of 150\u2009pg of hNR6A1 mRNA resulted in microphthalmia and heart edema with a straight body axis (n\u2009=\u200991/108) (Supplementary Fig.\u00a017c, c\u2019). At 200\u2009pg, overexpression of hNR6A1 mRNA, phenotypes were more severe including colobomatous microphthalmia, heart edema and a bent body axis (n\u2009=\u200960/92), with 26% (n\u2009=\u200924/92) (Supplementary Fig.\u00a017 d-f\u2019), exhibiting noticeable shortening and loss of chevron-shaped somites (Supplementary Fig.\u00a020); a minority of embryos (n\u2009=\u20098/92) developed no discernible eyes (Supplementary Fig.\u00a017f, f\u2019). Taken together, these experiments demonstrate that normal zebrafish eye development is sensitive to nr6a1 dosage and both reduced and increased nr6a1 expression result in developmental phenotypes analogous to human colobomatous microphthalmia.",
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+        {
+            "section_name": "Discussion",
+            "section_text": "Here we describe six NR6A1 variants that cause an autosomal dominant syndromic form of colobomatous microphthalmia and missing vertebrae with or without congenital kidney abnormalities, which we term OVR syndrome. As with many other cases of syndromic and non-syndromic microphthalmia/coloboma, the OVR syndrome show, incomplete penetrance and variable expressivity1. By 2015 ACMG/AMP variant interpretation criteria, we considered chr9:g.124536516_124643457del pathogenic (criteria: PVS1, PP1_Strong, PM2) and other MAC-associated variants likely pathogenic (criteria: Ser76del, PM1, PM2, PM4, PP3; Arg92Trp, PS3, PM1, PM2, PP3; Arg436Cys, PS3, PM2, PP3; Ser301Ter & Ser322Ter, PVS1, PM2). Thus, NR6A1 variants were causative among 1.3%\u20131.4% families in two independent patient cohorts (3 out of 224 in the NEI coloboma cohort and 3 out of 215 in the MAC cohort in the UK100KGP).\n\nThe NEI study, which specifically recruits patients with coloboma/microphthalmia, performs extensive phenotypic analysis on probands including complete eye examination, kidney ultrasound, neuropsychological testing, physical exam/dysmorphology exam, spine x-ray, routine bloodwork/urinalysis, ECHO (in the presence of a murmur), and audiology. Additional testing (e.g., brain MRI) may be performed on an as needed basis. In addition, all available first-degree relatives undergo a complete dilated fundus exam. As such, we have greater certainty that a patient is truly unaffected, say, by coloboma, rather than being simply asymptomatic. Indeed, the mother of the proband in family COL034 (COL034.2), for example, was visually asymptomatic and unaware of a forme fruste of coloboma or a missing thoracic vertebra prior to her exam with us. Conversely, the Genomics England database spans an entire population in a gene and phenotype-agnostic manner but may contain incomplete or unrelated phenotypic information. As such, phenotypes such as intellectual disability (Individual B1, Supplementary Data\u00a01) may be spurious associations or may be uncommon manifestations of an NR6A1-related syndrome. Confirmation of these and other possible phenotypes awaits description of additional cases. We include congenital renal disease as part of this syndrome not only because two individuals in two separate pedigrees exhibited these phenotypes, but also because Rasouly et al. have simultaneously identified presumed loss-of-function variants in thirteen individuals with congenital renal abnormalities, with or without congenital eye abnormalities, providing further validation of our findings42. Using a combination of imaging and genetic data, Sun et al. recently reported that NR6A1 was a key gene associated with differences in vertebral number43. In addition, Jacquinet et al. subsequently noted congenital kidney, uterine, and vertebral anomalies in three patients and in zebrafish mutant line44. None of our patients reported uterine abnormalities or difficulty with pregnancy; however, pelvic ultrasounds were not generally performed, so subclinical phenotypes cannot be ruled out. Because none of our affected patients displayed heart defects, we currently do not include this as part of the syndrome, even though heart edema was noted in the morphants. However, we cannot rule out that congenital heart anomalies will be found in subsequent patients as more are identified.\n\nAdditional studies are required to understand the detailed disease mechanisms of NR6A1 variants. Deletion and presumed truncating variants are generally associated with a haploinsufficiency mechanism such as nonsense-mediated decay. This may be tested by expression profiling in patient cells. However, the subcellular localization defects of the two missense variants in NR6A1 hint at more than one mechanism of disease. The early expression of NR6A1 homologs in mouse and zebrafish are consistent with the previous data21 and suggest that the colobomatous microphthalmia observed in our patients may result from effects on early eye morphogenesis rather than a defect in optic fissure closure per se. Given the known roles of Nr6a1 in stem cell biology, we posit that the developmental trajectory of the optic cup neuroepithelium is altered in a way not consistent with optic fissure closure. However, given the expression of nr6a1a/nr6a1b in the lens vesicle in zebrafish and mouse, a non-cell autonomous effect on optic fissure closure cannot be excluded. In fact, evidence from Mexican surface and cave fish (Astyanax mexicanus) experiments show that early neural retina development and maintenance relies on a healthy lens45,46.\n\nRecently, NR6A1 has been shown to be important for somite development and, consequently, vertebral number, thus strengthening the phenotyping link with missing vertebrae we describe in humans18,19,20,21,47. Vertebrae differentiate from somites which develop their stereotyped segmentation pattern in an anterior to posterior progression during early development, with successive HOX genes specifying different regions of the spine via a process called temporal collinearity. Homozygous germline inactivation of Nr6a1 in mice results in embryonic lethality around E10.5 with cardiovascular, neural tube and hindgut abnormalities as well as fewer somites (13, rather than the normal 25)21,48. In Sus domesticus (pig), NR6A1 was identified as a quantitative trait locus for vertebral number, which is known to vary between breeds18,20. In Equus assinus (donkey), an NR6A1 intronic polymorphism is associated with body size/vertebral number and a single nucleotide polymorphism in exon 8 is associated with the number of lumbar vertebrae in Kazakh sheep19,47. In developing Xenopus, NR6A1 is expressed in late tailbud and neurula stages; overexpression results in posterior defects and disturbed somite formation, while expression of a dominant negative form of the receptor results in abnormal neural tube differentiation, loss of head structure including eyes41, and downregulation of a retinoic acid receptor (RAR\u03b32) anteriorly49. Retinoic acid treatment of embryos upregulates expression of NR6A1, increasing primary neurogenesis via factors such as NeuroD, XDelta1 and x-ngnrl. Retinoic acid is a known and important regulator of both ocular and kidney development50,51; whether retinoic acid receptor signaling is disrupted in model systems of Nr6a1/nr6a1 is currently under investigation. However, all phenotypes previously observed when modulating the activity of NR6A1 in animal models are consistent with the developmental defects in the eyes, kidneys, and vertebrae that we observe in patients carrying deleterious mutations in NR6A1.\n\nIn this study, we identified novel NR6A1 variants in three unrelated families with an OVR syndrome; these findings were further corroborated in an independent cohort using a genome first approach. Using in silico prediction and molecular studies we demonstrated that these highly conserved variants disrupt NR6A1 protein structure leading to mis-localization at the cellular level. We further demonstrated enrichment of coloboma-associated genes with NR6A1 in fetal, but not adult tissues. Expression of NR6A1 homologs in mouse and zebrafish embryos suggests disease relevant tissue-specific gene expression pattern. This was further confirmed by in vivo experiments where the knockdown of zebrafish nr6a1a and nr6a1b resulted in ocular, renal and vertebral phenotypes that were partially rescued with WT human NR6A1 mRNA but not with the two variants tested. This data implicates the human NR6A1 gene variants with the OVR syndrome.",
+            "section_image": []
+        },
+        {
+            "section_name": "Methods",
+            "section_text": "The design and the conduct of the study complied with all relevant regulations governing research on human subjects and according to the principles of the Declaration of Helsinki. Complete eye examinations and genetic testing at the National Eye Institute (NEI) were conducted after informed consent from all participants under National Institutes of Health-Internal Review Board-approved clinical protocols (NCT01778543, NCT01087320, NCT02077894, www.clinicaltrials.gov). This consent included permission to publish deidentified data. No compensation was provided to the participants. Probands underwent systemic testing as clinically indicated, which included physical exam, kidney ultrasound, routine blood chemistries, audiology, and spine x-ray. Eye examinations included age-appropriate testing of visual acuity, refraction, ocular motility/alignment, slit lamp exam, dilated fundus exam, and ophthalmic photography. Specific informed consent for exome/genome sequencing was obtained under an IRB-approved protocol, along with pre- and post-test genetic counseling (NCT02077894). Family COL005 and COL034 were previously reported as Family 1 and 2, respectively, without molecular characterization and detailed individual phenotyping data16. For patients and relatives recruited from the Genomics England 100,000 Genomes Project (UK100KGP), informed consent for whole genome sequencing (GS) was obtained in accordance with approval from the HRA committee East of England-Cambridge South (REC 14/EE/1112)17. Sex was not considered as an independent variable as OVR syndrome is autosomal dominant, affecting both males and females, and due to the relatively small size of the studied families. Sex reported in Table\u00a01 is self-identified by the participants.\n\nGenomic DNA samples prepared from blood or saliva from NEI patients, and their family members were subjected to short-read Next-generation sequencing (NGS) using Illumina platforms. In total, 101 proband samples were subjected to amplicon sequencing of the NR6A1 gene (Supplementary Data\u00a02) using a MiSeq sequencer (2\u2009\u00d7\u2009300\u2009bp paired-end), 57 samples subjected to exome sequencing (2\u2009\u00d7\u2009150\u2009bp paired-end, xGen exome v1 supplemented with additional probes, Blueprint Genetics), 66 samples subjected to GS (2\u2009\u00d7\u2009150\u2009bp paired-end, PCR-free library, NIH Intramural Sequencing Center). Reads were aligned to the GRCh38 reference genome, small variants and structural variants were then called, annotated, and prioritized using a custom NGS analysis pipeline (https://github.com/NIH-NEI/NGS_genotype_calling & https://github.com/NIH-NEI/variant_prioritization).\n\nSanger sequencing was performed to confirm select variants in probands and family members using the BigDye-direct sequencing kit (Thermo Fisher) using primers provided in Supplementary Data\u00a02. The deletion breakpoint in family COL005 was also determined by PCR and Sanger sequencing (Supplementary Data\u00a02). Breakpoint PCR was further used for genotyping of the COL005 family. The logarithm of the odds (LOD) score in family COL005 was estimated using the formula log10(1/0.5Segregations).\n\nAdditional patients and family members underwent Genome Sequencing (GS) as part of the UK100KGP including the clinical variant interpretation pipeline (The National Genomics Research Library v5.1, Genomics England. doi:10.6084/m9.figshare.4530893/7. 2020.). Genome data from affected individuals recruited with a clinical phenotype in keeping with microphthalmia, anophthalmia or coloboma were interrogated for rare (minor allele frequency <0.001, gnomAD v3.1 dataset) biallelic or de novo protein altering variants across the genome. Candidate variants underwent manual curation including in silico prediction, literature search and pathway analysis to establish biological plausibility as a pathogenic variant in developmental eye disease. Additional analyses of all rare protein altering variants in NR6A1 across the entire UK100KGP was performed to identify any individuals outside of the ophthalmology cohort who harbored a candidate pathogenic variant. All variants were manually inspected in the Integrative Genomics Viewer (IGV) after loading sample bam files. Variants appeared to be artifacts were not reported.\n\nThe 2015 ACMG/AMP sequence variant interpretation guidelines were followed for variant classification52,53. The PM1 (functional domain) criterion was applied to variants in part of the DNA binding domain, a.a. Thr68-Lys119, as the region is highly constrained for missense variations in gnomAD (v2.1.1, missense observed/expected\u2009=\u20090.19, p value\u2009=\u20096\u2009\u00d7\u200910\u22126). The PP3 criterion was applied to missense variants based on a collection of in-house in silico prediction tools (https://github.com/NIH-NEI/variant_prioritization) and the inframe deletion variant based on five in silico prediction tools (CAPICE, FATHMM-indel, MutationTaster, MutPred-Indel, and SIFT).\n\nA structural model of NR6A1 was generated using the AlphaFold server, AF-Q15405-F1-model_v4). The Zn-finger domain (ZFD) and nuclear receptor ligand binding domain (NR_LBD) were saved as two PDB files. The binding of DNA to the ZFD of NR6A1 was modeled using a single ZFD domain of the retinoid X receptor alpha-liver X receptor beta (PDB ID: 4NQA) in a complex with DNA. Two variants (R92W and R436C) were generated using the Edit\u2009>\u2009Swap\u2009>\u2009Residue function on the respective domain PDB files in YASARA. Variant models were optimized and minimized using gradient descent. All two minimized mutants and the two WT, ZFD and NR_LBD models were subjected to 10\u2009ns of Molecular Dynamics (MD) using YASARA\u2019s \u201crun.mcr\u201d macro. Ion concentration was added as a mass fraction with 0.9% NaCl. The simulation temperature was set to 310\u2009K with a water density of 0.997\u2009g/mL. For each domain, the cell size extended to 10\u2009\u00c5 beyond each side of the protein in the shape of a cube. Dimensions were 90.2\u2009\u00c5\u2009\u00d7\u200990.2\u2009\u00c5\u2009\u00d7\u200990.2\u2009\u00c5 and 82.5\u2009\u00c5\u2009\u00d7\u200982.6\u2009\u00c5\u2009\u00d7\u200982.6\u2009\u00c5 for the nuclear receptor Zn-finger and ligand-binding domains, respectively. Each simulation was run in YASARA using an AMBER14 forcefield, with a timestep of 2.5\u2009fs. Simulation snapshots were outputted for every 0.1\u2009ns, resulting in 100 simfiles for each simulation.\n\nDanio rerio were maintained under standard conditions. Embryos were staged according to Kimmel et al., 199554. ABTL stocks were used for all the experiments, which were carried out in accordance with National Eye Institute, Animal Care and Use Committee Protocol Number NEI-648 and NIH Animal Research Advisory Committee.\n\nEmbryo were fixed in 4% paraformaldehyde (PFA) overnight at 4\u2009\u00b0C and dehydrated in methanol for 1\u2009h at \u221230\u2009\u00b0C. The embryos were rehydrated, treated with proteinase-K and re-fixed with 4% PFA. Pre-hybridization and hybridization were carried out at 65\u2009\u00b0C. RNA probes were synthesized using a DIG labeling kit (Millipore-Sigma, 112770739) following manufacturer\u2019s protocol. nr6a1a RNA probe was synthesized from a CDS clone in TOPO TA vector (ThermoFischer Scientific), while nr6a1b was synthesized using PCR product as a template. Primers are noted in Supplementary Data\u00a03. Samples were hybridized overnight with RNA probes at 65\u2009\u00b0C, washed, incubated with Anti-DIG antibody (Millipore-Sigma, 1109327490); color was developed using BCIP/NBT substrate (Millipore-Sigma, 11681451001) in alkaline phosphatase buffer. Embryos were imaged with Leica DM6 dissecting microscope.\n\nAll morpholinos (MO) were obtained from Gene Tools LLC. MOs used to target zebrafish nr6a1a and nr6a1b are given in Supplementary Data\u00a04. Human NR6A1-wild-type, variants NR6A1-R92W and NR6A1-R436C DNA fragments were synthesized and cloned in pCS2+ (Azenta Life Sciences). Plasmids were linearized with Not I restriction enzyme and capped mRNA was synthesized using mMessage mMachine T7 Transcription kit (ThermoFischer Scientific). MOs and mRNA were co-injected into zebrafish embryos at single cell stage. nr6a1a and nr6a1b translation blocking (TB) MOs were used at 2\u2009ng and 1.25\u2009ng respectively. Nr6a1a and nr6a1b, SB-MOs were injected at 2\u2009ng and 1\u2009ng respectively. Human NR6A1-wild-type was used at 100\u2009pg and 150\u2013200\u2009pg for RNA rescue and over expression studies respectively. NR6A1-R92W and NR6A1-R436C RNAs were used at 100\u2009pg for rescue experiments. For over-expression experiments, doses of 100\u2009pg\u2013200\u2009pg hNR6A1 mRNA were injected at the single cell stage. Embryo phenotypes were scored and imaged at 72\u2009hours post-fertilization (hpf) using Leica DM6 dissecting microscope.\n\nHEK293T cells maintained in DMEM with 10% FBS and 1% penicillin-streptomycin were seeded onto 4-well chamber slides, maintained for 24\u2009h and transiently transfected with GFP tagged WT and/or mutant NR6A1 constructs (Azenta Life Science, Burlington, MA, USA) using X-treme Gene HP (Roche, Indianapolis, IN, USA) following manufacturers\u2019 instructions. After 24\u201348\u2009h of transfection, transfected cells were fixed for 15\u2009min in 4% paraformaldehyde (PFA) in PBS. After washing with 1 \u00d7 PBS cells were incubated for 1\u2009h at room temperature with Hoechst33342 (1:250 dilution in PBST). Subsequently, the slides were washed and mounted with Fluoromount-G\u00ae (SouthernBiotech, Birmingham, AL, USA). Zeiss confocal microscopes 880 coupled with an Airyscan\u00ae detector was used for confocal imaging. The images were analyzed using ZEN Software (Carl Zeiss Microscopy LLC, Thornwood, NY). The cell culture experiments were repeated at least three times for each for variant localization studies. Co-transfected cells with both WT and mutant forms of the NR6A1 constructs were fixed for 15\u2009min in 4% paraformaldehyde (PFA) in PBS. After washing with 1 \u00d7 PBS and permeabilization and blocking in ICC buffer (0.5% BSA 0.5% Tween and 0.1% triton X100 1 \u00d7 PBS). Cells were then incubated overnight at 4\u2009\u00b0C with the Fibrillarin antibody (MA3\u221216771, Thermo Fisher Scientific) in ICC buffer. After multiple washes in PBS, the cells were incubated for 1\u2009hr at room temperature in Alexa Fluor\u2122 555 conjugated goat anti-mouse antibody (A-21422, Thermo Fisher Scientific) and Hoechst33342 (1:1000 dilution in ICC buffer). Cells were then washed in PBST before mounting with Fluoromount-G\u00ae (SouthernBiotech, Birmingham, AL, USA) imaging.\n\nTransfection efficiency was determined by measuring the expression of GFP after 48 hrs post transfection. HEK293 cells were detached from the plates using Trypsin for 5\u2009min followed by neutralization with serum containing media. The cells were then fixed for 15\u2009min in 4% paraformaldehyde (PFA) in PBS and then collected in 1\u00d7 PBS containing 2% FBS (FACS buffer) and washed 2 times by centrifugation. The cell suspension was filtered through a 50\u2009\u00b5m cell strainer. Data was acquired with a CytoFlex NUV instrument (Beckman Coulter, Brea CA) using the blue light excitation and 525\u2009nm emission to detect GFP and violet light excitation and 450\u2009nm emission to detect DAPI detection. Data analysis was done using CytExpert software Version 2.5 (Beckman Coulter, Brea CA). Interesting cells were identified as DAPI negative, in the whole cell cluster in a FSC vs. SSC plot and being in a single cell state in the FSC-A vs. FSC-Width. Transfection efficiency was quantified as the Stain Index of GFP fluorescence intensity, which was calculated using the median fluorescent intensity and robust Standard Deviation as described. The cell culture experiments were repeated at least three times for each for variant localization studies.\n\nC57Bl/6 mice (The Jackson laboratory, Strain #:000664) were housed in individually ventilated cages (five per cage) under conditions of a 14\u2009h/10\u2009h light/dark cycle and ambient temperature of 22\u2009\u2009\u00b1\u2009\u20092\u2009\u00b0C with 30\u201370% humidity. Experiments were carried out in accordance with National Eye Institute, Animal Care and Use Committee Protocol Number NEI-605 and NIH Animal Research Advisory Committee. Nr6a1 mRNA expression in mouse was assayed by RNA in situ hybridization with Nr6a1(Cat: 1314941-C1) probe using the RNAScope Assay, Multiplex fluorescent Reagent Kit V2 (Advanced Cell Diagnostics (ACD), Newark, CA, USA) on E10.5 and E11.5 cryosections55. The manufacturer\u2019s control against a bacterial sequence was used for comparison, RNAscope\u2122 3-plex Negative Control Probe (Cat. #320871). Exposure settings were identical for all samples to facilitate comparisons in expression levels. Expression levels in the eye were quantitated relative to brain and periocular tissue using a free open source bioimaging QuPath software56 for comparison. A \u201cbest fit\u201d model was applied to all samples analyzed.\n\nFIBRILLARIN antibody from Invitrogen with Cat#-MA1-91878, Lot#-ZA389553, Clone#- DYKDDDDK Tag Monoclonal Antibody (FG4R) raised in mouse was used at 1:1000 dilution.\n\nThe h5ad (d27a79a1-8a5f-404d-8063-52e19122ef49.h5ad for adult and 88444d73-7f55-4a62-bcfe-e929878c6c78.h5ad for fetal) from the HRCA project were downloaded from cellxgene.cziscience.com and the raw counts were summed at the sample and cell type level to create a pseudobulk matrix with the python package ADPBulk (https://github.com/noamteyssier/adpbulk). The eyeIntegration (which includes GTEx) gene counts and sample level metadata were downloaded from eyeIntegration.nei.nih.gov (https://hpc.nih.gov/~mcgaugheyd/eyeIntegration/2023/gene_counts.csv.gz and https://hpc.nih.gov/~mcgaugheyd/eyeIntegration/2023/eyeIntegration23_meta_2023_09_01.built.csv.gz). The pseudobulk and bulk RNA-seq counts were normalized by counts per million (CPM) and transformed in R/4.3 to have a mean of zero and a standard deviation of one. Plots were created in R/4.3 with the ggplot2, cowplot, and ggbeeswarm packages.\n\nThe same data used in the plotting was used to create separate gene expression matrices that for either fetal primary tissue (retina and RPE) or adult tissue (retina and RPE). We used spatial quantile normalization (spqn) analysis to derive gene correlation matrices that were not biased by higher gene expression.\u00a0The same data used in the plotting was used to create separate gene expression matrices that for either fetal primary tissue (retina and RPE) or adult tissue (retina and RPE). We used spatial quantile normalization (spqn) analysis to derive gene correlation matrices that were not biased by higher gene expression57. Briefly, the first four principal components were removed with the WGCNA tool removePrincipalComponents. The correlation matrices were created with the base R \u201ccor\u201d function. The correlation scores were expression transformed with the spqn package\u2019s \u201cnormalize_correlation\u201d function with the parameters \u201cngrp\u2009=\u200920, size_grp\u2009= 300, ref_grp\u2009=\u200918\u201d. The correlation matrix was filtered to only contain correlations between NR6A1 and all other genes. Code for all bioinformatic analyses have been deposited in 10.5281/zenodo.14.\n\nFurther information on research design is available in the\u00a0Nature Portfolio Reporting Summary linked to this article.",
+            "section_image": []
+        },
+        {
+            "section_name": "Data availability",
+            "section_text": "The genome sequencing data from NEI participants generated in this study have been deposited in the dbGaP database under accession code phs003996.v1. The genome data are available under controlled access due to restriction in participant informed consent; access can be obtained by following dbGaP data access policy. The application process, time frame for review of requests will be according to the published governance structure: https://sharing.nih.gov/accessing-data/accessing-genomic-data/how-to-request-and-access-datasets-from-dbgap. Data for all bioinformatic analyses have been deposited in 10.5281/zenodo.14757568. All other data are provided in the main text or in the Supplementary Information. Source data files are provided with this research article.\u00a0Source data are provided with this paper.",
+            "section_image": []
+        },
+        {
+            "section_name": "Code availability",
+            "section_text": "Code for scRNA-seq and Multiple Sequence Alignment can be found at GitHub (https://github.com/davemcg/nr6a1/releases/tag/1.3)58. NGS analysis code can be found at GitHub (https://github.com/NIH-NEI/variant_prioritization/releases/tag/v0.1)59.",
+            "section_image": []
+        },
+        {
+            "section_name": "References",
+            "section_text": "Williamson, K. A. & FitzPatrick, D. R. The genetic architecture of microphthalmia, anophthalmia and coloboma. Eur. J. Med. Genet. 57, 369\u2013380 (2014).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nChang, L., Blain, D., Bertuzzi, S. & Brooks, B. P. Uveal coloboma: clinical and basic science update. Curr. Opin. Ophthalmol. 17, 447\u2013470 (2006).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nPatel, A. & Sowden, J. C. Genes and pathways in optic fissure closure. Semin. Cell Dev. Biol. 91, 55\u201365 (2019).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nAS, A. L., Gregory-Evans, C. Y. & Gregory-Evans, K. An update on the genetics of ocular coloboma. Hum. Genet. 138, 865\u2013880 (2019).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nChan, B. H. C., Moosajee, M. & Rainger, J. Closing the gap: mechanisms of epithelial fusion during optic fissure closure. Front. Cell Dev. Biol. 8, 620774 (2020).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nNakamura, K. M., Diehl, N. N. & Mohney, B. G. Incidence, ocular findings, and systemic associations of ocular coloboma: a population-based study. Arch. Ophthalmol. 129, 69\u201374 (2011).\n\nArticle\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nRoos, L., Jensen, H., Gronskov, K., Holst, R. & Tumer, Z. Congenital microphthalmia, anophthalmia and coloboma among live births in Denmark. Ophthalmic Epidemiol. 23, 324\u2013330 (2016).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nManta, A. S., Olsson, M., Ek, U., Wickstr\u00f6m, R. & Fahnehjelm, K. T. Optic disc coloboma in children - prevalence, clinical characteristics and associated morbidity. Acta Ophthalmol. 97, 478\u2013485 (2019).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMorrison, D. et al. National study of microphthalmia, anophthalmia, and coloboma (MAC) in Scotland: investigation of genetic aetiology. J. Med. Genet. 39, 16\u201322 (2002).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKallen, B. & Tornqvist, K. The epidemiology of anophthalmia and microphthalmia in Sweden. Eur. J. Epidemiol. 20, 345\u2013350 (2005).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDas, A. V., Rauniyar, D., Chaurasia, S., Jalali, S. & Padhi, T. R. Clinical and demographic profile of uveal coloboma: a hospital-based study of 14,371 eyes of 9557 Indian patients. Am. J. Ophthalmol. 242, 1\u20136 (2022).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMaumenee, I. H. & Mitchell, T. N. Colobomatous malformations of the eye. Trans. Am. Ophthalmol. Soc. 88, 123\u2013132 (1990).\n\nCAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nPatel, A. et al. The oculome panel test: next-generation sequencing to diagnose a diverse range of genetic developmental eye disorders. Ophthalmology 126, 888\u2013907 (2019).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKalaskar, V. K. et al. High-throughput custom capture sequencing identifies novel mutations in coloboma-associated genes: mutation in DNA-binding domain of retinoic acid receptor beta affects nuclear localization causing ocular coloboma. Hum. Mutat. 41, 678\u2013695 (2020).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nJackson, D. et al. Molecular diagnostic challenges for non-retinal developmental eye disorders in the United Kingdom. Am. J. Med Genet. C Semin. Med. Genet. 184, 578\u2013589 (2020).\n\nArticle\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nHuynh, N. et al. Systemic diagnostic testing in patients with apparently isolated uveal coloboma. Am. J. Ophthalmol. 156, 1159\u20131168.e1154 (2013).\n\nArticle\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMark Caulfield, J. D. et al. In The National Genomic Research Library v5.1, Genomics England (National Genomic Research Library, 2019).\n\nBurgos, C. et al. Allelic frequencies of NR6A1 and VRTN, two genes that affect vertebrae number in diverse pig breeds: a study of the effects of the VRTN insertion on phenotypic traits of a Duroc x Landrace-Large White cross. Meat Sci. 100, 150\u2013155 (2015).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nFang, X. et al. A novel 13 bp deletion within the NR6A1 gene is significantly associated with growth traits in donkeys. Animals 9, 681 (2019).\n\nMikawa, S. et al. Fine mapping of a swine quantitative trait locus for number of vertebrae and analysis of an orphan nuclear receptor, germ cell nuclear factor (NR6A1). Genome Res. 17, 586\u2013593 (2007).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nChang, Y. C. et al. Nr6a1 controls Hox expression dynamics and is a master regulator of vertebrate trunk development. Nat. Commun. 13, 7766 (2022).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWang, Y. et al. NR6A1 couples with cAMP response element binding protein and regulates vascular smooth muscle cell migration. Int J. Biochem. Cell Biol. 69, 225\u2013232 (2015).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBryan, J. M. et al. Identifying core biological processes distinguishing human eye tissues with precise systems-level gene expression analyses and weighted correlation networks. Hum. Mol. Genet. 27, 3325\u20133339 (2018).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nAguet, F. et al. Genetic effects on gene expression across human tissues. Nature 550, 204 (2017).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nHoshino, A. et al. Molecular anatomy of the developing human retina. Dev. Cell 43, 763\u2013779.e764 (2017).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMellough, C. B. et al. An integrated transcriptional analysis of the developing human retina. Development 146 https://doi.org/10.1242/dev.169474 (2019).\n\nLi, J. et al. Integrated multi-omics single cell atlas of the human retina. Res. Sq. https://doi.org/10.21203/rs.3.rs-3471275/v1 (2023).\n\nSur, A. et al. Single-cell analysis of shared signatures and transcriptional diversity during zebrafish development. Dev. Cell 58, 3028\u20133047.e3012 (2023).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nFarrell, J. A. et al. Single-cell reconstruction of developmental trajectories during zebrafish embryogenesis. Science 360 https://doi.org/10.1126/science.aar3131(2018).\n\nEisen, J. S. & Smith, J. C. Controlling morpholino experiments: don\u2019t stop making antisense. Development 135, 1735\u20131743 (2008).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nStainier, D. Y. R. et al. Guidelines for morpholino use in zebrafish. PLoS Genet. 13, e1007000 (2017).\n\nArticle\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMorcos, P. A., Vincent, A. C. & Moulton, J. D. Gene editing versus morphants. Zebrafish 12, 319 (2015).\n\nArticle\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nRobu, M. E. et al. p53 activation by knockdown technologies. PLoS Genet. 3, e78 (2007).\n\nArticle\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDrummond, I. A. Kidney development and disease in the zebrafish. J. Am. Soc. Nephrol. 16, 299\u2013304 (2005).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKramer-Zucker, A. G., Wiessner, S., Jensen, A. M. & Drummond, I. A. Organization of the pronephric filtration apparatus in zebrafish requires Nephrin, Podocin and the FERM domain protein Mosaic eyes. Dev. Biol. 285, 316\u2013329 (2005).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nO\u2019Brien, L. L. et al. Wt1a, Foxc1a, and the Notch mediator Rbpj physically interact and regulate the formation of podocytes in zebrafish. Dev. Biol. 358, 318\u2013330 (2011).\n\nArticle\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nChrist, B. & Wilting, J. From somites to vertebral column. Ann. Anat. 174, 23\u201332 (1992).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nStickney, H. L., Barresi, M. J. & Devoto, S. H. Somite development in zebrafish. Dev. Dyn. 219, 287\u2013303 (2000).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMise, T., Iijima, M., Inohaya, K., Kudo, A. & Wada, H. Function of Pax1 and Pax9 in the sclerotome of medaka fish. Genesis 46, 185\u2013192 (2008).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nPeters, H. et al. Pax1 and Pax9 synergistically regulate vertebral column development. Development 126, 5399\u20135408 (1999).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDavid, R., Joos, T. O. & Dreyer, C. Anteroposterior patterning and organogenesis of Xenopus laevis require a correct dose of germ cell nuclear factor (xGCNF). Mech. Dev. 79, 137\u2013152 (1998).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMilo Rasouly, H. et al. Exome-wide analysis of congenital kidney anomalies reveals new genes and shared architecture with developmental disorders. medRxiv. https://doi.org/10.1101/2024.11.05.24316672 (2024).\n\nZhuopin Sun, J. H., Liam G. Fearnley, Edwina McGlinn, Melanie Bahlo. Identification of novel vertebral development factors through UK Biobank driven genetic and body imaging analysis reveals markers for back pain. medRxiv. https://doi.org/10.1101/2025.02.13.25322190 (2025).\n\nAdeline, J. et al. Variants in NR6A1 as a cause for congenital renal, vertebral and uterine anomalies. medRxiv. https://doi.org/10.1101/2025.01.08.24319478 (2025).\n\nYamamoto, Y. & Jeffery, W. R. Central role for the lens in cave fish eye degeneration. Science 289, 631\u2013633 (2000).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nStrickler, A. G., Yamamoto, Y. & Jeffery, W. R. The lens controls cell survival in the retina: evidence from the blind cavefish Astyanax. Dev. Biol. 311, 512\u2013523 (2007).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nZhang, X. et al. Association analysis of polymorphism in the NR6A1 gene with the lumbar vertebrae number traits in sheep. Genes Genom. 41, 1165\u20131171 (2019).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nChung, A. C. et al. Loss of orphan receptor germ cell nuclear factor function resultsin ectopic development of the tail bud and anovel posterior truncation. Mol. Cell. Biol. 21, 663\u2013677 (2001).\n\nArticle\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBarreto, G., Borgmeyer, U. & Dreyer, C. The germ cell nuclear factor is required for retinoic acid signaling during Xenopus development. Mech. Dev. 120, 415\u2013428 (2003).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nCvekl, A. & Wang, W. L. Retinoic acid signaling in mammalian eye development. Exp. Eye Res. 89, 280\u2013291 (2009).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBurrow, C. R. Retinoids and renal development. Exp. Nephrol. 8, 219\u2013225 (2000).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nRichards, S. et al. Standards and guidelines for the interpretation of sequence variants: a joint consensus recommendation of the American College of Medical Genetics and Genomics and the Association for Molecular Pathology. Genet. Med. 17, 405\u2013424 (2015).\n\nArticle\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nJarvik, G. P. & Browning, B. L. Consideration of cosegregation in the pathogenicity classification of genomic variants. Am. J. Hum. Genet. 98, 1077\u20131081 (2016).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKimmel, C. B., Ballard, W. W., Kimmel, S. R., Ullmann, B. & Schilling, T. F. Stages of embryonic development of the zebrafish. Dev. Dyn. 203, 253\u2013310 (1995).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBoobalan, E. et al. Zfp503/Nlz2 is required for RPE differentiation and optic fissure closure. Investig. Ophthalmol. Vis. Sci. 63, 5 (2022).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBankhead, P. et al. QuPath: open source software for digital pathology image analysis. Sci. Rep. 7, 16878 (2017).\n\nArticle\u00a0\n    ADS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWang, Y., Hicks, S. C. & Hansen, K. D. Addressing the mean-correlation relationship in co-expression analysis. PLoS Comput. Biol. 18, e1009954 (2022).\n\nNeelathi, U. M. et al. Variants in NR6A1 cause a novel oculo vertebral renal syndrome. https://doi.org/10.5281/zenodo.15232521 (2025).\n\nNeelathi, U. M. et al. Variants in NR6A1 cause a novel oculo vertebral renal syndrome. https://doi.org/10.5281/zenodo.14757568 (2025).\n\nDownload references",
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+            "section_name": "Acknowledgements",
+            "section_text": "We are grateful to the patients and their families for participation in this research, which spanned over 20 years. We thank the staff at the NIH Clinical Center and the NEI Eye Clinic for patient phenotyping, ophthalmic testing, and ophthalmic imaging. This work utilized the computational resources of the NIH HPC Biowulf cluster (https://hpc.nih.gov). This study was supported by the Intramural Research Program of the NIH. This research was made possible through access to data in the National Genomic Research Library, which is managed by Genomics England Limited (a company owned by the Department of Health and Social Care). The National Genomic Research Library holds data provided by patients and collected by the NHS as part of their care and data collected as part of their participation in research. GA is supported by a Fight For Sight (UK) Early Career Investigator Award (5045/46), the National Institute of Health Research Biomedical Research Centre (NIHR-BRC) at Moorfields Eye Hospital, and the UCL Institute of Ophthalmology, and Moorfields Eye Charity (Stephen and Elizabeth Archer in memory of Marion Woods) and NIH-P20GM139769. RY was supported by the Moorfields Eye Charity Career Development Award and Springboard (GR001155 and GR001210), Medical Research Council (MR/X001067/1) and FODNECYT (1221843). MIM was supported by Moorfields Eye Charity PhD Studentship (GR001661).",
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+        },
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+            "section_name": "Funding",
+            "section_text": "Open access funding provided by the National Institutes of Health.",
+            "section_image": []
+        },
+        {
+            "section_name": "Author information",
+            "section_text": "These authors contributed equally: Uma M. Neelathi, Ehsan Ullah.\n\nThese authors jointly supervised this work: Rodrigo M. Young, Bin Guan, Brian P. Brooks.\n\nOphthalmic Genetics & Visual Function Branch, National Eye Institute, National Institutes of Health, Bethesda, MD, USA\n\nUma M. Neelathi,\u00a0Ehsan Ullah,\u00a0Aman George,\u00a0Elangovan Boobalan,\u00a0Daniel Sanchez-Mendoza,\u00a0Chloe Adams,\u00a0David McGaughey,\u00a0Yuri V. Sergeev,\u00a0Ranya AI Rawi,\u00a0Amelia Naik,\u00a0Chelsea Bender,\u00a0Delphine Blain,\u00a0Robert B. Hufnagel,\u00a0Bin Guan\u00a0&\u00a0Brian P. Brooks\n\nUCL Institute of Ophthalmology, University College London, London, UK\n\nMara I. Maftei,\u00a0Michel Michaelides,\u00a0Siying Lin,\u00a0Gavin Arno\u00a0&\u00a0Rodrigo M. Young\n\nHarkness Eye Institute, Columbia University, New York, NY, USA\n\nIrene H. Maumenee\n\nMoorfields Eye Hospital, NHS Foundation Trust, London, UK\n\nMichel Michaelides\u00a0&\u00a0Siying Lin\n\nTorbay Hospital, Torbay and South Devon NHS Foundation Trust, Devon, UK\n\nTun Giap Tan\n\nFlow Cytometry Core, National Eye Institute, Bethesda, MD, USA\n\nRafael Villasmil\n\nCenter for Integrated Health Care Research, Kaiser Permanente Hawai\u2019i; Hawai\u2019i Permanente Medical Group, Honolulu, HI, USA\n\nRobert B. Hufnagel\n\nGreenwood Genetic Center, Greenwood, SC, USA\n\nGavin Arno\n\nCenter for Integrative Biology, Universidad Mayor, Santiago, Chile\n\nRodrigo M. Young\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nE.U., R.B.H., M.I.M., G.A., and B.G. performed exome/genome analysis and variant confirmation in the NIH and UK100KGP populations. R.A., A.N., and C.B. performed variant confirmation, including confirmation of deletion breakpoints. I.H.M., D.B., S.L., T.G.T., M.M., and B.P.B. performed patient examination/phenotyping. Y.V.S. performed molecular dynamic modeling. D.M. performed bioinformatic analyses of NR6A1. E.B. preformed RNA scope analysis. U.M.N. designed, performed and analyzed zebrafish morpholino knockdown, mRNA rescue experiments and imaging. U.M.N. and D.S.M. performed zebrafish in situ hybridization. R.Y. assisted in interpretation of zebrafish data. A.G. and C.A. performed cell culture and transfection experiments. A.G. performed confocal microscopy. R.V. performed flow cytometry. All co-authors provided draft language and experimental design for their portions of the manuscript, as well as a critical review of the entire manuscript. BPB provided overall project conception and experimental design, drafting of the manuscript and project support.\n\nCorrespondence to\n                Brian P. Brooks.",
+            "section_image": []
+        },
+        {
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+            "section_text": "The authors declare no competing interests.",
+            "section_image": []
+        },
+        {
+            "section_name": "Peer review",
+            "section_text": "Nature Communications thanks Edwina McGlinn and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. A peer review file is available.",
+            "section_image": []
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+            "section_text": "Open Access  This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article\u2019s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article\u2019s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.\n\nReprints and permissions",
+            "section_image": []
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+            "section_name": "About this article",
+            "section_text": "Neelathi, U.M., Ullah, E., George, A. et al. Variants in NR6A1 cause a novel oculo vertebral renal syndrome.\n                    Nat Commun 16, 6111 (2025). https://doi.org/10.1038/s41467-025-60574-y\n\nDownload citation\n\nReceived: 09 November 2024\n\nAccepted: 29 May 2025\n\nPublished: 03 July 2025\n\nVersion of record: 03 July 2025\n\nDOI: https://doi.org/10.1038/s41467-025-60574-y\n\nAnyone you share the following link with will be able to read this content:\n\nSorry, a shareable link is not currently available for this article.\n\n\n\n\n                            Provided by the Springer Nature SharedIt content-sharing initiative\n                        ",
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+            ]
+        },
+        {
+            "section_name": "This article is cited by",
+            "section_text": "Nature Communications (2025)",
+            "section_image": []
+        }
+    ]
+}

25a1db52868bd6993ac74e75dd961147bc73fd48a03630df813924b331c71afa/metadata.json

@@ -0,0 +1,136 @@
+{
+    "title": "Unlocking ultra-high holographic information capacity through nonorthogonal polarization multiplexing",
+    "pre_title": "Unlocking Ultra-High Holographic Information Capacity through Nonorthogonal Polarization Multiplexing",
+    "journal": "Nature Communications",
+    "published": "26 July 2024",
+    "supplementary_0": [
+        {
+            "label": "Supplementary Information",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-024-50586-5/MediaObjects/41467_2024_50586_MOESM1_ESM.pdf"
+        },
+        {
+            "label": "Peer Review File",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-024-50586-5/MediaObjects/41467_2024_50586_MOESM2_ESM.pdf"
+        }
+    ],
+    "supplementary_1": NaN,
+    "supplementary_2": NaN,
+    "source_data": [],
+    "code": [],
+    "subject": [
+        "Metamaterials",
+        "Nanophotonics and plasmonics"
+    ],
+    "license": "http://creativecommons.org/licenses/by/4.0/",
+    "preprint_pdf": "https://www.researchsquare.com/article/rs-3981683/v1.pdf?c=1722078543000",
+    "research_square_link": "https://www.researchsquare.com//article/rs-3981683/v1",
+    "nature_pdf": "https://www.nature.com/articles/s41467-024-50586-5.pdf",
+    "preprint_posted": "07 Mar, 2024",
+    "research_square_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Contemporary studies in polarization multiplexing are hindered by the intrinsic orthogonality constraints of polarization states, which restrict the scope of multiplexing channels and their practical applications. This research transcends these barriers by introducing an innovative nonorthogonal polarization-basis multiplexing approach. Utilizing spatially varied local polarization states within metaatoms, we successfully reconstruct globally nonorthogonal channels that exhibit minimal crosstalk. This method not only facilitates the generation of free-vector holograms, achieving complete degrees-of-freedom in three nonorthogonal channels with ultra-low energy leakage, but it also significantly enhances the dimensions of the Jones matrix, expanding it to a groundbreaking 10\u00d710 scale. The fusion of a controllable eigen-polarization engineering mechanism with a vectorial optical diffraction neural network culminates in the experimental creation of 55 intricate holographic patterns across these expanded channels. This advancement represents a profound shift in the field of polarization multiplexing, unlocking unprecedented opportunities in advanced holography and quantum encryption, among other applications.Physical sciences/Optics and photonics/Optical materials and structures/MetamaterialsPhysical sciences/Physics/Optical physics/Nanophotonics and plasmonicspolarization multiplexingnonorthogonal basisvector diffraction neural networkmetasurface holography",
+            "section_image": []
+        },
+        {
+            "section_name": "Additional Declarations",
+            "section_text": "There is NO Competing Interest.",
+            "section_image": []
+        },
+        {
+            "section_name": "Supplementary Files",
+            "section_text": "V6SupplementaryMateria.docx",
+            "section_image": []
+        }
+    ],
+    "nature_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Contemporary studies in polarization multiplexing are hindered by the intrinsic orthogonality constraints of polarization states, which restrict the scope of multiplexing channels and their practical applications. This research transcends these barriers by introducing an innovative nonorthogonal polarization-basis multiplexing approach. Utilizing spatially varied eigen-polarization states within metaatoms, we successfully reconstruct globally nonorthogonal channels that exhibit minimal crosstalk. This method not only facilitates the generation of free-vector holograms, achieving complete degrees-of-freedom in three nonorthogonal channels with ultra-low energy leakage, but it also significantly enhances the dimensions of the Jones matrix, expanding it to a groundbreaking 10\u2009\u00d7\u200910 scale. The fusion of a controllable eigen-polarization engineering mechanism with a vectorial diffraction neural network culminates in the experimental creation of 55 intricate holographic patterns across these expanded channels. This advancement represents a profound shift in the field of polarization multiplexing, unlocking opportunities in advanced holography and quantum encryption, among other applications.",
+            "section_image": []
+        },
+        {
+            "section_name": "Introduction",
+            "section_text": "Polarization orthogonality, a fundamental principle in photonics, demands that the inner product of two output fields, u1\u2192(x,y) and u2\u2192(x,y), equals zero. This orthogonality, stemming from polarization bases p^1 and p^2, confines polarization multiplexing to a mere two channels, dictated by a 2\u2009\u00d7\u20092 Jones matrix1,2. While this orthogonality ensures perfect isolation in applications such as polarization imaging and information encryption3,4,5,6,7,8,9,10, it inherently limits the maximum number of multiplexing channels free from cross-interference. Existing methods, like space- or time-division techniques11,12,13,14,15,16,17, compromise on spatial or temporal resolution, and typically can only expand to four orthogonal polarization channels. For instance, conventional configurations using bulk optical elements like polarizers and waveplates represent this limitation18. Attempts to incorporate additional dimensions19,20,21,22,23, such as wavelength or orbital angular momentum, typically exacerbate issues of crosstalk and noise. Even with advanced eigen-polarization modulation techniques, the reliance on orthogonal polarization bases persists, constraining applications like dynamic holography and information transmission within a narrow scope17,24,25,26.\n\nRecent advancements in metasurface technology have significantly expanded the potential for holographic information capacity. For instance, Bao et al. cascaded two single-layer metasurfaces to construct a spatially varying Jones matrix, enabling the manipulation of the amplitude and phase of light for intricate holographic applications8. Furthermore, Wang et al. demonstrated high-efficiency metasurfaces capable of complex vectorial holography using polarization multiplexing, showing that engineered metasurfaces can achieve high-density information encoding9. Additionally, Xiong et al. introduced the concept of engineered noise to break the fundamental limit of polarization multiplexing capacity, demonstrating up to 11 independent holographic images using a single metasurface17. These studies demonstrate the possibility of breaking traditional limitations by employing innovative strategies, such as engineered noise and complex light manipulation techniques, to enhance polarization multiplexing. Despite these advancements, the number of achievable independent channels remains a critical area for further research, as the lack of full exploitation of metasurfaces restricts high-capacity holographic applications, particularly in fields requiring extensive data encoding and secure information transmission.\n\nHere, our work pioneers a nonorthogonal polarization-basis multiplexing technique by engineering spatially variable eigen-polarization states p^1(x,y) and p^2(x,y) at a subwavelength scale using metaatoms. We meticulously control the local eigen-polarization of each metaatom, thereby achieving a unique collective effect across multiple nonorthogonal polarization channels. This method, deviating from the norm, permits a nonzero product of u1\u2217\u2192(x,y) and u2\u2192(x,y) at each metaatom, culminating in a precise overall polarization output. Our approach\u2019s efficacy is demonstrated both theoretically and experimentally by showcasing three holograms cycled through asymmetric polarization channels, achieving full degrees-of-freedom coverage without compromising spatial, temporal, or other dimensions. Furthermore, we introduce a controllable local eigen-polarization modulation mechanism that expands the Jones matrix dimensionality to 10\u00d710. By employing a vectorial diffraction neural network (VDNN)27, we optimize multiplexing efficiency and reduce crosstalk, as evidenced by a set of 55 holograms integrating 10 input and 10 output polarization states. Notably, there is no compromise of spatial, temporal, or other dimensions in the realization of three-channel nonorthogonal polarization multiplexing. For cases involving more than three channels, the spatial dimension along the propagation direction is adopted in this work. Our work represents a substantial advance in polarization multiplexing channels and it also offers a robust and scalable solution for ultra-high capacity holographic multiplexing. This nonorthogonal strategy promises new possibilities for dynamic holography and advanced information transmission in the realm of photonics.",
+            "section_image": []
+        },
+        {
+            "section_name": "Results",
+            "section_text": "The polarization manipulation capabilities of a single-layer metaatom are elegantly encapsulated by the Jones matrix, represented as:\n\nHere, A, B, C, and D govern the complex amplitude control of both eigen and cross channels in standard polarization representation. The eigen-polarizations e1^ and e2^, along with the eigenvalues \u039b1 and \u039b2, define the polarization control. Equation (1) highlights that the polarization control is simultaneously constrained by space-time reciprocity and the inherent form of the eigen-polarization.\n\nTraditionally, using orthogonal basis vectors |H\u3009 and |V\u3009, the Jones matrix is decomposed into components such as |H\u3009\u3008H|, |H\u3009\u3008V|, etc. Due to the reciprocity of single-layer metasurfaces, it\u2019s established that B\u2009=\u2009C, thus limiting the polarization control to three degrees of freedom.\n\nHowever, this approach simplifies the complex relationship between the local eigen-polarization control J of a metaatom and the global output polarization from an input. For in-plane symmetric metaatoms, the inherent linearity of the eigen-polarization constrains input-output combinations to linear orthogonal polarization bases in conventional scenarios.\n\nOur work transcends these limitations by modulating the local linear eigen- polarizations of metaatoms, thus constructing globally nonorthogonal output polarization states (see Fig.\u00a01a). This fine-tuning of each metaatom\u2019s local eigen-polarization results in distinct collective effects on multiple nonorthogonal output polarization channels.\n\na Illustration of a dynamically polarized holographic metadevice. It is engineered to generate holograms for each of the 55 arbitrary polarization channels, analogous to the elements in the periodic table. b Schematic of the controllable eigen-polarization modulation mechanism. An arbitrary input polarization is initially decomposed into circular polarization bases |L\u3009 and |R\u3009. For demonstrative purposes, linear polarization is selected. Upon interaction with a local metaatom, the polarization undergoes transformations in both eigen and conjugate channels, namely ALL, BLR, CRL, and ARR. Following this, a dynamically rotating polarizer is applied, assigning aij manipulation to the \u3008L| and \u3008R| channels, respectively. This process enables the modulation of local eigen-polarization at the metaatom level, facilitating global polarization multiplexing. The cumulative and coherent interference of various metaatoms at the imaging plane realizes the envisioned nonorthogonal polarization multiplexing.\n\nFor arbitrary input pi and output pj(i, j=1, 2, \u2026, n), the responses Oij(x,y)=\u27e8pj|J|pi\u27e9 of metaatoms at different positions (x, y) differ from each other. Combining with Eq. (1), we have Oij(x,y)=pj\u2020\u22c5[e1^,e2^]\u22121\u22c5\u039b\u22c5[e1^,e2^]\u22c5pi, where \u2020 represents the transpose and conjugate operation. Since the system is unitary, [e1^,e2^]\u22121=[e1^,e2^]\u2020, thus:\n\nwhere pi\u2032, and pj\u2032 include the role of eigenvectors in their interaction with pi and pj.\n\nAt this point, we have derived the fundamental equation Oij(x,y) for the modulation of incident/output polarization along with the metaatoms, which serves as the basis for extending arbitrary polarization channel modulation. By incorporating this equation into the tools of machine learning or neural networks, it offers an efficient way to address the challenge of maximizing the isolation between channels that jointly modulate global perturbations and local controls under limited degrees of freedom. In this situation, we can achieve desired nonorthogonal multiplexing channels for any combined input and output polarization pairs.\n\nTo demonstrate this, we choose circular polarization basis vectors to rewrite Eq. (2) and get Eq. (3):\n\nIn this scenario, we can decompose the metaatom\u2019s matrix into eigen and conjugate components Jeigen=[ALL00ARR] and Jcon=[0BLRCRL0], as shown in Fig.\u00a01b, where each element represents the circular-based modulation channel, ALL/ARR and BLR/CRL are co- and cross-polarization channel respectively. |pi\u27e9=a1i|L\u27e9+a2i|R\u27e9 and \u27e8pj|=a3j\u2217\u27e8L|+a4j\u2217\u27e8R|, where a is decomposition factor, * denotes conjugation, and |L\u3009/|R\u3009 are left/right circular polarization. This decomposition enables us to explore various combinations of incident and output polarizations, showing how the global response of the metasurface and the local response of the metaatoms are intricately cross-coupled.\n\nIntuitively, the metaatom\u2019s response based on eigen-polarization modulation can be denoted by a matrix O(x, y) (Eq. (4)), in which different combinations of input and output polarizations are selective extractions of this response matrix. The out-of-plane symmetry leads to physical transport reciprocity in our system, which gives the response matrix the form of a symmetric matrix, i.e., the upper (lower) triangular form, the relevant discussion can be seen in Supplementary Note\u00a01.\n\nThe global response of metasurface for nonorthogonal polarization multiplexing is then the integral of Eq. (4) with respect to position: \u03a9=\u222cO(x,y)dxdy. In this way, the change of the response matrix due to the tuning of the input-output polarization will be fully attributed to the modulation effect of the eigenvectors on the input-output polarization. According to this integral formula and the diffraction process, we can build an efficient network and optimize the parameters so that the response matrix \u03a9 can optimally extract different channels selectively. Details can be found in Supplementary Note\u00a02.\n\nIt\u2019s worth noting that we utilize the spatially varied eigen-polarization states of the metaatoms to successfully reconstruct globally nonorthogonal channels that exhibit minimal crosstalk. This leads to a modulation capability that is no longer limited to symmetric channels (\u03a9ij, i\u2009=\u2009j), but can also be extended to asymmetric channels (\u03a9ij, i \u2260 j). Equation (4) represents a pivotal development in our study. It enables the reconstruction of the control matrix over various nonorthogonal input-output polarization channels, significantly expanding the conventional dimension of the Jones matrix.\n\nEmploying the methodology delineated, we executed a series of sample designs to empirically validate our proposed nonorthogonal polarization-basis multiplexing approach. This included an array of tri-fold cyclic nonorthogonal linear polarization multiplexes, tri-fold cyclic nonorthogonal circular and elliptical polarization multiplexes, and an extensive suite of 55 diverse nonorthogonal polarization multiplexes.\n\nIn the implementation of our triple nonorthogonal linear polarization asymmetric holography model, we simplified the metasurface to exhibit a transmittance of 1. The corresponding diffraction neural network was configured with a single hidden layer for streamlined efficiency. It should be noted that the definition of the diffraction neural network28,29,30 follows that outlined in ref. 27. However, our approach differs in that we integrate the polarization dimension of light into a single-layer metasurface, rather than using a series of cascading optical elements. The optimization is conducted using electronic neural networks31. As depicted in Fig.\u00a02a, the training process is illustrated, highlighting the incident polarization, output polarization, and the targeted holographic pattern. Operating at a wavelength of 3\u03bcm, we precisely calibrated incident polarization angles at 0, 60, and 120 degrees to correspond with output polarization angles of 60, 120, and 0 degrees, respectively. This calibration resulted in the generation of gray-scale holographic images: a puppy, a kitten, and a mouse. The distance between the metasurface layer and the output layer was meticulously maintained at 500 \u03bcm. The loss for each target pattern is evenly distributed with its respective weight during the optimization process, promoting a fair allocation of energy across all patterns. More details can be found in Supplementary Note\u00a02.\n\na Conceptual model of vectorial diffraction neural network illustrating the training process. Here, different polarized lights constitute the input layer, the metasurfaces function as the hidden layers, and the image plane serves as the output layer. b Training outcomes for the nonorthogonal linear polarization channel. This section highlights the loss maps and the correlation coefficients that measure the congruence between the output and target patterns. c Anisotropic response and orientation of the metaatoms within the systematically arranged metadevice. d Scanning electron microscope images, offering both oblique and cross-sectional views of the metadevice. Each image includes a scale bar of 2 \u03bcm to provide a sense of scale. e Depicts the optical characterization system used for evaluating the performance of the designed metadevices. LP stands for linear polarization, PR for phase retarder, and FPA for focal plane array.\n\nFigure\u00a02b offers insight into the neural network training, showcasing the loss profile and the variation in correlation coefficients across channels as a function of iteration numbers. Over successive iterations, the three patterns gradually converge towards the target patterns at varying rates, ultimately attaining a nearly flawless alignment as the iteration count rises. The vectorial diffraction neural network\u2019s output results, including the parameters \u03c6x, \u03c6y, and the metasurface orientation \u03b8, are elucidated in Fig.\u00a02c. The metasurface consisted of a 400\u2009\u00d7\u2009400-pixel array, each with a period of 1.5 \u03bcm. The nano-elliptic metaatoms, made of pure silicon, have a height of 4 \u03bcm, the length and width of the metaatom varied between 0.3 and 1.2\u2009\u03bcm. More details are in Supplementary Note\u00a03. In Fig.\u00a02d, scanning electron microscopy images provide both oblique and cross-sectional views of the metasurface, showcasing the robustness of the fabrication process and underscoring the precision achieved in metasurface manufacturing. The scale bar is 2 \u03bcm. Lastly, Fig.\u00a02e delineates the experimental setup, where the camera captures the holographic pattern following the transmission of infrared light through the polarizer, metasurface, and analyzer. The phase retarder was omitted in the linear polarization experiment. Further details on simulations and experiments can be found in the Methods section.\n\nFigure\u00a03a\u2013c displays the outcomes of the tri-fold cyclic nonorthogonal linear polarization asymmetric holography experiments. These figures are systematically organized, featuring the training targets (top left), simulation results (top right), and experimental data (middle). The asymmetric polarization channels are distinctly highlighted in purple boxes at the bottom of each figure. Notably, these results showcase vivid and crosstalk-free asymmetric holograms achieved through nonorthogonal polarization multiplexing. This alignment serves as a testament to the robustness and efficacy of the proposed methodology. Supplementary Note\u00a04 illustrates the degrees of freedom in the conventional Jones matrix for metasurface design.\n\na\u2013c Training targets (upper left), simulation results (upper right), and experimental results (middle) for the tri-fold cyclic nonorthogonal polarization holography. The bottom section of each panel, highlighted in purple boxes, denotes the distinct polarization channels. The images illustrate the holographic patterns: a puppy in (a) with polarization transitioning from 0 to 60 degrees, a kitten in (b) with polarization from 60 to 120 degrees, and a mouse in (c) with polarization from 120 to 0 degrees, all within the nonorthogonal polarization channel. d Crosstalk analysis. This panel presents a detailed crosstalk analysis, using selected metaatoms from experimental results (a)\u2013(c), as indicated by yellow (Area 1), orange (Area 2), and green (Area 3) boxes. This analysis quantifies the interference between different polarization channels. e\u2013g Longitudinal intensity statistics derived from the target patterns, simulation results, and experimental data, corresponding to (a), (b), and (c), respectively. These statistics provide a quantitative comparison between the intended patterns and both the simulated and actual experimental outcomes.\n\nTo further quantify crosstalk among these hologram channels, we adopted partitioned summation statistics across three randomly chosen, disjoint regions, as detailed in the Supplementary Note\u00a05. Figure\u00a03d presents the crosstalk computations, indicating an almost negligible interference between hologram channels, thus affirming the method\u2019s precision.\n\nFurther statistical analysis is provided in Fig.\u00a03e\u2013g, where we juxtapose the experimental results with both target and simulated images. The employed statistical approach involves summing and normalizing each image along its longitudinal axis. It can be seen that the measured results agree well with the simulations. Moreover, the curve alterations exhibit a high degree of consistency with the target variations, emphasizing the fidelity and accuracy of our experimental findings. This quantitative evaluation not only substantiates the alignment of our results with the intended outcomes but also underscores the reliability of our experimental approach. The holographic efficiency is defined as \u03b7=EholoEtotal, where Eholo refers to the measured total energy of the hologram patterns, and Etotal refers to the total incident energy received by the metasurface area. The measured holographic efficiencies are 26.04% (0\u00b0\u2009\u2192\u200960\u00b0 polarized channel), 25.25% (60\u00b0\u2009\u2192\u2009120\u00b0 polarized channel), and 27.83% (120\u00b0\u2009\u2192\u2009180\u00b0 polarized channel) respectively.\n\nTo demonstrate the extensive engineering capabilities in creating asymmetric holograms across various nonorthogonal polarization channels, we developed tri-fold cyclic nonorthogonal holograms specifically designed for arbitrary circular and elliptical polarization channels. This process necessitated meticulous amplitude manipulation during the polarization layer mapping phase, as detailed in Fig.\u00a04a.\n\na The operation mechanism that enables the extension of nonorthogonal polarization to a variety of forms. This is achieved through the strategic recombination and distribution of circular and elliptical polarization components, which facilitates the creation of a spectrum of nonorthogonal polarization channels. b Simulation and experimental results for two metasurfaces. It exemplifies the linear-circular polarization channel (using Metasurface 1, MS1) and demonstrate the mutual conversion capabilities for arbitrary elliptical polarization (using Metasurface 2, MS2). The deer image has been designed using images from Flaticon.com. c, d Quantitative analysis of the correlation coefficients between target patterns, simulation outcomes, and experimental images for both circular and elliptical polarization channels. It highlights the exceptional isolation maintained between the various distinct polarization channels.\n\nFor empirical validation, two distinct metasurface samples were rigorously designed and fabricated. The first sample was engineered to respond to incident light composed of x-, y-, and right-hand circularly polarized components. This configuration was achieved by setting \u03b2 at \u03c0/2, and \u03b1 at 0, 90, and 135 degrees within the Jones vector [cos\u2061\u03b1sin\u2061\u03b1\u22c5ei\u03b2], resulting in holographic representations of the letters \u2018A\u2019, \u2018B\u2019, and \u2018C\u2019. The second sample was tailored to process three nonorthogonal elliptical polarizations, with \u03b2 consistently at \u03c0/3, and \u03b1 at 30, 70, and 140 degrees, producing holographic depictions of a deer, squirrel, and wolf, respectively. The training, simulation, and experimental results of these implementations are presented in Fig.\u00a04b. Furthermore, the multiplexing of arbitrarily nonorthogonal linear polarizations is demonstrated in Supplementary Note\u00a06.\n\nTo quantitatively assess the quality of the reconstructed images, we employed correlation coefficients between the reconstructed, target, and simulated images, as depicted in Fig.\u00a04c, d. The correlation coefficient is defined as corr(T,R)=COV(T,R)D(T)\u22c5D(R), where T and R denote the two images, COV (T, R) is their covariance, and D(T) and D(R) are their variances. Both metasurfaces were operated at a wavelength of 3 \u03bcm, with a pixel configuration of 400\u2009\u00d7\u2009400 and a diffraction distance of 500\u2009\u03bcm. Despite the inherent challenges in metaatom determination and sample fabrication, the experimental results demonstrated a close alignment with the design targets. This congruence attests to the feasibility and effectiveness of realizing arbitrary nonorthogonal polarization multiplexed holography. A nine-channel multiplexing with the introduction of wavelength is illustrated in Supplementary Note\u00a07. The measured efficiencies of the Metasurface 1 are 19.13%, 22.16%, and 20.12%, corresponding to the letters \u2018A\u2019, \u2018B\u2019, and \u2018C\u2019, respectively, and the Metasurface 2 are 22.08%, 24.61%, and 21.4% in that order.\n\nBuilding on the innovative nonorthogonal polarization multiplexing framework, we have developed a continuous polarization-based tunable Vectorial Diffraction Neural Network (VDNN). This groundbreaking approach is designed for the full exploitation of global polarization degrees of freedom, thereby significantly enhancing the information channel capacity. By integrating the controllable eigen-polarization modulation mechanism and introducing a subtle focal plane mismatch, we have successfully generated 55 distinct holographic patterns, as showcased in Fig.\u00a05a.\n\na Schematic illustration of 55 distinct elements selected from the periodic table, each serving as a target pattern for holograms across various orthogonal polarization channels. b Correlation coefficient matrix derived from the simulation results. This matrix exemplifies the exceptional global performance achieved in optimizing metaatoms for nonorthogonal polarization multiplexing, highlighting the accuracy and fidelity of our simulation process. c Experimental results of 55 nonorthogonal polarization channels. The arrows within the outer gray box signify the input and output polarizations. This representation emphasizes our method\u2019s ability to transcend conventional boundaries in polarization multiplexing, thereby demonstrating the superior capability of our approach in facilitating nonorthogonal polarization multiplexing across multiple channels.\n\nIn this system, ten linear polarizations (at angles 0\u00b0, 18\u00b0, 36\u00b0, 54\u00b0, 72\u00b0, 90\u00b0, 108\u00b0, 126\u00b0, 144\u00b0, 162\u00b0) are chosen for each input and output, cumulatively resulting in 55 multiplexing channels. These channels are systematically arranged in a lower triangular matrix of dimension 10\u2009\u00d7\u200910, akin to a periodic table of elements, with each channel representing a unique matrix element, as depicted in Fig.\u00a05a. Relevant design process is seen in Supplementary Note\u00a08. The correlation coefficient matrix, presented in Fig.\u00a05b, confirms the high degree of effective isolation achieved between these distinct channels.\n\nAdhering to this methodology, we fabricated a metasurface comprising an array of 640,000 (800\u2009\u00d7\u2009800) metaatoms. The target pattern was tailored for experimental validation, with comprehensive details provided in the Supplementary Note\u00a09. Experimental results are illustrated in Fig.\u00a05c, where the input polarization is displayed at the bottom, the output polarization on the left, and the intersecting pattern depicting the experimentally measured channel results. The measured holographic efficiencies can be found in Supplementary Note\u00a010. It\u2019s worth noting that the images in Fig.\u00a05c are captured at slightly different spatial positions along the z-axis to ensure the best possible resolution and image quality for each holographic pattern. In addition, the nonuniform brightness distribution observed in some holographic patterns (e.g., Ni, Te, Fe) in Fig.\u00a05c become more pronounced with an increase in the number of operating channels. This phenomenon occurs because, as the number of multiplexing channels increases, the repeated use of each metaatom also increases. Consequently, the control capacity of each metaatom may not fully meet the requirements, leading to changes in the brightness of the holographic patterns due to interference at the focal plane. To mitigate this effect, several strategies can be employed: 1. Increase the height of metaatoms: This can enhance the phase control range of each metaatom, thereby reducing brightness variations. 2. Use of combined metaatoms: Implementing complicated metaatoms with more design degrees of freedom can provide better control over the holographic output. 3. Adopt multiple layered metasurfaces: Utilizing multiple layers can distribute the control load more evenly across different metaatoms, improving uniformity. 4. Increase the number of metaatoms: Adding more metaatoms can enhance the overall control precision and reduce nonuniform brightness. These methods can improve the control degree of each metaatom more effectively and regulate the distribution of the holographic target pattern, thereby minimizing the nonuniformity in brightness.",
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+            ]
+        },
+        {
+            "section_name": "Discussion",
+            "section_text": "The nonzero analytical solution of the derived formulas in Supplementary Notes\u00a01 and 4 indicates that the largest rank of the coefficient matrix of the Jones matrix is 3. This means that for given metaatoms with similar profiles, the maximum number of channels for nonorthogonal polarization multiplexing without compromising other dimensions is three. Beyond three channels, crosstalk becomes significant, and different methods must be employed to extend the multiplexing channels. Our approach involves the use of a controllable local eigen-polarization modulation mechanism, as well as optimization through a vectorial diffraction neural network. Additionally, methods such as noise assistance, as described in ref. 17, can also be utilized to further extend the number of multiplexing channels. To achieve more multiplexing channels, it imposes a higher requirement on the metaatoms to possess stronger control abilities, such as enhanced phase coverage, more design degrees of freedom, etc. This necessitates metaatoms with larger depth-to-width ratios, higher refractive index differences, more complex shapes, or additional metasurface layers to expand their controlling capabilities. These factors can influence the efficiency, crosstalk, and the number of achievable multiplexing channels.\n\nAs for the potential to implement other types of functionalities, such as a continuous zoom lens by varying the input-output polarization, our method theoretically allows for such implementations. By precisely controlling the eigen-polarizations of the metaatoms and optimizing the metasurface\u2019s global response, we could potentially develop functionalities beyond holography, including adaptive lenses and other dynamic optical devices. This methodology offers the potential to further expand the Jones matrix to even higher dimensions. Such expansion facilitates the manipulation of more complex polarization states and channels. The compact and versatile nature of these metadevices, underpinned by the controllable eigen-polarization engineering mechanism, solidifies their role as a robust platform for advanced hyper-polarization dynamic holography.\n\nIn summary, this study marks a significant breakthrough in the field of photonics by pioneering a coupled recombination design that leverages local eigen-polarization degrees of freedom. The integration of this mechanism with a sophisticated vectorial diffraction neural network design has been instrumental in achieving a high level of polarization multiplexing holography, encompassing 55 distinct channels. This feat not only facilitates the creation of arbitrary polarization forms and asymmetric channels but also greatly expands the dimensional capacity of the Jones matrix through our controllable eigen-polarization modulation mechanism.\n\nFurthermore, by harmonizing various multiplexing techniques, our strategy significantly boosts the capacity and security of information transmission while maintaining minimal crosstalk. The introduction of nonorthogonal polarization-basis multiplexing represents a pivotal development, establishing a robust foundation for future innovations in optical communications and quantum information sciences. This work not only exemplifies state-of-the-art scientific exploration but also opens new horizons for more secure and versatile channels in the ever-evolving domain of photonics.",
+            "section_image": []
+        },
+        {
+            "section_name": "Methods",
+            "section_text": "The fabrication of the all-silicon metasurface begins with the deposition of a 50\u2009nm chromium (Cr) layer onto a double-sided polished silicon wafer, utilizing electron beam evaporation. A photoresist layer is then spin-coated onto this chromium-coated wafer, followed by a baking process on a hot plate. The metasurface pattern is intricately defined using electron beam lithography (JBX-6300FS). Post-lithography, the samples are developed in a 300-MIF solution, rinsed thoroughly with deionized water, and dried. The fabrication is completed through the use of inductively coupled plasma (ICP) dry etching, targeting both the chromium and silicon layers. This etching process involves selective material removal using various gases, ensuring the precise realization of the desired metasurface configuration.\n\nThe experimental setup involves the generation of mid-infrared light using the Electro MIR 4.8 laser system (Leukos laser). The light is first filtered to a wavelength of 3 \u03bcm with a 200\u2009nm bandwidth, then passes through a polarizer and a full-wave liquid crystal retarder (Thorlabs, LCC1113-MIR, LCC25) for light manipulation before reaching the sample. The sample\u2019s image plane is aligned with the focal plane of an imaging lens set, comprising a 4\u2009mm aspheric lens and a 25\u2009mm lens. The transmitted light is captured and visualized using a high-resolution 640\u2009\u00d7\u2009512 pixels home-made MCT focal array, post-analyzer. Notably, the MWIR camera is cooled to approximately 80\u2009K for optimal measurement performance. In linear polarization experiments, the full-wave liquid crystal retarder is intentionally omitted, reflecting a specific experimental choice. This precise and controlled setup underlines the reliability of our measurements in the mid-infrared range.\n\nFor designing metaatoms, we employ the three-dimensional finite difference time domain (FDTD) method, provided by Lumerical Inc., to calculate transmittance and phase distributions. The holograms are constructed using Python v3.8.13 and PyTorch v1.12.1 (Facebook Inc.), with the vectorial diffraction neural network (VDNN) formulated within this environment. The Adam optimizer in PyTorch is used as the automatic differentiation library, essential for holographic design optimization, while Numpy v1.21.5 enhances data processing efficiency. The angular spectrum diffraction algorithm is incorporated for computational efficiency in diffraction calculations. For arbitrary input polarization state, neural network models were trained with a fixed learning rate of 0.015. The number of iterations varied depending on the model\u2019s complexity. For instance, the linear, elliptic, and circular polarization models underwent 300 iterations each due to their smaller sizes, while the three-wavelength nine-channel model underwent 800 iterations, and the 55-channel model underwent 1500 iterations. To train the vectorial diffraction neural network, a workstation was specifically configured with two NVIDIA GeForce RTX 3090 GPUs (Nvidia Inc.), an AMD EPYC 7513 32-Core Processor (AMD Inc.), and 256 GB of RAM, running the Windows 10 operating system (Microsoft Inc.). The training time for a diffractive model with 55 polarization channels was approximately 0.5\u2009h.\n\nFor large array hologram simulations (800\u2009\u00d7\u2009800 metaatoms), we utilize the vector integration algorithm based on Rayleigh-Sommerfeld diffraction theory, chosen to overcome the computational limitations of FDTD software, allowing for practical simulation of extensive metaatom arrays.",
+            "section_image": []
+        },
+        {
+            "section_name": "Data availability",
+            "section_text": "Relevant data supporting the key findings of this study are available in the article and Supplementary Information file. All raw data generated in this study are available from the corresponding authors upon reasonable request.",
+            "section_image": []
+        },
+        {
+            "section_name": "Code availability",
+            "section_text": "The code used for data analysis during this study is available upon reasonable request from the corresponding authors.",
+            "section_image": []
+        },
+        {
+            "section_name": "References",
+            "section_text": "Mueller, J. P. B., Rubin, N. A., Devlin, R. C., Groever, B. & Capasso, F. Metasurface polarization optics: Independent phase control of arbitrary orthogonal states of polarization. Phys. Rev. Lett. 118, 113901 (2017).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nRubin, N. A., Shi, Z. J. & Capasso, F. Polarization in diffractive optics and metasurfaces. Adv. Opt. Photonics 13, 836\u2013970 (2021).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nOvervig, A. C. et al. Dielectric metasurfaces for complete and independent control of the optical amplitude and phase. Light Sci. Appl. 8, 92 (2019).\n\nArticle\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nGuo, X. et al. Full-color holographic display and encryption with full-polarization degree of freedom. Adv. Mater. 34, 2103192 (2022).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nYang, H. et al. Angular momentum holography via a minimalist metasurface for optical nested encryption. Light Sci. Appl. 12, 79 (2023).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nZang, X. et al. Polarization encoded color image embedded in a dielectric metasurface. Adv. Mater. 30, 1707499 (2018).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nFeng, Z. et al. Dual-band polarized upconversion photoluminescence enhanced by resonant dielectric metasurfaces. eLight 3, 21 (2023).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBao, Y. et al. Observation of full-parameter Jones matrix in bilayer metasurface. Nat. Commun. 13, 7550 (2022).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWang, Z.-Y. et al. Vectorial liquid-crystal holography. eLight 4, 5 (2024).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nChen, Y. et al. Compact spin-valley-locked perovskite emission. Nat. Mater. 22, 1065\u20131070 (2023).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nChen, S., Liu, W., Li, Z., Cheng, H. & Tian, J. Metasurface-empowered optical multiplexing and multifunction. Adv. Mater. 32, 1805912 (2020).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBao, Y., Wen, L., Chen, Q., Qiu, C.-W. & Li, B. Toward the capacity limit of 2D planar Jones matrix with a single-layer metasurface. Sci. Adv. 7, eabh0365 (2021).\n\nArticle\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLiu, M. et al. Multifunctional metasurfaces enabled by simultaneous and independent control of phase and amplitude for orthogonal polarization states. Light Sci. Appl. 10, 107 (2021).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nGeorgi, P. et al. Optical secret sharing with cascaded metasurface holography. Sci. Adv. 7, abf9718 (2021).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nChen, J. et al. Polychromatic full-polarization control in mid-infrared light. Light Sci. Appl. 12, 105 (2023).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nFan, Z.-B. et al. Integral imaging near-eye 3D display using a nanoimprint metalens array. eLight 4, 3 (2024).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nXiong, B. et al. Breaking the limitation of polarization multiplexing in optical metasurfaces with engineered noise. Science 379, 294\u2013299 (2023).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDeng, Z.-L. et al. Vectorial compound metapixels for arbitrary nonorthogonal polarization steganography. Adv. Mater. 33, 2103472 (2021).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nRen, H. et al. Metasurface orbital angular momentum holography. Nat. Commun. 10, 2986 (2019).\n\nArticle\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nRen, H. et al. Complex-amplitude metasurface-based orbital angular momentum holography in momentum space. Nat. Nanotechnol. 15, 948\u2013955 (2020).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nFang, X., Ren, H. & Gu, M. Orbital angular momentum holography for high-security encryption. Nat. Photonics 14, 102\u2013108 (2020).\n\nArticle\u00a0\n    CAS\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWang, J. et al. Continuous-spectrum-polarization recombinant optical encryption with a dielectric metasurface. Adv. Mater. 35, 2304161 (2023).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nJin, L. et al. Dielectric multi-momentum meta-transformer in the visible. Nat. Commun. 10, 4789 (2019).\n\nArticle\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nQu, G. et al. Reprogrammable meta-hologram for optical encryption. Nat. Commun. 11, 5484 (2020).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKim, I. et al. Pixelated bifunctional metasurface-driven dynamic vectorial holographic color prints for photonic security platform. Nat. Commun. 12, 3614 (2021).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nNeshev, D. N. & Miroshnichenko, A. E. Enabling smart vision with metasurfaces. Nat. Photonics 17, 26\u201335 (2023).\n\nArticle\u00a0\n    CAS\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLin, X. et al. All-optical machine learning using diffractive deep neural networks. Science 361, 1004\u20131008 (2018).\n\nArticle\u00a0\n    MathSciNet\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBai, B. et al. To image, or not to image: class-specific diffractive cameras with all-optical erasure of undesired objects. eLight 2, 14 (2022).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nQian, C. et al. Performing optical logic operations by a diffractive neural network. Light Sci. Appl. 9, 59 (2020).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLuo, Y. et al. Computational imaging without a computer: seeing through random diffusers at the speed of light. eLight 2, 4 (2022).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nChen, Z. & Segev, M. Highlighting photonics: looking into the next decade. eLight 1, 2 (2021).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDownload references",
+            "section_image": []
+        },
+        {
+            "section_name": "Acknowledgements",
+            "section_text": "This work was supported by Strategic Priority Research Program (B) of Chinese Academy of Sciences (XDB0580000, GJ0090406, XDB43010200); National Key Research and Development Program of China (2023YFA1406900); National Natural Science Foundation of China (62222514, 62350073, U2341226, 61991440, 62204249, 62305363); Shanghai Science and Technology Committee (23ZR1482000, 22JC1402900, 21ZR1402200); Natural Science Foundation of Zhejiang Province (LR22F050004); Shanghai Municipal Science and Technology Major Project (2019SHZDZX01); Youth Innovation Promotion Association (Y2021070) and International Partnership Program (112GJHZ2022002FN) of Chinese Academy of Sciences; Shanghai Human Resources and Social Security Bureau (2022670), Fundamental Research Funds for the Central Universities (2232022A-11) and China Postdoctoral Science Foundation (2023T160661, 2022TQ0353, 2022M713261). This work was partially carried out at the Center for Micro and Nanoscale Research and Fabrication in University of Science and Technology of China and Soft Matter Nanofab (SMN180827) in ShanghaiTech University.",
+            "section_image": []
+        },
+        {
+            "section_name": "Author information",
+            "section_text": "These authors contributed equally: Jie Wang, Jin Chen, Feilong Yu.\n\nState Key Laboratory of Infrared Physics, Shanghai Institute of Technical Physics, Chinese Academy of Sciences, 500 Yu-Tian Road, Shanghai, 200083, China\n\nJie Wang,\u00a0Jin Chen,\u00a0Feilong Yu,\u00a0Rongsheng Chen,\u00a0Jiuxu Wang,\u00a0Zengyue Zhao,\u00a0Xuenan Li,\u00a0Guanhai Li,\u00a0Xiaoshuang Chen\u00a0&\u00a0Wei Lu\n\nCollege of Physics, DongHua University, 2999 North Renmin Road, Shanghai, 201620, China\n\nJie Wang\u00a0&\u00a0Huaizhong Xing\n\nHangzhou Institute for Advanced Study, University of Chinese Academy of Sciences, No.1 SubLane Xiangshan, Hangzhou, 310024, China\n\nGuanhai Li,\u00a0Xiaoshuang Chen\u00a0&\u00a0Wei Lu\n\nUniversity of Chinese Academy of Science, No. 19 Yuquan Road, 100049, Beijing, China\n\nGuanhai Li,\u00a0Xiaoshuang Chen\u00a0&\u00a0Wei Lu\n\nShanghai Research Center for Quantum Sciences, 99 Xiupu Road, Shanghai, 201315, China\n\nGuanhai Li,\u00a0Xiaoshuang Chen\u00a0&\u00a0Wei Lu\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nG.H.L. conceived the idea. J.W., J.C. and F.L.Y. performed the theoretical calculation and numerical simulation. G.H.L. and J.C. fabricated the sample. J.W., J.C., F.L.Y., J.X.W. and R.S.C. built the optical platform and conducted metasurface experiments. J.W., Z.Y.Z. and X.N.L analyzed the data. G.H.L., J.W., J.C., F.L.Y. and H.Z.X. prepared the manuscript with input from all authors. G.H.L., X.S.C. and W.L. initialized and supervised the project.\n\nCorrespondence to\n                Guanhai Li.",
+            "section_image": []
+        },
+        {
+            "section_name": "Ethics declarations",
+            "section_text": "The authors declare no competing interests.",
+            "section_image": []
+        },
+        {
+            "section_name": "Peer review",
+            "section_text": "Nature Communications thanks the anonymous reviewers for their contribution to the peer review of this work. A peer review file is available.",
+            "section_image": []
+        },
+        {
+            "section_name": "Additional information",
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+            "section_image": []
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+            "section_name": "Rights and permissions",
+            "section_text": "Open Access  This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article\u2019s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article\u2019s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.\n\nReprints and permissions",
+            "section_image": []
+        },
+        {
+            "section_name": "About this article",
+            "section_text": "Wang, J., Chen, J., Yu, F. et al. Unlocking ultra-high holographic information capacity through nonorthogonal polarization multiplexing.\n                    Nat Commun 15, 6284 (2024). https://doi.org/10.1038/s41467-024-50586-5\n\nDownload citation\n\nReceived: 05 March 2024\n\nAccepted: 16 July 2024\n\nPublished: 26 July 2024\n\nVersion of record: 26 July 2024\n\nDOI: https://doi.org/10.1038/s41467-024-50586-5\n\nAnyone you share the following link with will be able to read this content:\n\nSorry, a shareable link is not currently available for this article.\n\n\n\n\n                            Provided by the Springer Nature SharedIt content-sharing initiative\n                        ",
+            "section_image": [
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+            ]
+        },
+        {
+            "section_name": "This article is cited by",
+            "section_text": "PhotoniX (2025)\n\nCommunications Physics (2025)\n\nOptical and Quantum Electronics (2025)\n\nPlasmonics (2025)\n\nOptical Review (2025)",
+            "section_image": []
+        }
+    ]
+}

266d2bdaff4671eda29f45925e187839557438136a8b463f7af726b39e8ebce5/metadata.json

@@ -0,0 +1,139 @@
+{
+    "title": "Environmental control on the productivity of a heavily fished ecosystem",
+    "pre_title": "Environmental Control on the Productivity of a Heavily Fished Ecosystem",
+    "journal": "Nature Communications",
+    "published": "06 June 2025",
+    "supplementary_0": [
+        {
+            "label": "Supplementary Information",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-60453-6/MediaObjects/41467_2025_60453_MOESM1_ESM.pdf"
+        },
+        {
+            "label": "Reporting Summary",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-60453-6/MediaObjects/41467_2025_60453_MOESM2_ESM.pdf"
+        },
+        {
+            "label": "Transparent Peer Review File",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-60453-6/MediaObjects/41467_2025_60453_MOESM3_ESM.pdf"
+        }
+    ],
+    "supplementary_1": NaN,
+    "supplementary_2": NaN,
+    "source_data": [
+        "https://doi.org/10.5281/zenodo.15359627",
+        "https://psl.noaa.gov"
+    ],
+    "code": [
+        "https://doi.org/10.5281/zenodo.15359627"
+    ],
+    "subject": [
+        "Marine biology",
+        "Physical oceanography"
+    ],
+    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
+    "preprint_pdf": "https://www.researchsquare.com/article/rs-4108948/v1.pdf?c=1749294351000",
+    "research_square_link": "https://www.researchsquare.com//article/rs-4108948/v1",
+    "nature_pdf": "https://www.nature.com/articles/s41467-025-60453-6.pdf",
+    "preprint_posted": "27 Mar, 2024",
+    "research_square_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Sustainable fisheries management requires an understanding of the links between environmental conditions and fish stock populations, especially in the context of climate change. From this perspective, identifying phases where ocean climate fluctuations and changes in ecosystem productivity coincide could provide a powerful tool to help inform fisheries management. Using more than 70 years of climate and fisheries data, this study shows that the Newfoundland and Labrador (NL) ecosystem productivity, from primary producers to piscivorous fish, changes in relative synchronicity with the climate of the northern hemisphere over decadal time scales. Such correspondence between the climate and lower and higher trophic levels has not been achieved previously in the Northwest Atlantic in the context of fisheries. This work advances ideas for incorporating environmental knowledge into fisheries management on the NL shelves, or in other regions facing similar dynamics.Earth and environmental sciences/Climate sciences/Ocean sciences/Marine biologyEarth and environmental sciences/Climate sciences/Ocean sciences/Physical oceanographyClimateFisheriesEcosystemBottom-Up controlNW Atlantic Ocean",
+            "section_image": []
+        },
+        {
+            "section_name": "Additional Declarations",
+            "section_text": "There is NO Competing Interest.",
+            "section_image": []
+        }
+    ],
+    "nature_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Sustainable fisheries management requires an understanding of the links between environmental conditions and fish populations, especially in the context of climate change. From this perspective, identifying the phases in which ocean climate fluctuations and changes in ecosystem productivity coincide could provide a powerful tool to help inform fisheries management. Using more than 70 years of climate and fisheries data, we show that cyclical changes in the Newfoundland and Labrador (NL) ecosystems productivity, from primary producers to piscivorous fish, coincide with changes in the regional ocean climate and the atmospheric settings of the northern hemisphere. This broad correspondence between climate and lower and higher trophic levels advances ideas for incorporating environmental knowledge into fisheries management on the NL shelves or in other regions facing similar dynamics.",
+            "section_image": []
+        },
+        {
+            "section_name": "Introduction",
+            "section_text": "Fisheries productivity is known to be affected by broad-scale environmental processes such as those captured by the North Atlantic Oscillation (NAO)1, the Pacific Decadal Oscillation2 or the El Ni\u00f1o Southern Oscillation (ENSO)3. However, separating the effects of changes in recruitment or fishing mortality and varying ecosystem productivity due to variations in environmental conditions remains a major challenge in the evaluation of fish stocks around the world4. These considerations are even more pressing in the face of anthropogenic climate change5. Integrating environmental knowledge into stock assessment processes is a key step, along with moving beyond single-species approaches6, to achieving ecosystem-based fisheries management (EBFM)7,8. One practical limitation often put forward for not including environmental information in fisheries management is the fact that their quantitative impact on resources is often poorly understood9,10.\n\nThe Newfoundland and Labrador (NL) shelves are a broad region of the northwest (NW) Atlantic\u00a0ocean that includes the Labrador shelf, the Newfoundland shelf, and the Grand Banks of Newfoundland (Fig.\u00a01). Following centuries of exploitation, the NL Northern Cod (Gadus morhua) stock, together with other groundfish stocks, collapsed in the early 1990s11. More than 30 years later, most of these stocks have yet to recover to their pre-collapse levels, and the region\u2019s ecosystems have shown important changes in their community structure (shifting from groundfish-dominated to shellfish-dominated, and are now returning to a groundfish-dominated structure)12,13,14,15. Although the exact causes of these changes continue to be investigated, it appears that both overfishing and environmental changes contributed to the collapse of many populations16,17,18. More specifically, the collapse of groundfish stocks occurred during one of the coldest periods of the last century in the NW Atlantic19 and coincided with the collapse of capelin (Mallotus villosus), a key pelagic forage fish species for the NL ecosystems, and several groundfish species that were not subjected to directed commercial fishing13,20.\n\nThe color map shows the bathymetric features obtnained from the General Bathymetric Chart of the Oceans92. A sketch of the main surface currents is shown in black. NAFO Divisions 2H, 2J, 3K and 3L, 3N, 3O, 3M and 3Ps are shown in slate gray for reference. The red dots aligned in sections (also identified) represent the hydrographic stations where zooplankton samples used in this study were collected. Hydrographic Station 27 is shown with a red star.\n\nSeveral studies have investigated the role of environmental changes in the collapse of fish stocks on the NL shelves12,21,22,23,24,25. Less work has been directed towards the period prior to the collapse, when a recently mechanized fleet achieved record-high catches during the warmest and potentially most productive period of the last century in the NW Atlantic26,27. Could the collapse of NL fish stocks have been prevented if the changes in environmental conditions and related productivity regimes of the ecosystem (e.g., the recognition of anomalously warm and productive 1960s and anomalously cold and less productive 1980s/90s) been factored into fisheries stock assessments at the time? Although we cannot definitively answer this question, as it involves both science and policy or political considerations, we propose an approach to identify when an ecosystem is characterized by particular productivity regimes and argue that it offers a mechanism for adjusting fisheries management given changes in climatic conditions going forward.\n\nIn this work, we argue that the lack of precise quantitative knowledge on the effect of the environment on fish stocks does not preclude its integration into stock assessments and its consideration in fisheries management decisions. Using more than 70 years of data from the NL shelves, we show that the ecosystem goes through productivity phases on decadal time scales. We also show that these phases can be identified using proper environmental monitoring and be used to guide fisheries management. For example, more conservative fisheries management policies (e.g., lower extraction rates, stronger emphasis on conservation when evaluating the trade-off between stock conservation and socio-economic objectives) could be used in phases of low productivity, and more relaxed fisheries management policies (e.g., higher extraction rates, increased emphasis on socio-economic objectives) could be used in phases of higher productivity.",
+            "section_image": [
+                "https:////media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41467-025-60453-6/MediaObjects/41467_2025_60453_Fig1_HTML.png"
+            ]
+        },
+        {
+            "section_name": "Results",
+            "section_text": "Located in Atlantic Canada at the confluence of Arctic, sub-Arctic, and subtropical currents, the NL shelves (Fig.\u00a01) are strongly influenced by changes in ocean circulation at the scale of the NW Atlantic. These changes impact not only the regional ocean climate but also the overall composition of water masses and the immediate habitat of numerous commercial and non-commercial fish and invertebrate species.\n\nThe environmental conditions on the NL shelves and the NW Atlantic can be described using a climate index19,28. Presented as a composite graph showing the average and relative contributions of standardized anomalies from 10 environmental time series, the NL Climate Index (NLCI; https://doi.org/10.20383/101.0301 [consulted 5 May 2024]) shows annual changes in ocean climatic conditions for more than seven decades (Fig.\u00a02). Different climate phases can be identified by looking at periods where the NLCI is mostly positive or mostly negative. These phases are delimited here using the simple rule that a new phase occurs when the mean value of the NLCI (scorecard at the bottom of Fig.\u00a02) has a positive or negative run for at least three consecutive years (minimum number of years for which a linear regression can be fitted with uncertainty).\n\nThe NLCI (unitless) is the average of 10 environmental time series: the Winter North Atlantic Oscillation (NAO) index, air temperature (Air Temp), sea ice season duration and maximum area, the number of icebergs drifting on the NL shelves, sea surface temperature (SST) of the NL shelves, vertically averaged temperature (T) and salinity (S) at Station 27 (S27), cold intermediate layer (CIL) core temperature at Station 27, summer CIL area on the hydrographic sections Seal Island, Bonavista Bay and Flemish Cap, and spring and fall bottom temperatures in NAFO Div. 3LNOPs and 2HJ3KLNO (See Cyr and Galbraith, 2021 for details19). The relative contribution of each sub-index to the NLCI is proportional to the length of each bar in the stacked bar plot, while the averaged value is reported in a scorecard at the bottom of the figure. Different climate phases are identified with orange and blue shades for warm and cold, respectively. A new phase is identified when the NLCI is positive or negative for at least three successive years. Qualitative information on the fisheries during the different climate phases has been added with black arrows.\n\nEight climate phases, generally characterized by warmer or colder ocean conditions, were identified between 1951 and 2017 (orange and blue shades in Fig.\u00a02). A ninth warm and potentially more productive climate phase has emerged since 2018. Although its effect on fish stocks has yet to be quantified, some signs of improvement in the finfish community have already been detected (see Discussion). These phases are driven by large-scale atmospheric conditions, shown here with mean sea level pressure (SLP) anomalies over the northern hemisphere (Fig.\u00a03). Phases characterized by warmer climate (1951\u20131971, 1979\u20131981, 1999\u20132006, and 2010\u20132013) have mostly positive SLP anomalies above the pole and negative anomalies in the subtropics (except the 1999\u20132006 phase, where the patterns are unclear). In contrast, the phases characterized by a colder climate (1972\u20131978, 1982\u20131998, 2007\u20132009, and 2014\u20132017) all have negative SLP anomalies above the pole and positive anomalies in the subtropics.\n\nb 1951\u20131971, (i) 1972\u20131978, (d) 1979\u20131981, (k) 1982\u20131998, (f) 1999\u20132006, (m) 2007\u20132009, (h) 2010\u20132013 and (o) 2014\u20132017). Each of these periods correspond to the climate phases identified in Fig.\u00a02, recalled in a side panel showing the NLCI (gray bars, unitless) with orange/blue shades showing the warm/cold phase of interest (subfigures a, j, c, l, e, n, g and p, respectively). Anomalies in the annual primary production above the NW Atlantic and Calanus finmarchicus density on the NL shelves are shown in the top of each SLP panel (where available). The trends in capelin biomass, multi-species bottom trawl survey biomass density, and groundfish biomass are indicated in the bottom of SLP subfigures (see legend). The anomalies and trends have been highlighted in orange, blue and gray for positive, negative and non-significant, respectively.\n\nNegative SLP anomalies above the pole are associated with positive phases of the NAO and are accompanied by a strengthening of the westerlies and the atmospheric jet stream above the NW Atlantic. This in turn leads to more frigid Arctic airflow above the NW Atlantic, particularly in winter, which promotes deeper convection in the Labrador Sea29, larger volumes of cold water on the Labrador shelf30, and changes in the pathways and strength of the Labrador current31 and the subpolar gyre32,33.\n\nImportant milestones for the NL fisheries have been linked to the ocean climate (Fig.\u00a02). Following centuries of relatively small-scale fisheries, the post-World War II period saw the introduction of large mechanized fishing vessels, including factory trawlers34. Historical reconstructions suggest that cod catches remained below 300,000 tonnes/year for hundreds of years before rapidly increasing in the 1950s and 1960s, reaching a peak of more than 800,000 tonnes in 196835 (see also Supplementary Fig.\u00a06). Although the capabilities of this new fishing fleet were undeniable, it should be noted that record catches of the 1960s were achieved during one of the warmest period in (at least) seven decades on the NL shelves19. This period was characterized as uniquely favorable for groundfish productivity26.\n\nA first partial collapse of the groundfish fisheries occurred in the early 1970s34 during a relatively cold phase that was in sharp contrast to the warm climate of the 1950s and 1960s (note that 1972 is the third coldest year recorded by the NLCI, tied with 1984). This collapse on the NL shelves coincided with general decreases in Atlantic Cod stocks across the NW Atlantic and was attributed to poor environmental conditions36. A partial recovery followed in the late 1970s, a period again characterized by warmer ocean conditions and positive SLP anomalies above the pole. This partial recovery of groundfish stocks was also aided by a reduction in fishing pressure in coastal waters following international agreements that led to the establishment of exclusive economic zones of 200 miles for maritime nations36,37.\n\nFrom the early 1980s to the late 1990s, the NW Atlantic entered its coldest phase in the last 70 years (a first cold pulse was recorded in the mid-1980s and a second in the early 1990s). Multiple commercial and non-commercial fish populations successively collapsed during this period13. The biomass of the capelin stock in Northwest Atlantic Fisheries Organization (NAFO) Divisions (Div.) 2J3KL rapidly collapsed from 5800 kt in spring 1990 to 600 kt in fall 1990 \u2014 probably due to environmental drivers rather than fishing \u2014 before the collapse of the northern cod stock20. The collapse of cod led to the eventual establishment of a series of moratoria on groundfish fisheries beginning in 1992, while 1991 and 1993 were the coldest years recorded by the NLCI (Fig.\u00a02). In the following decades, some cold water shellfish stocks became more productive15, although their increases in biomass never fully compensated for losses in groundfish biomass14,38. Although some finfish stocks have shown signs of improvement in the following decades39, the recovery of many groundfish and pelagic stocks appears to have stalled during the 2014\u20132017 phase40,41,42. This period again coincides with a shift in climate towards colder conditions, with the 2014\u20132017 phase sharing some similarities with that of the early 1990s29, albeit of much shorter duration. Following a reanalysis of cod stocks using a longer time series43, the Northern cod commercial fishing moratorium ended in 2024.\n\nWe also note that in addition to 2014\u20132017, another cold phase of lesser magnitude (2006\u20132009) interrupted the otherwise positive run of the NLCI that occurred between the late 1990s and the mid-2010s. Since the late 1990s, the NL climate has exhibited alternating colder and warmer conditions over relatively short phases, and the NLCI has not returned to a positive run similar to the one observed in the 1950s and 1960s. Provided that the ocean climate is influential on fish stocks, this means that the climatic conditions and the setup preceding the record catches of the 1960s have not been replicated over the past 50 years.\n\nTo better quantify and explain the changes observed in the ecosystems, we examined, for the different phases of the climate introduced above, the evolution in primary and secondary production, forage and groundfish biomass, and the biomass density of finfish and commercial shellfish collected during scientific surveys. We treated these five time series differently (see Methods section). For primary and secondary production, we look at the mean level for each climate phase compared to the average of the entire time series (that is anomalies, because biomass cannot generally accumulate from one year to the next). For fish and finfish biomass, we look at trends during the different climate phases because surplus production can accumulate over time.\n\nPrimary production levels in the NW Atlantic, as well as the density of Calanus finmarchicus, a key zooplankton species on the NL shelves, were generally above average during warmer climate phases and below average during colder climate phases (Supplementary Figs.\u00a01 and 2).\n\nSimilarly, trends in the capelin biomass index derived from acoustic-trawl surveys, the finfish and shellfish biomass density index derived from scientific multi-species bottom trawl surveys, and the groundfish excess-biomass derived from a surplus production model accounting for density-dependent effects and fisheries catches generally increased during warm climate phases and decreased during cold phases. Here, trends refer to the slopes of linear regression fits to annual biomass, biomass index and density time series during climate phases (Supplementary Figs.\u00a03\u20135).\n\nFor nearly all climate phases identified with the NLCI, there is a good correspondence between the atmospheric large-scale SLP patterns, the regional NL climate and, where data are available, the productivity of the ecosystems determined by the mean level of primary and secondary production, as well as the trends in surplus groundfish biomass and multispecies biomass density. For example, during warmer phases of the climate (Fig.\u00a03a\u2013h), primary and secondary production levels were generally above average, and the three biomass metrics described above increased (mostly orange numbers). In contrast, during the colder phases of the climate (Fig.\u00a03i\u2013p), primary and secondary production levels were generally below average, and the three biomass metrics described above decreased (mostly blue numbers). Exceptions include above average primary production during the cold 2007\u20132009 phase (Fig.\u00a03m) and near-average abundance of Calanus finmarchicus during the warm 1999\u20132006 phase (Fig.\u00a03f). Furthermore, the evidence for the importance of climate phases in trends in capelin biomass is not as compelling as that of groundfish and multispecies biomasses. Specifically, although the capelin biomass is marked by a decline during the groundfish collapse phase (1982\u20131998; Fig.\u00a03k), its biomass increased between 1982-1990 before collapsing in 1990-1991 (Supplementary Fig.\u00a03). The reasons for this increase in capelin biomass in the 1980s are unclear. It may be associated with a reduction in predation pressure when groundfish stocks began to decrease in the mid to late 1980s13. Alternatively, capelin stocks may have had reduced spatial overlaps with their predators during the cold 1980s44, but then the capelin also collapsed during the very cold anomaly of 1990\u20131993. Trends in capelin biomass were also not significantly different from zero during the 1999\u20132006 and 2007\u20132009 climate phases, unlike the trends in the groundfish and multi-species biomasses (Fig.\u00a03f, m). However, the SLP patterns during these two phases did not exhibit clear positive or negative signals centered around the pole as seen in other phases, which corresponded to rapid fluctuations of the NLCI (especially during the 1999\u20132006 phase). This may suggest changes in predation dynamics upon capelin or that the species responds more rapidly to environmental changes.\n\nOverall, the NLCI, the SLP patterns and the productivity of the different components of the NL ecosystems track each other well. Autocorrelation in the environmental time series provides a challenge in detecting changes in climate conditions, but it also highlights the consistency in the signal for extended periods of time, particularly when consistent across multiple trophic levels. Collectively, this suggests that not only does the ocean climate, driven by large-scale atmospheric forcing, change on decadal time scales, but also that the overall productivity of the ecosystems (from primary and secondary production to forage fish and higher trophic levels) changes in relative synchronicity with climate fluctuations. These results support the description of the fisheries made in Fig.\u00a02 and suggest that productivity changes may have also occurred in periods where no fisheries-independent data were available (e.g., productive 1960s and less productive early 1970s)16. This is supported by historical Northern Cod catches reconstructed for the NW Atlantic35 that shows periods of increase and decline aligned with the different climate phases, especially before the 1990s collapse (Supplementary Fig.\u00a06). This study also supports the idea that the period preceding the late 1960s, when the highest extraction rates by fisheries occurred, was likely a period with an unusually large climatic anomaly for the NL shelves26; and that those sustained warm and productive conditions during the 1950s and 1960s have not been observed since.",
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+            ]
+        },
+        {
+            "section_name": "Discussion",
+            "section_text": "In ecology, bottom-up trophic control refers to ecosystems that are resource-driven and limited by biotic or abiotic factors (physical environment, primary and secondary production, etc.), while top-down trophic control refers to a consumer-driven cascade where the dominant control is exerted by predators such as fish, marine mammals and/or fisheries45. By demonstrating a consistent correspondence between the atmospheric setting on ocean climate and the influence of climate on primary and secondary production, forage fish, groundfish, and overall biomass density, this study provides evidence for strong bottom-up control of the NL shelves ecosystems.\n\nWith the NL shelf being located in the coldest part of the range for many groundfish species, it is not surprising to find a positive relationship between recruitment and temperature for some stocks, such as Atlantic cod46. However, it is important to acknowledge that the effects of warmer and colder climate phases go far beyond the simple physiological response of organisms to temperature. Changes in climate phases involve changes in ocean circulation, water mass composition, plankton phenology, etc. Here, a series of hypotheses linking climate and ecosystem productivity and fish biomass are reviewed.\n\nThe NL shelves are characterized by the presence of near-freezing(<\u20090\u2009\u00b0C) Arctic-origin waters in their subsurface for most of the year47. In colder climate phases, larger volumes of these cold waters are found on the NL shelves19, potentially limiting the distribution of species that are less cold tolerant48, or resulting in distributional changes of some stocks toward areas with more suitable conditions21. The different climate phases on the NL shelves also imply changes in the severity of winter and sea ice conditions, which alter the timing of post-winter ocean re-stratification and the phenology of spring phytoplankton blooms, with earlier blooms associated with warmer climate, and vice versa49.\n\nWarmer climate phases are also associated with higher densities of Calanus finmarchicus, a key copepod species in the NL ecosystems49. The increases in their density can be explained not only by increases in primary production, but also by a better match between the end of the C. finmarchicus winter diapause and the timing of the phytoplankton bloom50,51. In addition, there may be better retention of secondary production on the NL shelves during warm phases due to the weaker subpolar gyre associated with reduced wind curl over the North Atlantic32,52. The energy rich C. finmarchicus is a key prey for capelin, a keystone forage fish species that is responsible for the transfer of energy between secondary producers and higher trophic levels53,54. Thus, it is not unexpected to see capelin biomass trend upwards when C. finmarchicus abundances are high. Higher capelin biomass also has a direct effect on higher trophic levels, such as cod, a key predator of capelin55, and other groundfish species. In general, this study supports the idea that the availability of energy at the base of the food web is an important limiting factor for overall ecosystem productivity, as indicated by concurrent increases in capelin, groundfish, and other fish species biomasses in periods when C. finmarchicus densities are high (and vice versa).\n\nWe have been able to identify climate phase as an underlying mechanism that explains prolonged periods of low and high productivity for multiple trophic levels in the NL ecosystems. Unlike previous studies that have typically focused on single characteristics of the climate system (e.g., the NAO1), our approach builds on the simple concept that no single indicator can fully encapsulate all relevant environmental processes that impact ecosystem productivity. We leverage environmental indicators provided by the NLCI to uncover the relationship between the ocean climate state and ecosystem function.\n\nThe NLCI used in this study includes the winter NAO as well as nine other subindices. The advantage of integrating these additional climate indices (both on a regional scale and on a broad scale) into a climate index is that we do not rely on the trend of one index alone to identify climate phases. While we have time series of variable lengths, especially for lower trophic levels, the relative concordance between productivity trends across trophic levels supports the use of the NLCI to identify periods of low and high productivity.\n\nPrevious studies on Atlantic cod stocks across the North Atlantic basin have noted a general coherence in stock collapses during the 1980s and 1990s, suggesting that environmental forcing was an important underlying factor in addition to fishing impacts36,56,57. In the northeast Atlantic, the prevalence of warmer ocean conditions since the 1980s, combined with the application of precautionary biological reference points in applied fisheries management, has contributed to the rebuilding of the Atlantic Cod stock to record levels58. Additional work on some of these stocks has shown how changing environmental conditions affected cod through impacts in lower trophic levels59, and how the availability of a forage species like capelin emerges as a common driver for two cod stocks with very different trajectories in the northwest and northeast Atlantic55. These observations from several North Atlantic ecosystems are consistent with our finding that ecosystem productivity appears to be generally associated with the prevailing phase of ocean climate, and suggest that identifying such phases could provide information on overall ecosystem functioning more generally.\n\nIt has been hypothesized that the lack of recovery of most commercial fisheries to pre-collapse biomass levels was due to a sustained low productivity regime since the early 1990s57,60,61. This study offers a perspective on this hypothesis. First, it confirms that the climatic setting that led to record high cod catches in the 1960s \u2014 e.g., sustained warmer than average ocean conditions with potentially earlier spring blooms and higher levels of primary and secondary production \u2014 have not been observed since. Second, warm phases since 1998 provide an explanation for the modest improvements experienced by capelin and some groundfish stocks since the collapses in the early 1990s20,62,63, but the lack of further recovery to pre-collapse levels may be associated with what appears to be an increased variability in the periodicity of changes in climate phases such as the short-lived but intense cold and low productivity phases for groundfish between about 2006 and 2009, and 2014 and 201714,64 (Figs.\u00a02 and 3). The warmer phase emerging since about 2018 may, however, signify a transition to a more productive phase in the coming years, consistent with a recent improvement of the capelin fall condition index65.\n\nDisentangling fishing mortality (e.g., overfishing) and natural fluctuations of fish populations is a challenge because they are intrinsically related36,57. Favorable environmental conditions can allow for fishing levels that may not be otherwise sustainable. That may have been the case, for example, on the NL shelves in the 1960s. In contrast, fishing mortality can exacerbate the impacts of poor environmental conditions on ecosystems and accelerate the decline of fish stocks66. A stock historically fished sustainably may become over-fished if its production declines below a certain level due to changes in environmental conditions.\n\nLinking environmental fluctuations with fish stock dynamics is a key step in the implementation of EBFM67,68. Towards this goal, this study demonstrates how 70 years of fluctuations in NL ecosystems productivity and changes in fish biomass can be explained using a simple climate index. Recognizing the phases (or productivity regimes) that an ecosystem is subject to, such as the ones described in this study, provides a powerful tool to inform fisheries management. This environmental information can be taken into account either qualitatively or quantitatively.\n\nQualitatively, it allows setting more conservative extraction targets, or even ecosystem quotas, during periods when environmental conditions are deemed less favorable for productivity, or more permissive ones when these conditions appear favorable. Although conceptually a straightforward approach, real-life applications of these concepts would be expected to be more complex and likely involve the use of environmental conditions to inform risk assessments aimed at evaluating trade-offs between the conservation of the exploited stocks and socioeconomic pressures. A recent illustration of this idea is the decision of Peru to suspend the 2023 anchoveta fishery season as a trade-off for conservation69. This decision was motivated by the high number of juvenile fish in the exploratory fishery as a result of the developing El Ni\u00f1o phase of the ENSO in 2023, a situation known to impact the anchoveta fishery70.\n\nQuantitatively, environmental trend analyses could be used to adjust target levels of fishing mortality (sensu Feco)6 or these trends could be explicitly included in the operating models used in management strategy evaluations (MSE) to fully integrate environmental signals in the development of harvest control rules71. Another alternative would be to adjust ecosystem-level quotas based on a scaling factor determined by ocean climate. This is analogous to the idea of establishing ecosystem overfishing thresholds based on primary production metrics72, except this time on the basis of a climate index. This type of approach would be well suited for current applications of ecosystem indicators for total sustainable catches, such as the one implemented by NAFO that scales estimates of fisheries production potential using total biomass density, and which our study has shown responds to identified climate phases18,73,74. However, in the context of fisheries management based on maximum sustainable yield (MSY), factoring in changes in ecosystem productivity may, in some circumstances, have the unintended consequence of increasing anthropogenic pressure on a stock by lowering its limit reference point75. Climate-adaptive fisheries management strategies in the context of MSY should therefore be carefully studied if the protection of marine resources is the priority.\n\nFisheries management actions in relation to a changing climate are plagued by many unknown unknowns76 that should nevertheless be considered when setting management objectives, since these decisions can affect the future state of natural resources77. This work joins a growing body of literature that proposes pragmatic solutions to how to overcome these challenges.",
+            "section_image": []
+        },
+        {
+            "section_name": "Methods",
+            "section_text": "Monthly SLP between 1948 and 2021 were retrieved from the National Centers for Environmental Prediction (NCEP) and the National Center for Atmospheric Research (NCAR) (NCEP-NCAR Reanalysis 1 data). These are provided by the National Oceanic and Atmospheric Administration Physical Science Laboratory in Boulder, Colorado, USA, and accessible on their website at https://psl.noaa.gov [consulted 4 May 2022]78. The SLP anomalies for each of the climate phases discussed above were calculated as the difference between the average for each time window (all months considered) and the average of the 1950\u20132020 period (Fig.\u00a03).\n\nThe annual net primary production (in mgC\u2009m\u22123\u2009d\u22121) over the NW Atlantic was obtained from a Mercator-Ocean biogeochemistry hindcast for the global ocean at https://doi.org/10.48670/moi-00019 [consulted 4 October 2022]. The monthly resolution data were averaged in annual means and over a geographical region covering the NW Atlantic [47-65\u00b0N; 47-65\u00b0W] (dashed box in Fig.\u00a03). The resulting time series runs from 1993 to 2020 (Supplementary Fig.\u00a01). The average primary production for each climate phase were reported as horizontal dashed-green lines with shading representing the 80% confidence interval (Supplementary Table\u00a01). The anomalies of primary production for each climate phase are calculated as the difference between the average of each climate phase and the average of the entire time series (1993\u20132020). These anomalies are reported in Fig.\u00a03 in orange when positive and blue when negative.\n\nPhysical and biogeochemical data are regularly collected on the NL shelves at standard stations along oceanographic transects since 1999 as part of Fisheries and Oceans Canada\u2019s (DFO) Atlantic Zone Monitoring Program (AZMP)79. Up to three missions (spring, summer and fall) occur annually in the NL waters as part of the AZMP. During the spring and fall, Southeast Grand Bank, Flemish Cap and Bonavista Bay transects were occupied in most years while the Seal Island transect was only occupied from 2009 to 2015 during fall missions (Fig.\u00a01). In the summer, the Flemish Cap and Seal Islands transects were occupied in most years while the White Bay transect was occupied every 1 to 3 years between 1999 and 2007.\n\nIn addition to those transects, zooplankton samples were also collected at Station 27 (47\u221832.8\u2019N, 52\u221835.2\u2019W) two to four times per month on average, from April through December. This Station is located just east of St. John\u2019s, NL and has a total depth of 176 m (Fig.\u00a01). It is downstream from the incoming flow from the Labrador shelf, and its local oceanographic conditions are considered representative of the climate of the NL shelves and the NW Atlantic19,80,81.\n\nZooplankton samples were collected at the stations described above by vertically towing a pair of conical ring nets (200\u2009\u03bcm) that were mounted side by side (e.g., \u201cbongo nets\u201d) from 10 m off the bottom to the surface at a speed of \u00a0~\u20091\u2009m\u2009s\u22121. Material collected from each of the conical ring nets was preserved separately in a buffered 2% formaldehyde solution. The material from one net was sent to a taxonomy lab for species identification and counting. For each vertical tow, the copepod density per surface area (C in ind\u2009m\u22122) was estimated by dividing the number of individuals in the tow (N) by the area of the net opening (0.44\u2009m2). Annual estimates of copepod Calanus finmarchicus (\\(\\overline{C}\\)) were obtained by fitting a linear model of the form shown in equation (1):\n\nHere \\(\\overline{C}\\) is the mean annual density of Calanus (in ind m\u22122), \u03b1 is the intercept, \u03f5 is the error, and \u03b2, \u03b4, \u03b3 are the categorical effects of the factors Year, Station and Season, respectively. \\(\\overline{C}\\) was log-transformed (ln) to normalize the skewed distribution of the observations. This model accounts for the fact that the number of stations and seasons sampled annually by the AZMP may slightly vary from year to year. To control for the order of the variables in the model, annual means were estimated using adjusted sums of squares82. The assumptions of the models were assessed, i.e., the residuals were examined for independence as well as for normality and homogeneity of variance.\n\nAnnual C. finmarchicus densities are reported in Supplementary Fig.\u00a02. The horizontal dashed brown lines correspond to the average level for each climate phase identified in the study, with shading representing the 80% confidence interval (Supplementary Table\u00a01). The anomalies in C. finmarchicus density for each climate phase are calculated as the difference between the average of each climate phase and the average of the entire time series (1999\u20132021). These anomalies are reported in Fig.\u00a03 in orange text when positive and blue text when negative.\n\nThe capelin biomass index (in kt) was estimated during the annual DFO spring capelin acoustic survey (Supplementary Fig.\u00a03). The spring capelin acoustic survey has taken place annually in its current form since 1982, except for 1983-84 and 2021, and there were no acoustic surveys in 1993\u20131995, 1997-1998, 2006, 2016, and 202060.\n\nThe acoustic survey is typically conducted in May and covers the majority of NAFO Div. 3L, and since 1996, the southern NAFO Div. 3K. Div. 3L is an area of particular importance for juvenile and non-migratory age-1\u2009+ capelin, although all age classes acoustically surveyed are included in the annual capelin biomass index. A depth-delimited stratified survey design is conducted each year, although the transect design, stratum boundaries, and areas covered have changed over time83,84. Acoustic backscatter attributed to capelin was converted to capelin biomass using biological data from directed mid-water and bottom trawls.\n\nLinear trends were calculated for each climate phase previously identified by a least squares regression with bootstrap (1000 repetitions). The mean trends, defined as the average of all repetitions, are reported in Fig.\u00a03 in orange text when positive and in blue text when negative, while the 80% confidence intervals are reported in Supplementary Table\u00a01. Slopes for which the confidence interval bounds have different signs are left gray.\n\nThe total biomass density index from DFO multi-species bottom-trawl scientific surveys (in kt\u2009km\u22122) was calculated from DFO Fall and Spring surveys for NAFO Div. 2J3KLNOPs (Supplementary Fig.\u00a04). The large marine ecosystem in the NL shelves is typically subdivided into Ecosystem Production Units (EPUs) which correspond to relatively well defined, but still interconnected, functional ecosystems85,86,87. DFO multi-species surveys have covered these EPUs differently over time. The Fall surveys have systematically surveyed the Newfoundland Shelves (NAFO Div. 2J3K) EPU since 1981, and the Grand Bank (NAFO Div. 3LNO) EPU since 1990. The Spring surveys have systematically covered the Grand Bank EPU since 1985, and the Southern Newfoundland (NAFO Div. 3Ps) EPU since 1982. The gear used in these surveys changed in 1995 for the Fall surveys and 1996 for the Spring surveys when the Campelen trawl replaced the Engel trawl. The introduction of the Campelen trawl permitted the beginning of the systematic recording of commercial shellfish species in DFO surveys. This was important given that shellfish species like Northern shrimp and snow crab had increased after the collapse of the groundfish community14,38. While these biomass increases were substantial, especially in the mid-late 1990s, they did not compensate for the losses of groundfish14. Northern shrimp was the dominant species among commercial shellfish, and available approximations of its biomass prior to the introduction of the Campelen gear indicate that it was only starting to increase in a significant way when the Campelen gear was introduced88. The available evidence88,89 suggest that commercial shellfish biomass was a relatively modest fraction of the total biomass before the collapse. It follows that considering only finfish for the Engel period, when groundfish heavily dominated the total biomass, is a reasonable approximation to the total biomass signal.\n\nFor each EPU and season, total biomass density was calculated as the total biomass for all finfish and commercial shellfish, when shellfish data is available, species divided by the total area surveyed. Total biomass was obtained as the sum of individual species biomass estimates calculated as the standard areal expansion of survey biomass based on the random-stratified survey design. Scaling factors were applied to the Engel series to provide comparability in the order of magnitude between the Engel and Campelen data14,38. These scaling factors are not available for the Southern Newfoundland EPU, so only Campelen data (i.e., 1996 forward) was considered in this analysis for this EPU. Given that the Grand Bank EPU is typically surveyed twice a year (spring and fall surveys), the biomass density signal for this EPU was summarized as the average of the estimated biomass densities from these two surveys. The total biomass density signal at the scale of the NL shelf was estimated as the median of all available total biomass densities by EPU in a given year.\n\nLinear trends were calculated for each climate phase previously identified by a least squares regression with bootstrap (1000 repetitions). The mean trends, defined as the average of all repetitions, are reported in Fig.\u00a03 in orange text when positive and in blue text when negative, while the 80% confidence intervals are reported in Supplementary Table\u00a01. Slopes for which the confidence interval bounds have different signs are left gray.\n\nGroundfish biomass was estimated using a state-space multi-species surplus production model for the NL shelves. Within each region (NAFO Div. 2J3K and 3LNO), the biomass of each species at the start of year y was given by equation (2):\n\nwhere rs is the maximum per-capita rate of change for species s, K is the carrying capacity, Cy\u22121,s is the catch through year y\u00a0\u2212\u00a01 for species s, and \u03b4y,s is process error. Process errors were modeled using a multivariate normal distribution, estimating temporal and species-to-species correlation. Relative biomass indices for species s in year y from survey i was given by equation (3):\n\nwhere qi,s is the time-invariant catchability coefficient for the survey index i, and \u03b5y,i,s is the observation error, which was assumed to be normally distributed. This model was implemented using template model builder (TMB)90 within R91.\n\nThe process errors of this model, \u03b4y,s, correspond to the variance unexplained by density-dependent processes and fishing mortality (i.e., changes presumably caused by environmental variables). The changes in biomass imposed by these errors were calculated (in kt) and averaged for all species (Supplementary Fig.\u00a05).\n\nLinear trends were calculated for each climate phase previously identified by a least squares regression with bootstrap (1000 repetitions). The mean trends, defined as the average of all repetitions, are reported in Fig.\u00a03 in orange text when positive and in blue text when negative, while the 80% confidence intervals are reported in Supplementary Table\u00a01. Slopes for which the confidence interval bounds have different signs are left gray.\n\nFurther information on research design is available in the Nature Portfolio Reporting Summary linked to this article.",
+            "section_image": []
+        },
+        {
+            "section_name": "Data availability",
+            "section_text": "All data needed to evaluate the conclusion are provided here at https://doi.org/10.5281/zenodo.15359627. In addition, updates of the Newfoundland and Labrador Climate Index (NLCI), sea level pressure and primary production data are available at 10.20383/101.0301 [consulted 5 May 2024], https://psl.noaa.gov [consulted 4 May 2022], and 10.48670/moi-00019 [consulted on 4 October 2022], respectively.",
+            "section_image": []
+        },
+        {
+            "section_name": "Code availability",
+            "section_text": "All relevant code used to generate the figures are available at https://doi.org/10.5281/zenodo.15359627.",
+            "section_image": []
+        },
+        {
+            "section_name": "References",
+            "section_text": "B\u00e1ez, J. C., Gimeno, L. & Real, R. North Atlantic Oscillation and fisheries management during global climate change. Rev. Fish Biol. Fish. 31, 319\u2013336 (2021).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMantua, N. J. & Hare, S. R. The Pacific Decadal Oscillation. J. Oceanogr. 58, 35\u201344 (2002).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLehodey, P. et al. In El Ni\u00f1o Southern Oscillation in a Changing Climate, Geophysical Monograph. (2021).\n\nSkern-Mauritzen, M. et al. Ecosystem processes are rarely included in tactical fisheries management. Fish. Fish. 17, 165\u2013175 (2016).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBarange, M. et al. Impacts of climate change on fisheries and aquaculture: synthesis of current knowledge, adaptation and mitigation options. FAO Fish. Aquac. Tech. Pap. 627, 628 (2018).\n\n\n                    Google Scholar\u00a0\n                \n\nHowell, D. et al. Combining ecosystem and single-species modeling to provide ecosystem-based fisheries management advice within current management systems. Front. Mar. Sci. 7, 607831 (2021).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nTownsend, H. et al. Progress on implementing ecosystem-based fisheries management in the United States through the use of ecosystem models and analysis. Front. Mar. Sci. 6, 641 (2019).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nPepin, P. et al. Fisheries and Oceans Canada\u2019s Ecosystem Approach to Fisheries Management Working Group: Case Study Synthesis and Lessons Learned. (2023).\n\nGarcia, S. M. & Cochrane, K. L. Ecosystem approach to fisheries: A review of implementation guidelines. ICES J. Mar. Sci. 62, 311\u2013318 (2005).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nPepin, P. et al. Incorporating knowledge of changes in climatic, oceanographic and ecological conditions in Canadian stock assessments. Fish Fish. 23, 1332\u20131346 (2022).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLear, W. H. History of fisheries in the Northwest Atlantic: The 500-year perspective. J. Northw. Atl. Fish. Sci. 23, 41\u201373 (1998).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKoen-Alonso, M., Pepin, P. & Mowbray, F. Exploring the role of environmental and anthropogenic drivers in the trajectories of core fish species of the Newfoundland-Labrador marine community. NAFO SCR Doc. 10/37, 16 (2010).\n\n\n                    Google Scholar\u00a0\n                \n\nPedersen, E. J. et al. Signatures of the collapse and incipient recovery of an overexploited marine ecosystem. R. Soc. Open Sci. 4, 170215 (2017).\n\nArticle\u00a0\n    ADS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKoen-Alonso, M. & Cuff, A. Status and trends of the fish community in the Newfoundland Shelf (NAFO Div. 2J3K), Grand Bank (NAFO Div. 3LNO) and Southern Newfoundland Shelf (NAFO Div. 3Ps) Ecosystem Production Units. NAFO SCR Doc. 18/70, 11 (2018).\n\n\n                    Google Scholar\u00a0\n                \n\nMullowney, D. R. J. & Baker, K. D. Gone to shell: Removal of a million tonnes of snow crab since cod moratorium in the Newfoundland and Labrador fishery. Fish. Res. 230, 105680 (2020).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nRose, G. A. Reconciling overfishing and climate change with stock dynamics of Atlantic cod (Gadus morhua) over 500 years. Can. J. Fish. Aquat. Sci. 61, 1553\u20131557 (2004).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLilly, G.R. in Resiliency of Gadid Stocks to Fishing and Climate Change. (2008).\n\nKoen-Alonso, M., Pepin, P., Fogarty, M. & Gamble, R. Review and assessment of the ecosystem production potential (EPP) model structure, sensitivity, and its use for fisheries advice in NAFO. NAFO SCR Doc. 22/002, 52 (2022).\n\n\n                    Google Scholar\u00a0\n                \n\nCyr, F. & Galbraith, P. S. A climate index for the Newfoundland and Labrador shelf. Earth Syst. Sci. Data 13, 1807\u20131828 (2021).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBuren, A. D. et al. The collapse and continued low productivity of a keystone forage fish species. Mar. Ecol. Prog. Ser. 616, 155\u2013170 (2019).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDe Young, B. & Rose, G. A. On recruitment and distribution of Atlantic cod (Gadus morhua) off Newfoundland. Can. J. Fish. Aquat. Sci. 50, 2729\u20132741 (1993).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nHutchings, J. A. & Myers, R. A. What can be learned from the collapse of a renewable Resource? Atlantic cod, Gadus morhua, of Newfoundland and Labrador. Can. J. Fish. Aquat. Sci. 51, 2126\u20132146 (1994).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMyers, R. A. & Cadigan, N. G. Was an increase in natural mortality responsible for the collapse of northern cod? Can. J. Fish. Aquat. Sci. 52, 1274\u20131285 (1995).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMyers, R. A., Hutchings, J. A. & Barrowman, N. J. Hypotheses for the decline of cod in the North Atlantic. Mar. Ecol. Prog. Ser. 138, 293\u2013308 (1996).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMullowney, D. R. J. et al. Temperature influences on growth of unfished juvenile Northern cod (Gadus morhua) during stock collapse. Fish. Oceanogr. 28, 612\u2013627 (2019).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nHalliday, R. G. & Pinhorn, A. T. The roles of fishing and environmental change in the decline of Northwest Atlantic groundfish populations in the early 1990s. Fish. Res. 97, 163\u2013182 (2009).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nTableau, A., Collie, J. S., Bell, R. J. & Minto, C. Decadal changes in the productivity of new England fish populations. Can. J. Fish. Aquat. Sci. 76, 1528\u20131540 (2019).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nCyr, F., Galbraith, P.S. Newfoundland and Labrador climate index https://doi.org/10.20383/101.0301 (2020).\n\nYashayaev, I. & Loder, J. W. Further intensification of deep convection in the Labrador Sea in 2016. Geophys. Res. Lett. 44, 1429\u20131438 (2017).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nCyr, F. et al. Physical oceanographic conditions on the Newfoundland and Labrador Shelf during 2021. DFO Can. Sci. Advis. Sec. Res. Doc 2022/040, 48 (2022).\n\n\n                    Google Scholar\u00a0\n                \n\nHan, G., Chen, N. & Ma, Z. Is there a north-south phase shift in the surface Labrador Current transport on the interannual-to-decadal scale? J. Geophys. Res. Oceans 119, 276\u2013287 (2014).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nHolliday, N. P. et al. Ocean circulation causes the largest freshening event for 120 years in eastern subpolar North Atlantic. Nat. Commun. 11, 585 (2020).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDesbruy\u00e8res, D., Chafik, L. & Maze, G. A shift in the ocean circulation has warmed the subpolar North Atlantic Ocean since 2016. Commun. Earth Environ. 2, 48 (2021).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nRose, G.A. Cod: The Ecological History of the North Atlantic Fisheries. (2007).\n\nSchijns, R., Froese, R., Hutchings, J. A. & Pauly, D. Five centuries of cod catches in Eastern Canada. ICES J. Mar. Sci. 78, 2675\u20132683 (2021).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nRothschild, B. J. Coherence of Atlantic Cod Stock Dynamics in the Northwest Atlantic Ocean. Trans. Am. Fish. Soc. 136, 858\u2013874 (2007).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nChurchill, R., Lowe, V., Sander, A. The Law of the Sea. (Manchester University Press, Manchester, UK, 2022).\n\nDempsey, D. P., Koen-Alonso, M., Gentleman, W. C. & Pepin, P. Compilation and discussion of driver, pressure, and state indicators for the Grand Bank ecosystem, Northwest Atlantic. Ecol. Indic. 75, 331\u2013339 (2017).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nRowe, S. & Rose, G. A. Don\u2019t derail cod\u2019s comeback in Canada. Nature 545, 412 (2017).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nRowe, S. & Rose, G. Canadian cod comeback derailed. Nature 556, 436 (2018).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDFO: Assessment of 2J3KL capelin in 2020. DFO Canadian Science Advisory Secretariat Science Advisory Report 2022/013 (2022).\n\nDFO: Stock assessment of Northern cod (NAFO Div. 2J3KL) in 2021. DFO Canadian Science Advisory Secretariat Science Advisory Report 2022/041 (2022).\n\nDFO. Northern (2J3KL) Atlantic Cod Assessment Framework. Can. Sci. Adv. Sec. Sci. Adv. Rep. 2024/046, 18 (2024).\n\n\n                    Google Scholar\u00a0\n                \n\nKrohn, M., Reidy, S. & Kerr, S. Bioenergetic analysis of the effects of temperature and prey availability on growth and condition of northern cod (Gadus morhua). Can. J. Fish. Aquat. Sci. 54, 113\u2013121 (1997).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nFrank, K. T., Petrie, B. & Shackell, N. L. The ups and downs of trophic control in continental shelf ecosystems. Trends Ecol. Evol. 22, 236\u2013242 (2007).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nPlanque, B. & Fr\u00e9dou, T. Temperature and the recruitment of Atlantic cod (Gadus morhua). Can. J. Fish. Aquat. Sci. 56, 2069\u20132077 (1999).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nPetrie, B., Akenhead, S. A., Lazier, S. A. & Loder, J. The cold intermediate layer on the Labrador and Northeast Newfoundland Shelves, 1978-86. NAFO Sci. Counc. Stud. 12, 57\u201369 (1988).\n\n\n                    Google Scholar\u00a0\n                \n\nChawarski, J., Klevjer, T. A., Cot\u00e9, D. & Geoffroy, M. Evidence of temperature control on mesopelagic fish and zooplankton communities at high latitudes. Front. Mar. Sci. 9, 917985 (2022).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nCyr, F. et al. Physical controls and ecological implications of the timing of the spring phytoplankton bloom on the Newfoundland and Labrador shelf. Limnol. Oceanogr. Lett. 9, 191\u2013198 (2024).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nHead, E. J. H., Harris, L. R. & Campbell, R. W. Investigations on the ecology of Calanus spp. in the Labrador Sea. I. Relationship between the phytoplankton bloom and reproduction and development of Calanus finmarchicus in spring. Mar. Ecol. Prog. Ser. 193, 53\u201373 (2000).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nHead, E. J. H., Gentleman, W. C. & Ringuette, M. Variability of mortality rates for Calanus finmarchicus early life stages in the Labrador Sea and the significance of egg viability. J. Plankton Res. 37, 1149\u20131165 (2015).\n\n\n                    Google Scholar\u00a0\n                \n\nH\u00e1t\u00fan, H. et al. An inflated subpolar gyre blows life toward the northeastern Atlantic. Prog. Oceanogr. 147, 49\u201366 (2016).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDalpadado, P. & Mowbray, F. Comparative analysis of feeding ecology of capelin from two shelf ecosystems, off Newfoundland and in the Barents Sea. Progr. Oceanogr. 114, 97\u2013105 (2013).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLewis, K. P., Buren, A. D., Regular, P. M., Mowbray, F. K. & Murphy, H. M. Forecasting capelin Mallotus villosus biomass on the Newfoundland shelf. Mar. Ecol. Prog. Ser. 616, 171\u2013183 (2019).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKoen-Alonso, M., Lindstr\u00f8m, U. & Cuff, A. Comparative modeling of Cod-Capelin dynamics in the Newfoundland-Labrador Shelves and Barents Sea Ecosystems. Front. Mar. Sci. 8, 579946 (2021).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nGarrod, D. J. & Schumacher, A. North Atlantic cod: the broad canvas. ICES Mar. Sci. Symposia 198, 59\u201376 (1994).\n\n\n                    Google Scholar\u00a0\n                \n\nHilborn, R. & Litzinger, E. Causes of decline and potential for recovery of Atlantic Cod populations. Open Fish Sci. J. 2, 32\u201338 (2009).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKjesbu, O. S. et al. Synergies between climate and management for Atlantic cod fisheries at high latitudes. Proc. Natl. Acad. Sci. USA 111, 3478\u20133483 (2014).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nAlheit, J. et al. Synchronous ecological regime shifts in the central Baltic and the North Sea in the late 1980s. ICES J. Mar. Sci. 62, 1205\u20131215 (2005).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDFO: 2022 Stock Status Update for Capelin in NAFO Divisions 2J3KL. Can. Sci. Advis. Sec. Sci. Advis. Rep. 2023/010 (2023).\n\nDFO: Stock Assessment of Witch Flounder Glyptocephalus cynoglossus in NAFO Div. 2J3KL. DFO Can. Sci. Advis. Sec. Sci. Advis. Rep. 2023/012 (2023).\n\nRegular, P. M. et al. Indexing starvation mortality to assess its role in the population regulation of Northern cod. Fish. Res. 247, 106180 (2022).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nRose, G. A. & Rowe, S. Northern cod comeback. Can. J. Fish. Aquat. Sci. 72, 1789\u20131798 (2015).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nPedersen, E. J., Koen-Alonso, M. & Tunney, T. D. Detecting regime shifts in communities using estimated rates of change. ICES J. Mar. Sci. 77, 1546\u20131555 (2020).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDFO: Assessment of 2J3KL Capelin in 2020. DFO Can. Sci. Advis. Sec. Sci. Advis. Rep. 2022/013 (2022).\n\nEssington, T. E. et al. Fishing amplifies forage fish population collapses. Proc. Natl. Acad. Sci. USA 112, 6648\u20136652 (2015).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nPikitch, E. K. et al. Ecosystem-based fishery management. Science 305, 346\u2013347 (2004).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMuffley, B., Gaichas, S., DePiper, G., Seagraves, R. & Lucey, S. There Is no I in EAFM Adapting Integrated Ecosystem Assessment for Mid-Atlantic Fisheries Management. Coast. Manag. 49, 90\u2013106 (2021).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMolinari, C. Peru\u2019s Canceled Anchovy Fishing Season seen as Necessary Trade-off for Sustainability. (2023).\n\nHobday, A. J. et al. With the arrival of El Ni\u00f1o, prepare for stronger marine heatwaves. Nature 621, 38\u201341 (2023).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nPunt, A. E. et al. Capturing uncertainty when modelling environmental drivers of fish populations, with an illustrative application to Pacific Cod in the eastern Bering Sea. Fish. Res. 272, 106951 (2024).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLink, J. S. & Watson, R. A. Global ecosystem overfishing: Clear delineation within real limits to production. Sci. Adv. 5, eaav0474 (2019).\n\nArticle\u00a0\n    ADS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nNAFO Report of the Scientific Council Meeting, 03-16 June 2022. NAFO SCS Doc. 22/18, 241 (2022).\n\n\n                    Google Scholar\u00a0\n                \n\nNAFO Report of the NAFO Commission and its Subsidiary Bodies (STACTIC and STACFAD), 19-23 September 2022. NAFO/COM Doc. 22-27, 168 (2022).\n\n\n                    Google Scholar\u00a0\n                \n\nSzuwalski, C., Aydin, K., Fedewa, E., Garber-Yonts, B. & Litzow, M. Canaries of the Arctic: the collapse of eastern Bering Sea snow crab. Science 382, 306\u2013310 (2023).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWalter, J. F. et al. When to conduct, and when not to conduct, management strategy evaluations. ICES J. Mar. Sci. 80, 719\u2013727 (2023).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nPunt, A. E., Butterworth, D. S., de Moor, C. L., De Oliveira, J. A. A. & Haddon, M. Management strategy evaluation: Best practices. Fish Fish. 17, 303\u2013334 (2016).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKalnay, E. et al. The NCEP NCAR 40-year reanalysis project. 1996.pdf. Bull. Am. Meteorol. Soc. 77, 437\u2013472 (1996).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nTherriault, J. C. et al. Proposal for a Northwest Zonal Monitoring Program. Can. Tech. Rep. Hydrogr. Ocean Sci. 194, 57 (1998).\n\n\n                    Google Scholar\u00a0\n                \n\nPetrie, B., Loder, J. W., Lazier, J. & Akenhead, S. Temperature and salinity variability on the eastern Newfoundland shelf: The residual field. Atmos. Ocean 30, 120\u2013139 (1992).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nColbourne, E., Narayanan, S. & Prinsenberg, S. Climatic changes and environmental conditions in the Northwest Atlantic, 1970-1993. ICES J. Mar. Sci. Symposia 198, 311\u2013322 (1994).\n\n\n                    Google Scholar\u00a0\n                \n\nQuinn, G. P., Keough, M. J. Experimental Design and Data Analysis for Biologists. (Cambridge University Press, Cambridge, 2002).\n\nMowbray, F. K. Some results from spring acoustic surveys for capelin (Mallotus villosus) in NAFO Div. 3L between 1982 and 2010. Can. Sci. Advis. Sec. Res. Doc. 2012/143, 34 (2012).\n\n\n                    Google Scholar\u00a0\n                \n\nMowbray, F. K. Recent spring offshore acoustic survey results for capelin, Mallotus villosus, in NAFO Div. 3L. Can. Sci. Advis. Sec. Res. Doc. 2013/040, 25 (2013).\n\n\n                    Google Scholar\u00a0\n                \n\nNAFO Report of the 7th Meeting of the NAFO Scientific Council (SC) Working Group on Ecosystem Science and Assessment (WGESA). NAFO SCS Doc. 14/023, 126 (2014).\n\n\n                    Google Scholar\u00a0\n                \n\nPepin, P., Higdon, J., Koen-Alonso, M., Fogarty, M. & Ollerhead, N. Application of ecoregion analysis to the identification of Ecosystem Production Units (EPUs) in the NAFO Convention Area. NAFO SCR Doc. 14/069, 13 (2014).\n\n\n                    Google Scholar\u00a0\n                \n\nKoen-Alonso, M., Pepin, P., Fogarty, M. J., Kenny, A. & Kenchington, E. The Northwest Atlantic Fisheries Organization Roadmap for the development and implementation of an Ecosystem Approach to Fisheries: structure, state of development, and challenges. Mar. Policy 100, 342\u2013352 (2019).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nPedersen, E. J., Skanes, K., le Corre, N., Alonso, M. K. & Baker, K. D. A new spatial ecosystem-based surplus production model for Northern Shrimp in Shrimp Fishing Areas 4 to 6. DFO Can. Sci. Advis. Sec. Res. Doc. 2022/062, 64 (2022).\n\n\n                    Google Scholar\u00a0\n                \n\nKoen-Alonso, M. et al. Analysis of the overlap between fishing effort and Significant Benthic Areas in Canada\u2019s Atlantic and Eastern Arctic marine waters. DFO Can. Sci. Advis. Sec. Res. Doc. 2018/015, 270 (2018).\n\n\n                    Google Scholar\u00a0\n                \n\nKristensen, K., Nielsen, A., Berg, C. W., Skaug, H. & Bell, B. M. TMB: Automatic differentiation and laplace approximation. J. Stat. Softw. 70, 1\u201321 (2016).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nR Core Team. R: A Language and Environment for Statistical Computing. (2021).\n\nGEBCO Compilation Group: GEBCO 2023 Grid. https://doi.org/10.5285/f98b053b-0cbc-6c23-e053-6c86abc0af7b (2023).\n\nDownload references",
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+        },
+        {
+            "section_name": "Acknowledgements",
+            "section_text": "While no dedicated funding was used for this study, this work was made possible thanks to open-access data made available by the National Oceanic and Atmospheric Administration (NOAA) and Mercator-Ocean (see data availability section), and to historical data collected as part of multiple Fisheries and Oceans Canada (DFO) monitoring programs such as the Atlantic Zone Monitoring Program, the Capelin Research Program and the NAFO Div. 2J3KL Fall Multi-Species bottom trawl survey. FC thanks Flore C. for the permission to use her drawings in Fig.\u00a03.",
+            "section_image": []
+        },
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+            "section_name": "Author information",
+            "section_text": "Fr\u00e9d\u00e9ric Cyr\n\nPresent address: Centre for Fisheries and Ecosystem Research, Fisheries and Marine Institute of Memorial University, St. John\u2019s, Newfoundland and Labrador, Canada\n\nNorthwest Atlantic Fisheries Centre, Fisheries and Oceans Canada, St. John\u2019s, Newfoundland and Labrador, Canada\n\nFr\u00e9d\u00e9ric Cyr,\u00a0Aaron T. Adamack,\u00a0David B\u00e9langer,\u00a0Mariano Koen-Alonso,\u00a0Darrell Mullowney,\u00a0Hannah Murphy,\u00a0Paul Regular\u00a0&\u00a0Pierre Pepin\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nF.C. conceptualized the study and led the data analysis, writing and editing. A.A. and H.M. curated capelin data and contributed to the writing and editing. D.B. and P.P. curated zooplankton data and contributed to the writing and editing. M.K.A. curated scientific survey biomass density data and contributed to the writing and editing. P.R. curated groundfish excess biomass data and contributed to the writing and editing. D.M. curated data that did not make the final version of this study and contributed to the writing and editing.\n\nCorrespondence to\n                Fr\u00e9d\u00e9ric Cyr.",
+            "section_image": []
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+        {
+            "section_name": "About this article",
+            "section_text": "Cyr, F., Adamack, A.T., B\u00e9langer, D. et al. Environmental control on the productivity of a heavily fished ecosystem.\n                    Nat Commun 16, 5277 (2025). https://doi.org/10.1038/s41467-025-60453-6\n\nDownload citation\n\nReceived: 15 March 2024\n\nAccepted: 22 May 2025\n\nPublished: 06 June 2025\n\nVersion of record: 06 June 2025\n\nDOI: https://doi.org/10.1038/s41467-025-60453-6\n\nAnyone you share the following link with will be able to read this content:\n\nSorry, a shareable link is not currently available for this article.\n\n\n\n\n                            Provided by the Springer Nature SharedIt content-sharing initiative\n                        ",
+            "section_image": [
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+            ]
+        },
+        {
+            "section_name": "This article is cited by",
+            "section_text": "Reviews in Fish Biology and Fisheries (2025)\n\nReviews in Fish Biology and Fisheries (2025)",
+            "section_image": []
+        }
+    ]
+}

2a7545a262e748ebc0ab9d89acde6b8030a0183dd22cadb6d94fc17e681cfcc7/metadata.json

@@ -0,0 +1,147 @@
+{
+    "title": "Unraveling the role of water in mechanism changes for economically viable catalytic plastic upcycling",
+    "pre_title": "Unraveling the Role of Water in Mechanism Changes for Economically Viable Catalytic Plastic Upcycling",
+    "journal": "Nature Communications",
+    "published": "29 November 2024",
+    "supplementary_0": [
+        {
+            "label": "Supplementary Information",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-024-54495-5/MediaObjects/41467_2024_54495_MOESM1_ESM.pdf"
+        },
+        {
+            "label": "Transparent Peer Review file",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-024-54495-5/MediaObjects/41467_2024_54495_MOESM2_ESM.pdf"
+        }
+    ],
+    "supplementary_1": [
+        {
+            "label": "Source Data",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-024-54495-5/MediaObjects/41467_2024_54495_MOESM3_ESM.xlsx"
+        }
+    ],
+    "supplementary_2": NaN,
+    "source_data": [
+        "/articles/s41467-024-54495-5#Sec24"
+    ],
+    "code": [],
+    "subject": [
+        "Catalytic mechanisms",
+        "Chemical engineering",
+        "Heterogeneous catalysis"
+    ],
+    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
+    "preprint_pdf": "https://www.researchsquare.com/article/rs-4284309/v1.pdf?c=1732972161000",
+    "research_square_link": "https://www.researchsquare.com//article/rs-4284309/v1",
+    "nature_pdf": "https://www.nature.com/articles/s41467-024-54495-5.pdf",
+    "preprint_posted": "22 Apr, 2024",
+    "research_square_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "The surge in global plastic production, reaching to 390.7\u00a0million tons in 2021, exacerbates environmental pollution, with only 11% of plastic being recycled. Catalytic recycling, particularly through hydrogenolysis and hydrocracking, offers a promising avenue for upcycling polyolefin plastic, comprising 55% of global plastic waste. This study investigates the influence of water on polyolefin depolymerization using Ru catalysts, revealing a promotional effect only when both metal and acid sites, particularly Br\u00f8nsted acid, are present. Findings highlight the impact of Ru content, metal-acid balance, and their proximity on this interaction, as well as their role in modulating the isomerization process, affecting product selectivity. Additionally, the interaction facilitates the suppression of coke formation, ultimately enhancing catalyst stability. A comprehensive techno-economic and life cycle assessment underscores the viability and environmental benefits of the process, particularly in the presence of water. These insights advance understanding and offer strategies for optimizing polyolefin plastic recycling processes.Physical sciences/Engineering/Chemical engineeringPhysical sciences/Chemistry/Catalysis/Heterogeneous catalysis",
+            "section_image": []
+        },
+        {
+            "section_name": "Additional Declarations",
+            "section_text": "There is NO Competing Interest.",
+            "section_image": []
+        },
+        {
+            "section_name": "Supplementary Files",
+            "section_text": "WatereffectSupplementarydatafinal.docx",
+            "section_image": []
+        }
+    ],
+    "nature_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "The surge in global plastic production, reaching 400.3 million tons in 2022, has exacerbated environmental pollution, with only 11% of plastic being recycled. Catalytic recycling, particularly through hydrogenolysis and hydrocracking, offers a promising avenue for upcycling polyolefin plastic, comprising 55% of global plastic waste. This study investigates the influence of water on polyolefin depolymerization using Ru catalysts, revealing a promotional effect only when both metal and acid sites, particularly Br\u00f8nsted acid site, are present. Findings highlight the impact of Ru content, metal-acid balance, and their proximity on this interaction, as well as their role in modulating the isomerization process, affecting product selectivity. Additionally, the interaction facilitates the suppression of coke formation, ultimately enhancing catalyst stability. A comprehensive techno-economic and life cycle assessment underscores the viability and environmental benefits of the process, particularly in the presence of water. These insights advance understanding and offer strategies for optimizing polyolefin plastic recycling processes.",
+            "section_image": []
+        },
+        {
+            "section_name": "Introduction",
+            "section_text": "Global plastic production has surged over the years, escalating from 1.7 million tons in 1954 to a staggering 400.3 million tons in 20221. However, the management of plastic waste predominantly relies on landfill disposal (~75%) or incineration (~14%), with a mere 11% of plastic being recycled2. This concerning trend exacerbates environmental pollution, highlighting the urgent need for sustainable solutions in plastic waste management. In response to these challenges, there is a critical demand for innovative recycling technologies aimed at mitigating environmental risks3. While mechanical recycling has traditionally been utilized, it often leads to downcycling of plastics, compromising their mechanical properties4. Chemical recycling methods, particularly catalytic recycling, are increasingly recognized as promising alternatives5,6,7. Catalytic recycling enables the conversion of plastic waste into drop-in fuels at lower temperatures (250\u2013400\u2009\u00b0C) compared to conventional chemical recycling methods (500\u2013800\u2009\u00b0C)8. Furthermore, it facilitates selective cleavage of the C-C bonds in plastic wastes, yielding higher yields of liquid fuels compared to conventional methods9. These advantages reduce separation costs and energy inputs, making catalytic recycling an economically and environmentally friendly solution to the escalating concerns surrounding plastic waste management10.\n\nHydrogenolysis and hydrocracking are prominent catalytic recycling methods extensively studied for their efficacy in upcycling polyolefin plastic waste, which constitutes over half of the global plastic waste due to its short lifecycle9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35. Hydrogenolysis operates at relatively low temperatures, employing Ru or Pt supported on metal oxides such as CeO2, TiO2, Al2O3, SBA-15, and ZrO2, to produce liquid fuels with high yields13,14,15,16,17,18,19. In hydrogenolysis, both C-H bond activation and C-C bond cleavage primarily occur at metal sites, emphasizing the critical role of the geometric structure of Ru and Pt in influencing activity17,18,19,20,21. Conversely, hydrocracking involves C-H bond activation at metal sites and C-C bond cracking at acid sites, typically employing Pt and Ru metals paired with acidic supports such as WO3/ZrO2 or zeolite22,23,24. The metal-to-acid molar ratio, known as the metal-acid balance (MAB), has been reported to significantly influence hydrocracking reactivity9,23,24,25,26.\n\nPrevious studies on hydrogenolysis and hydrocracking of polyolefin plastics have mainly been conducted without solvents, but recent research has shed light on the impact of solvents on catalytic activity, particularly in HDPE hydrogenolysis over Ru/C12. Among various solvents tested, such as water, n-pentane, n-hexane, methylcyclohexane, and decalin, only n-hexane and methylcyclohexane were found to enhance HDPE hydrogenolysis activity12. Molecular dynamics simulations have revealed that the interaction between HDPE and solvent molecules changes the conformation of HDPE12. For instance, in n-hexane, HDPE tends to coil, facilitating access to the catalyst\u2019s active sites and increasing activity, whereas, in decalin, HDPE maintains extended conformations, resulting in decreased catalytic activity12. Notably, previous studies have explored the influence of water in the hydrocracking of n-hexadecane36,37,38. The addition of water was found to reduce the hydrocracking conversion of n-hexadecane over H-ZSM-5 due to competitive adsorption between water and reactants on the acidic sites of the zeolite at relatively low reaction temperatures (<350\u2009\u00b0C)37. Conversely, water addition was reported to promote the activity of Pd/NaX zeolite in the hydrocracking of n-hexadecane38. Therefore, we hypothesize that water addition enhances the depolymerization of polyolefin plastic waste in the presence of both metal and acid sites.\n\nIn this study, we investigate the influence of water on the depolymerization of polyolefin plastics by synthesizing a series of Ru catalysts supported on various materials, including SiO2, SBA-15, \u03b3-Al2O3, TiO2, and zeolite-Y. Our findings reveal that the promotional effect of water is only observed in the presence of both metal and acid sites, particularly Br\u00f8nsted acid sites, via the metal-acid interaction, leading to an increase in conversion from 51% to 82%. Additionally, we identify MAB and their proximity as crucial factors in facilitating the metal-acid interaction. Notably, the presence of water also influences the degree of isomerization, with a selectivity toward isomers of 1.6% with water compared to 72.1% without water. Through a comprehensive set of characterization techniques, including GC-MS, MS, and pyridine-DRIFTS, we propose a bifunctional depolymerization reaction mechanism, elucidating key distinctions from hydrogenolysis and hydrocracking processes. Techno-economic analysis (TEA) and life-cycle assessments (LCA) further demonstrate that the addition of water positively impacts both economic and environmental performance. This mechanistic insight not only advances our comprehension of catalytic activity but also provides strategies for regulating the degree of isomerization in polyolefin plastic waste catalytic processes.",
+            "section_image": []
+        },
+        {
+            "section_name": "Results",
+            "section_text": "The LDPE depolymerization reactions were conducted using various Ru catalysts supported on SiO2, SBA-15, \u03b3-Al2O3, TiO2, and zeolite-Y. In most cases, the addition of water resulted in lower or comparable activity (Table\u00a01, entries 1\u201314), consistent with previous findings12. However, 5% Ru/zeolite-Y exhibited a notable 16.3%-point increase in conversion, rising from 80.6% to 96.9% after water addition. This increase in conversion was accompanied by a shift in product distribution toward mid-range (C5-C22) alkanes, which are desirable for liquid fuel production (Fig.\u00a01a). Pyridine-DRIFTS analysis revealed that among the various Ru catalysts, only Ru/zeolite-Y exhibited Br\u00f8nsted acid sites (BAS) (Fig.\u00a01b and Table\u00a02), suggesting a potential association between enhanced activity in the presence of water and BAS.\n\na Product distributions after LDPE depolymerization reaction over 5% Ru/zeolite-Y. Raw data from GC-FID and GC-TCD spectra are shown in Supplementary Figs.\u00a014 and 15. Reaction conditions: 250\u2009\u00b0C, 3\u2009h, 30\u2009bar H2 (at 25\u2009\u00b0C), 1.70\u2009g of LDPE (Mn: ~1700, Mw: ~4000), 50\u2009mg of catalyst, 50\u2009mg of water (if needed). b. Pyridine-DRIFTS spectra of Zeolite-Y and various Ru-based catalysts. c Conversion as a function of reaction time. d. Conversion as a function of Water/Catalyst ratio. Unless otherwise mentioned, the reaction conditions are as follows: 250\u2009\u00b0C, 1.5\u2009h, 30\u2009bar H2 pressure (at 25\u2009\u00b0C), 1.70\u2009g LDPE (Mn: ~1700, Mw: ~4000), 50\u2009mg of Ru/zeolite-Y (Metal: 5\u2009wt%), and 50\u2009mg of water (if needed). e Representative STEM image and Ru particle size distribution histogram of Ru/zeolite-Y. f, g X-ray photoelectron spectra of Ru 3p3/2 of Ru/zeolite-Y before and after reaction with or without water; f 5% Ru/zeolite-Y and g 0.2% Ru/zeolite-Y. h Pore size distribution of fresh and spent Ru/zeolite Y in the presence or absence of water based on the N2 adsorption-desorption. i. Reusability test results of Ru/zeolite Y. Reaction conditions: 250\u2009\u00b0C, 3\u2009h, 30\u2009bar H2 pressure (at 25\u2009\u00b0C), 1.70\u2009g of LDPE (Mn: ~1700, Mw: ~4000), 50\u2009mg of spent Ru/zeolite Y (Metal: 5\u2009wt%), 50\u2009mg of water (if required). Error bars = standard deviation. Source data are provided as a Source Data file.\n\nTo understand the promotional effect of water over Ru/zeolite-Y, a series of experiments were conducted by changing the reaction conditions. The results revealed a time-dependent enhancement in conversion with the addition of water (Fig.\u00a01c). Additionally, the conversion displayed a bell-shaped curve as a function of the water/catalyst ratio, peaking at a water/catalyst ratio of 1.0 (Fig.\u00a01d). This observation suggests that the presence of water gradually enhances LDPE conversion as the water/catalyst ratio increases, but beyond this optimal ratio, reactivity diminishes, possibly due to a dilution effect39. Further investigations were conducted to explore the influence of reaction temperature, H2 pressure, and additional Ar (Supplementary Table\u00a01).\n\nTo further investigate the role of Ru metal, we prepared Ru/zeolite-Y catalysts with weight loadings of 1% and 0.2%. Given the potential influence of Ru dispersion and acid sites on catalytic activity, we conducted analyses to measure particle size using STEM, acid density through NH3-TPD, and BAS/LAS ratio via pyridine-DRIFTS (Table\u00a02, entries 7, 8 and Fig.\u00a01e). Similar particle size and acidic properties were observed, ruling out the potential influence of Ru dispersion and acidic properties of Ru/zeolite-Y on catalytic activity. STEM analysis of spent catalysts was further conducted to investigate the particle size changes. The spent Ru/zeolite-Y exhibited a slight increase in mean particle sizes with and without water (Supplementary Fig.\u00a03), suggesting that water did not strongly contribute to aggregation. Furthermore, XPS was conducted to determine the electronic structure of Ru/zeolite-Y. The binding energy of spent Ru/zeolite-Y remained constant at 461.7\u2009eV regardless of water and weight loadings (Fig.\u00a01f, g), a characteristic indicative of pure metallic states of Ru (Ru0)40. This suggests that the electronic state of Ru catalysts remained unchanged after the reaction, irrespective of the presence of water.\n\nWith evidence that both geometric and electronic structures of Ru catalysts remained similar regardless of the presence of water, we conducted BET analysis to characterize the pore structure of the fresh and spent catalysts. While the general shape of the hysteresis loop remained consistent (Supplementary Fig.\u00a04), the pore size distribution of the spent catalyst shifted to smaller diameters, particularly in the absence of water (Fig.\u00a01h). This shift suggests increased coke formation during the reaction, as evidenced by a decrease in both surface area and pore volume (Supplementary Table\u00a02)41. This inhibition of coke formation was further confirmed by post-calcination characterization, where the presence of water was essential for restoring the catalyst\u2019s performance (Supplementary Table\u00a02). To further assess the stability of the catalyst under different conditions, we conducted control experiments without LDPE at 300\u2009\u00b0C for 24 to 48\u2009hours. These experiments showed that the zeolite structure remained largely intact, with only minor reductions in surface area and pore volume for the 5% Ru/zeolite-Y, regardless of water exposure (Supplementary Table\u00a03). The preservation of the zeolite structure can be explained by the low n/n0 ratio in our experiments. The ratio of the amount of water present in the zeolite plus the added water to the molar number of the saturated state (n/n0) was calculated to be 0.056, well below the critical threshold of 0.3 known to cause zeolite crystal structure collapse42. Additionally, the presence of Ru metal helped mitigate structural changes in the zeolite.\n\nTo quantify the amount of coke deposited during the reaction, TGA was conducted15,26. The weight loss was approximately 12% following the reaction with water, contrasting with about 22% without water, providing compelling evidence that water suppresses coke formation (Supplementary Fig.\u00a09). Additional TGA results of 0.2% Ru/zeolite-Y and visual comparisons of the catalysts showed the similar trend, reinforcing our conclusions (Supplementary Figs.\u00a010 and 11). This observation aligns with earlier findings in methane reforming, where coke formation was higher without water (dry reforming of methane) than with water (steam reforming of methane)43. Further analysis revealed that the coke removed by water was primarily in the form of CO2, with the amount of CO2 extracted increasing with both reaction time and water/catalyst ratio (Supplementary Fig.\u00a012).\n\nThe reusability test was performed to investigate the impact of coke deposition on the reactivity of Ru/zeolite-Y in LDPE depolymerization (Fig.\u00a01i). Upon reusing Ru/zeolite-Y with water, the initial conversion was 96.9%, with subsequent 1st and 2nd regenerations yielding conversions of 94.5% and 90.1%, respectively (Table\u00a01, entries 15\u201318). These results suggest that the reactivity of the catalyst remained nearly unchanged in the presence of water. In contrast, when the reaction was conducted without water, a significant decrease in conversion was observed, dropping from 80.6% to 31.8% after the 1st regeneration and 24.1% in the 2nd. These findings indicate that the addition of water in LDPE depolymerization using Ru/zeolite-Y suppresses coke formation, resulting in improved reactivity and reusability of the catalyst.\n\nTo understand how water enhances reactivity and reusability, a control experiment was conducted with pyridine. Interestingly, the poisoned Ru/zeolite-Y catalysts exhibited a negligible promotional effect with water (Table\u00a01, entries 19 and 20), different from the fresh catalyst. Additionally, the product distribution of poisoned catalysts remained similar regardless of water (Fig.\u00a02a), unlike the fresh catalyst (Fig.\u00a01a). These findings strongly suggest the involvement of acid sites in LDPE depolymerization for the promotional effect of water. Given that pyridine poisons both Lewis acid sites (LAS) and BAS26, pyridine-DRIFTS, and NH3-TPD analyses of spent Ru/zeolite-Y were performed to discern the role of the BAS. The peaks at 1450\u2009cm-1 (LAS) and 1540\u2009cm-1 (BAS) were present over Ru/zeolite-Y before and after the reaction with water (Fig.\u00a02b). However, the pyridine-DRIFTS spectra of the spent catalyst without water showed a noticeable decrease in the peak at 1540\u2009cm-1. Indeed, the BAS of the catalyst decreased from 185.0 \u03bcmol/g to 44.1 \u03bcmol/g after the reaction without water (Supplementary Table\u00a07). Conversely, the BAS was maintained at 160.8 \u03bcmol/g after the reaction with water. This trend was also observed for the 0.2% Ru/zeolite-Y catalyst. The substantial decrease in the BAS after the reaction without water can be attributed to coke deposition on the BAS during the reaction without water23,26. This also suggests that the reaction predominantly occurs at the BAS rather than the LAS.\n\na Product distributions after the LDPE depolymerization reaction over pyridine-poisoned 5% Ru/zeolite-Y. b Pyridine-DRIFTS spectra of Ru/zeolite-Y before and after the reaction or controlled reaction in the presence or absence of water. The spent catalyst was obtained under the following conditions: 250\u2009\u00b0C, 12\u2009h, 30\u2009bar H2 pressure (at 25\u2009\u00b0C), 50\u2009mg of Ru/zeolite-Y (Metal: 5\u2009wt%), 50\u2009mg of water (if required), 1.70\u2009g of LDPE (Mn: ~1700, Mw: ~4000). LDPE was not added in the controlled reaction. c\u2013k Product distributions after LDPE depolymerization reaction. Reaction over: c 5% Ru/zeolite-Y (Si/Al=30), d 5% Ru/zeolite-Y (Si/Al=80), e 5% Ru/zeolite-Y (2.5\u2009mg Ru), f 1% Ru/zeolite-Y (0.5\u2009mg Ru), g Physical mixture of 1% Ru/zeolite-Y and zeolite-Y (0.5\u2009mg Ru), h 1% Ru/zeolite-Y (2.5\u2009mg Ru), i 0.2% Ru/zeolite-Y (2.5\u2009mg Ru), j Physical mixture of 5% Ru/SiO2 and zeolite-Y (2.5\u2009mg Ru), and k 5% Pt/zeolite-Y. l Isomer selectivity with different catalysts. Reaction conditions: 250\u2009\u00b0C, 3\u2009h, 30\u2009bar H2 (at 25\u2009\u00b0C), 1.70\u2009g of LDPE (Mn: ~1700, Mw: ~4000). Other conditions are shown in Table\u00a01. Error bars = standard deviation. Source data are provided as a Source Data file.\n\nTo discern whether the decrease in the BAS was caused by coke deposition during LDPE depolymerization or by catalyst structure deformation at the reaction temperature, additional control experiments were conducted without LDPE under identical reaction conditions. The pyridine-DRIFTS spectra of control experiments with and without water (Fig.\u00a02b) remained similar to that of the fresh catalyst (Fig.\u00a01b), indicating that the loss of the BAS without water is associated with coke formation during LDPE depolymerization. This suggests that the reduction of the BAS coincides with coking occurrences. To further evaluate the relationship between reactivity and acid strength, we synthesized and tested catalysts with SiO2/Al2O3 ratios of 30 and 80, different from our reference catalyst with a SiO2/Al2O3 ratio of 60. All catalysts showed similar levels of conversion enhancement (Table\u00a01, entries 19-22). However, differences in isomer selectivity were observed based on the concentration of the BAS, particularly in the absence of water (Table\u00a02, entries 9, 10). High Ru loading generally led to reduced isomer selectivity, with selectivity decreasing further to 3.35%, 1.97%, and 1.11% as the SiO2/Al2O3 ratio increased to 30, 60, and 80, when water was absent. In contrast, isomer selectivities remained relatively stable, ranging from 1.08% to 1.51%, in the presence of water, regardless of the SiO2/Al2O3 ratio (Fig.\u00a02c\u2013e). This behavior indicates that selectivity is influenced by both the presence of water and the density of BAS, which varies with the SiO2/Al2O3 ratio.\n\nConsidering the involvement of Br\u00f8nsted acid in LDPE depolymerization, additional experiments were performed to investigate how water influences this process (Table\u00a01, entries 23-34). As shown in Figs.\u00a02e, 5% Ru/zeolite-Y exhibited an enhanced conversion of 96.9% in the presence of water, compared to 80.6% in the absence of water after a 3-hour reaction. Conversely, 1% Ru/zeolite-Y exhibited negligible differences in conversion, with conversions of 34.3% with water and 35.3% without, indicating negligible promotional effect of water (Fig.\u00a02f). To understand this further, additional zeolite-Y was added to increase the number of acid sites. However, despite this addition, no significant water-induced enhancement occurred for 1% Ru/zeolite-Y (Fig.\u00a02g). When the quantity of 1% Ru/zeolite-Y was adjusted to match the Ru content of 5% Ru/zeolite-Y while keeping acid sites constant, a notable increase in conversion was observed\u2014from 56.8% to 94.5% with water (Fig.\u00a02h). A similar trend was observed for 0.2% Ru/zeolite-Y, where conversion increased from 54.5% to 82.8% with water (Fig.\u00a02i). These findings highlight the importance of MAB in the promotional effect of water.\n\nTo explore the influence of proximity between metal and acid sites, experiments were performed with a physical mixture of 5% Ru/SiO2 and zeolite-Y (Fig.\u00a02j). The mixture exhibited a negligible promotional effect, suggesting the pivotal role of metal-acid proximity in inducing the promotional effect of water via the metal-acid interactions in LDPE depolymerization. Additional experiments using Pt/zeolite-Y (Fig.\u00a02k) revealed minimal enhancement in conversion, but changes in isomer selectivity were observed (Fig.\u00a02l), consistent with previous findings44. This can be attributed to Pt\u2019s relatively lower C-C bond dissociation ability compared to Ru. Previous studies have shown that the ability to dissociate C-C bonds follows the order Ru > Rh > Ir > Pt45, which may explain why Pt, despite interacting with water and acid sites to modify selectivity, does not significantly enhance conversion\u2014similar to the effect seen with insufficient Ru amounts (0.5\u2009mg, Fig.\u00a02f).\n\nFurthermore, notable variations in product distribution were observed with and without water. The product distribution remained relatively consistent with water; however, significant variations were observed depending on the Ru loading without water, particularly in catalysts with lower Ru loading (Supplementary Figs.\u00a025 and 26). Considering that hydrocracking reactions typically produce shorter alkanes (C3-C4) in the presence of dominant acid sites and longer alkanes (C21+) or methane in the presence of prevalent metal sites23,24,26, this observation suggests that reactions primarily occur at Ru sites rather than zeolite sites with water, regardless of the Ru loading.\n\nTo elucidate the influence of water on the reaction mechanism, we employed deuterated water (D2O) alongside regular water (H2O). The results revealed a similar product distributions with both H2O and D2O (Fig.\u00a03a). Further analysis using mass spectrometry (MS) showed the absence of HDO and D2O peaks in the catalyst after reaction without water, while HDO peaks appeared in the catalyst after reactions with D2O, indicating the incorporation of deuterium atoms (Supplementary Fig.\u00a027). Additionally, isotopic composition analysis of gas products (Fig.\u00a03b, c) showed a selectivity of 0.3% for substituted deuterium atoms without water, which increased to 4.1% with D2O, suggesting the replacement of some hydrogen atoms by deuterium. These results support the hypothesis that water acts as a proton donor in the reaction38. Furthermore, MS and GC-MS analyses were conducted to examine the effect of water on the degree of isomerization reaction. Using n-dodecane as a surrogate, we aimed to elucidate the role of acid sites, crucial for isomerization46. Comparing reactions with and without water over 0.2% and 5% Ru/zeolite-Y catalysts (Fig.\u00a03d\u2013f), we observed significant differences in isomer selectivity. Specifically, the selectivity for isomers over 0.2% Ru/zeolite-Y decreased from 72.1% without water to 1.6% with water (Fig.\u00a03e, f), indicating a profound shift in the reaction pathway in the presence of water, especially with low metal loading. Conversely, reactions over 5% Ru/zeolite-Y exhibited an isomer selectivity of 1.2% without water and 3.0% with water, indicating a dominant role of metal sites in these conditions regardless of the presence of water (Fig.\u00a03d\u2013f). This suggests that water alters the reaction pathways in LDPE depolymerization, potentially by promoting the protonation of carbon cations rather than skeletal rearrangement, leading to the predominant production of linear alkanes. Additionally, the detection of aromatic compounds via acid sites chemistry indicates a complex interplay of reaction mechanisms30.\n\na\u2013c LDPE depolymerization reaction over 5% Ru/zeolite-Y. a Detailed carbon distributions after 3\u2009h reaction with H2O or D2O (b\u2013c). Selectivity of isotopes in gaseous products after 12\u2009h reaction: b After the reaction without water, and c After the reaction with D2O. Reaction conditions: 250\u2009\u00b0C, 30\u2009bar H2 (at 25\u2009\u00b0C), 1.70\u2009g of LDPE (Mn: ~1700, Mw: ~4000), 50\u2009mg of 5% Ru/zeolite-Y, 50\u2009mg of H2O or 55.6\u2009mg of D2O (if required). d\u2013f Dodecane decomposition reaction over: d 5% Ru/zeolite-Y, e 0.2% Ru/zeolite-Y, f total normal and isomer yield. Reaction conditions: 250\u2009\u00b0C, 3\u2009h, 30\u2009bar H2 (at 25\u2009\u00b0C), 1.0\u2009g of n-Dodecane, m(Ru): 2.5\u2009mg, Water/Catalyst ratio: 1 or 0. Error bars = standard deviation. Source data are provided as a Source Data file.\n\nGiven that MAB is widely recognized as a crucial factor in small alkane hydrogenolysis or hydrocracking24,47,48,49, we incorporated MAB as a classification criterion. An acid-catalyzed reaction tends to slow at a high MAB, whereas a low MAB shifts the rate-determining step toward hydrogenation/dehydrogenation reactions. Reflecting these shifts, the molar ratio of C21+/C4-6 was reported to increase with an elevated MAB24 (Fig.\u00a04a). To illustrate this, we plotted the molar ratio of C21+/C4-6 using Ru/zeolite-Y with varying Ru loading. In alignment with prior findings, the molar ratio of C21+/C4-6 rises with increasing MAB without water (Fig.\u00a04a)24. However, results with water show a noticeable difference in product distribution, implying a mechanism distinct from hydrogenolysis and hydrocracking. For example, the yield of gasoline is highest without water, while the yield of diesel and lubricant peaks with water over 0.2% Ru/zeolite-Y (Fig.\u00a02i). In addition to the C21+/C4-6 ratio, the ratio of the average carbon number of the gas and liquid phases was influenced by MAB24. Similar to the previous findings24, the Cliq/Cgas ratio of the average carbon number without water increases with increasing MAB (Fig.\u00a04b). However, even with similar MAB levels, the distribution differs significantly with water, resulting in different Cliq/Cgas. Therefore, we consider both the MAB and the all-product distribution to categorize the depolymerization of polyolefins into three groups (see details in Supplementary Note\u00a01).\n\na Molar ratio of C21+ to C4-6 products as a function of MAB, ref. 24. b Average carbon number ratio of the liquid (C5\u2013C35) to gaseous phase (C1\u2013C4) as a function of MAB, ref. 24. c Reactivity-mechanism map of the PE depolymerization reaction. d Average product distribution. e Color of products after PE depolymerization reactions. Reaction conditions: 250\u2009\u00b0C, 3\u2009h, 30\u2009bar H2 (at 25\u2009\u00b0C), 1.70\u2009g of PE (Mn: ~1700, Mw: ~4000), 50\u2009mg of water (if required). Error bars = standard deviation. Source data are provided as a Source Data file.\n\nConsidering both MAB and the corresponding ratios, a lower MAB and a lower Cliq/Cgas correspond to reactions closer to hydrocracking (see full details in Methods). Conversely, a higher MAB and a higher Cliq/Cgas align with reactions closer to hydrogenolysis, with moderate cases being classified as bifunctional depolymerization reactions (Fig.\u00a04c). The mechanisms of each reaction categorized in Fig.\u00a04c are described in Fig.\u00a059,22,24,50,51. The distribution shown in Fig.\u00a04d represents the average of all reaction results. In instances of high Ru loading and low concentration of acid sites, hydrogenolysis is the dominant reaction. This reaction proceeds through the dehydrogenation of the reactant, followed by the cleavage of the C-C bond at the metal site, as illustrated in the Fig.\u00a05a pathway (II). Although the introduction of water may facilitate intermediates to undergo protonation (Fig.\u00a05a, II-ii), \u03b2-scission does not occur due to the absence of, or few, acid sites even in the presence of water. Consequently, the hydrogenolysis reaction over Ru catalysts primarily produces methane (Figs.\u00a05b and 4d). The Ru/zeolite-Y catalyst, subjected to pyridine poisoning, is also categorized as a hydrogenolysis reaction due to the absence of acid sites, specifically because C-C bond dissociation occurs solely on Ru.\n\na Overall reaction mechanism for PE depolymerization reactions. b Simplified reaction mechanism for high, intermediate, and low MAB.\n\nIn instances of low Ru loading and a high concentration of acid sites, the primary reaction is hydrocracking. This process involves dehydrogenation at the metal site, followed by protonation at the acid sites, leading to skeletal rearrangement for isomerization. The protonated intermediate then undergoes \u03b2-scission to cleave the C-C bond at the acid site (Fig.\u00a05a, pathway I). Notably, the \u03b2-scission rates of the reaction intermediate differ based on the skeleton structure, with deep skeletal rearrangement showing the fastest rate, while reactions lacking branches are slower or forbidden (Fig.\u00a05a, I-iv)9. As previously shown in Fig.\u00a04d\u2013e, the quantity of iso-C12 is relatively larger than other Cn(<12) products in both 0.2% and 5% Ru/zeolite-Y, irrespective of water. This is mainly associated with the rate-determining step, \u03b2-scission, in LDPE depolymerization (Fig.\u00a05). Alkanes undergo protonation after dehydrogenation, leading to isomerization through skeletal rearrangement, followed by conversion to a short alkane via \u03b2-scission. In this series of steps, the \u03b2-scission reaction works as the rate-determining step; thus, the preceding skeletal rearrangement step produces a larger amount of iso-C12. Interestingly, products obtained from hydrocracking exhibit a yellow hue, signifying the formation of isomeric products, as previously reported (Fig.\u00a04e)32.\n\nIn cases where the MAB falls within an intermediate range, it is categorized as bifunctional depolymerization (Fig.\u00a04c). While the roles of the metal and acid sites are well-defined in hydrogenolysis and hydrocracking reactions, bifunctional depolymerization involves the simultaneous occurrence of hydrocracking and hydrogenolysis reactions. Essentially, the cleavage of C-C bonds occurs concurrently at both the metal and acid sites, resulting in superior activity compared to other mechanisms (Fig.\u00a04c). For instance, catalysts with relatively low MABs, such as 0.2% and 1% Ru/zeolite-Y, exhibited enhanced reactivity in the presence of water compared to its absence due to the bifunctional depolymerization mechanism. Water can protonate or deprotonate intermediates at the metal or acid site, as illustrated by the two-way arrow highlighted in green in Fig.\u00a05a. This process facilitates the simultaneous dissociation of C-C bonds at both the metal and acid sites, resulting in an enhancement in PE depolymerization.\n\nUnderstanding the influence of water on reaction mechanisms, we conducted depolymerization reactions using substances with varying degrees of branching. The product distribution exhibited notable differences between the more branched substance (PP) and the less branched one (HDPE) (Fig.\u00a06a, b). In substances with more branching, such as PP, \u03b2-scission occurs more rapidly due to the stabilization provided by neighboring carbons9, allowing it to occur without the need for skeletal rearrangement. Conversely, in substances like HDPE with fewer branches, skeletal rearrangement becomes essential for \u03b2-scission. Additionally, water plays a significant role by facilitating the protonation or deprotonation of the carbon cation to achieve a more stable state (Fig.\u00a06a). In the presence of water, HDPE predominantly produced methane due to the dissociation of terminal C-C bonds at Ru sites rather than undergoing skeletal rearrangement. Conversely, PP exhibited a more stable carbon cation skeleton in the presence of water, leading to the dissociation of internal C-C bonds rather than terminal ones. This resulted in higher yields of high-value materials in the gasoline and jet fuel range compared to short alkanes of C3-6.\n\nDepolymerization reaction over 0.2% Ru/zeolite-Y both with and without water of a PP, b HDPE, c Commercial LDPE, and d LDPE bottle. Reaction conditions: 300\u2009\u00b0C, 9\u2009h, 30\u2009bar H2 (at 25\u2009\u00b0C), 1.70\u2009g of reactant, 2.5\u2009mg of Ru, and a water/catalyst ratio of 1.0 for the reactions with water. Detailed reaction results are shown in Supplementary Table\u00a08. Error bars\u2009=\u2009standard deviation. Source data are provided as a Source Data file.\n\nThe promotional effect of water was also evident involving commercial LDPE and LDPE bottles. For commercial LDPE, the gas yield decreased from 32.2% without water to 2.5% with water, while the diesel yield increased from 0.7% without water to 34.3% with water (Fig.\u00a06c). Similarly, for LDPE bottles, the gasoline yield decreased from 34.1% without water to 8.8% with water, while the diesel yield increased from 9.2% without water to 21.1% with water, reflecting a noticeable shift in product distribution (Fig.\u00a06d). This shift highlights the practical feasibility of directing the depolymerization pathway toward the desired carbon range products, representing a significant advancement in plastic waste upcycling. Additionally, the observation of CO/CO2 peak only in the presence of water indicates that water not only influences product distribution but also facilitates the removal of coke (Supplementary Fig.\u00a029).\n\nTo assess the economic viability of implementing a real commercial-scale process utilizing a 0.2% Ru/zeolite-Y catalyst, a comprehensive techno-economic analysis was performed52,53,54. It was found that the LDPE fractionation, both with and without water, emerged as a major cost-driver mainly due to high material expenses and high capital cost, resulting from multiple reactors to continuously depolymerize LDPE (Figs.\u00a07a and 7b). Specifically, approximately 62.1% and 66.3% of the total costs occurred from purchasing waste LDPE, respectively. Notably, while the same amount of LDPE (240 tons/day) was supplied in both scenarios, the relatively lower contribution of LDPE cost in the process without water can be primarily attributed to a higher hydrogen consumption (192.0\u2009kg/hr)55. The reaction with water requires relatively less hydrogen (94.6\u2009kg/hr), primarily because of the production of heavier carbon-range products (C22+). However, to further enhance the value of the products, particularly those in the gasoline or diesel range, an additional fluidized catalytic cracking subsystem ($0.49/GGE) is required in the process with water to convert C22+ into more valuable fuel products, leading to an increase in the total capital investment compared to the process without water ($114.7\u2009\u00d7\u2009106 vs. $132.0\u2009\u00d7\u2009106) (see Supplementary Table\u00a012 for detailed capital cost). However, when considering the cost per gasoline gallon eq. (GGE), the process of utilizing water incurs a higher material cost ($3.10/GGE) mainly due to LDPE ($2.90/GGE) and hydrogen ($0.19/GGE). This higher cost is attributed to the lower production rate (1978\u2009gal/hr vs. 2941\u2009gal/hr) despite slightly higher energy content (30.4 kWh/gal vs. 28.7 kWh/gal) compared to that process without water (28.7 kWh/gal, 2941\u2009gal/hr). The black arrows representing carbon flows confirm that when LDPE\u2019s carbon content is 100%, the carbon efficiency of gasoline is 75% for processes without water and 54% for the process with water. Notably, although the carbon efficiency of gasoline in the process with water is lower than that in the process without water, the total carbon efficiency, considering both gasoline and diesel, is higher in the process with water (94%) than in the process without water (87%).\n\nCost contributions for a process without water and b process with water. Carbon flows (black arrows) and major three heat networks (dashed arrows) are represented. The storage ($0.04/GGE and $0.05/GGE, respectively) and utility ($0.01/GGE and $0.01/GGE, respectively) subsystems are not represented. c Comparison of economic performance between processes with and without water. Detailed economic parameters and results are specified in Supplementary Tables\u00a011 and 12. Source data are provided as a Source Data file.\n\nThe economics of the process with water is improved primarily due to higher carbon efficiency, which increases production rates and, in turn, boosts product revenues, including byproduct credits ($2.97/GGE). This occurs despite the higher total cost compared to the process without water ($5.13/GGE vs. $3.63/GGE). Specifically, the production costs, including LDPE and hydrogen costs, are the most significant factors, accounting for 75.8% and 72.1%, respectively. The MSP of gasoline for each process is determined by subtracting the income generated from diesel and electricity from the overall cost54,56,57. Consequently, the MSP of the process with water is $2.16/GGE, whereas for the process without water, it is $2.95/GGE, indicating the economic advantage of the process with water. The MSP of the processes without and with water can be increased by 10.2% to $3.25/GGE and by 9.3% to $2.36/GGE, respectively, due to changes in the hydrogen price\u2014which is one of the most influential parameters on the MSP\u2014from $3640/ton to $7280/ton. Considering the conventional retail gasoline price range ($1.66/GGE - $4.84/GGE), both processes are market-competitive even with a higher discount rate (20%) compared to a typical rate in the nth plant assumption (10%)54,58. In conclusion, despite the increased overall cost, the addition of water results in a 26.8% reduction in MSP, making it the more economically preferred.\n\nTo quantitatively evaluate the environmental impacts of the processes without water and with water, a life-cycle assessment (LCA) was conducted following the guidelines provided by ISO 14040 and 1404459,60,61,62. Based on the environmental impacts of one gallon of conventional gasoline production (100%), the relative environmental impacts of the processes are represented in Fig.\u00a08a. Unlike conventional gasoline, the environmental impacts of gasoline produced from both processes yield negative values, indicating environmental benefits. The environmental impacts of the process without water range from -2% to -42%, while those of the process with water range from -10% to -103%. This implies that the process with water offers both economic and environmental advantages. The beneficial impacts of the process with water are derived from the production of diesel. As shown in Fig.\u00a08b, the environmental impacts attributed to input materials and energy in the process with water are offset by the production of diesel, while the process without water mitigates the environmental impacts via the production of diesel and electricity. Notably, these coproducts can substitute conventional counterparts that largely rely on fossil fuels. Consequently, the production of coproducts from these processes contributes to reducing the reliance on fossil fuels, resulting in environmentally favorable outcomes.\n\na An environmental impact radar chart for the major categories, and b heatmaps of environmental contributions. The major categories include global warming potential (GWP), stratospheric ozone depletion (SOD), terrestrial acidification (TA), marine ecotoxicity (MEu), fossil resource scarcity (FRS), and fine particulate matter formation (FPMF). Additional life-cycle assessment (LCA) results are specified in Supplementary Table\u00a013. Source data are provided as a Source Data file.\n\nFurthermore, the process with water exhibits a larger offset impact in diesel production due to its higher production rate compared to the process without water. Additionally, the analysis revealed that the disposal of boiler slag, generated during the incineration of byproducts such as C22+, is the most environmentally intensive component. The major environmental impacts originated from disposal of residue are freshwater eutrophication (FWEu), freshwater ecotoxicity (FWEc), marine ecotoxicity (MEc), human carcinogenic toxicity (HCT), and human non-carcinogenic toxicity (HNCT) of both processes, respectively. Especially, disposal of residue accounts for 96% and 94% of HCT of both processes. This significant influence of disposing of residue is attributed to the cement used for its solidification.",
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+        {
+            "section_name": "Discussion",
+            "section_text": "The catalytic depolymerization of polyolefins presents a promising route for recycling plastic waste in terms of process economics and sustainability. In this study, we found the significant impact of water addition on plastic depolymerization, elevating the yield of valuable liquid fuels from 41.8% to 71.0% and effectively suppressing coke formation to preserve catalyst activity. Through our investigation into reaction mechanisms with water, we categorized reactions into three groups based on catalytic properties and product distribution including hydrogenolysis, hydrocracking, and bifunctional depolymerization. Among these, the proposed bifunctional depolymerization reaction demonstrated the highest activity, where the cleavage of C-C bonds occurs simultaneously at the metal and acid sites. This promotional effect of water extends across various waste plastics, promising implications for the recycling of plastic waste. Moreover, the addition of water not only enhances carbon efficiency, improving economic and environmental performance based on TEA and LCA analysis, but also increases conversion to gasoline and diesel. This results in a 26.8% reduction in the MSP of gasoline and enhances economic efficiency. Additionally, the increased production rate achieved by adding water substantially mitigates environmental impacts and reduces reliance on fossil fuels, thereby replacing diesel derived from fossil fuels. This opens up the possibility to advance the entire chemical recycling of plastic waste, while simultaneously addressing environmental pollution caused by plastic waste.",
+            "section_image": []
+        },
+        {
+            "section_name": "Methods",
+            "section_text": "All chemicals were analytical or higher grade and used as received without further treatment. RuCl3\u00b7xH2O (product no. 11043) was purchased from Alfa Aesar. SiO2 (product no. 236845) of Davisil grade 646, SBA-15 (product no. 806862), \u03b3-Al2O3 (product no. 544,833), and TiO2 (product no. 634662) of P25 were purchased from Sigma-Aldrich. Zeolite Y with SiO2:Al2O3 ratios of 30:1 (product no. 045870), 60:1 (product no. 045871), and 80:1 (product no. 045872) was purchased from Alfa Aesar. PE (Mn: ~1700, Mw: ~ 4000, product no. 427772) was purchased from Sigma Aldrich, commercial LDPE was purchased from Hanwha Total (product code: 530\u2009G), and LDPE bottle was purchased from Korea Ace Scientific. Mesitylene (product no. 12558) was purchased from Acros Organics, toluene (product no. 22903) was purchased from Alfa Aesar, and pyridine (product no. 270407) was purchased from Sigma-Aldrich. High-density polyethylene (product no. 427985), polypropylene (product no. 427888), deuterium oxide (product no. 151882), alkane standard solution C8-C20 (product no. 04070) and C21-C40 (product no. 04071) were purchased from Sigma-Aldrich. n-pentane (product no. 16787), and n-dodecane (product no. 43459) were purchased from Acros Organics. n-hexane (product no. L09938), n-heptane (product no. A19894), n-octane (product no. A13181), n-nonane (product no. A16177), n-docosane (product no. A18050) were purchased from Alfa Aesar. n-octadecane (product no. O652) was purchased from Sigma-Aldrich.\n\nSupported Ru catalysts were prepared by a wet impregnation method. The support (0.96\u2009g) and RuCl3\u00b7xH2O (133.0\u2009mg, 0.50\u2009mmol) were added to deionized water (100\u2009mL) for 5\u2009wt% Ru/support catalyst. The suspension was stirred at 600\u2009rpm for 2\u2009hours for mixing and heated to 50\u2009\u00b0C until completely dried. Subsequently, the obtained catalyst was dried 12\u2009hours at 100\u2009\u00b0C and reduced under a 10% H2/Ar flow (50\u2009mL/min) at 500\u2009\u00b0C for 3\u2009hours, with a ramping rate of 2.5\u2009\u00b0C/min. Prior to the reaction, the catalyst was ex-situ reduced for 1.5\u2009hours at 400\u2009\u00b0C under a 10% H2/Ar flow (50\u2009mL/min), with a ramping rate of 5\u2009\u00b0C/min. A similar procedure was performed using the support (2.50\u2009g) and RuCl3\u00b7xH2O (66.5\u2009mg, 0.25\u2009mmol) for 1\u2009wt% Ru/support, and the support (3.78\u2009g) and RuCl3\u00b7xH2O (19.9\u2009mg, 0.075\u2009mmol) for 0.2\u2009wt% Ru/support catalyst. To distinguish between zeolites with different SiO2:Al2O3 ratios, zeolite Y with a SiO2:Al2O3 ratio of 30:1 termed Ru/zeolite-Y (Si/Al=30), 60:1 termed Ru/zeolite-Y, and 80:1 termed Ru/zeolite-Y (Si/Al=80).\n\nA glass-coated magnetic stir bar, pretreated catalyst, water (if required), and PE were added to the glass liner in this order, and the liner was then placed into 50\u2009mL 316\u2009L stainless-steel high-pressure batch reactors fitted with a spiral wound gasket (Hanwoul Engineering CO., LTD). For depolymerization of post-consumer plastic waste, the commercial LDPE was used as received, and the LDPE bottle was cut into small pieces (3\u2009mm x 3\u2009mm) as shown in Supplementary Fig.\u00a030. The reactor was purged three times with Ar (30\u2009bar) and then three times with H2 (30\u2009bar), followed by pressurized to H2 (30\u2009bar). The pressurized reactor was placed in a heater, and heated at the reaction temperature (200 \u2013 300\u2009\u00b0C) for approximately 1\u2009h. The reaction temperature was monitored by a thermocouple, which was inserted into the reactor. Once the temperature reached 150\u2009\u00b0C, stirring at a rate of 500\u2009rpm was initiated for the target reaction time. After the reaction, the reactor was cooled down to room temperature in an ice bath. The gas and liquid products were transferred to a 2\u2009L PVC gas bag and a 50\u2009mL centrifuge tube, respectively. Mesitylene solution (125\u2009mmol/L) was used as an internal standard, and toluene was used as a washing solvent for the collection of the liquid phase. The unreacted reactant and catalyst were separated and subsequently dried in an oven set to 60\u2009\u00b0C for 48\u2009hours. The centrifuge tube, containing the reaction products and catalyst, was then weighed after drying. The weight of the initial empty tube and added catalyst were subsequently subtracted from the measurement, yielding the exact amount of unreacted reactant. The products were analyzed using a gas chromatograph (Agilent 8890 GC System) equipped with a flame ionization detector (FID) and thermal conductivity detector (TCD). A GS-Carbon PLOT (Agilent) column was used for the gas phase and an HP-1 column (Agilent) was used for the liquid phase. Analysis of gaseous products was performed using an Agilent 8890 GC System, with a ramping rate of 20\u2009\u00b0C/min from 38 to 325\u2009\u00b0C, and hold 10\u2009min. The corresponding retention times of C1-C6 hydrocarbons were identified and FID area signals were calibrated by a reference gas mixture obtained from Union gas comprising CH4, C2H4, C2H6, C3H8, and n-C4H10 in Ar. TCD area signals were calibrated by high-purity hydrogen (99.999%) obtained from Union gas. Analysis of liquid product was also performed using an Agilent 8890 GC System, with a ramping rate of 15\u2009\u00b0C/min from 50 to 325\u2009\u00b0C, and hold 45\u2009min. The corresponding retention times of C5-C40 hydrocarbons were identified and FID area signals were calibrated by n-pentane, n-hexane, n-heptane, n-octane, n-nonane, n-dodecane, n-octadecane, n-docosane and an alkane standard solution C8-C20 and C21-C40 from Sigma-Aldrich.\n\nThe spent catalyst was collected after 12\u2009h of reaction to attain full conversion to extractable. After the drying of the reaction mixture, the spent catalyst underwent a two-step process. Firstly, it was calcined at a temperature of 300\u2009\u00b0C under an air flow (80\u2009mL/min). Subsequently, the catalyst was pretreated at 400\u2009\u00b0C under a 10% H2/Ar flow (50\u2009mL/min). The preceding reaction was repeated more than twice to ensure an adequate amount of catalyst for the subsequent reaction due to a loss of approximately 5% in catalyst recovery as in a previous work15.\n\nThe reactivity mechanism map is plotted with the summation of the normalized average carbon number ratio and metal acid balance on the x-axis and the corresponding conversion on the y-axis. To consider the MAB and average carbon number ratios as equivalent ratios, each was normalized to 0 for the lowest value and 5 for the highest, and the sum was expressed from 0 to 10. From 0 to 3.3, we denoted hydrocracking, from 3.3 to 6.7, bifunctional hydrocracking, and from 6.7 to 10, hydrogenolysis. The formula is as follows:\n\nwhere \\({v}_{m}\\) is a volume occupied by an atom in bulk Ru metal63, \\({a}_{m}\\) is an area occupied by a surface atom63, and \\({d}_{{VA}}\\) is an average particle size determined by CO-chemisorption.\n\nThe catalyst underwent ex-situ reduction at a ramping rate of 5\u2009\u00b0C/min, maintaining a temperature of 400\u2009\u00b0C for 1.5\u2009h under a 10% H2/Ar flow (50\u2009mL/min). Pyridine (100\u2009mg, 1.27\u2009mmol) was added dropwise using a pipette to poison 50\u2009mg of 5% Ru/zeolite-Y, 40 times the estimated acid site density by NH3-TPD to ensure sufficient poisoning. The mixture was dried for 12\u2009hours at room temperature in a vacuum desiccator and used immediately in the reaction.\n\nThe BAS/LAS ratio was calculated as follows64:\n\nwhere IBAS and ILAS are the integrated absorbance of the BAS and LAS band (cm 1); r is the radius of the sample disk (cm); msample is the weight of the sample (mg). The molar extinction coefficient used was 1.8\u2009cm/\u03bcmol for BAS and 1.5\u2009cm/\u03bcmol for LAS65,66.\n\nConversion and yield were calculated as follows:\n\nWe developed two integrated processes to produce gasoline and diesel based on experimental data (Supplementary Fig.\u00a031): (1) one employing the depolymerization reaction with water, and (2) the other using the reaction without water (hereafter, referred to as the process with and without water, respectively). In both processes, the downstream separation system was designed to efficiently recover gasoline and diesel, considering the contaminants present in the effluent stream of the depolymerization reactor. In the process without water, since the effluent stream consists primarily of light hydrocarbons with carbon numbers below those of gasoline and diesel, a series of flash drums and distillation columns was employed for separation. On the other hand, in the process with water, heavier carbon-range products (C22+) are present in the effluent stream, requiring an additional fluidized catalytic cracking (FCC) subsystem to upgrade these C22+ into valuable fuel products.\n\nBased on the heat and mass balance of the developed process (Supplementary Fig.\u00a031 and Supplementary Tables\u00a09 and 10), capital and operating costs are computed. To calculate the capital cost, equipment costs are estimated by using the Aspen Process Economic Analyzer (V12.1) or by adopting the cost data from the literature67,68. The adopted cost data is adjusted to the capacity of the process as follows:\n\nThe variable n represents the scaling exponent that quantifies the economic impact of scale. The computed capital and operating costs are adjusted to the common basis of 2020 USD using the following formula.\n\nWith the adjusted capital and operating costs, the MSP of gasoline is determined. The MSP, which means the selling price at the breakeven point, is one of the economic indicators. Supplementary Table\u00a011 contains the detailed economic parameters and assumptions.\n\nAccording to the international standards (ISO 14040 and 14044), LCA is conducted with four interconnected steps: goal and scope definition, life-cycle inventory analysis, life-cycle impact assessment, and life-cycle interpretation. The system boundary is from waste LDPE fractionation to product separation. To compare the environmental impact of processes, both input and output materials and energy are normalized based on a functional unit of 1 GGE of gasoline production. The environmental impacts are calculated by employing SimaPro 9.1 and the ReCiPe 2016 Midpoint with a hierarchical approach. Moreover, to consider the general region, rather than focusing on a particular local location. a global region dataset from Ecoinvent 3.6 is used.\n\nPyridine adsorption spectra were acquired using a Nicolet iS20 FTIR spectrometer equipped with a Hg/Cd/telluride detector cooled using liquid nitrogen. Prior to measurements, the catalysts were reduced in situ at 400\u2009\u00b0C for 1.5\u2009hours under 10% H2/Ar, followed by cooled to ambient temperature (25\u2009\u00b0C) under an Ar atmosphere. To measure the acid sites of the catalyst after the reaction, the spent catalyst was treated with in situ reduction at 400\u2009\u00b0C for 1.5\u2009hours under 10% H2/Ar only. A baseline spectrum was recorded prior to introducing pyridine. Subsequently, the catalysts were exposed to pyridine vapor in Ar for 20\u2009min, generated by passing Ar flow through a bubbler filled with liquid pyridine24. Physically adsorbed pyridine was subsequently removed with pure Ar for 50\u2009minutes. All spectra were obtained using 128 scans with a resolution of 2\u2009cm\u22121. The peaks at 1450\u2009cm\u22121 and 1540\u2009cm\u22121 correspond to the Lewis acid sites (LAS) and the Br\u00f8nsted acid sites (BAS)65,66,69,70, respectively. The ratio of Br\u00f8nsted acid site density to Lewis acid site density (BAS/LAS) was estimated by pyridine-DRIFTS analysis69,70. The pyridine vibration bands were classified as following70: Br\u00f8nsted acid site (BAS) exhibiting peaks around 1540\u2009cm\u22121, Lewis acid site (LAS) characterized by peaks near 1450\u2009cm\u22121.\n\nScanning transmission electron microscopy (STEM) was conducted using a NEOARM (JEOL) with a Cs probe aberration corrector operated at 200\u2009kV with a spatial resolution of <0.1\u2009nm. STEM images were recorded after ex situ reduction of the fresh and spent catalysts at 400\u2009\u00b0C under 10% H2/Ar. The high-angle annular dark-field (HAADF) mode was applied to acquire images under the following conditions: HAADF detector angle: 68 to 270 mrad; probe convergence angle (2\u03b1): 1.5 to 20 mrad; probe current: 1.0\u2009nA; and probe diameter: 0.2\u2009nm. Over 200 randomly selected particles were examined to calculate the mean particle size, which exhibited a narrow Gaussian distribution in the histogram.\n\nA Thermo Scientific NEXSA XPS system equipped with a monochromatic Al K\u03b1 X-ray source was used for XPS. XPS spectra were recorded after ex situ reduction of the fresh and spent catalysts at 400\u2009\u00b0C under 10% H2/Ar. The number of scans and dwell time were 10 and 50\u2009ms, respectively. To accurately calibrate the binding energies, the reference for this calibration was the lattice oxygen (O 1\u2009s) peak at 529.9\u2009eV, instead of the C 1\u2009s peak19. This selection was primarily based on the overlap between the binding energy of the C 1s peak and the Ru 3d5/2 peak, rendering the C 1\u2009s peak unsuitable for precise calibration40.\n\nBrunauer\u2013Emmett\u2013Teller (BET) analysis were conducted using an automated gas adsorption analyzer (TriStar 3000, Micromeritics). Prior to analysis, fresh and spent catalysts weighing ~0.1\u2009g was subjected to degassing by heating at 90\u2009\u00b0C for 2\u2009h, followed by further heating at 300\u2009\u00b0C for 6\u2009h under He flow (60\u2009mL/min). BET surface area was determined through a standard multipoint analysis (P/P0\u2009=\u20090.05-0.3), while the pore volume was measured using the single-point method at P/P0\u2009=\u20090.995. The adsorption average pore width (4\u2009V/A) was calculated based on the BET results. Additionally, pore size distribution was obtained using the Barrett-Joyner-Halenda (BJH) method.\n\nAmmonia temperature-programmed desorption (NH3-TPD) spectra were collected by AutoChem II 2920 (Micromeritics) instrument. Before conducting NH3-TPD, the catalyst underwent in situ reduction at 400\u2009\u00b0C for 1.5\u2009hours under a 10% H2/Ar flow (50\u2009mL/min). Subsequently, the catalyst was purged with He and cooled down to 50\u2009\u00b0C under He flows (50\u2009mL/min). Adsorption of NH3 onto the catalyst surfaces occurred by flowing 10% NH3/He at 50\u2009\u00b0C and 50\u2009mL/min for 1\u2009hour, followed by purging with He for 1\u2009hour. The desorption process was quantified using a thermal conductivity detector (TCD) with a temperature ramp of 5\u2009\u00b0C/min, starting from 100\u2009\u00b0C and reaching 900\u2009\u00b0C. The acid site density was estimated by calculating a coefficient multiplied by the area divided by the weight, and the coefficient was obtained using a specified reference.\n\nDEPT 135 13C NMR analysis was conducted using a 600\u2009MHz Agilent DD2 NMR Spectrometer at room temperature to characterize the product structure. The product was diluted in CDCl3, and the spectra were recorded over 500 scans.\n\nTPO-MS analysis was conducted using a BEL CAT II and BEL mass analyzer (MicrotracBEL). Prior to analysis, catalysts were heated to 200\u2009\u00b0C for 2\u2009hours under a He flow (30\u2009mL/min) to remove physically adsorbed water. Thereafter, the catalyst was heated to 1000\u2009\u00b0C at a rate of 5\u2009\u00b0C/min under a 5% O2/He flow (30\u2009mL/min). The analysis was performed using thermal conductivity (TCD) and mass spectrometry.\n\nTo estimate the amount of coke in the spent catalysts, thermogravimetric analysis (TGA) was performed using a DTG-60H (Simadzu). Prior to analysis, catalysts were heated to 200\u2009\u00b0C for 1\u2009hour under nitrogen flow (50\u2009mL/min) to remove physically adsorbed water. Thereafter, the catalyst was heated to 800\u2009\u00b0C at a rate of 10\u2009\u00b0C/min under airflow (50\u2009mL/min) within an alumina cell.",
+            "section_image": []
+        },
+        {
+            "section_name": "Data availability",
+            "section_text": "The data generated in this study are provided in the Source Data file.\u00a0Source data are provided with this paper.",
+            "section_image": []
+        },
+        {
+            "section_name": "References",
+            "section_text": "Plastics Europe. Plastics \u2013 The Fast Facts 2023 (2023).\n\nGeyer, R., Jambeck, J. R. & Law, K. L. Production, use, and fate of all plastics ever made. Sci. Adv. 3, e1700782 (2017).\n\nArticle\u00a0\n    ADS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nJung, S. & Ro, I. Strategic use of thermo-chemical processes for plastic waste valorization. Korean J. Chem. Eng. 40, 693\u2013705 (2023).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nVollmer, I. et al. Beyond mechanical recycling: giving new life to plastic waste. Angew. Chem. Int. Ed. 59, 15402\u201315423 (2020).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMusa, A., Jaseer, E. A., Barman, S. & Garcia, N. Review on catalytic depolymerization of polyolefin waste by hydrogenolysis: state-of-the-art and outlook. Energy Fuels 38, 1676\u20131691 (2024).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDong, S. et al. Catalytic conversion of model compounds of plastic pyrolysis oil over ZSM-5. Appl. Catal. B: Environ. 324, 122219 (2023).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nRagauskas, A. J. et al. New technologies are needed to improve the recycling and upcycling of waste plastics. ChemSusChem 14, 3982\u20133984 (2021).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nFont, R., Marcilla, A., Garcia, A. N., Caballero, J. A. & Conesa, J. A. Comparison between the pyrolysis products obtained from different organic wastes at high temperatures. J. Anal. Appl. Pyrolysis 32, 41\u201349 (1995).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWeitkamp, J. Catalytic hydrocracking-mechanisms and versatility of the process. ChemCatChem 4, 292\u2013306 (2012).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWang, Y.-Y. et al. Catalytic hydrogenolysis of polyethylene under reactive separation. ACS Catal. 14, 2084\u20132094 (2024).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nZhao, Z. et al. Catalytic hydrogenolysis of plastic to liquid hydrocarbons over a nickel-based catalyst. Environ. Pollut. 313, 120154 (2022).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nJia, C. et al. Deconstruction of high-density polyethylene into liquid hydrocarbon fuels and lubricants by hydrogenolysis over Ru catalyst. Chem. Catal. 1, 437\u2013455 (2021).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nRorrer, J. E., Beckham, G. T. & Rom\u00e1n-Leshkov, Y. Conversion of polyolefin waste to liquid alkanes with Ru-based catalysts under mild conditions. JACS Au 1, 8\u201312 (2021).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nEllis, L. D. et al. Chemical and biological catalysis for plastics recycling and upcycling. Nat. Catal. 4, 539\u2013556 (2021).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nNakaji, Y. et al. Low-temperature catalytic upgrading of waste polyolefinic plastics into liquid fuels and waxes. Appl. Catal. B: Environ. 285, 119805\u2013119805 (2021).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nNakagawa, Y. et al. Regioselectivity and reaction mechanism of Ru-catalyzed hydrogenolysis of squalane and model alkanes. ChemSusChem 10, 189\u2013198 (2017).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nChen, S. et al. Ultrasmall amorphous zirconia nanoparticles catalyse polyolefin hydrogenolysis. Nat. Catal. 6, 161\u2013173 (2023).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nNguyen-Phu, H. et al. Investigating the influence of Ru structures and supports on hydrogenolysis of polyethylene plastic waste. Chem. Eng. J. 475, 146076 (2023).\n\nKim, T., Nguyen-Phu, H., Kwon, T., Kang, K. H. & Ro, I. Investigating the impact of TiO(2) crystalline phases on catalytic properties of Ru/TiO2 for hydrogenolysis of polyethylene plastic waste. Environ. Pollut. 331, 121876 (2023).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nCelik, G. et al. Upcycling single-use polyethylene into high-quality liquid products. ACS Cent. Sci. 5, 1795\u20131803 (2019).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWu, X. et al. Size-controlled nanoparticles embedded in a mesoporous architecture leading to efficient and selective hydrogenolysis of polyolefins. J. Am. Chem. Soc. 144, 5323\u20135334 (2022).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWang, C. et al. Polyethylene hydrogenolysis at mild conditions over ruthenium on tungstated zirconia. J. Am. Chem. Soc. 1, 1422\u20131434 (2021).\n\nCAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nRorrer, J. E. et al. Role of bifunctional Ru/Acid catalysts in the selective hydrocracking of polyethylene and polypropylene waste to liquid hydrocarbons. ACS Catal. 12, 13969\u201313979 (2022).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nVance, B. C. et al. Single pot catalyst strategy to branched products via adhesive isomerization and hydrocracking of polyethylene over platinum tungstated zirconia. Appl. Catal. B: Environ. 299, 120483\u2013120483 (2021).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMunir, D., Irfan, M. F. & Usman, M. R. Hydrocracking of virgin and waste plastics: a detailed review. Renew. Sust. Energ. Rev. 90, 490\u2013515 (2018).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLiu, S., Kots, P. A., Vance, B. C., Danielson, A. & Vlachos, D. G. Plastic waste to fuels by hydrocracking at mild conditions. Sci. Adv. 7, 1\u201310 (2021).\n\n\n                    Google Scholar\u00a0\n                \n\nVance, B. C., Kots, P. A., Wang, C., Granite, J. E. & Vlachos, D. G. Ni/SiO2 catalysts for polyolefin deconstruction via the divergent hydrogenolysis mechanism. Appl. Catal. B: Environ. 322, 122138 (2023).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nSun, J. A. et al. Size and structure effects of carbon-supported ruthenium nanoparticles on waste polypropylene hydrogenolysis activity, selectivity, and product microstructure. ACS Catal. 14, 3228\u20133240 (2024).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nTamura, M. et al. Structure-activity relationship in hydrogenolysis of polyolefins over Ru/support catalysts. Appl. Catal. B: Environ. 318, 121870 (2022).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDu, J. et al. Efficient solvent- and hydrogen-free upcycling of high-density polyethylene into separable cyclic hydrocarbons. Nat. Nanotechnol. 18, 772\u2013779 (2023).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKwon, T. & Ro, I. Advancing towards a sustainable future: recent trends in catalytic upcycling of waste plastics. Korean Chem. Eng. Res. 61, 505\u2013516 (2023).\n\nCAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLee, W. T. et al. Mechanistic classification and benchmarking of polyolefin depolymerization over silica-alumina-based catalysts. Nat. Commun. 13, 4850 (2022).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKots, P. A., Vance, B. C., Quinn, C. M., Wang, C. & Vlachos, D. G. A two-stage strategy for upcycling chlorine-contaminated plastic waste. Nat. Sustain. 6, 1258\u20131267 (2023).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nChen, L. et al. Disordered, sub-nanometer Ru structures on CeO2 are highly efficient and selective catalysts in polymer upcycling by hydrogenolysis. ACS Catal. 12, 4618\u20134627 (2022).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKwon, T., Jeong, H., Kim, M., Jung, S. & Ro, I. Catalytic approaches to tackle mixed plastic waste challenges: a review. Langmuir 40, 17212\u201317238 (2024).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMart\u00ednez, A. et al. A detailed study of the activity and deactivation of zeolites in hybrid Co/SiO2-zeolite Fischer\u2013Tropsch catalysts. J. Catal. 249, 162\u2013173 (2007).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nOppmann, N. & Jess, A. Hydrocracking of model substances on Pt/H\u2010ZSM\u20105 under an imitated fischer\u2010tropsch product gas composition. Chem. Eng. Technol. 46, 1924\u20131934 (2023).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nYan, T. Y. The promotional effect of water in hydrocracking. J. Catal. 25, 204\u2013211 (1972).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nZhao, Y. X. & Wojciechowski, B. W. The consequences of steam dilution in catalytic cracking: I. Effect of steam dilution on reaction rates and activation energy in 2-methylpentane cracking over USHY. J. Catal. 163, 365\u2013373 (1996).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMorgan, D. J. Resolving ruthenium: XPS studies of common ruthenium materials. Surf. Interface Anal. 47, 1072\u20131079 (2015).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWood, J. & Gladden, L. F. Effect of coke deposition upon pore structure and self-diffusion in deactivated industrial hydroprocessing catalysts. Appl. Catal. A: Gen. 249, 241\u2013253 (2003).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLu, Z., Kuizhi, C. & Banghao, C. Factors that determine zeolite stability in hot liquid water. J. Am. Chem. Soc. 137, 11810\u201311819 (2015).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWolf, M. Thermodynamic assessment of the stability of bulk and nanoparticulate cobalt and nickel during dry and steam reforming of methane. RSC Adv. 11, 18187\u201318197 (2021).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBrosius, R., Kooyman, P. J. & Fletcher, J. C. Selective formation of linear alkanes from n-hexadecane primary hydrocracking in shape-selective MFI zeolites by competitive adsorption of water. ACS Catal. 6, 7710\u20137715 (2016).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nZong, X., Xie, T. & Vlachos, D. G. Predicting hydrogenolysis reaction barriers of large hydrocarbons on metal surfaces using machine learning: Implications for polymer deconstruction. Appl. Catal. B: Environ. 353, 124070 (2024).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWang, C. et al. A general strategy and a consolidated mechanism for low-methane hydrogenolysis of polyethylene over ruthenium. Appl. Catal. B: Environ. 319, 121899\u2013121899 (2022).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDegnan, T. F. & Kennedy, C. R. Impact of catalyst acid/metal balance in hydroisomerization of normal paraffins. AIChE J. 39, 607\u2013614 (2004).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nThybaut, J. W. et al. Acid-Metal Balance of a Hydrocracking Catalyst: Ideal versusNonideal Behavior. Ind. Eng. Chem. Res. 44, 5159\u20135169 (2005).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nAlvarez, F. F. R. R., G. Perot, C. Thomazeau, M. Guisnet. Hydroisomerization and Hydrocracking of Alkanes: 7. Influence of the Balance between Acid and Hydrogenating Functions on the Transformation ofn-Decane on PtHY Catalysts. J. Catal. 162, 179\u2013189 (1996).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nZecevic, J., Vanbutsele, G., De Jong, K. P. & Martens, J. A. Nanoscale intimacy in bifunctional catalysts for selective conversion of hydrocarbons. Nature 528, 245\u2013254 (2015).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nChen, L. et al. Effect of reaction conditions on the hydrogenolysis of polypropylene and polyethylene into gas and liquid alkanes. React. Chem. Eng. 7, 844\u2013854 (2022).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nJeong, S., Kim, J., Liu, J. J. & Won, W. A lignocellulosic 2, 3-butanediol strategy: process development and integrative analyses. J. Environ. Chem. Eng. 11, 110085 (2023).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nOh, M.-Y., Gujjala, L. K. S. & Won, W. Process development for production of platform chemicals from white birch: Insights from techno-economic and life-cycle assessment. Chem. Eng. J. 472, 144955 (2023).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWiatrowski, M., Klein, B., Kinchin, C., Huang, Z. & Davis, R. Opportunities for Utilization of Low-Cost Algae Resources: Techno-Economic Analysis Screening for Near-Term Deployment (Parts 1 and 2). (National Renewable Energy Lab.(NREL), 2022).\n\nYadav, G. et al. Techno-economic analysis and life cycle assessment for catalytic fast pyrolysis of mixed plastic waste. Energy Environ. Sci. 16, 3638\u20133653 (2023).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nGong, C., Lee, S. & Won, W. Process development and analyses for the co\u2010production of 2\u2010methyltetrahydrofuran and 1, 4\u2010pentanediol from lignocellulosic biomass. GCB Bioenergy 15, 900\u2013915 (2023).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKang, C., Liu, J. J., Woo, N. & Won, W. Process design for the sustainable production of butyric acid using techno-economic analysis and life cycle assessment. ACS Sustain. Chem. Eng. 11, 4430\u20134440 (2023).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nAhn, B., Jin, G., Kim, J. & Won, W. Integrated process design and analysis for co-production of biofuels with adipic acid and tetrahydrofuran. Ind. Crop. Prod. 200, 116830 (2023).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nAhn, B., Park, C., Liu, J. J., Ok, Y. S. & Won, W. Maximizing the utilization of lignocellulosic biomass: Process development and analysis. Renew. Energy 215, 119004 (2023).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nISO, I. 14044: 2006/AMD 2: 2020\u2014Environmental Management\u2014Life Cycle Assessment\u2014Requirements and Guidelines\u2014Amendment 2. International Organization for Standardization: Geneva, Switzerland (2020).\n\nPark, D., Lee, H. & Won, W. Unveiling the environmental gains of biodegradable plastics in the waste treatment Phase: A Cradle-to-Grave life cycle assessment. Chem. Eng. J. 487, 150540 (2024).\n\nTechnical Committee ISO/TC 207, E. M. Environmental Management-life Cycle Assessment-principles And Framework (International Organization for Standardization, 2006).\n\nErtl, G., Kn\u00f6zinger, H. & Weitkamp, J. Handbook of Heterogeneous Catalysis. Vol. 2 (VCH Weinheim, 1997).\n\nEmeis, C. A. Determination of integrated molar extinction coefficients for IR absorption bands of pyridine adsorbed on solid acid catalysts. J. Catal. 141, 347\u2013354 (1993).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nS. Khabtou, T. C., J.C. Lavalley. Quantitative infrared study of the distinct acidic hydroxyl groups contained in modified Y zeolites. Microporous Mater. 3, 133\u2013148 (1994).\n\nZholobenko, V. et al. Probing the acid sites of zeolites with pyridine: quantitative AGIR measurements of the molar absorption coefficients. J. Catal. 385, 52\u201360 (2020).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDavis, R., Wiatrowski, M., Kinchin, C. & Humbird, D. Conceptual Basis and Techno-Economic Modeling for Integrated Algal Biorefinery Conversion of Microalgae to Fuels and Products (2019 NREL TEA Update: Highlighting Paths to Future Cost Goals via a New Pathway for Combined Algal Processing) (National Renewable Energy Lab.(NREL), 2020).\n\nDavis, R. E. et al. Process Design And Economics For The Conversion Of Lignocellulosic Biomass To Hydrocarbon Fuels And Coproducts: 2018 Biochemical Design Case Update; Biochemical Deconstruction And Conversion Of Biomass To Fuels And Products Via Integrated Biorefinery Pathways (National Renewable Energy Lab.(NREL), Golden, 2018).\n\nZepeda, T. A. et al. Synergetic effect in RuxMo(1-x)S2/SBA-15 hydrodesulfurization catalysts: comparative experimental and DFT studies. Appl. Catal. B: Environ. 251, 143\u2013153 (2019).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKumar, V. V. et al. An investigation on the influence of support type for Ni catalysed vapour phase hydrogenation of aqueous levulinic acid to \u03b3-valerolactone. RSC Adv. 6, 9872\u20139879 (2016).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDownload references",
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+        },
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+            "section_name": "Acknowledgements",
+            "section_text": "This work was supported by the Korea Environment Industry & Technology Institute(KEITI) through the Center of plasma process for organic material recycling project, funded by Korea Ministry of Environment(MOE) (2022003650002 to I.R.), the National Research Foundation of Korea (NRF) grant funded by The Ministry of Science and ICT (MSIT) under grant NRF-2022R1F1A1074392 to I.R., and the Korea Institute of Energy Technology Evaluation and Planning(KETEP) and the Ministry of Trade, Industry & Energy(MOTIE) of the Republic of Korea (RS-2024-00419764 to W. W.)",
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+        },
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+            "section_name": "Author information",
+            "section_text": "These authors contributed equally: Taeeun Kwon, Byeongchan Ahn.\n\nDepartment of Chemical and Biomolecular Engineering, Seoul National, University of Science and Technology, Seoul, Republic of Korea\n\nTaeeun Kwon\u00a0&\u00a0Insoo Ro\n\nDepartment of Chemical and Biological Engineering, Korea University, Seoul, Republic of Korea\n\nTaeeun Kwon,\u00a0Byeongchan Ahn\u00a0&\u00a0Wangyun Won\n\nChemical & Process Technology Division, Korea Research Institute of Chemical Technology (KRICT), Daejeon, Republic of Korea\n\nKi Hyuk Kang\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nI.R. conceived the project idea and contributed to the experiment design. T.K. conducted the experiments, while T.K. and K.H.K. handled catalyst characterization and data analysis. B.A. and W.W. provided insights into process analysis. Project supervision was carried out by I.R. and W.W. The manuscript was collectively written by T.K., B.A., W.W., and I.R. All authors participated in result discussions and manuscript review.\n\nCorrespondence to\n                Wangyun Won or Insoo Ro.",
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+            "section_text": "Kwon, T., Ahn, B., Kang, K.H. et al. Unraveling the role of water in mechanism changes for economically viable catalytic plastic upcycling.\n                    Nat Commun 15, 10239 (2024). https://doi.org/10.1038/s41467-024-54495-5\n\nDownload citation\n\nReceived: 17 April 2024\n\nAccepted: 11 November 2024\n\nPublished: 29 November 2024\n\nVersion of record: 29 November 2024\n\nDOI: https://doi.org/10.1038/s41467-024-54495-5\n\nAnyone you share the following link with will be able to read this content:\n\nSorry, a shareable link is not currently available for this article.\n\n\n\n\n                            Provided by the Springer Nature SharedIt content-sharing initiative\n                        ",
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+            ]
+        },
+        {
+            "section_name": "This article is cited by",
+            "section_text": "Korean Journal of Chemical Engineering (2025)",
+            "section_image": []
+        }
+    ]
+}

2af794e8bdc6d7671634e08f6af1da53069c1fb5bf84792aa87006addcb20726/metadata.json

@@ -0,0 +1,138 @@
+{
+    "title": "In situ atomic observations of aggregation growth and evolution of penta-twinned gold nanocrystals",
+    "pre_title": "In-situ atomic observations unveil the aggregation growth and evolution of five-fold twin structures",
+    "journal": "Nature Communications",
+    "published": "25 October 2024",
+    "supplementary_0": [
+        {
+            "label": "Supplementary Information",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-024-53501-0/MediaObjects/41467_2024_53501_MOESM1_ESM.pdf"
+        }
+    ],
+    "supplementary_1": [
+        {
+            "label": "Transparent Peer Review file",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-024-53501-0/MediaObjects/41467_2024_53501_MOESM2_ESM.pdf"
+        },
+        {
+            "label": "Source Data",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-024-53501-0/MediaObjects/41467_2024_53501_MOESM3_ESM.zip"
+        }
+    ],
+    "supplementary_2": NaN,
+    "source_data": [
+        "/articles/s41467-024-53501-0#Sec18"
+    ],
+    "code": [],
+    "subject": [
+        "Nanoparticles",
+        "Nanoscale materials"
+    ],
+    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
+    "preprint_pdf": "https://www.researchsquare.com/article/rs-4283157/v1.pdf?c=1729940830000",
+    "research_square_link": "https://www.researchsquare.com//article/rs-4283157/v1",
+    "nature_pdf": "https://www.nature.com/articles/s41467-024-53501-0.pdf",
+    "preprint_posted": "22 Apr, 2024",
+    "research_square_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "The unique twin boundaries and inherent lattice strain of five-fold twin (5-FT) structures offer a promising and innovative approach to tune nanocrystal configurations and properties, enriching nanomaterial performance. However, due to constraints imposed by small thermodynamically stable size and complex twin configurations, gaps persist in understanding the nonclassical growth models of 5-FT nanoparticles. Here, we in-situ investigated the mechanisms underlying size-dependent and twin configuration-related aggregation growth phenomena between 5-FT and other nanoparticles at the atomic scale. The results find that surface diffusion shapes the morphology of aggregated nanoparticles, promoting symmetrical 5-FT formation, particularly involving smaller nanoparticles. Additionally, the inherent structure of 5-FT mitigates the dominance of surface diffusion in its morphological evolution, retarding the aggregation evolution process and fostering intricate twin structures. Our findings contribute to advancing our ability to manipulate the configuration of twinned particles and achieve a more predictable synthesis of novel functional nanomaterials for engineering applications.Physical sciences/Materials science/Nanoscale materials/NanoparticlesPhysical sciences/Physics/Particle physics/Experimental particle physics",
+            "section_image": []
+        },
+        {
+            "section_name": "Additional Declarations",
+            "section_text": "There is NO Competing Interest.",
+            "section_image": []
+        },
+        {
+            "section_name": "Supplementary Files",
+            "section_text": "SupplementaryInformation.docx",
+            "section_image": []
+        }
+    ],
+    "nature_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "The twin boundaries and inherent lattice strain of five-fold twin (5-FT) structures offer a promising and innovative approach to tune nanocrystal configurations and properties, enriching nanomaterial performance. However, a comprehensive understanding of the nonclassical growth models governing 5-FT nanocrystals remains elusive, largely due to the constraints of their small thermodynamically stable size and complex twin configurations. Here, we conducted in situ investigations to elucidate the atomic-scale mechanisms driving size-dependent and twin configuration-related aggregation phenomena between 5-FT and other nanoparticles at the atomic scale. Our results reveal that surface diffusion significantly shapes the morphology of aggregated nanoparticles, promoting the symmetrical formation of 5-FT, especially in smaller nanoparticles. Moreover, the inherent structural characteristics of 5-FT mitigate the dominance of surface diffusion in its morphological evolution, retarding the aggregation evolution process and fostering intricate twin structures. These findings contribute to advancing our capacity to manipulate the configuration of twinned particles, enabling more predictable synthesis of functional nanomaterials for advanced engineering applications.",
+            "section_image": []
+        },
+        {
+            "section_name": "Introduction",
+            "section_text": "Uncovering the growth mechanisms of nanoparticles (NPs) is significant not only for elucidating the underlying formation mechanisms of minerals and comprehensively understanding the evolution of natural environments but also for its scientific and engineering significance in tuning the size, morphology, and properties of synthetic nanomaterials. Despite numerous pieces of evidence challenging the classical interpretations of crystal growth, which emphasize surface reactions and the monomer diffusion to the surface1,2, nonclassical crystal growth scenarios have only begun to be recognized gradually just over the past decade2,3,4,5. As a main nonclassical crystal growth mechanism, particle-based aggregation3,6,7 generally includes orientated attachment (OA)4,6, nearly OA (such as meso-crystal8,9 and dislocation-induced tilt attachment4), and non-OA (such as intraparticle growth10,11, aggregation and transformation of thermodynamically metastable particle to stable phases8,12, and aggregation and grain boundary/surface atom migration dominated growth10,13). These mechanisms require systematic and intensive investigation due to unresolved and challenging aspects, such as the need for high spatial and temporal resolution to study atomic diffusion and migration, particle relative movement, interfacial interactions, and grain boundary evolution.\n\nThe 5-FT structure has been extensively detected in diverse natural and synthetic systems14,15,16 and exhibits special properties attributed to its crystallographically forbidden pentagonal symmetry and inherent lattice strain, such as enhanced mechanical properties17, attractive catalytic properties18, and improved optic properties19. In addition to NP size, morphology, and composition, the twin plane and inherent lattice strain of 5-FT provide an appealing avenue to tailor the configuration and properties of nanocrystals, thus diversifying and enhancing the performance of nanomaterials. For instance, 5-FT structure holds the potential for producing hierarchical materials20,21,22, which preserve the properties of the nanoscale building blocks and may exhibit attractive performance characteristics22,23. Nevertheless, limited by complicated twin structures (5 twin units), significantly small size (3\u201314\u2009nm) under a thermodynamic stability state24,25,26, together with movement of NPs, and the only proper \\([110]\\) twin pole observation direction, revealing the atomic formation and growth mechanisms of 5-FT remains experimentally challenging. By trigging NPs aggregation through electron-beam-induced decomposition of the organic ligands surrounding the NPs, we uncovered two underlying atomic formation mechanisms of 5-FT within Au, Pd, and Pt nanomaterials6. However, nonclassical growth mechanisms of 5-FT are still elusive, particularly potentially under the coupling effect of thermodynamic and kinetics landscapes, involving but not limited to the atomic formation and evolution of complicated twin structure (twining and de-twinning processes), atom surface diffusion, and relative slip and configuration modulation of NPs. Therefore, clarifying the nanoparticle-based aggregation growth of 5-FT is scientifically significant and important from an engineering perspective.\n\nIn this work, in situ high-resolution transmission electron microscopy (HRTEM) combined with molecular dynamics (MD) simulation was utilized to study the atomic aggregation growth and evolution mechanisms involving 5-FT and diverse NPs, i.e., NPs with varied size ratios and twinned configurations (single crystal (SC) and 5-FT). Additionally, the impact of various thermodynamic and kinetic landscapes on aggregation evolution was systematically investigated.",
+            "section_image": []
+        },
+        {
+            "section_name": "Results and discussion",
+            "section_text": "Spherical Au NPs with various twin configurations (\u22484.4\u2009nm, Supplementary Fig.\u00a01) embedded in 1-dodecanethiol organic matrix were drop-casted onto a TEM grid. Then, NP aggregation was induced by decomposing organics under electron-beam irradiation (see \u201cMethods\u201d). As shown in Fig.\u00a01a, b, aggregation between a 2.1\u2009nm SC and a 3.6\u2009nm symmetrical 5-FT (S5-FT, size ratio R\u2009=\u20090.58) induces obvious growth of the twin units 1 and 5, resulting in the formation of an asymmetrical 5-FT (AS5-FT). Nevertheless, the AS5-FT evolves into a symmetrical twin structure (Fig.\u00a01c) and transforms into a stable re-entrant \\(\\left\\{111\\right\\}\\) (highlighted by white arrows in Fig.\u00a01d) S5-FT at last. Considering none visible twin boundaries (TBs) migrations, the above evolution process is supposed to be dominated by surface diffusion from the small NP to the 5-FT, which will be further discussed in Fig.\u00a02. Wherein, the formation of highly faceted structure (Fig.\u00a01d) has been proved to be associated with the balance between surface and strain energy27,28, i.e., the re-entrant \\(\\left\\{111\\right\\}\\) 5-FT can significantly release the intrinsic lattice strain energy and slightly increases the surface energy of the 5-FT structure.\n\na\u2013d Configuration evolution after a 2.1\u2009nm SC NP attached with a 5-FT NP (3.6\u2009nm) with R\u2009=\u20090.58. White arrows show the formation of the re-entrant surface. e\u2013o Configuration evolution after a 4.6\u2009nm SC NP aggregated with a 4.2\u2009nm 5-FT NP (R\u2009=\u20091.10). p The surface outlines of the aggregated NP. The migration directions of the surface outline with durations are denoted by red arrows. Twin boundaries are highlighted by red lines. Twin units are denoted by numbers ranging from 1 to 5 in (a) and (e). Yellow numbers and arrows show migration layers and directions of the TBs, compared with the immediate prior image. Partial dislocations are denoted by blue \u201c\u2514\u201d and their slip directions are denoted by the blue arrows.\n\na\u2013e Evolution of an aggregated 5-FT NP, formed by attaching of a 5.0\u2009nm symmetrical 5-FT NP (yellow, A5F) and a 2.6\u2009nm SC NP (cyan, B3S) with R\u2009=\u20090.52. Re-entrant \\(\\left\\{111\\right\\}\\) surfaces are highlighted by gray solid lines. f The biggest cross-section perpendicular to the Z-axis showing atomistic distribution of the initial SC NP. g Variation of the relative energy of the simulated system from (a) to (e). h\u2013r The aggregation evolution process after a 5\u2009nm 5-FT Au NP (A5F) attached with a 4.8\u2009nm SC NP (B5S) with R\u2009=\u20090.96. The relative slip and layers between the 5-FT and the SC are represented by cyan arrows and numbers in (i\u2013k) and (m), respectively. s Variation of the relative energy of the simulated system from (h) to (r). t TBs slip induced migrations of the twin pole from 2.5\u2009ns (i) to 4.8\u2009ns (o). u A double Thompson tetrahedron with an FCC crystal structure. Vertex-to-vertex (e.g., AB), vertex-to-orthocenter (e.g., A\u03b3), and orthocenter-to-orthocenter (e.g., \u03b1\u03b3) denote a perfect, partial, and stair-rod dislocations, respectively. v Relationship of the Thompson tetrahedron in 5-FT units verifying that dislocations within different twin units can undergo mutual transformations via various dislocation reactions. w Schematic illustration of twin pole migration (o to o\u2019). TBs before and after slip are denoted by dashed yellow lines and solid red lines, respectively. Yellow arrows and numbers show migration directions and layers of the TBs, respectively, compared with the immediate prior image. Partial dislocations are denoted by blue \u201c\u2514\u201d and their slip directions are denoted by the blue arrows. Twin units are denoted by numbers ranging from 1 to 5 in (a) and (h). Source data are provided as a Source Data file.\n\nDifferent from the above small size ratios (Fig.\u00a01a, b), the large SC (R\u2009=\u20091.10) only stimulates continuous growth of the twin unit 1 with substantially de-twinning process until the final manifestation of a SC (Fig.\u00a01e\u2013o). The detailed evolution processes are as follows: Initially, a 4.6\u2009nm SC-1 attaches with a 2.1\u2009nm SC-2 and a 4.2\u2009nm S5-FT successively, resulting in attractive growth of the twin unit 1 (Fig.\u00a01e\u2013g). Then, a partial dislocation nucleates at the TB \u03a331 from the periphery of the NP and slips toward the center of the 5-FT, leading to a single layer of migration of the \u03a331 near the periphery (Fig.\u00a01h). Subsequently, continuous nucleation and slip of partial dislocations at TBs induces de-twinning process of the 5-FT (Fig.\u00a01i\u2013o), giving rise to reduction of the twin units 2, 3, and 4. During this process, when the twin pole of the 5-FT is close to overlap (Fig.\u00a01j), specifically, it involves one layer of migrations of the four TBs (\u03a331, \u03a332, \u03a333, and \u03a334). Alternatively, there is obvious split of the twin pole. At last, when the 5-FT twin pole is close to (\u22482\u20133 layers of \\(\\left\\{111\\right\\}\\) planes away from) the periphery of the NP, 5-FT structure disappears within 0.8\u2009s, resulting in the formation of the SC NP (Fig.\u00a01n, o). To assess the influence of surface diffusion on the entire aggregation process, further analysis is conducted on the variations in surface outlines. As presented in Fig.\u00a01g\u2013p, distinct variations of the surface outlines are detected from 83.2 to 179.4\u2009s, especially at the concave surfaces and the region near the 5-FT twin pole (Fig.\u00a01p), nevertheless, the variation can be ignored from 179.4 to 220.8\u2009s (Fig.\u00a01p). Therefore, during the above aggregation induced evolution process, the surface diffusion mainly occurs at the initial stage (Fig.\u00a01g\u2013k), and the partial dislocations induced twin boundaries slip mainly happens at the subsequent stage (Fig.\u00a01i\u2013o) with an overlapping duration from 142.6 to 179.4\u2009s (Fig.\u00a01i\u2013k). In addition, surface diffusion without significant morphology variations, such as mutual diffusion, remains undetectable in Fig.\u00a01. The relative slip between the initial 5-FT and SC NPs is also indistinguishable, which can potentially induce morphological variations. These phenomena will be comprehensively analyzed in Fig.\u00a02 based on high time-resolution data and 3-D atomic evolution tracing using MD simulations.\n\nTherefore, as presented in Fig.\u00a01, after attachment between a 5-FT NP with a small (R\u2009=\u20090.58, Fig.\u00a01a\u2013d) or a relatively large (R\u2009=\u20090.73, Supplementary Fig.\u00a06) SC NP, surface diffusion dominates the aggregation growth processes, resulting in formation of a S5-FT or an asymmetrical 5-FT (AS5-FT) NP, respectively. Nevertheless, during the aggregation growth process of a 5-FT with a large (R\u2009=\u20091.10, Fig.\u00a01e\u2013o) SC NP, surface diffusion exclusively dominates the initial stage of surface modulation. Subsequent to this, the activation of partial dislocations governs the de-twinning process, resulting in the manifestation of a newly formed SC NP. Additionally, based on our previous observation6, asymmetrical 5-FTs can also evolve into symmetrical ones through NPs aggregation at small twin units. Meanwhile, with the growing of 5-FT NPs, its inherent lattice strain29 can be relieved through various mechanisms, including but not limited to the formation of plane defects in twin units30, the migration of the 5-FT twin pole30,31, and the formation of re-entrant decahedral morphology32. Thereby, the aforementioned AS5-FT, including various unstable intermediate 5-FT NPs, can be potentially stabilized via attachment with other NPs in conjunction with the modulation of the inherent lattice strain.\n\nTo uncover detailed evolution mechanisms of NPs\u2019 3D configurations, the aggregation processes between S5-FT and SC NPs are further investigated by employing high temporal resolution MD simulation (see \u201cMethods\u201d, Supplementary Fig.\u00a02 and Supplementary Table\u00a01). As shown in Fig.\u00a02a\u2013c, the SC NP (B3S, R\u2009=\u20090.52, Fig.\u00a02a) was initially designed to attach with the twin unit 1. However, a portion of the surface of the SC NP evolves into an amorphous state and its atoms diffuse symmetrically toward the S5-FT surface quickly (Fig.\u00a02b and Supplementary Fig.\u00a07), inducing significant growth of the twin units 1 and 2, resembling the phenomena detected in Fig.\u00a01a, b. The mutual diffusion of surface several layers\u2019 atoms is also detected after 4.0\u2009ns with the formation of re-entrant \\(\\left\\{111\\right\\}\\) surfaces (Fig.\u00a02c\u2013f). Additionally, significantly fewer atoms diffuse from the 5-FT to the B3S SC NP, and the atoms from the initial NP can even diffuse to the far-away twin unit 4 of the 5-FT (Fig.\u00a02f). Correspondingly, the system experiences a substantial decrease in relative energy primarily at the initial stage (0.0\u20134.0\u2009ns, Fig.\u00a02g), indicating significant configuration modifications. Therefore, the surface diffusion from the small SC NP to the big 5-FT NP dominates the aggregation growth processes, consistent with the experimental results detected in Fig.\u00a01a\u2013d. Similar mutual diffusion is also detected at the initial stage of the simulated system with a relatively large particle size ratio (0.76, Supplementary Fig.\u00a08). Nevertheless, the 5-FT structure swiftly transforms into a bi-crystal within 0.1\u2009ns (Supplementary Fig.\u00a08d, e), accompanying with significant decreasing of the relative energy (Supplementary Fig.\u00a08g). Additionally, there is also diffusion induced growth of both twin units, i.e., the twin units 1 and 5 (Supplementary Fig.\u00a08d). This verifies that the formation of initial asymmetrical configuration, i.e., significant growth of both twin units (Fig.\u00a01a, b and Supplementary Figs.\u00a06 and 8), is an inherent characteristic of surface diffusion dominated aggregation processes when R\u2009<\u20090.76.\n\nDivergent from the aforementioned surface diffusion dominated NPs aggregation evolution mechanisms (R\u2009<\u20090.76, Fig.\u00a02a\u2013f and Supplementary Fig.\u00a08), MD simulation indicates that the de-twinning process induced by TBs\u2019 migrations governs the aggregation evolution as the R increases to 0.96 (Fig.\u00a02h\u2013r). This aligns with the experimental results delineated in Fig.\u00a01i\u2013o. The aggregation evolution process can be segmented into the following three distinct stages: (1) The initial relative slip. As presented in Fig.\u00a02h, i, the interaction between the 5-FT and the SC gives rise to the relative slip of 2 layers of \\(\\left\\{111\\right\\}\\), and the slip direction of the 5-FT aligns parallel to the \u03a335 (highlighted by the cyan arrow). (2) TB migration dominated de-twinning process. This process is triggered by nucleation and slip of partial dislocations (Fig.\u00a02j\u2013o). As shown in Fig.\u00a02j, the nucleation and slip of a partial dislocation from the periphery of the concave surface to the twin pole instigate the migration of the TB \u03a335 toward the initial SC. Additionally, there are also relative slips between the 5-FT and the SC (Fig.\u00a02j, k, m). These determinations arise from the layer variation of \\(\\left\\{200\\right\\}\\) planes between the twin pole and the periphery of the initial SC (prior to the migration of the twin pole, Fig.\u00a02h, i), alternatively, the layer variations of \\(\\left\\{111\\right\\}\\) planes from the \u03a334 (without migration) to the \\(\\left\\{111\\right\\}\\) intersection plane in the twin unit 5 with the initial \\(\\left\\{200\\right\\}\\) interface between the 5-FT and the SC (Fig.\u00a02j, k, m). (3) Surface diffusion dominated de-twinning process. When the twin units are as small as 3 layers of \\(\\left\\{111\\right\\}\\) planes (Fig.\u00a02o\u2013r), surface diffusion takes precedence as the predominant mechanism during the final de-twinning process, while no discernible TB migration can be detected. This differs from the detected TB migration-dominated de-twinning process in Fig.\u00a01n, o, and is supposed to be associated with NP\u2019s configuration. That is, when the twin pole of the AS5-FT is close to the convex surface (Fig.\u00a01n, o and Supplementary Fig.\u00a010f, g), TB migration induces the fast de-twinning process. Nevertheless, when the serious AS5-FT twin structures are close to the concave surface (Fig.\u00a02o\u2013r), surface diffusion dominates the de-twinning process. Figure\u00a02s shows there is a significant increase in the system energy during the initial stage of the relative slip (Fig.\u00a02h\u2013k), followed by a substantial energy decrease attributed to the de-twinning process dominated by partial dislocations. This is mainly associated with the reduction of TB energy and lattice strain energy31,33. After that, the variation in the system energy becomes moderate. Throughout the entire evolution process, mutual diffusion was detected consistently. The surface amorphous detected in MD simulations (Fig.\u00a02b, c and Supplementary Fig.\u00a08), as opposed to experimental observation (Fig.\u00a01a\u2013c), is supposed to correlate with the relatively elevated simulation temperature employed to expedite the simulated experimental process (see \u201cMethods\u201d).\n\nEffective TBs migration layers during the TBs migrations dominated de-twinning process (Fig.\u00a02i\u2013o) are illustrated in Fig.\u00a02t. That is, TBs \u03a331 and \u03a332 migrate 4 layers, TBs \u03a333 and \u03a335 migrate 5 layers, remaining \u03a334 are unchanged. The migration of TBs is closely associated with nucleation and slip of partial dislocations, and the detailed mechanisms are depicted in Fig.\u00a02u\u2013w. A double Thompson tetrahedron is generally employed to define various dislocations in face-centered cubic crystal34, including perfect dislocation (vertex to vertex, such as AB and BD), partial dislocation (vertex to orthocenter, such as A\u03b4 and B\u03b4), and stair-rod dislocation (orthocenter to orthocenter, such as \u03b1\u03b2 and \u03b2\u03b4). Dislocations have the capability to undergo transformation into one another through reactions, guided by the principles of vector geometry addition and subtraction rules34. For instance, DB\u2009=\u2009DA\u2009+\u2009AB, \u03b2\u03b4\u2009=\u20091/3DB, DB\u2009=\u2009D\u03b2\u2009+\u2009\u03b2\u03b4\u2009+\u2009\u03b4B\u2009=\u20091/3DB\u2009+\u2009D\u03b2\u2009+\u2009\u03b4B, DB\u2009=\u20093/2(D\u03b2\u2009+\u2009\u03b4B). Here, the 5-FT NP can be regarded as a five Thompson tetrahedron (Fig.\u00a02v), and dislocations can transform into one another by diverse dislocation reactions. Based on experimental observation (Fig.\u00a01h) and MD simulation (Fig.\u00a02j), partial dislocations initially nucleate at the periphery of the NPs. For instance, a partial dislocation C\u03b2\u2032 nucleates on \u03a335 (Fig.\u00a02w) and slips toward the twin pole O, inducing one layer migration of \u03a335. Then, C\u03b2\u2032 dissociates into other two partial dislocations at the twin pole, i.e., C\u03b2\u2032\u2009\u2192\u2009C\u03b7\u2009+\u2009\u03b7\u03b2\u2032, and C\u03b7 can slip along \u03a333, resulting in one layer of migration of \u03a333. Meanwhile, \u03b7\u03b2\u2032 can be equivalent to 1/2DB (\u03b7\u03b2\u2032 serves as the median of the triangle FBD, Fig.\u00a02v). And as analyzed above, DB\u2009=\u20093/2(D\u03b2\u2009+\u2009\u03b4B), thereby, \u03b7\u03b2\u2032 can be dissociated into D\u03b2 and \u03b4B, i.e., \u03b7\u03b2\u2032\u2009=\u20091/2DB\u2009=\u20093/4(D\u03b2\u2009+\u2009\u03b4B). Correspondingly, partial dislocations D\u03b2 and \u03b4B can trigger migration of TBs \u03a331 and \u03a332, resulting in migration of the twin pole form O to O\u2032 (Fig.\u00a02w), i.e., one layer of de-twinning process of 5-FT. Based on the above dislocation reactions, one C\u03b2\u2032 only generates 3/4(D\u03b2\u2009+\u2009\u03b4B), that is, a single layer of migration of \u03a335 results in 3/4 layer of migrations of \u03a331 and \u03a332. Nevertheless, based on the geometrical relation of 5-FT, one C\u03b2\u2032 still generates approximately 0.18 more D\u03b2 and \u03b4B than that to maintain the perfect overlap of the twin pole. This residual mismatch can be mediated by various migration layers of TBs, such as 5 layers of \u03a333 and \u03a335 and 4 layers of \u03a331 and \u03a332 (5 \u00d7 0.18\u2009=\u20090.90 layer, closed to a single layer of difference, Fig.\u00a02i\u2013o, t). This observation is also consistent with the experimental observation (Fig.\u00a01h\u2013j), i.e., the TBs \u03a331, \u03a332, \u03a333, and \u03a334 migrate one layer to maintain the nearly overlapped twin pole.\n\nAggregation-induced growth and TB evolution process are also investigated between 5-FT NPs with various size ratios (Fig.\u00a03). As presented in Fig.\u00a03a, b, aggregation between a 3.7\u2009nm S5-FT and a 4.6\u2009nm S5-FT induces the formation of an AS5-FT (Fig.\u00a03d). And the AS5-FT can potentially evolve into S5-FT by aggregating with other NPs (denoted by a white arrow, Fig.\u00a03d), as discussed above. With increasing the size ratio between the two aggregated 5-FT NPs, intricate twin structures can be induced (R\u2009=\u20090.82, Fig.\u00a03e\u2013l), and the detailed evolution processes are as follows. At first, the twin unit 4 of the small S5-FT NP orientationally attaches with the twin unit 2 of the big S5-FT NP (Fig.\u00a03e, f), followed by the formation of a TBs sealed region. This is introduced by the relative slip between the two NPs (layers variation without corresponding TBs migration, highlighted by cyan arrows in Fig.\u00a03f, g), the surface diffusion toward the concave surface (denoted by red arrows, Fig.\u00a03f\u2013h), and the TBs migration (highlighted by yellow arrows, Fig.\u00a03f\u2013i). Then, the sealed region remains unchanged until the small 5-FT evolves into three-fold twin at 72.0\u2009s (Fig.\u00a03i\u2013k). This process is dominated by surface diffusion, verified by significant morphology variation and two reserved TBs, i.e., only disappearing of the twin units 1 and 2 of the S5-FT NP. Thereby, the de-twinning process (Fig.\u00a03j, k) is significantly different from the TB migration decided de-twinning process (Fig.\u00a01n, o), in which the morphology variation can be ignored. Thereby, the TBs sealed region can stabilize the 5-FT structures and modify the evolution pathway of the aggregation growth mechanism between 5-FT NPs. Nevertheless, the sealed region becomes unstable after 5-FT evolving into 3-fold twin within 1.0\u2009s (Fig.\u00a03k, l), resulting in the formation of a complicated twin structure, which can potentially evolve into AS5-FT by de-twinning of the TB at bottom left. Additionally, when the size ratios between two aggregated 5-FT are small, such as 0.47 and 0.53 (Supplementary Fig.\u00a09), S5-FT NPs ultimately formed. Besides the orientation attachment dominated NPs aggregation (with no detectable formation of newly formed GBs at attachment sites, Fig.\u00a03e, f), another scenario emerged, where a zig-zag \\(\\{200\\}\\)/\\(\\{111\\}\\) GB was induced after aggregation (R\u2009=\u20090.72, see Supplementary Fig.\u00a010 for details).\n\na\u2013d Atomic evolution process between a 3.7\u2009nm 5-FT and a 4.6\u2009nm 5-FT with R\u2009=\u20090.78. e\u2013l Atomic evolution process between a 3.3\u2009nm 5-FT and a 4.0\u2009nm 5-FT with a size ratio of 0.82. Twin units are denoted by numbers ranging from 1 to 5 in (a) and (e). TBs and unclear TBs are highlighted by red solid and dashed lines, respectively. The white arrow shows the aggregation of another NP in (d). Yellow arrows and numbers show migration directions and layers of the TBs, respectively, compared with the immediate prior image. The relative slip between the two 5-FT is represented by cyan arrows in (g). Partial dislocation is denoted by blue \u201c\u2514\u201d and its slip direction is denoted by the blue arrow.\n\nFigure\u00a04 shows aggregation growth between 5-FT NPs with various size ratios. As presented in Fig.\u00a04a, b, after orientation attachment with the twin unit 1 of the 5.0\u2009nm 5-FT, the small 5-FT NP evolves into surface amorphous state within 0.1\u2009ns (Fig.\u00a04b). There is no detectable TB migration. Then, mutual diffusion dominates the subsequent evolution process and induces the formation of a symmetrical 5-FT (Fig.\u00a04c\u2013e). Cross-section (Fig.\u00a04f) shows that atoms originating from the initial small 5-FT can even diffuse over a considerable distance to the twin units 3 and 4 (Fig.\u00a04f). The system energy variation is presented in Fig.\u00a04g. The above process analogous to that detected in Fig.\u00a01a\u2013g. Thereby, when the size ratio is small enough, such as 0.52 in Fig.\u00a02a\u2013g and 0.62 in Fig.\u00a04a\u2013g, the aggregation kinetics is governed by surface diffusion from small NPs to the big NPs, resulting in the formation of the S5-FT structure. With increasing of the size ratio to 0.82, apparent relative slip (Supplementary Fig.\u00a013a, b) and TBs migration (Supplementary Fig.\u00a013b, c) are detected, corresponding to a significant decrease of the system energy (Supplementary Fig.\u00a013h). Although relatively small 5-FT NP still evolves into surface amorphous state accompanying with surface diffusion toward the big 5-FT (Supplementary Fig.\u00a013c\u2013g), an AS5-FT ultimately forms.\n\na\u2013e, h\u2013m Evolution of the aggregated 5-FT NPs, formed by attaching of a 5.0\u2009nm S5-FT NP (yellow, A5F) with 3.2\u2009nm (B3F) and 5.0\u2009nm (B5F) S5-FT NPs (cyan), respectively. The corresponding size ratios are 0.64 and 1.00, respectively. f, n The biggest cross-sections perpendicular to the Z-axes showing atomistic distribution of the initial 5-FT NPs of B3F and B5F, respectively. g, o Variation of the relative energies of the corresponding simulated systems. TBs are highlighted by red lines. Twin units are denoted by numbers ranging from 1 to 5 in (a) and (h). The relative slip between the two 5-FT is represented by cyan arrows in (I). Source data are provided as a Source Data file.\n\nFor the large size ratio between two aggregated 5-FT NPs, MD simulation shows there is also relative slip at the initial stage (Fig.\u00a04h, i), inducing the formation of a sealed stable region S1 (Fig.\u00a04i). The region S1 can stabilize for a long time until the twin units 3 and 4 of the left 5-FT decrease to three and four layers, respectively, resulted by surface diffusion (Fig.\u00a04i\u2013l). Then, TBs migration induces \u03a332, \u03a333, \u03a334, and \u03a335 TBs to disappear within 0.02\u2009ns (Fig.\u00a04k, l), accompanied by significant decreasing of the system energy (Fig.\u00a04o). Therefore, MD simulation results are consistent with the phenomena detected during in situ observation (Fig.\u00a03e\u2013l). As for the reserved TB \u03a331, it disappears at last with the forming of an AS5-FT (Fig.\u00a03l, m). The system energy decreases slowly during the initial 69.50\u2009ns, accompanied by moderate surface modulation, and decreases seriously with de-twinning of the left 5-FT NP. This means that the system energy of the aggregated 5-FT NPs is mainly introduced by the 5-FT structures. Additionally, while the surface diffusion remains a dominated factor during 5-FT NP\u2019s aggregation, de-twinning process, i.e., TB migration, is often observed across experimental (Fig.\u00a03) and simulated (Fig.\u00a04) conditions. This phenomenon stems from the intricate and highly strained twin configuration inherent in 5-FT NPs, as opposed to the SC NPs. Due to the formation of the stable sealed region S1, a significant long simulation duration was employed in Fig.\u00a04 (80.00\u2009ns) compared with that of the previous MD simulations (30.00\u2009ns, Fig.\u00a02 and Supplementary Figs.\u00a08, 12, 13).\n\nSymmetry evolution of the aggregated 5-FT NPs is closely associated with surface diffusion and TBs migration. As observed in all experimental results (Figs.\u00a01, 3), during aggregation between various NPs, surface diffusion occurs almost throughout the whole evolution process. Surface diffusion generally promotes the generation of S5-FT (formed based on the big 5-FT NPs), especially for small particle size ratios, by transferring atoms from small NPs to the twin units far away from the attached regions (Figs.\u00a01a\u2013d, 2a\u2013f, 3a\u2013h, 4a\u2013f). Nevertheless, the effect of TBs migration on the symmetry of the aggregated NPs depends on the twin pole migration direction. The migration of the reserved 5-FT twin pole toward the periphery of the NPs results in a reduction in symmetry, and vice versa. Based on dozens of experimental observations, the size effect of the aggregation growth between 5-FT and various NPs (SC and 5-FT) is illustrated in Fig.\u00a05. Correspondingly, to obtain the S5-FT, the critical ratios should be roughly smaller than 0.83 and 0.72, respectively. Otherwise, AS5-FT (Fig.\u00a05a) or complex twin structures (Fig.\u00a05b) form. In addition, SC can be also introduced at the final stage if the size ratio between the SC and the 5-FT is larger than approximately 1.0 (Fig.\u00a05a) under experimentally observed conditions. According to the theoretical models (Supplementary Table\u00a01), the number of atoms of SC is significantly larger than that of the 5-FT with the same particle size. And even R\u2009=\u20090.76 (model 1-2, Supplementary Table\u00a01, smaller than the critical R\u2009=\u20090.83), the number of atoms of SC is also larger than that of the corresponding attached 5-FT. This indicates that: (1) under investigated particles size (several nanometers), S5-FT exhibits relative stability, maintaining its symmetrical structure after attaching with small SC NP, and even the SC possesses a slightly larger number of atoms than that of the 5-FT. That is, surface diffusion predominantly governs the aggregation evolution, rendering negligible the migration of TBs or twin poles. (2) Relatively small critical R (0.72, atoms significantly less than that of the attached 5-FT, model 2-2, Supplementary Table\u00a01) between two aggregated 5-FT also verifies the stability of the 5-FT NP, i.e., the 5-FT structure can greatly mitigate surface diffusion. (3) The mutual surface diffusion from small NP to 5-FT is markedly greater than the reverse diffusion, i.e., the surface energy plays a significant role during NP\u2019s aggregation growth.\n\na Configuration obtained after aggregation between SC and 5-FT NPs. b Configuration obtained after aggregation between two 5-FT NPs. Source data are provided as a Source Data file.\n\nTo maintain the symmetrical configuration of 5-FT NPs, the critical transfer ratio registers at \u22480.72 for 5-FT/5-FT, which is smaller than that of SC/5-FT (\u22480.83). As discussed above, the surface diffusion persists throughout the entire evolution process and facilitates to maintain the symmetrical configuration of the big 5-FT NPs. Thereby, for two aggregated 5-FT NPs, the formation of S5-FT is mainly associated with the de-twinning process of the small 5-FT. This can be introduced by TBs migration (Fig.\u00a03c, d and Supplementary Figs.\u00a012, 13) and/or surface diffusion (Fig.\u00a04a\u2013e and Supplementary Figs.\u00a012, 13). Nevertheless, the S5-FT remains relatively stable and maintains its symmetry even when attaching to SC NPs with a slightly larger number of atoms compared to the 5-FT, that is, it is relative difficult to trigger TBs migration of symmetrical 5-FT NPs. Additionally, van der Waals (vdW) force calculation (Supplementary Fig.\u00a014) shows that the force between 5-FT and SC NPs is significantly stronger than that between two 5-FT NPs. This is introduced by the structural difference between 5-FT and SC, i.e., a greater number of atoms can exhibit a close interatomic distance in the 5-FT/SC interactions compared to the 5-FT/5-FT (see Supplementary Fig.\u00a014 and related discussion). Thereby, the force exerted on the small S5-FT is minimal, which not only results in a diminished driving force to initiate TBs migration but also mitigates morphological modulation. Therefore, the relatively smaller critical transfer ratio for 5-FT/5-FT (0.72) than that of the SC/5-FT (\u22480.83) is determined by the stable twin structure and decreases the interaction force introduced by the small S5-FT. It is noteworthy that the particle size of various aggregated NPs investigated is smaller than 10\u2009nm (Fig.\u00a05). The above critical transfer ratio is supposed to vary slightly with further growth of the particle size of 5-FT, considering the size effect on 5-FT, which is stable with the size of 3\u201314\u2009nm owing to thermodynamics24,25,26.\n\nIn conclusion, our findings reveal the fundamental atomic-scale mechanisms governing the aggregation growth and evolution of 5-FT NPs. We have demonstrated that when a 5-FT attaches to small NPs (R\u2009<\u20090.83 for SC and R\u2009<\u20090.72 for 5-FT), surface diffusion of the small nanoparticles to the big 5-FT dominates the configuration evolution, resulting in the formation of S5-FT NPs and a decrease of the system energies. Nevertheless, when a 5-FT attaches to a larger SC NP, besides surface diffusion, TB migration induced de-twinning process contributes significantly to the evolution process. This dynamic interplay induces the formation of a SC or a simple twinned structure. Additionally, in the case of attachment to another larger 5-FT NP (R\u2009>\u20090.72), this results in the development of intricate 5-FT configurations.\n\nComprehending the mechanisms and dynamics underlying the process of particle aggregation growth is critical to constructing quantitative models to elucidate formation and evolution mechanisms of diverse twinned mineral materials in natural environments. Simultaneously, mastering the deterministic manipulation of NP growth holds the innovative synthesis pathways to fabricate twinned crystals endowed with precisely controlled morphologies and properties. Consequently, this endeavor provides guidance to unlock the full potential of twinned crystal structures and promotes materials design and synthesis.",
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+        {
+            "section_name": "Methods",
+            "section_text": "Synthesis of Au NPs: Gold(III) chloride trihydrate (HAuCl4\u2009\u2219\u20093H2O, \u226599.9 % trace metals basis), tetrakis(decyl)ammonium bromide (\u226599.0 %, TDAB), sodium borohydride (NaBH4, 98 %), 1-dodecanethiol (\u226598 %) and toluene (\u226599.5 %) were purchased from Sigma-Aldrich and used without further purification. The Au NPs were synthesized by the TDAB method6,35. 0.27\u2009mmol of TDAB was dissolved in 4\u2009mL toluene. The TDAB solution was mixed with 6\u2009mL of a 0.01\u2009M HAuCl4\u2009\u2219\u20093H2O aqueous solution for 1\u2009h. When the color of the toluene layer was changed to yellow due to the migration of AuCl4\u2212 ions, the only toluene layer was collected. Then, 200\u2009\u03bcL of a 26\u2009mM NaBH4 aqueous solution, which was prepared under an ice bath, was injected into the Au-TDAB toluene solution. After 20\u2009min, 800\u2009\u03bcL of 1-dodecanethiol was added to this mixture. The product was precipitated by excessive ethanol and then collected by centrifuge (3000\u00d7g).\n\nAfter centrifuge, the sample was dispersed in 5\u2009mL toluene solution, drop-cast onto a TEM grid, and labeled as the as-prepared sample. As shown in Supplementary Fig.\u00a01a\u2013c, the as-prepared sample is SC dominated Au NPs with an average size of 3.5\u2009\u00b1\u20090.6\u2009nm. To tune particles\u2019 structure and size, half (2.5\u2009mL) of the above toluene solution was sealed and kept in the dark at room temperature for approximately 2 months (Supplementary Fig.\u00a01d\u2013f), and another half (2.5\u2009mL) of the above toluene solution with centrifuged samples was cleaned four times with toluene to remove 1-dodecanethiol on the Au NP surface (Supplementary Fig.\u00a01g\u2013i). About 1/3 of NPs has evolved into 5-FT after staying for 2 months, and the particle size increases into 4.4\u2009\u00b1\u20091.4\u2009nm (Supplementary Fig.\u00a01e, f). After purifying for 4 times, besides the formation of some 5-FT NPs, significant aggregation of NPs was also detected (highlighted by yellow arrows in Supplementary Fig.\u00a01h). And the average particle size grows into 6.2\u2009\u00b1\u20092.6\u2009nm (Supplementary Fig.\u00a01i). To investigate aggregation growth and evolution of 5-FT nanoparticles, the sample after staying for 2 months was employed for further study. Particle sizes were statistically analyzed based on more than 300 particles for each sample, and the standard errors were employed (Supplementary Fig.\u00a01).\n\nTo investigate atomic-scale 5-FT NPs growth and evolution mechanisms by particle aggregation, electron-beam induced NPs aggregation method6 was employed. This method has been engaged to tune the formation kinetics of 5-FT Au nanoparticles by controlling the decomposition process of organic ligand coated on the Au nanoparticles under various electron-beam dose rates6. Here, a cold-field emission aberration-corrected TEM (Spectra 300, Thermal Fisher, USA), was employed at 300\u2009kV for the above in situ HRTEM imaging with an image frame rate of \u22480.5\u2009s. An optimized dose rate of \u2248(2\u20134) \u00d7 106 e nm\u22122 s\u22121 was applied. When the ratio between the longest TB and the shortest TB of 5-FT is smaller than 2.0, the 5-FT NT is referred to as a S5-FT. When the ratio is larger than 2.0, the 5-FT NP is referred to as an AS5-FT. Theoretically, the configuration of NPs evolves continuously under the employed electron-beam dose rate with time. Here, the terminal time was roughly determined according to the evolution rate of the NPs\u2019 configurations, including morphologies and twin structures. The ultimate configurations were obtained if their variation can be ignored within \u224820\u2009s. Correspondingly, most of the in situ experimental durations are \u2248150\u2013200\u2009s under the employed electron-beam dose rate. Slip directions of partial dislocations are determined by TBs migration directions based on the immediate prior and subsequent images.\n\nMD simulations were conducted to explore the evolution processes of both the three-dimensional configuration and energy of simulated models of Au NPs (Supplementary Figs.\u00a02, 3). Two types of models were employed in our experiment, and all invariable decahedral 5-FT NPs (left side, Supplementary Figs.\u00a02, 3) are the same, i.e., all surfaces of the big 5-FT are \\(\\{111\\}\\) planes with 1773 atoms. Model 1 was built with a 5\u2009nm decahedral 5-FT NP attached with SC NPs in a box with a side length of 20\u2009nm. The SC NPs with \u22482.6, 3.8, and 4.8\u2009nm (Supplementary Fig.\u00a02), present truncated octahedral morphologies and have corresponding numbers (Supplementary Table\u00a01) of 811, 1862, and 4033 atoms, respectively. Model 2 was built with a 5\u2009nm decahedral 5-FT NP attached with decahedral 5-FT NPs in a box with a side length of 20\u2009nm. The size and numbers of atoms of various 5-FT NPs are 3.2, 4.1, 5.0\u2009nm and 569, 1061, 1773, respectively (Supplementary Fig.\u00a03 and Supplement Table\u00a01). The models were visualized by OVITO software36.\n\nMD simulations were performed using the LAMMPS code37. The Au embedded atom potential developed by Ackland et al38. was employed in the simulation. This interatomic potential has been applied in previous investigations on the evolution of Au NPs during OA process successfully6. A Nos\u00e9\u2013Hoover thermostat39 in the canonical ensemble was used to maintain the temperature of 1100\u2009K, and the time step was configured to 1\u2009fs. The simulation temperature was determined based on the evolution kinetics of the aggregated nanoparticles and the computational resources and duration required for the MD simulation.\n\nAlthough the electrostatic force may be argued as the source of the jump connection during the orientation attachment4, in our experiment, when the distance between the two aggregated NPs is smaller than \u22482\u2009nm, the vdW force is supposed to be the determining force35, especially the evolution process after aggregation, such as the relative slip between NPs.\n\nvdW interactions between two NPs (NP1 and NP2) were performed based on Hamaker\u2019s approach. To describe the vdW interactions of heterogeneous structures such as 5-FT structures, each NP was divided into many small cubes with length (L)\u2009=\u20090.2882\u2009nm, which is the closest Au-Au separation distance. Next, the vdW interactions between the two NPs were calculated by the summations of each pairwise interaction.\n\nThe center positions of the small cubes of the NP1 and the NP2 were defined as (x1,i, y1,i, z1,i) and (x2,j, y2,j, z2,j), respectively.\n\nThe vdW interaction potentials between the small cubes of the NP1 and the small cubes of the NP2 were calculated based on the formulation shown in previous work that followed Hamaker\u2019s approach with geometrical consideration40. The formulations can produce the vdW interaction energy (V) between small cube-\u03b1,i and cube-\u03b2, j with parallel configurations at arbitrary separations.\n\nwhere A is the Hamaker constant 359.579 \u00d7 10\u221221\u2009J obtained from ref. 41, which calculated dielectric responses of Au in vacuum based on the Lifshitz theory. VR is the London-vdW interaction energy between cubes,\n\nwhere, r is the distance between an arbitrary point in the small cube-\u03b1,i and an arbitrary point in the small cube-\u03b2,j, v\u03b1,I, and v\u03b2,j are the volume of the respective bodies. For the numerical computations, the integrations of the Eq. (2) were modified by\n\nParameter am, bn, and cp were defined as below,\n\nwhere hx, hy, and hz were denoted, which are shown in Supplementary Fig.\u00a04.\n\nNext, the vdW interaction potentials (V) between NP1 and NP2 were calculated by\n\nThe interparticle distance between NP1 and NP2 (hd) was defined as the distance between closed atoms of each NC, which is shown in Supplementary Fig.\u00a05.\n\nBased on the vdW potential as a function of hd, the vdW force was calculated numerically.\n\nHere, \u0394d\u2009=\u20090.05\u2009nm was employed.",
+            "section_image": []
+        },
+        {
+            "section_name": "Data availability",
+            "section_text": "The data that support the findings of this study are available from the corresponding authors upon request.\u00a0Source data are provided with this paper.",
+            "section_image": []
+        },
+        {
+            "section_name": "References",
+            "section_text": "Sugimoto, T. Monodispersed Particles 2nd edn (Elsevier, 2001).\n\nPolte, J. Fundamental growth principles of colloidal metal nanoparticles\u2014a new perspective. Cryst. Eng. Comm. 17, 6809\u20136830 (2015).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDe Yoreo, J. J. et al. Crystallization by particle attachment in synthetic, biogenic, and geologic environments. Science 349, aaa6760 (2015).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLi, D. et al. Direction-specific interactions control crystal growth by oriented attachment. Science 336, 1014\u20131018 (2012).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nYe, H., Zhang, Z. & Wang, R. Nucleation and growth of nanocrystals investigated by in situ transmission electron microscopy. Small 19, 2303872 (2023).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nSong, M. et al. Oriented attachment induces fivefold twins by forming and decomposing high-energy grain boundaries. Science 367, 40 (2020).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nNelli, D. et al. Structure and orientation effects in the coalescence of Au clusters. Nanoscale 12, 7688\u20137699 (2020).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nZhu, G. et al. Self-similar mesocrystals form via interface-driven nucleation and assembly. Nature 590, 416\u2013422 (2021).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nPark, B. C. et al. Surface-ligand-induced crystallographic disorder\u2013order transition in oriented attachment for the tuneable assembly of mesocrystals. Nat. Commun. 13, 1144 (2022).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLi, J. et al. In situ atomic-scale study of particle-mediated nucleation and growth in amorphous bismuth to nanocrystal phase transformation. Adv. Sci. 5, 1700992 (2018).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nThanh, N. T. K., Maclean, N. & Mahiddine, S. Mechanisms of nucleation and growth of nanoparticles in solution. Chem. Rev. 114, 7610\u20137630 (2014).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBaumgartner, J. et al. Nucleation and growth of magnetite from solution. Nat. Mater. 12, 310\u2013314 (2013).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nHuang, B. et al. Identification of plasmon-driven nanoparticle-coalescence-dominated growth of gold nanoplates through nanopore sensing. Nat. Commun. 13, 1402 (2022).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nRose, G. Ueber die krystallformen des goldes und des silbers. Ann. Phys. 99, 196\u2013204 (1831).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nHofmeister, H. Fivefold twinned nanoparticles. Encyclopedia Nanosci. Nanotechnol. 3, 431\u2013452 (2004).\n\nCAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nZhou, S., Zhao, M., Yang, T. H. & Xia, Y. Decahedral nanocrystals of noble metals: synthesis, characterization, and applications. Mater. Today 22, 108\u2013131 (2019).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWu, J. Y., Nagao, S., He, J. Y. & Zhang, Z. L. Role of five-fold twin boundary on the enhanced mechanical properties of fcc Fe nanowires. Nano Lett. 11, 5264\u20135273 (2011).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWang, X. et al. Pd@Pt core\u2013shell concave decahedra: a class of catalysts for the oxygen reduction reaction with enhanced activity and durability. J. Am. Chem. Soc. 137, 15036\u201315042 (2015).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nPietrobon, B. & Kitaev, V. Photochemical synthesis of monodisperse size-controlled silver decahedral nanoparticles and their remarkable optical properties. Chem. Mater. 20, 5186\u20135190 (2008).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMaksimuk, S., Teng, X. & Yang, H. Roles of twin defects in the formation of platinum multipod nanocrystals. J. Phys. Chem. C 111, 14312\u201314319 (2007).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nClasen, P., Tiruvalam, R., Ma, S., Harmer, M. P. & Kiely, C. Effect of synthesis parameters on the gold nanostructures produced using an oleamine reductant. Microsc. Microanal. 13, 776\u2013777 (2007).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLakes, R. Materials with structural hierarchy. Nature 361, 511\u2013515 (1993).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nHan, H. et al. Multiscale hierarchical structures from a nanocluster mesophase. Nat. Mater. 21, 518\u2013525 (2022).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBarnard, A. S. et al. Nanogold: a quantitative phase map. ACS Nano. 3, 1431\u20131436 (2009).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nYoung, N. P., van Huis, M. A., Zandbergen, H. W., Xu, H. & Kirkland, A. I. Transformations of gold nanoparticles investigated using variable temperature high-resolution transmission electron microscopy. Ultramicroscopy 110, 506\u2013516 (2010).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKoga, K., Ikeshoji, T. & Sugawara, K. Size- and temperature-dependent structural transitions in gold nanoparticles. Phys. Rev. Lett. 92, 115507 (2004).\n\nArticle\u00a0\n    ADS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMarks, L. D. Surface structure and energetics of multiply twinned particles. Philos. Mag. A 49, 81\u201393 (1984).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nCleveland, C. L. et al. Structural evolution of smaller gold nanocrystals: the truncated decahedral motif. Phys. Rev. Lett. 79, 1873\u20131876 (1997).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nJohnson, C. L. et al. Effects of elastic anisotropy on strain distributions in decahedral gold nanoparticles. Nat. Mater. 7, 120 (2007).\n\nArticle\u00a0\n    ADS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nGryaznov, V. G. et al. Pentagonal symmetry and disclinations in small particles. Cryst. Res. Technol. 34, 1091\u20131119 (1999).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nSong, M., Wu, Z., Lu, N. & Li, D. Strain relaxation-induced twin interface migration and morphology evolution of silver nanoparticles. Chem. Mater. 31, 842\u2013850 (2019).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nPatala, S., Marks, L. D. & Olvera de la Cruz, M. Elastic strain energy effects in faceted decahedral nanoparticles. J. Phys. Chem. C 117, 1485\u20131494 (2013).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nSong, M. et al. Uneven strain distribution induces consecutive dislocation slip, plane gliding, and subsequent detwinning of penta-twinned nanoparticles. Nano Lett. 24, 1153\u20131159 (2024).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nZhu, Y. T. et al. Dislocation-twin interactions in nanocrystalline fcc metals. Acta Mater. 59, 812\u2013821 (2011).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLee, J. et al. Mechanistic understanding of the growth kinetics and dynamics of nanoparticle superlattices by coupling interparticle forces from real-time measurements. ACS Nano. 12, 12778\u201312787 (2018).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nStukowski, A. Visualization and analysis of atomistic simulation data with OVITO\u2014the open visualization tool. Model. Simul. Mater. Sci. Eng. 18, 015012 (2010).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nThompson, A. P. et al. LAMMPS\u2014a flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales. Comput. Phys. Commun. 271, 108171 (2022).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nAckland, G. J., Tichy, G., Vitek, V. & Finnis, M. W. Simple N-body potentials for the noble metals and nickel. Philos. Mag. A 56, 735\u2013756 (1987).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nNos\u00e9, S. A unified formulation of the constant temperature molecular dynamics methods. J. Chem. Phys. 81, 511\u2013519 (1984).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMaeda, H. & Maeda, Y. Orientation-dependent London\u2013van der Waals interaction energy between macroscopic bodies. Langmuir 31, 7251\u20137263 (2015).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nPinchuk, P. & Jiang, K. Size-dependent Hamaker constants for silver and gold nanoparticles. Proc. SPIE 14, 95491J (2015).\n\nDownload references",
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+        },
+        {
+            "section_name": "Acknowledgements",
+            "section_text": "This project is supported by the National Natural Science Foundation of China (No. 52471025, M.S. and 52101025, G.Z.), State Key Laboratory of Crystal Materials, Shandong University (No. KF2206, M.S.), Natural Science Foundation of Hunan Province (No. 2023JJ30684, M.S.), and the Changsha Municipal Natural Science Foundation (kq2202091, M.S.). We acknowledge the support from the State Key Laboratory of Powder Metallurgy, Central South University, Changsha, China. The support from the aberration-corrected spectra 300 in the State Key Laboratory of Powder Metallurgy is also greatly acknowledged.",
+            "section_image": []
+        },
+        {
+            "section_name": "Author information",
+            "section_text": "State Key Laboratory of Powder Metallurgy, Central South University, Changsha, Hunan, 410083, China\n\nMiao Song,\u00a0Dingri Zhang,\u00a0Dan Leng,\u00a0Ziang Yang,\u00a0Jiaxuan Chen,\u00a0Dan Li\u00a0&\u00a0Kechao Zhou\n\nState Key Laboratory of Crystal Materials, Shandong University, Jinan, Shandong, 250100, China\n\nMiao Song\u00a0&\u00a0Lei Wang\n\nDepartment of Mechanical and Aerospace Engineering, College of Engineering, University of Missouri, Columbia, MO, 65203, USA\n\nJaewon Lee\n\nShi-changxu Innovation Center for Advanced Materials, Institute of Metal Research, Chinese Academy of Sciences, Shenyang, Liaoning, 110016, China\n\nGang Zhou\u00a0&\u00a0Rui Yang\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nM.S. designed the experiments, conducted experiments and data analysis, wrote the manuscript, and supervised the study. D.Z. assisted with image processing and data analysis. D.Leng revised the manuscript. J.L. synthesized Au NPs and conducted force calculation. Z.Y., J.C., D.Li, Z.G., and L.W. contributed to the discussion of the results and commented on the manuscript. G.Z. conducted MD simulations and wrote the manuscript. R.Y. and K.Z. supervised the study and commented on the manuscript.\n\nCorrespondence to\n                Miao Song or Gang Zhou.",
+            "section_image": []
+        },
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+            "section_image": []
+        },
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+            "section_name": "Peer review",
+            "section_text": "Nature Communications thanks Francis Deepak and the other anonymous reviewers for their contribution to the peer review of this work. A peer review file is available.",
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+            "section_text": "Song, M., Zhang, D., Leng, D. et al. In situ atomic observations of aggregation growth and evolution of penta-twinned gold nanocrystals.\n                    Nat Commun 15, 9217 (2024). https://doi.org/10.1038/s41467-024-53501-0\n\nDownload citation\n\nReceived: 17 April 2024\n\nAccepted: 15 October 2024\n\nPublished: 25 October 2024\n\nVersion of record: 25 October 2024\n\nDOI: https://doi.org/10.1038/s41467-024-53501-0\n\nAnyone you share the following link with will be able to read this content:\n\nSorry, a shareable link is not currently available for this article.\n\n\n\n\n                            Provided by the Springer Nature SharedIt content-sharing initiative\n                        ",
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+            ]
+        },
+        {
+            "section_name": "This article is cited by",
+            "section_text": "Structural Chemistry (2025)",
+            "section_image": []
+        }
+    ]
+}

2b8c98fb229297a1262aa712f9c884323c7fbe1c918252cec11c83d0130a8dc7/metadata.json

@@ -0,0 +1,151 @@
+{
+    "title": "Hurricane Ida\u2019s blackout-heatwave compound risk in a changing climate",
+    "pre_title": "Hurricane Ida\u2019s blackout-heatwave compound hazard risk in a changing climate",
+    "journal": "Nature Communications",
+    "published": "15 May 2025",
+    "supplementary_0": [
+        {
+            "label": "Supplementary Information",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-59737-8/MediaObjects/41467_2025_59737_MOESM1_ESM.pdf"
+        },
+        {
+            "label": "Reporting Summary",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-59737-8/MediaObjects/41467_2025_59737_MOESM2_ESM.pdf"
+        },
+        {
+            "label": "Transparent Peer Review file",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-59737-8/MediaObjects/41467_2025_59737_MOESM3_ESM.pdf"
+        }
+    ],
+    "supplementary_1": [
+        {
+            "label": "Source Data",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-59737-8/MediaObjects/41467_2025_59737_MOESM4_ESM.xlsx"
+        }
+    ],
+    "supplementary_2": NaN,
+    "source_data": [
+        "/articles/s41467-025-59737-8#ref-CR15",
+        "https://doi.org/10.5281/zenodo.15012708",
+        "/articles/s41467-025-59737-8#Sec15"
+    ],
+    "code": [
+        "https://doi.org/10.5281/zenodo.15012708"
+    ],
+    "subject": [
+        "Civil engineering",
+        "Climate-change impacts",
+        "Natural hazards"
+    ],
+    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
+    "preprint_pdf": "https://www.researchsquare.com/article/rs-4096843/v1.pdf?c=1747393752000",
+    "research_square_link": "https://www.researchsquare.com//article/rs-4096843/v1",
+    "nature_pdf": "https://www.nature.com/articles/s41467-025-59737-8.pdf",
+    "preprint_posted": "28 Mar, 2024",
+    "research_square_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "The emerging tropical cyclone (TC)-blackout-heatwave compound hazard under climate change are not well understood. In this study, we employ future projections of TCs, sea levels, and heatwaves, in conjunction with power system resilience modeling, to evaluate historical and future TC-blackout-heatwave compound hazard risks in Louisiana, US. We find that the return period for a compound hazard event comparable to Hurricane Ida (2021), with approximately 35 million customer hours of simultaneous power outage and heatwave exposure in Louisiana, is around 278 years in the historical climate (1980-2005).  Under the emissions scenario SSP5 8.5 (SSP2 4.5), this return period may decrease by a factor of ~17\u00d7(10x) to 16.2 (28.4) years in the future climate (2070-2100). The significant increase in risk can be primarily attributed to projected escalations in heatwaves, which result in an approximate 5(2)-fold decrease in compound hazard return period, and in TC activity, which cause an estimated 2(1)-fold decrease in the return period. The findings contribute to our knowledge of and adaptation to compound climate hazards.Earth and environmental sciences/Climate sciences/Climate change/Climate-change impactsPhysical sciences/Engineering/Civil engineeringEarth and environmental sciences/Natural hazards",
+            "section_image": []
+        },
+        {
+            "section_name": "Additional Declarations",
+            "section_text": "There is NO Competing Interest.",
+            "section_image": []
+        },
+        {
+            "section_name": "Supplementary Files",
+            "section_text": "smncidacompoundMarch13.pdf",
+            "section_image": []
+        }
+    ],
+    "nature_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "The emerging tropical cyclone (TC)-blackout-heatwave compound risk under climate change is not well understood. In this study, we employ projections of TCs, sea level\u00a0rise, and heatwaves, in conjunction with power system resilience modeling, to evaluate historical and future TC-blackout-heatwave compound risk in Louisiana, US. We find that the return period for a compound event comparable to Hurricane Ida (2021), with approximately 35 million customer hours of simultaneous power outage and heatwave exposure in Louisiana, is around 278 years in the historical climate of 1980\u20132005. Under the SSP5-8.5 emissions scenario, this return period is projected to decrease to 16.2 years by 2070\u20132100, a ~17 times reduction. Under the SSP2-4.5 scenario, it decreases to 23.1 years, representing a ~12 times reduction. Heatwave intensification is the primary driver of this increased risk, reducing the return period by approximately 5 times under SSP5-8.5 and 3 times under SSP2-4.5. Increased TC activity is the second driver, reducing the return period by 40% and 34% under the respective scenarios. These findings enhance our understanding of compound climate hazards and inform climate adaptation strategies.",
+            "section_image": []
+        },
+        {
+            "section_name": "Introduction",
+            "section_text": "In August 2021, Hurricane Ida, a Category 4 storm, struck Louisiana with intense winds, heavy rainfall, and storm surges, resulting in widespread flooding and damage to the state\u2019s infrastructure systems. Subsequent to the hurricane\u2019s landfall, the state experienced a loss of ~200 million customer hours of electricity, affecting roughly 2.15 million customers for an average power outage duration of 96\u2009h. Data from the United States (U.S.) Department of Energy reveals that Hurricane Ida caused the most extensive power outage in Louisiana\u2019s history, largely surpassing Hurricane Katrina (Category 5; 2005) and Hurricane Laura (Category 4; 2020), which led to losses of approximately 140 million and 100 million customer hours of electricity, respectively1,2,3.\n\nFurthermore, a prolonged heatwave occurred in the aftermath of Hurricane Ida, particularly affecting households that lost power and thus had no air conditioning (3; 93% of Louisiana households used air conditioning in 2020 corresponding to ref. 4). Consequently, Louisiana residents experienced a total of 35 million customer hours of compound blackout-heatwave risk (with a heat index surpassing 37.8\u2009\u00b0C/100\u2009\u00b0F; 5). Customers exposed to the compound hazard endured an average of approximately 98\u2009h of heatwave conditions5. Prolonged heat exposure can cause hospitalization and mortality risks6, especially among vulnerable populations7. Understanding how often Ida-like compound blackout-heatwave events may occur is critical for the development of risk mitigation strategies for populations vulnerable to hurricanes.\n\nA \u201ccompound climate event\u201d can result in large impacts due to the combination of climate drivers and hazards such as floods, wildfires, heatwaves, and droughts8. Traditional risk assessment methods typically consider one hazard at a time, potentially leading to an underestimation of risk, since the physical drivers causing extreme events may exhibit spatial and/or temporal dependencies and interact to exacerbate the overall impact. Hurricanes or more generally tropical cyclones (TCs), as drivers of extreme wind, rainfall, and storm surge, inherently lead to compound impacts on coastal regions9 and are responsible for nine of the ten largest power outages in the United States over a recent two-decade period10. While extreme winds are the primary source of damage to power systems, the presence of storm surges and heavy rainfall resulted in extensive flood inundation during Hurricane Ida, which caused additional physical damage and hindered power system resilience as repair crews were unable to access affected areas2. In addition, sea-level rise (SLR) may intensify coastal flood inundation by extending and prolonging the flood coverage, further exacerbating power system damage and delaying recovery operations.\n\nDue to the seasonal peak of intense heat being ahead of that of major TCs, TC-heatwave compound events have so far been rare worldwide11. However, a previous study12 found that for Harris County (a portion of Houston situated on higher ground and affected by hurricane winds), Texas (TX), the percentage of residents experiencing 5-day TC-blackout-heatwave compound hazard conditions could increase by a factor as large as 23 over the course of the 21st century under the high emissions scenario RCP8.5. Also, in recent years, TC-heatwave compound events have happened in the Gulf Coast region. Hurricane Ida may represent the first hurricane landfall on the mainland United States associated with a long-lasting (i.e., multi-day), large-scale blackout-heatwave compound hazard (during Hurricane Laura the state-average heat index was also high but did not reach the threshold of 37.8\u2009\u00b0C/100\u2009\u00b0F). During Hurricane Ida and Laura, at least eleven and eight Louisianans, respectively, died of heat-related illnesses1,13. Investigating this emerging compound threat, enhanced by climate change, will contribute to our knowledge of and adaptation to compound climate hazards.\n\nIn this study, we integrate hazard projection and power system analysis to examine TC-blackout-heatwave compound risk for Louisiana over the 21st century under the combined influence of SLR and changes in heatwave and storm climatology. We highlight the change in the return period/recurrence interval of Ida-like compound events from the historical to future climates. We further quantify the relative importance of the change in various climatological variables (i.e., heat stress, sea level, storm frequency, storm intensity) in driving the changes in the compound risk.\n\nOur framework is an extension of the previous study in ref. 12 to incorporate multiple hazards, including storm surge, rainfall, and SLR, in addition to wind and heatwave, to more comprehensively model TC-blackout-heatwave compound risk, for the entire State of Louisiana under various climate conditions. Specifically, we combine projections of heatwaves14, TC hazards (including wind, storm surge, and rainfall15), and SLR16,17,18, driven by CMIP6 GCMs14 under a moderate (Shared Socioeconomic Pathway 2\u20134.5) and a high (SSP5-8.5) emissions scenarios, to assess both a likely scenario and an upper bound of the risk. We generate a large number of compound hazard events (~30,000 stochastic sequences) based on the projections for historical (1980\u20132005) and future (2081\u20132100) climates to estimate how hazard probabilities may change over the 21st century (Methods). Then we utilize a physics-based power outage and restoration model for Louisiana to simulate wind/surge/rainfall-induced power system failure and recovery for each hazard event, to estimate the TC-blackout-heatwave compound risk. In doing so, we extend the existing wind-impact-only simulation method (county level12,19) to a wind-rainfall-surge coupled framework for power damage and recovery process modeling to consider a larger study area including coastal regions (state level; Methods). Considering the uncertainty surrounding the impact of climate change on the frequency of TCs making landfall along the Gulf Coast, we assume a constant TC frequency but also assess the sensitivity of the compound risk to TC frequency projection. To focus on the impact of climate change, we assume that the power system, population distribution, and recovery plans in the study region will remain unchanged. However, we assume that the coastal levees will be elevated following design guidance, as this enhancement may be considered necessary to prevent the region from frequent inundation due to SLR (\u201cMethods\u201d).",
+            "section_image": []
+        },
+        {
+            "section_name": "Results",
+            "section_text": "We first examine power outage simulations of the historical cases of Hurricanes Ida and Laura, which are the two major events over the last decade that caused widespread power disruptions in Louisiana1. Ida devastated the eastern half of Louisiana, which is more densely populated (including the city of New Orleans), whereas Laura grazed the western side. Ida destroyed 31,000 poles (reported by local utility company Entergy20) that carry lower-voltage distribution lines in the neighborhoods, twice as many as those in Hurricane Laura (14,000 poles) and Katrina (2005; 17,000 poles).\n\nAs shown in Fig.\u00a01a and b, the model\u2019s estimates for the overall impact of Hurricanes Ida and Laura on Louisiana compare relatively well with the observation. Hurricane Ida led to 47% (48% in simulation) of customers being out of power within the first 24\u2009h, and it took ~10 days (11 days in simulation) for 90% of customers to restore power. Meanwhile, up to 60% of Louisiana customers were under heatwave conditions within 6 days after Hurricane Ida\u2019s landfall. About 42% independent customers experienced compound power outage and heatwave hazards for at least one day after the hurricane\u2019s landfall, and the percentage of customers experiencing the compound hazard surpassed 15% during a period of time (see Supplementary Fig.\u00a01). Hurricane Laura led to 27% (29% in simulation) of customers being out of electricity initially and it took ~6 days (8 days in simulation) for 90% of customers to restore power (see Supplementary Fig.\u00a02 for spatial distribution).\n\na Ida and b Laura. The red curve shows median values, with 5% to 95% quantile range shown by shade and the blue curve shows the observation. The yellow curve in (a) shows the percent of customers impacted by heatwaves (value reads the right axis). c Comparison of observed and simulated spatial distribution of power outage for Hurricane Ida. Source data are provided as a Source Data file.\n\nTo measure the overall severity of the blackout associated with each TC, we compute the cumulative interruption hours throughout Louisiana (the total of all customers\u2019 power outage duration), a commonly used metric in evaluating power system reliability21. The model simulation estimates in total 189 (156\u2013242; \u00b13 standard deviations) million power interruption hours for Ida, which is consistent with the observed 206 million hours, and 110 (77\u2013153) million power interruption hours for Laura, which compares relatively well with the observed 99 million interruption hours. As a comparison, Hurricane Katrina led to ~140 million power interruption hours. The model estimation for the spatial and temporal distribution of power outage also correlates well with observations (the average relative error is <10% between the modeled and observed county-level power outage), as illustrated in Fig.\u00a01c for the power outages at 24\u2009h, 5 days, and 8 days after landfall at the county level for Hurricane Ida.\n\nIntegrating power outage and recovery modeling with projections of future TC, SLR, and heatwaves, we examine the TC-induced blackout-heatwave compound risk in Louisiana. We generate 10,000 simulations of synthetic hazard events for each of the historical (1980\u20132005) and future (2081\u20132100) SSP5-8.5 and SSP2-4.5 scenarios. Each stochastic simulation includes a continuous 20-year sequence of TC occurrences, along with the physical simulation of TC tracks, wind speeds, rainfall amounts, storm surge levels, and heatwaves. We track each customer\u2019s exposure (i.e., duration) to blackout or compound blackout-heatwave hazard in the power outage and recovery modeling process for each synthetic hazard event. Then, we integrate the customer-level results to obtain state-level statistics and estimate the return periods (i.e., reciprocal of annual exceedance probability) of event total interruption hours for the historical and future climates. As demonstrated by the substantial shift of the return period curves (Fig.\u00a02), the power outage risk will increase dramatically from the historical to the future climate. Specifically, the historical return period of a power outage of 206 million customer hours, as in Hurricane Ida, is 64 years (Table\u00a01). The return period of a power outage like Hurricane Ida\u2019s total outage is projected to be 35.8 years in the future under the SSP5-8.5 emissions scenario, compared to 38.2 years under SSP2-4.5. The total power outage for an event with Ida\u2019s historical return period of 64 years is approximately 413 million customer hours under SSP5-8.5 and 265 million customer hours under SSP2-4.5. The return period of a TC-blackout-heatwave compound hazard of 35 million customer hours, as in Hurricane Ida, is 278 years in the historical climate. This return period is expected to decrease in the future climate to 16.2 years under SSP5-8.5 (~17\u00d7 reduction) and 23.1 years under SSP2-4.5 (~12\u00d7 reduction). A compound hazard event with Ida\u2019s historical return period of 278 years is projected to cause about 435 million customer hours of impact under SSP5-8.5 and 138 million under SSP2-4.5. Such an event would induce an average blackout-heatwave compound hazard duration of approximately 8.8 days (SSP5-8.5) or 2.8 days (SSP2-4.5) for each of Louisiana\u2019s 2.13 million customers.\n\na interruption hours under power outage, b interruption hours under blackout-heatwave compound hazard. The red curve shows median values for SSP5-8.5 for the future climate, with the 5\u201395% quantile range shown by shade, the yellow curve represents SSP2-4.5 for the future, and the blue for the historical climate. The dashed lines highlight Hurricane Ida\u2019s power outage and compound risk levels. Source data are provided as a Source Data file.\n\nThe power outage level under SSP2-4.5 is similar to that under SSP5-8.5 at Ida\u2019s return period or shorter, although the power outage level becomes higher in SSP5-8.5 at longer return periods (Fig.\u00a02a), due to higher extreme TC hazards and SLR in SSP5-8.5. The difference between the two emissions scenarios is larger for the compound risk. Specifically, the return period of the compound hazard impact at Ida\u2019s level under SSP5-8.5 is slightly shorter than that under SSP2-4.5, and the return period of larger compound impacts becomes dramatically shorter under SSP5 8.5 (Fig.\u00a02b), due to combined effects of larger increases in extreme heatwaves, TC hazards, and\u00a0the sea level under SSP5-8.5. For example, the return period of extremely severe compound events, such as those with triple the impact of Hurricane Ida (i.e., 100 million customer-hours of compound hazards), is expected to be 2.5 times longer under SSP2-4.5 compared to SSP5-8.5. However, for less severe events, such as those with a third of Ida\u2019s impact (i.e., 10 million customer-hours of compound hazards), we do not find a statistically significant difference in the\u00a0event return period/frequency between the two emissions scenarios. These findings suggest that the combined effects of global warming and increasing hurricane intensity amplify the risk of the most extreme compound events. Nonetheless, the moderate emission scenario may still lead to a similar increase of frequency for events of Ida\u2019s impact magnitude, compared to the high emissions scenario.\n\nTo investigate the spatial distribution of the compound risk, we estimate the county-average compound hazard interruption days for each synthetic hazard event. Figure\u00a03 shows the compound hazard interruption days with Ida\u2019s historical return period of 278 years for each county in Louisiana in the historical and future climates. The coastal counties face a greater compound risk than inland counties for both historical and future climates (Fig.\u00a03a\u2013c). For example, the counties with an average compound hazard impact larger than 20 days in the future climates are mostly coastal counties. Coastal counties often face a greater compound risk since hurricane winds reach peak strength before the storm makes landfall, and storms weaken as they move inland, causing less damage to the inland power infrastructure. Moreover, the floods induced by storm surge and heavy rainfall can severely damage coastal power sectors. The flooding also hampers the recovery efforts of local contractors by submerging electrical components in water and obstructing local traffic and logistics with debris.\n\na Historical average interruption, b future SSP5-8.5 average interruption, and c future SSP2-4.5 average interruption, for each county in Louisiana for a compound hazard event with a 278-year return period. d Distribution of affected Orleans Parish customers\u2019 compound hazard duration under a 278-year event. The solid lines show the percentage of affected customers experiencing compound hazard up to a certain temporal length in the historical and future climates. Source data are provided as a Source Data file.\n\nThe general spatial disparities in compound risks are also substantial and will increase with climate change. For example, in the historical climate, the most impacted county may face on average a 1.8-day compound hazard with the return period of 278 years, and the least impacted county does not face any compound risk (Fig.\u00a03a). In the future, under the SSP5-8.5 scenario, the county with the greatest impact may face an average of 12.7 days of compound hazard exposure for an event with the return period of 278 years. Under the SSP2-4.5 scenario, this average is 3.1 days. Conversely, the least impacted area is projected to experience only 1.1 days under SSP5-8.5 and 0.1 days under SSP2-4.5 (Fig.\u00a03b\u2013c). To assess the spatial disparity in the compound risk, we use the Gini coefficient22, a statistical measure of inequality commonly applied to income, wealth, or consumption distribution. The coefficient ranges from 0 (perfect equality, where all counties face the same average compound hazard duration) to 1 (full inequality, where only one county faces the hazard). In the historical climate, the Gini coefficient is approximately 0.312. However, under future scenarios, it increases to 0.632 for SSP5-8.5 and 0.411 for SSP2-4.5. These results suggest that intensifying hurricane hazards disproportionally impact coastal regions and vulnerable communities distant from substations, and thus, climate change is likely to exacerbate existing disparities and inequalities in TC-blackout-heatwave compound risks across Louisiana.\n\nWe also examine the distribution of compound hazard durations for residents in densely populated counties. Figure\u00a03d illustrates the distribution of compound hazard interruption days for affected customers in Orleans Parish, for a\u00a0278-year\u00a0compound event. In the historical climate, only 3% of affected customers may experience a compound hazard lasting more than 120\u2009h (5 days). In the future, under the SSP5-8.5 scenario, nearly 60% of affected customers are projected to face a compound hazard exceeding 120\u2009h, with nearly 30% experiencing durations longer than 240\u2009h (10 days) and 10% encountering durations exceeding 360\u2009h (15 days). Under SSP2-4.5, 20% of affected customers may face compound hazards exceeding 120\u2009h, 3% may experience durations longer than 240\u2009h, and no customers are expected to encounter durations beyond 360\u2009hours. Hence, climate change not only increases the average compound hazard impact but also intensifies the tail risk that vulnerable residents may encounter, especially under the high emissions scenario.\n\nThe change in the compound risk is driven by the change in three climate factors: 1) heatwaves (heat index) 2) TC climatology, and 3) the sea level. As we assume that TC frequency remains unchanged in the future, the changes in TC climatology include changes in TC characteristics, particularly intensity (which drives changes in wind, storm tide, and rainfall). To determine the relative effect of the changes in these factors, we estimate the changes in the compound risk due to changes in temperature, SLR, and TC climatology, respectively, by adjusting each variable to its future value or distribution and calculating the resulting return period of Ida\u2019s compound hazard (i.e., 35 million customer hours of simultaneous power outage and heatwave impact), as shown in Fig.\u00a04a.\n\na. Relative impact of each climate change factor assuming a consistent TC frequency. b Sensitivity to TC frequency change. Note that the combined impact of all climate factors on Ida\u2019s compound hazard return period is highly non-linear, and thus, the sum of the relative impact of individual factors does not equal the total impact. Data are presented as the mean value with 10\u201390% quantile. 10,000 stochastic samples of storm sequences for each climate case are used to derive the statistics. Source data are provided as a Source Data file.\n\nAs discussed earlier, when all climate change factors are considered, Ida\u2019s return period is projected to decrease from 278 years in the historical climate to 16.2 years under SSP5-8.5 and 23.1 years under SSP2-4.5 in the future climate. Among these factors, changes in heatwaves are the largest contributors to this reduction. Due to heatwave changes alone, Ida\u2019s return period would drop to 47.6 years under SSP5-8.5 and 84.3 years under SSP2-4.5, representing approximately a five-fold and three-fold decrease, respectively. This substantial impact is driven by dramatic increases in temperature and humidity: the annual number of heatwave days (above 37.8\u2009\u00b0C) is expected to rise eightfold from the historical climate to the future climate, based on the ensemble average of the six GCMs for the study region.\n\nChanges in TC characteristics, especially intensity also contribute to the reduction, decreasing Ida\u2019s return period to 167.8 years under SSP5-8.5 and 185.2 years under SSP2-4.5. By comparison, the impact of SLR is relatively small, reducing Ida\u2019s return period to 251.2 years under SSP5-8.5 and 263.3 years under SSP2-4.5. SLR appears to have a relatively low impact because we assume the levees along the coast will be elevated. Also, the impact of SLR is limited to coastal regions, and it is averaged out when the compound hazard impact is calculated for the entire state. The contribution of the various climatological drivers to future compound risk is consistent across the two different emission scenarios.\n\nConsidering that the projection of TC frequency is subject to considerable uncertainty23,24, we assumed a constant TC frequency in above analyses. Here, we investigate the sensitivity of the estimated compound risk to the projection of TC frequency change. In one scenario, we apply the TC frequency in the applied TC\u00a0model15, which projects relatively high increases in TC frequency in the future climates. Under SSP5-8.5, Ida\u2019s return period decreases to 7.9 years, and under SSP2-4.5, it decreases to 15.2 years, compared to 16.2 years (SSP5-8.5) and 23.1 years (SSP2-4.5) when accounting for all climate change factors except TC frequency changes. In another scenario, we consider a 30% decrease in TC frequency, the lower bound of TC frequency projections ensembled in ref. 24. In this case, Ida\u2019s return period becomes 28.4 years under SSP5-8.5 and 40.6 years under SSP2-4.5. While longer than the projections with increased or constant TC frequency, these return periods represent a similarly dramatic decrease from 278 years in the historical climate. This sensitivity test indicates the relatively small impact of TC frequency change compared to the combined effects of other climate change factors.",
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+        {
+            "section_name": "Discussion",
+            "section_text": "This analysis highlights the substantial increase in the frequency of Ida-level extreme power outage-heatwave compound hazards over time, resulting from the combined effect of temperature increase, SLR, and storm climatology change under climate change. Linear interpolation suggests that Hurricane Ida\u2019s return period has decreased from 278 years around the end of the last century to 225.6 years under SSP5-8.5 and 227.0 years under SSP2-4.5 in the 2020\u2009s, representing approximately a 19% reduction over the past two decades. This real-life observation of an emerging climate compound hazard motivates further research on projecting future compound climate risks and developing strategies to mitigate climate risks for various regions around the world.\n\nWhen examining the impact of various climate scenarios, such as the high emission scenario SSP5-8.5 and the moderate emission scenario SSP2-4.5, it appears that the risk associated with Ida-scale compound hazard events may not exhibit substantial difference. This result indicates that utility companies urgently need to prepare for the compound events to prevent major impacts, regardless of whether a moderate or high emissions scenario is considered. On the other hand, the frequency of larger compound impacts is expected to be significantly lower under the moderate emissions scenario. Moreover, the duration of interruptions caused by compound hazards will also be reduced with moderate emissions. This result highlights the importance of strengthening climate change mitigation policy to reduce the impact of extreme climate hazards.\n\nWe do not consider the potential change in the power grid or its operation in the future. In the future, localized solutions, including backup generators and solar panels, can provide temporary support to residents who lose power from the main grid, thus mitigating the impacts of compound hazards25. These solutions can help reduce the exposure of vulnerable populations to the effects of power outages and extreme heat, thereby lessening the overall impact of compound hazard events. However, backup generators and solar panels may be cost-prohibitive, limiting their effectiveness in reducing heat stress. Proactive policy measures, such as subsidies or tax breaks, may be needed to make these interventions accessible and effective for vulnerable populations. Also, equipping relief centers with reliable cooling and backup power systems can further enhance emergency response capacity. Prioritizing these interventions based on estimated compound risk can guide effective resource allocations. From the main power grid design perspective, adopting effective strategies like burying distribution networks and developing distributed power systems25 can bolster the resilience of power infrastructure against extreme weather events.\n\nWe also do not consider the potential changes in demographics and human habitat. As extreme climate events become more frequent, coastal megacities are also expected to develop rapidly26,27. Encouraging climate-resilient urban design principles that prioritize green spaces, water management systems, and heat-resistant building materials can enhance cities\u2019 resilience against compound risks28. Also, the implementation of advanced early warning systems and preparedness measures, combined with public awareness campaigns, can help minimize potential impacts on vulnerable communities29,30. Moreover, changes in population patterns, such as urbanization in low-elevation coastal zones and the concentration of populations in areas vulnerable to climate hazards, can influence the impact of compound hazards, emphasizing the need to account for these demographic shifts when devising adaptation strategies26,31.\n\nQuantifying the reliability and resilience of infrastructure systems under the impact of future compound hazards is essential for climate change adaptation. Developing an integrated risk assessment framework that combines climatology, civil and electric engineering, urban planning, and social sciences is crucial for comprehensively understanding the interconnected nature of compound risks and their societal impacts, and the formulation of effective mitigation strategies32,33. For example, conventional statistical methods may fail to detect significant changes in compound risk, especially for the most extremes. Our analysis shows that the intensity of relatively frequent hazards may not change significantly in the future, especially under moderate emissions scenarios. However, if such a conclusion for frequent, observable events is statistically extrapolated to that for extreme events, we may transform events like Ida, which could have been foreseen and prepared for, into \u201cblack swan\u201d events\u2014unpredictable extreme disasters with unimaginable losses. Only physics-based modeling integrating climate and hazards projection and infrastructure/social system analysis may provide reliable estimates of future risks. This multidisciplinary perspective is essential for capturing the complex interactions between different hazards and their cascading effects on infrastructure systems and society as a whole, ultimately enabling the development of robust and resilient strategies to mitigate the impacts of compound hazards. Also, given various uncertainties in the projections of climate change and social development, there is a need for continuous refinement and updating of risk analysis techniques as improved modeling approaches and new data become available. By adopting a comprehensive approach that integrates various disciplines and continuously enhances our understanding of compound risks, we can work towards developing effective adaptation strategies for a sustainable future in the face of a changing climate.",
+            "section_image": []
+        },
+        {
+            "section_name": "Methods",
+            "section_text": "We use the synthetic TC hazard dataset generated in ref. 15 for the North Atlantic basin and select the TC tracks passing within 300\u2009km of Louisiana, with a maximum wind speed of at least 22\u2009m/s. The dataset contains synthetic TC tracks generated with the statistical-deterministic TC model34, which has been applied to TC hazard assessment9,35,36. The synthetic TC tracks for the historical period (between 1980 and 2005) were generated based on the National Centers for Environmental Prediction (NCEP) reanalysis. The dataset also contains bias-corrected and weighted-average climate projections of TCs for the future period (2070 to 2100) under Shared Socioeconomic Pathway (SSP) emissions scenarios, SSP5 8.5 and SSP2 4.5. The dataset was generated based on projections from six CIMP6 models (selected given data availability and following previous studies): Canadian Earth System Model (CanESM5), Centre National de Recherches M\u00e9t\u00e9orologiques Climate Model (CNRM-CM6-1), UK Earth System Model (UKESM1-0-LL), EC-Earth3, IPSL-CM6A-LR (Institut Pierre-Simon Laplace Climate Model), and Model for Interdisciplinary Research on Climate (MIROC6). The TC storm tides were modeled in ref. 15 using the Advanced Circulation (ADCIRC) hydrodynamic model37,38. We extract peak storm tides at nodes (~1\u2009km resolution) along the coastline of Louisiana for each TC and match these to the county level. The rain fields were simulated in ref. 15 for each synthetic TC using the physics-based Tropical Cyclone Rainfall (TCR) model39. We apply area-averaged TCR estimates at the county level, and we employ the maximum 24\u2009h rainfall accumulation from each storm event, since the 24-hour storm duration is often utilized for rainfall risk assessment39,40.\n\nTo perform sequential risk analysis, we generate 10,000 stochastic samples of storm sequences for each of the historical and future climate conditions. These samples were derived by sampling storms (according to a Poisson process with a rate as the TC annual frequency) and their associated hazards from the TC hazard datasets described above. Each stochastic sequence consists of 20 consecutive years of TC activity. For the primary analysis in this study, we maintain a constant TC frequency in the future climate. For the sensitivity analysis, we consider the increased TC frequency projected by the statistical-deterministic TC model in ref. 15 and the decreased TC frequency by up to 30% projected by a range of climate models ensembled in ref. 24.\n\nFor each sampled storm, we generate the spatial-temporal wind field, employing the classical Holland wind profile41 and accounting for the effects of surface friction and large-scale background wind following ref. 42, and converting one-minute mean winds to 3\u2009s wind gusts using gust factors43. We estimate the coastal flood area by comparing the height of peak storm tide (if over levee height) to the ground surface elevation specified by the USGS 30\u2009m DEM44, assuming that areas would be inundated when the storm tide exceeds the ground elevation.\n\nIn Louisiana, the actual seawall heights vary largely along the coastline, ranging from 2 to 5 meters and often changing over short distances. Due to the difficulty in acquiring the precise data, our simulations do not incorporate partially available measurements45,46,47. We assigned the current seawall level based on estimated 100-year flood level (estimated in ref. 15) for each coastal county in Louisiana, according to the typical design guidance. For example, the 100-year flood level for New Orleans is approximately 3.4 meters above the North American Vertical Datum of 1988 (NAVD 88)9. This approximation introduces a degree of inaccuracy into our flood modeling. Acknowledging this limitation, we subsequently focused on binary flood data\u2014whether a flood occurs or not\u2014when developing our power system damage and recovery models. We observe that the occurrence of flooding is a critical factor that largely hinders the restoration efforts of the power system in coastal counties. However, the inundation depth of the flooding appears to have a less substantial impact. When compared to the areas affected by the TC\u2019s wind and rainfall, the storm surge flooded regions are generally smaller. Therefore, the majority of the structural damage to the power system may not be caused by coastal flooding.\n\nThe future coastal levee plan is uncertain. In the future climate simulations, we assume the coastal levee will be elevated by ~ 2\u2009m, based on the historical 100-year return level plus one percentile SLR. This design strategy is commonly used by governmental agencies to plan the seawall height, and it is within the framework proposed by the U.S. Army Corps of Engineers for the New Orleans Region, Lafayette, and Lake Charles47. A sensitivity test was performed on future compound risks given different elevations of the coastal levee from 0-3 meters above the current level. If the levee were not elevated, the surge impact on the compound risk would be substantially higher than estimated in this study. On the other hand, when the levee is elevated by higher than 2\u2009m, the estimated compound risk is not sensitive to the variation of the assumed levee increment up to the test\u00a0case of\u00a03 meters (see Supplementary Fig.\u00a03). The generated wind, rainfall, and coastal flood conditions from each sampled storm drive the power grid outage and recovery analysis.\n\nFollowing ref. 11, the daily HI is determined as a function of daily maximum near-surface (2 m) air temperature, daily mean specific humidity, and daily mean surface pressure. To maintain consistency with the TC simulation, we obtain these data for Louisiana from the NCEP reanalysis and the six GCMs stated above during and after landfall for each sampled synthetic storm (each synthetic storm is associated with a climatological time of occurrence and development). The future HI projected by the GCM is bias-corrected12 by adding the difference between the NCEP reanalysis and the GCM-estimated historical HI. According to the historical analysis in ref. 11, the HI will drop upon TC landfall and will recover to the ambient average within around ten days. To account for this dependence between TCs and heatwaves, we add the composite of the impact of TC passage to the meteorological variables used to calculate the HI, where the composite impact is estimated based on historical data (Fig.\u00a03a in ref. 11).\n\nWe employ sea-level projections produced by the Intergovernmental Panel on Climate Change Sixth Assessment Report16,18 (AR6) using the Framework for Assessing Changes To Sea-level17 (FACTS). Localized probabilistic SLR projections under the SSP5-8.5 and SSP2-4.5 emission scenarios with \u201cmedium confidence\u201d are incorporated in this analysis (there are two confidence levels in the datasets, which are low and medium levels). The local sea level projection takes into account ground uplift or subsidence, oceanographic effects, and spatially variable responses of the geoid and the lithosphere to shrinking land ice. The projection of SLR was developed for tide-gauge stations. For each TC sequence realization, we first sample a near-by\u00a0SLR time series (a realization) from the projection\u00a0for each county. Then, we add the SLR to the storm tide level at each time point for each county.\n\nWe apply a physics-based power system model, which explicitly simulates component-level damage to predict the total power outage, accounting for the effects of future evolving factors, e.g., climate change, infrastructure upgrade, and utility maintenance. The physics-driven modeling of the power system allows us to better understand the impact of climate change and effectiveness of risk mitigation measures compared to if we used purely data-driven models48,49.\n\nSpecifically, we extend the power grid outage and recovery model developed by refs. 12,19 to simulate TC impact on the electric power system in Louisiana (see the methodology diagram in Supplementary Fig.\u00a04, power topology in Louisiana in Supplementary Figs.\u00a05, 6, and electric utility service areas in Louisiana in Louisiana Public Service Commission50). The power grid failure model first applies probabilistic fragility functions to estimate the damage states of five main vulnerable component types of the power network: transmission substations, transmission lines, distribution nodes, distribution lines, and local distribution circuits. Component failures alter the power grid topology and may separate the power grid into disconnected sub-grids. A direct-current (DC) flow simulation is then performed to capture the power availability in each sub-grid (similar to approaches in refs. 51,52,53,54). The power system is open and connects with systems outside the study area via transmission lines; the performance of the power grid outside the study area is assumed to be under normal operation.\n\nThe fragility curves in refs. 12,19 only considered the wind damage. Here we extend the fragility functions to consider the effects of coastal floods and rainfall. For example, the probability of failure of a substation given specific wind, rainfall, and coastal flood levels is estimated based on a log-normal fragility function as Eq. (1):\n\nwhere hazard (H/h) is considered as a linear combination of wind speed (w), rainfall amount (r), and flood condition (f, flooded or not; Boolean variable) with two parameters \u03b1 and \u03b2. With the shape (\u03c3i) and location (\u03bci) parameters, the log-normal distribution describes the probability of potential damage (D) in each of four states (di), i.e., i\u2009=\u2009{low, moderate, severe, complete} damage. Fragility function refers to the latent distribution of a component\u2019s ability to withstand outer forces (hazard). Some components may not withstand any force at all, while others can withstand very large outer force. Given a certain outer force, the probability of damage to the component is equal to the integral of fragility from 0 to that force level, i.e., the probability that the strength of the component is lower than outer force. The fragility functions for other components (support structures, distribution nodes, poles, conductors, and circuits) are similarly modeled with exponential, logistic, or uniform distributions. These fragility functions are similar to those in refs. 12,19 except that the effects of rainfall and flood are incorporated. The parameters are estimated by the Markov chain Monte Carlo (MCMC) method to minimize the mean squared error between simulated and observed county-level power outages1 under Hurricanes Laura and Ida with equal weight.\n\nThe recovery model, developed based on emergency response plans and operational data, applies estimated recovery resources based on a priority-oriented strategy to repair damaged transmission substations, transmission lines, and critical facilities vital to public safety, health, and welfare before local distribution networks12,19. Debris should be removed before utilities become able to reinstate the power system. This debris-cleaning time is sampled from a uniform distribution between 48 and 72\u2009h (estimated from utility reports)2. We also account for that, without structural failure of the distribution system, residents may turn on the main power switch themselves 24\u201348\u2009h after being flooded55.\n\nThere is a chance that TCs will make landfall in sequence, and the second TC comes before the damage caused by the first TC is fully recovered56. We account for this temporal compounding effect in our power system outage and recovery analysis. For each sampled sequential hazard time series, the initial state of the power system when a TC arrives is set based on the condition of the restoration state from the previous TC. If the power system is indeed not fully recovered from the previous TC impact, the emergency response plans following the second TC are also adjusted considering the recovery process for the first TC. Specifically, the response plans will re-evaluate and prioritize the restoration tasks and redirect the repair efforts based on this updated priority list.\n\nThe power grid outage and recovery models were calibrated (to determine the model parameters) for the study area using observed power outage data for Hurricane Ida and Laura using simulated wind and observed rainfall57 and flood58. The same wind field modeling method applied to the synthetic storms is used for these two historical storms with storm characteristics (i.e., track, intensity, and size) taken from the extended best track data59.\n\nFurther information on research design is available in the\u00a0Nature Portfolio Reporting Summary linked to this article.",
+            "section_image": []
+        },
+        {
+            "section_name": "Data availability",
+            "section_text": "The transmission network data is from Homeland Infrastructure Foundation Level Database (HIFLD). The distribution network data is from Louisiana Public Service Commission (LPSC). The hurricane hazard data were obtained from Ref. 15. The generated power system failure statistics are deposited to Github and Zenodo (https://doi.org/10.5281/zenodo.15012708). Source Data for figures are provided with this paper.\u00a0Source data are provided with this paper.",
+            "section_image": []
+        },
+        {
+            "section_name": "Code availability",
+            "section_text": "The codes for simulating power system failures are deposited to Github and Zenodo (https://doi.org/10.5281/zenodo.15012708).",
+            "section_image": []
+        },
+        {
+            "section_name": "References",
+            "section_text": "Hurricane Response Record, Office of Cybersecurity, Energy Security, and Emergency Response, U.S. Department of Energy (2021).\n\nHurricane Ida Power Restoration, Utility Report, Entergy Link: https://www.entergynewsroom.com/article/entergy-system-hurricane-ida-update-9-2-21-9-m/ (Last visited: 11/25/2024) (2021).\n\nNicholas Bogel-Burroughs and Katy Reckdahl. The Greatest Killer in New Orleans Wasn\u2019t the Hurricane. It Was the Heat. New York Times (2021).\n\nU.S. Energy Information Administration. State air conditioning. Retrieved from https://www.eia.gov/consumption/residential/data/2020/state/pdf/State%20Air%20Conditioning.pdf (2020).\n\nNational Weather Service, Heat Watch vs. Warning Link: https://www.weather.gov/news/250310-heat-hazard (Last visited 4/08/2025) (2024).\n\nEbi, K. L. et al. Hot weather and heat extremes: health risks. Lancet 398, 698\u2013708 (2021).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLee, D. H. K. Seventy-five years of searching for a Heat Index. Environ. Res. 22, 331\u2013356 (1980).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nZscheischler, J. et al. Future climate risk from compound events. Nat. Clim. Chang. 8, 469\u2013477 (2018).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nGori, A., Lin, N., Xi, D. & Emanuel, K. Tropical cyclone climatology change greatly exacerbates US extreme rainfall\u2013surge hazard. Nat. Clim. Change 12, 171\u2013178 (2022).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nHouser, T. & Marsters, P. The world\u2019s second largest blackout. 385 (Rhodium Group, 2018).\n\nMatthews, T., Wilby, R. L. & Murphy, C. An emerging tropical cyclone\u2013deadly heat compound hazard. Nat. Clim. Chang. 9, 602\u2013606 (2019).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nFeng, K., Ouyang, M. & Lin, N. Tropical cyclone-blackout-heatwave compound hazard resilience in a changing climate. Nat. Commun. 13, 4421 (2022).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLouisiana Department of Health verifies one additional hurricane-related death, bringing toll to 27. Louisiana Dep. Heal. Published online Sept 9. Available at: https://ldh.la.gov/index.cfm/newsroom/detail/5761 (2020) Accessed Oct 21, 2020).\n\nO\u2019Neill, B. C. et al. The scenario model intercomparison project (ScenarioMIP) for CMIP6. Geosci. Model Dev. 9, 3461\u20133482 (2016).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nXi, D., Lin, N. & Gori, A. Increasing sequential tropical cyclone hazards along the US East and Gulf Coasts. Nat. Clim. Chang. 13, 258\u2013265 (2023).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBaylor Fox-Kemper et al. Ocean, cryosphere and sea level change. in Climate Change 2021\u2013The Physical Science Basis: Working Group I Contribution to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change (ed. Intergovernmental Panel on Climate Change (IPCC)) 1211\u20131362 (Cambridge University Press, Cambridge, 2023). https://doi.org/10.1017/9781009157896.011.\n\nKopp, R. E. et al. The framework for assessing changes to sea-level (FACTS) v1.0: a platform for characterizing parametric and structural uncertainty in future global, relative, and extreme sea-level change. Geosci. Model Dev. 16, 7461\u20137489 (2023).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nGarner, G. G. et al. IPCC AR6 Sea Level Projections. Version 20210809 (2021).\n\nOuyang, M. & Duenas-Osorio, L. Multi-dimensional hurricane resilience assessment of electric power systems. Struct. Saf. 48, 15\u201324 (2014).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nEntergy, Restoration Times for Louisiana, including Hardest Hit Areas Link: https://www.entergynewsroom.com/article/entergy-louisiana-ida-update-9-20-2021/ (Last Visited: 4/08/2025) (2021).\n\nU.S. Energy Information Administration, Annual Electric Power Industry Report, Form EIA-861 detailed data files (2021).\n\nGastwirth, J.L. The estimation of the Lorenz curve and Gini index. The Review of Economics and Statistics, 306\u2013316 (1972).\n\nSobel, A. H. et al. Tropical cyclone frequency. Earth\u2019s Future 9, e2021EF002275 (2021).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKnutson, T. et al. Tropical cyclones and climate change assessment: part II: projected response to anthropogenic warming. Bull. Am. Meteor. Soc. 101, E303\u2013E322 (2020).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBennett, J. A. et al. Extending energy system modelling to include extreme weather risks and application to hurricane events in Puerto Rico. Nat. Energy 6, 240\u2013249 (2021).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nHauer, M. E. Migration induced by sea-level rise could reshape the US population landscape. Nat. Clim. Chang. 7, 321 (2017).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nFeng, K., Lin, N., Xian, S. & Chester, M. V. Can we evacuate from hurricanes with electric vehicles? Transp. Res. Part D: Transp. Environ. 86, 102458 (2020).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nGill, S. E., Handley, J. F., Ennos, A. R. & Pauleit, S. Adapting cities for climate change: the role of the green infrastructure. Built Environ. 33, 115\u2013133 (2007).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWamsler, C., Brink, E. & Rantala, O. Climate change, adaptation, and formal education: the role of schooling for increasing societies\u2019 adaptive capacities in El Salvador and Brazil. Ecol. Soc. 17, 2 (2012).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBirkmann, J. & von Teichman, K. Integrating disaster risk reduction and climate change adaptation: key challenges\u2014scales, knowledge, and norms. Sustain. Sci. 5, 171\u2013184 (2010).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nSeto, K. C., G\u00fcneralp, B. & Hutyra, L. R. Global forecasts of urban expansion to 2030 and direct impacts on biodiversity and carbon pools. Proc. Natl. Acad. Sci. USA 109, 16083\u201316088 (2012).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDT Cohen, 60 million live in the path of hurricanes. U.S. census bureau. Link: https://www.census.gov/library/stories/2018/08/coastal-county-population-rises.html (Last visited 4/08/2025) (2018).\n\nXu, L. et al. Resilience of renewable power systems under climate risks. Nat. Rev. Electr. Eng. 1, 53\u201366 (2024).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nEmanuel, K., Ravela, S., Vivant, E. & Risi, C. A statistical deterministic approach to Hurricane Risk Assessment. Bull. Am. Meteorol. Soc. 87, S1\u2013S5 (2006).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMarsooli, R., Lin, N., Emanuel, K. & Feng, K. Climate change exacerbates hurricane flood hazards along US Atlantic and Gulf Coasts in spatially varying patterns. Nat. Commun. 10, 1\u20139 (2019).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLin, N., Emanuel, K., Oppenheimer, M. & Vanmarcke, E. Physically based assessment of hurricane surge threat under climate change. Nat. Clim. Chang. 2, 462\u2013467 (2012).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLuettich, R.A., Westerink, J.J. & Scheffner, N.W. \u201cADCIRC: an advanced three-dimensional circulation model for shelves, coasts, and estuaries. Report 1, Theory and methodology of ADCIRC-2DD1 and ADCIRC-3DL.\u201d (1992).\n\nWesterink, J.J., Luettich, R.A., Blain, C.A. & Scheffner, N.W. \u201cADCIRC: An advanced three-dimensional circulation model for shelves, coasts, and estuaries. Report 2: User\u2019s Manual for ADCIRC-2DDI.\u201d (1992).\n\nXi, D., Lin, N. & Smith, J. Evaluation of a physics-based tropical cyclone rainfall model for risk assessment. J. Hydrometeorol. 21, 2197\u20132218 (2020).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nFagnant, C., Gori, A., Ensor, K.B., Sebastian, A. & Bedient, P.B. Characterizing spatiotemporal trends in extreme precipitation across the Southern Texas Coast. Nat. Hazards 104, 1597\u20131621 (2020).\n\nEmanuel, K. Assessing the present and future probability of Hurricane Harvey\u2019s rainfall. Proc. Natl. Acad. Sci. USA 114, 12681\u201312684 (2017).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nHolland, G. J. An analytic model of the wind and pressure profiles in hurricanes. Mon. Weather Rev. 108, 1212\u20131218 (1980).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLin, N. & Chavas, D. On hurricane parametric wind and applications in storm surge modeling. J. Geophys. Res. Atmos. 117 (2012).\n\nUSGS (U.S. Geological Survey). Digital Elevation Model https://pubs.usgs.gov/sim/3049/ Last accessed: Mar-19-2025 (2022).\n\nPalaseanu-Lovejoy, M., Thatcher, C. A. & Barras, J. A. Levee crest elevation profiles derived from airborne lidar-based high resolution digital elevation models in South Louisiana. ISPRS J. Photogramm. Remote Sens. 91, 114\u2013126 (2014).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nJohnson, D. R., Fischbach, J. R. & Ortiz, D. S. Estimating surge-based flood risk with the coastal Louisiana risk assessment model. J. Coast. Res. 67, 109\u2013126 (2013).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nUS Army Corps of Engineers, Hurricane & Storm Damage Risk Reduction System, New Orleans District (2021).\n\nNateghi, R., Guikema, S. D. & Quiring, S. M. Comparison and validation of statistical methods for predicting power outage durations in the event of hurricanes. Risk Anal. 31, 1897\u20131906 (2011).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nJi, C. et al. Large-scale data analysis of power grid resilience across multiple US Service Regions. Nat. Energy 1, 1\u20138 (2016).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLouisiana Public Service Commission Louisiana Electric Utility Service Area https://www.lpsc.louisiana.gov/Utilities_Map Last Accessed: Mar-19-25 (2025).\n\nYang, Y., Nishikawa, T. & Motter, A. E. Vulnerability and co-susceptibility determine the size of network cascades. Phys. Rev. Lett. 118, 048301 (2017).\n\nArticle\u00a0\n    ADS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nYang, Y., Nishikawa, T. & Motter, A. E. Small vulnerable sets determine large network cascades in power grids. Science 358, eaan3184 (2017).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nZhai, C., Chen, T. Y. J., White, A. G. & Guikema, S. D. Power outage prediction for natural hazards using synthetic power distribution systems. Reliab. Eng. Syst. Saf. 208, 107348 (2021).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nHines, P., Cotilla-Sanchez, E. & Blumsack, S. Do topological models provide good information about electricity infrastructure vulnerability? Chaos 20, 033122 (2010).\n\nArticle\u00a0\n    ADS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nSeven Steps to Restore Power After a Flood. New Equipment Digest https://www.newequipment.com/plant-operations/article/22059483/seven-steps-to-restore-power-after-a-flood (Last accessed: Mar-12-25) (2017).\n\nXi D., Lin, N. Sequential landfall of tropical cyclones in the United States: from historical records to climate projections. Geophys. Res. Lett. 48 (2021).\n\nDu, J. \u201cNCEP/EMC 4KM Gridded Data (GRIB) Stage IV Data. Version 1.0.\u201d UCAR/NCAR - Earth Observing Laboratory, https://doi.org/10.5065/D6PG1QDD (2011).\n\nDartmouth Flood Observatory. Link: https://floodobservatory.colorado.edu/ (Last Visited: 4/08/2025) (2021).\n\nDemuth, J., DeMaria, M. & Knaff, J. A. Improvement of advanced microwave sounder unit tropical cyclone intensity and size estimation algorithms. J. Appl. Meteor. 45, 1573\u20131581 (2006).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDownload references",
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+        },
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+            "section_name": "Acknowledgements",
+            "section_text": "K.F., N.L., A.G., D.X., and M. Oppenheimer were supported by the U.S. National Science Foundation (NSF) as part of the Megalopolitan Coastal Transformation Hub (MACH) under NSF award ICER-2103754\u00a0to Princeton University, with MACH contribution number 44. K.F. was also supported by the HMEI-STEP Graduate Fellowship\u00a0at Princeton University. K.F., A.G., and D.X moved\u00a0during revision, and\u00a0K.F. was then\u00a0supported by National Natural Science Foundation of China (Grant No. 62088101), Shanghai Municipal Science and Technology Major Project (Grant No.2021SHZDZX0100), Explorer Program (Grant No. 24TS1401600), and Xiaomi Foundation. M. Ouyang was supported by the National Natural Science Foundation of China (72371109,71821001), Strategic study project of Chinese Academy of Engineering (2022-JB-02), and Project of Interdisciplinary Research Support Program in HUST (2023-32). We thank the IPCC AR6 Sea Level projection team for developing and making the sea-level rise projections available, multiple funding agencies for supporting the development of the projections, and the NASA Sea Level Change Team for developing and hosting the IPCC AR6 Sea Level Projection Tool.",
+            "section_image": []
+        },
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+            "section_name": "Author information",
+            "section_text": "Department of Civil and Environmental Engineering, Princeton University, Princeton, NJ, USA\n\nKairui Feng,\u00a0Ning Lin,\u00a0Avantika Gori\u00a0&\u00a0Dazhi Xi\n\nThe National Key Laboratory of Autonomous Intelligent Unmanned Systems, Tongji University, Shanghai, China\n\nKairui Feng\n\nShanghai Innovation Institute, Shanghai, China\n\nKairui Feng\n\nDepartment of Civil and Environmental Engineering, Rice University, Houston, TX, USA\n\nAvantika Gori\n\nDepartment of Earth Sciences, The University of Hong Kong, Hong Kong, China\n\nDazhi Xi\n\nSchool of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan, China\n\nMin Ouyang\n\nSchool of Public and International Affairs, Princeton University, Princeton, NJ, USA\n\nMichael Oppenheimer\n\nDepartment of Geosciences, Princeton University, Princeton, NJ, USA\n\nMichael Oppenheimer\n\nHigh Meadows Environmental Institute, Princeton University, Princeton, NJ, USA\n\nMichael Oppenheimer\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nThe conceptualization of the project was carried out by K.F., N.L., M.O.Y., and M.O.P. The methodology was developed by K.F., N.L., A.G., D.X., and M.O.Y. The original draft of the writing was authored by K.F. and N.L., and K.F., N.L., A.G., D.X., M.O.Y., and M.O.P. reviewed and edited the manuscript.\n\nCorrespondence to\n                Ning Lin.",
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+            "section_text": "Feng, K., Lin, N., Gori, A. et al. Hurricane Ida\u2019s blackout-heatwave compound risk in a changing climate.\n                    Nat Commun 16, 4533 (2025). https://doi.org/10.1038/s41467-025-59737-8\n\nDownload citation\n\nReceived: 13 March 2024\n\nAccepted: 02 May 2025\n\nPublished: 15 May 2025\n\nVersion of record: 15 May 2025\n\nDOI: https://doi.org/10.1038/s41467-025-59737-8\n\nAnyone you share the following link with will be able to read this content:\n\nSorry, a shareable link is not currently available for this article.\n\n\n\n\n                            Provided by the Springer Nature SharedIt content-sharing initiative\n                        ",
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2bad4797b5cc24f4647b5de99a0eb4e23c0e77ca443e03e3c2737e1043560bec/metadata.json

@@ -0,0 +1,174 @@
+{
+    "title": "Three-dimensional atomic insights into the metal-oxide interface in Zr-ZrO2 nanoparticles",
+    "pre_title": "Three-dimensional atomic interface between metal and oxide in Zr-ZrO2 nanoparticles",
+    "journal": "Nature Communications",
+    "published": "02 September 2024",
+    "supplementary_0": [
+        {
+            "label": "Supplementary Information",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-024-52026-w/MediaObjects/41467_2024_52026_MOESM1_ESM.pdf"
+        },
+        {
+            "label": "Peer Review File",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-024-52026-w/MediaObjects/41467_2024_52026_MOESM2_ESM.pdf"
+        },
+        {
+            "label": "Description of Additional Supplementary Files",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-024-52026-w/MediaObjects/41467_2024_52026_MOESM3_ESM.pdf"
+        },
+        {
+            "label": "Supplementary Movie 1",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-024-52026-w/MediaObjects/41467_2024_52026_MOESM4_ESM.mp4"
+        },
+        {
+            "label": "Supplementary Movie 2",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-024-52026-w/MediaObjects/41467_2024_52026_MOESM5_ESM.mp4"
+        },
+        {
+            "label": "Supplementary Movie 3",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-024-52026-w/MediaObjects/41467_2024_52026_MOESM6_ESM.mp4"
+        },
+        {
+            "label": "Supplementary Movie 4",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-024-52026-w/MediaObjects/41467_2024_52026_MOESM7_ESM.mp4"
+        },
+        {
+            "label": "Supplementary Movie 5",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-024-52026-w/MediaObjects/41467_2024_52026_MOESM8_ESM.mp4"
+        }
+    ],
+    "supplementary_1": [
+        {
+            "label": "Source Data",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-024-52026-w/MediaObjects/41467_2024_52026_MOESM9_ESM.xlsx"
+        }
+    ],
+    "supplementary_2": NaN,
+    "source_data": [
+        "/articles/s41467-024-52026-w#ref-CR57",
+        "/articles/s41467-024-52026-w#Sec18"
+    ],
+    "code": [
+        "/articles/s41467-024-52026-w#ref-CR57"
+    ],
+    "subject": [
+        "Nanoscale materials",
+        "Structural properties"
+    ],
+    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
+    "preprint_pdf": "https://www.researchsquare.com/article/rs-3972857/v1.pdf?c=1725361732000",
+    "research_square_link": "https://www.researchsquare.com//article/rs-3972857/v1",
+    "nature_pdf": "https://www.nature.com/articles/s41467-024-52026-w.pdf",
+    "preprint_posted": "12 Mar, 2024",
+    "research_square_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Metal-oxide interfaces with poor coherency have unique properties comparing to the bulk materials and offer broad applications in the fields of heterogeneous catalysis, battery, and electronics. However, current understanding of the three-dimensional (3D) atomic metal-oxide interfaces remains limited because of their inherent structural complexity and limitations of conventional two-dimensional imaging techniques. Here, we determine the 3D atomic structure of metal-oxide interfaces in zirconium-zirconia nanoparticles using atomic-resolution electron tomography. We quantitatively analyze the atomic concentration and the degree of oxidation, and find the coherency and translational symmetry of the interfaces are broken. Moreover, we observe porous structures such as Zr vacancies and nano-pores and investigate their distribution. Our findings provide a clear 3D atomic picture of metal-oxide interface with direct experimental evidence. We anticipate this work could encourage future studies on fundamental problems of oxides such as interfacial structures in semiconductor and atomic motion during oxidation process.Physical sciences/Nanoscience and technology/Nanoscale materials/NanoparticlesPhysical sciences/Materials science/Nanoscale materials/Nanoparticles",
+            "section_image": []
+        },
+        {
+            "section_name": "Additional Declarations",
+            "section_text": "There is NO Competing Interest.",
+            "section_image": []
+        },
+        {
+            "section_name": "Supplementary Files",
+            "section_text": "ZrZrO2interfaceNatureSupplementaryInformation20240219final.pdfMovieS1.mp4SUPPLEMENTARY VIDEO 1MovieS2.mp4SUPPLEMENTARY VIDEO 2MovieS3.mp4SUPPLEMENTARY VIDEO 3MovieS4.mp4SUPPLEMENTARY VIDEO 4",
+            "section_image": []
+        }
+    ],
+    "nature_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Metal-oxide interfaces with poor coherency have specific properties comparing to bulk materials and offer broad applications in heterogeneous catalysis, battery, and electronics. However, current understanding of the three-dimensional (3D) atomic metal-oxide interfaces remains limited because of their inherent structural complexity and the limitations of conventional two-dimensional imaging techniques. Here, we determine the 3D atomic structure of metal-oxide interfaces in zirconium-zirconia nanoparticles using atomic-resolution electron tomography. We quantitatively analyze the atomic concentration and the degree of oxidation, and find the coherency and translational symmetry of the interfaces are broken. Atoms at the interface have low structural ordering, low coordination, and elongated bond length. Moreover, we observe porous structures such as Zr vacancies and nano-pores, and investigate their distribution. Our findings provide a clear 3D atomic picture of metal-oxide interface with direct experimental evidence. We anticipate this work could encourage future studies on fundamental problems of oxides, such as interfacial structures in semiconductor and atomic motion during oxidation process.",
+            "section_image": []
+        },
+        {
+            "section_name": "Introduction",
+            "section_text": "Most metals spontaneously form an oxidation layer on their surfaces. The metal-oxide interface plays a critical role in broad applications ranging from heterocatalysis1,2, batteries3,4, and electronics5,6. The thermodynamics and kinetics of oxidation processes have been extensively studied over the years7,8,9. Plenty of research has been focused on the metal\u2019s work function10, the transport of metal or oxygen species11,12,13, and the rate of oxidation14. A number of theories have been proposed in these studies to understand the oxidation behavior. For example, the Kirkendall effect is used to explain the formation of oxidized pores15,16,17; Wagner et al. proposed the law of oxidation kinetics in which the oxidation rate is controlled by the transport of ions under electrochemical potential gradient based on several assumptions12,14,18. However, owing to the lack of direct observation of the three-dimensional (3D) metal-oxide interface at nanoscale or atomic scale, most of the theories are based on the ideal atomistic interface model. Properties of the interface, including catalytic activity, phonon dispersion, and electron transportation, are strongly related to the local atomic arrangements of the metal-oxide interface, such as coordination numbers and atomic bond lengths19,20,21,22,23,24. It is, therefore, essential to determine the 3D atomic arrangements and understand the detailed oxidation structure of metal.\n\nWith the recent development in aberration-corrected transmission electron microscopy (TEM), local structures of metal-oxide interfaces such as Cu-Cu2O25,26, Ag-Ag2O27, and Ni-NiO28 have been studied at nanoscale or atomic scale; several of them were probed in-situ by atomic-resolution imaging and theoretical simulation25,26,27,28,29. Semi-coherent and incoherent interfaces between metal and oxide have been observed at sub-\u00c5 resolution from two-dimensional (2D) projections26. Luo et al. discovered the periodic dislocation in Cu-Cu2O semi-coherent interface, suggesting the mechanism of strain release by defects between metal and oxide25. Zhu et al. tracked the formation of voids in Ni-NiO nanoparticles at nanoscale, identifying a two-stage oxidation mechanism including early-stage nucleation and then the Wagner oxidation28. However, since the oxidized interfaces are usually non-epitaxial and inherently disordered due to the lattice mismatch, the atomic arrangements between some metals and their oxidation layer cannot be clearly elucidated using high-resolution TEM or crystallography. Conventional 3D characterization methods such as atom probe tomography30,31, electron tomography28,32,33,34,35, and depth sectioning36,37 have been used to study the 3D morphological structures of the metal-oxide interfaces, and these techniques could overcome the limitation of single images, which only provide the projected information of the 3D structures in 2D. However, the resolution of these techniques is limited to nanometer scale. Thus, determining the 3D atomic arrangements of the metal-oxide interface remains a major challenge. Although it remains notoriously difficult to image and identify each of the oxygen atoms of oxides in 3D, especially in annular dark-field scanning transmission electron microscopy (ADF-STEM) mode, atomic-resolution electron tomography (AET), which is an effective tool for determining the 3D atomic structure of nanomaterials32,33,34,35, can in principle resolve the positions of heavy metal atoms in oxides and therefore give important structural information on this long-standing problem.\n\nHere, using Zr-ZrO2 as a model system, we determined the 3D atomic structure of the metal-oxide interface using AET. We chose Zr-ZrO2 for two reasons. First, Zr can form oxide spontaneously in air, and the oxidation process is moderate10; second, the Zr-O bonding is strong among all the common metal oxides, and ZrO2 has excellent chemical stability. The Zr-ZrO2 interface can maintain its atomic structures after electron irradiation at a dose rate of 6\u2009\u00d7\u2009105\u2009e \u00c5\u22122, which is essential for electron tomography experiments. By determining all the Zr atomic positions in Zr-ZrO2 nanoparticles (NPs), we obtained the 3D atomic structure of a partially oxidized Zr NP; it has an uncommon face-centered cubic (FCC) Zr metal crystal nucleus as the core and amorphous/crystalline ZrO2 as the shell. The degree of oxidation decreases while Zr packing density increases from the oxide surface to the metal core. Instead of forming a coherent interface, most of the atoms at the Zr-ZrO2 interfaces connect with each other semi-coherently or incoherently. We discovered a bidirectional distortion including bending and twisting at the semi-coherent metal-oxide interface. Moreover, we identified numbers of voids in the oxides including Zr vacancies, nano-pores, and large pores; the oxidation process is related to the distribution of the voids. These findings expand our understanding of the atomic structures of metal-oxide interfaces with poor coherency, encourage future studies on oxidation process at 3D atomic resolution, and further inspire the designing and modeling of atomic metal-oxide interface in surface engineering, heterogeneous catalysis, and semiconductors.",
+            "section_image": []
+        },
+        {
+            "section_name": "Results",
+            "section_text": "NPs made of different monatomic metals with both disordered and crystalline structures can be achieved using fast-cooling vitrification process38,39. Zr NPs were synthesized using pulse laser ablation of pure Zr target (purity >\u200999.95%) in ethanol (Methods). This technique can provide a very high temperature to melt and vaporize the metal target and fast cooling to yield nanoparticles which have a large variety of morphologies38 including amorphous, partially amorphous, and crystalline metal nanoparticles (Supplementary Fig.\u00a01a). By naturally oxidizing the freshly prepared Zr NPs in air, we obtained Zr-ZrO2 NPs at different stages of the oxidation process. Some of the Zr-ZrO2 NPs have an oxidized shell and a metal core (Supplementary Fig.\u00a01c,e). To confirm the oxidation, we have employed high-resolution ADF-STEM and energy dispersive spectroscopy (EDS) to characterize the Zr-ZrO2 NPs (Supplementary Figs.\u00a01, 2); it is notable that the edges of the NPs have a high degree of oxidation since the oxygen signal of EDS at the edge are stronger while ADF-STEM intensities are weaker. The line profiles of Zr elemental intensity are particularly high at the core of the nanoparticles, also indicating the nanoparticles have a metallic Zr core and ZrO2 shell.\n\nIn this study, we selected Zr-ZrO2 particles with a suitable size (\u2248 10\u2009nm) and various of metal-oxide interfaces to perform AET experiments. We resolved the 3D atomic structures of all Zr atoms in several Zr-ZrO2 NPs using AET. In short, tomography tilt series (Supplementary Figs.\u00a03\u20138) were acquired from three Zr-ZrO2 NPs at different stages of the oxidation process using an aberration-corrected TEM in ADF-STEM mode (Supplementary Table\u00a01). After imaging processing including denoising, background subtracting, and alignment (Methods), the tilt series were reconstructed using the Real Space Iterative Reconstruction (RESIRE) algorithm40. Supplementary Fig.\u00a09 and Supplementary Movie\u00a01 show the volume rendering of raw reconstructions of these NPs. The 3D atomic coordinates of all Zr were traced from the computed reconstructions (Methods). We chose a partially oxidized Zr-ZrO2 (named Zr1) as our main interest to elucidate the metal-oxide interfaces. The other two particles are fully oxidized without obvious metal core (named as Zr2 and Zr3; Supplementary Fig.\u00a010).\n\nSince the image contrast of atoms in ADF-STEM mode is sensitive to the atomic number, the oxygen atoms are too light, and our current imaging parameters are not sufficient enough to detect oxygen (Supplementary Tables\u00a01, 2). To verify the contrast contribution of oxygen in 2D ADF-STEM images, we have constructed a slab model of cubic ZrO2 which is 8-nm-thick (similar thickness comparing to Zr NPs); and then performed the multi-slice simulation along the [100] zone axis. The contrasts of oxygen columns in the simulated images are very low, making the column of oxygen atoms barely seen (Supplementary Fig.\u00a011). To further validate our reconstruction and verify the contrast contribution of oxygen in 3D, we have performed multi-slice simulation of the tilt series and computed 3D reconstruction to show the oxygen contrast in 3D. The same number of projections have been generated from the experimental model with filling oxygens (Methods). By performing the same image processing, reconstruction, and atom tracing procedures, we obtained a multi-slice atomic model. We estimated that 97.2% of atoms were identified correctly with a 3D precision of \u2248 28\u2009pm by comparing the experimental model with the multi-slice one (Supplementary Fig.\u00a012). From either 3D reconstructed volume or traced atomic positions, we cannot distinguish the oxygen atoms in ZrO2 regions due to the low intensities of the oxygen atoms (Supplementary Figs.\u00a013, 14). These results reveal the low contrast of oxygen atoms, both in 2D ADF-STEM images and 3D AET reconstruction.\n\nFigure\u00a01a and Supplementary Movie\u00a02 show the experimental 3D atomic model of Zr1, with ordered crystalline grains and disordered structures in the particle. We calculated the normalized bond orientational order (BOO) parameters for all the atoms to quantify the disorder (Fig.\u00a01b and Methods); about 32% of all the Zr atoms are disordered. The particle has complicated phases, composed of a central metal grain, crystalline oxide grains (c-ZrO2), and an amorphous oxide phase (a-ZrO2) (Fig.\u00a01d and Supplementary Movie\u00a03). We calculated the Zr-Zr partial pair distribution functions (PDFs) of the atoms in c-ZrO2 and a-ZrO2 separately (Methods). The c-ZrO2 shows a well-matched cubic phase ZrO2 structure instead of monoclinic phase ZrO2 in both Zr1 and Zr2 (Fig.\u00a01c). The PDFs of the a-ZrO2 atoms in all three NPs exhibit similar shape; and the first peak position is located at 3.45\u2009\u00c5, which is close to the first peak position of monoclinic phase ZrO2 (Fig.\u00a01c). All the positions of main peaks and valleys in our Zr-Zr PDFs obtained from the atomic coordinates of our a-ZrO2 structures agree with those obtained from synchrotron X-ray diffraction41. The most populated Zr-Zr bond lengths in c-ZrO2 and a-ZrO2 are 3.6\u2009\u00c5 and 3.45\u2009\u00c5, respectively (Supplementary Fig.\u00a015). Interestingly, there is a small Zr metal core inside Zr1, confirmed by polyhedron template matching42 and atomic concentration analysis (Methods). Figure\u00a01e shows the atomic structure of the pure Zr metal core viewing from \u3008110\u3009 direction. The metal core has a distorted FCC structure with an averaged Zr-Zr bond length of 3.3\u2009\u00c5, slightly longer than the standard value in Zr metal (3.2\u2009\u00c5). These observations are different from the bulk behavior, where Zr typically forms hexagonal close-packed (HCP) or body-centered cubic (BCC) structures and usually forms monoclinic phase ZrO2 after natural oxidation43. This discrepancy highlights the distinctive behavior of materials at the nanoscale.\n\na Experimental 3D atomic model of the Zr1 NP with a-ZrO2 in blue, c-ZrO2 in green and metal core in red. b Normalized BOO parameters of all atoms. The red dashed curve is a criterion to distinguish the disordered atoms (32% in total, atoms below the curve) and ordered atoms (68% in total, atoms above the curve). The standard BCC, HCP and FCC parameters are marked as black dots for reference. c, d Zr-Zr PDFs of the c-ZrO2 (c) and a-ZrO2 (d), with Zr1 in red, Zr2 in blue and Zr3 in black. The gray peaks show the peak positions of the standard PDF of cubic phase ZrO2 (c) and monoclinic phase ZrO2 (d) for comparison. e The NP consists of a-ZrO2, c-ZrO2 and a metal core grain. f Magnified atomic structure of the pure Zr metal core viewing from \u3008110\u3009 direction. Source data are provided as a Source Data file.\n\nTo compare the local atomic packing density of Zr in all phases, we obtained the compactness of the NP by determining the Zr atomic concentration (\u03c1N) of all the regions present in Zr1 NP (Methods). Figure\u00a02a shows the 3D \u03c1N distribution of Zr1. The low packing density regions are not related to any voids in the NP as we exclude all the voids from consideration when performing calculation (Methods). The averaged \u03c1N of the metal core is 3.85\u2009\u00d7\u200910\u22122\u2009\u00c5\u22123 (Fig.\u00a02c), close to the \u03c1N of ideal close-packed metallic Zr (3.9\u2009\u00d7\u200910\u22122\u2009\u00c5\u22123). The \u03c1N of oxides (both c-ZrO2 and a-ZrO2 phases) are significantly lower than that of pure metal, being 2.92\u2009\u00d7\u200910\u22122\u2009\u00c5\u22123 and 2.89\u2009\u00d7\u200910\u22122\u2009\u00c5\u22123, respectively. They are comparable to the \u03c1N of ideal\u00a0cubic phase ZrO2 (3.0\u2009\u00d7\u200910\u22122\u2009\u00c5\u22123). We also observed 3D local \u03c1N heterogeneity in the oxides, particularly distributed around the metal-oxide interfaces. Figure\u00a02d shows the \u03c1N distribution as a function of the distance from the surface of the metal core (metal to c-ZrO2). The gradual decrease in \u03c1N suggests the metal-oxide interfaces are atomically smooth. The packing density gradient is attributed to the gradual change of the degree of oxidation of the Zr metal. Our PDFs and Zr-Zr bond length analysis suggest that c-ZrO2 is the cubic phase, and a-ZrO2 mainly forms the tetrahedral structure locally41; oxygen should be located in tetrahedral sites in both phases (Supplementary Fig.\u00a016). Next, we quantified the degree of oxidation by geometrically filling oxygen into the tetrahedral sites based on a reasonable Zr-specific knowledge (Methods). Since EDS measurements in other similar Zr-ZrO2 NPs suggest the oxide grain is almost fully oxidized, which is confirmed by our atomic concentration analysis, to satisfy the stoichiometric ratio of ZrO2, oxygen can be filled in eight tetrahedral sites (5.5 \u00c53) of the oxide (Supplementary Fig.\u00a016a); but those tetrahedral sites (4.2\u2009\u00c53) in Zr metal are too small (Supplementary Fig.\u00a016b). Figure\u00a02b and Supplementary Movie\u00a04 show the 3D oxidation maps of Zr1. The degree of oxidation distributions in all the phases are shown in Fig.\u00a02e and Supplementary Fig.\u00a017, where the degree of oxidation increases along with the decrease of Zr \u03c1N. The c-ZrO2 and a-ZrO2 grains are almost fully oxidized in their surfaces; and they become less oxidized as closer to their interfaces with the central Zr core (Fig.\u00a02e). The experimentally measured tetrahedral sites in the central Zr core are too small to be filled with oxygen, confirming the core is barely oxidized. There could be some heterogeneity in the degree of oxidation in some of the oxide grains, which makes the oxidation maps non-uniform. To further validate our oxygen filling method and partial oxidation, we have performed integrated differential phase-contrast STEM (iDPC-STEM) imaging on a similar nanoparticle with a known structure, the cubic ZrO2 phase (Methods, Supplementary Fig.\u00a018a, b). This technique provides improved sensitivity to light elements such as oxygens44. The line profiles of the iDPC image show the contrasts of different oxygen columns are different, indicating partial oxidation and non-uniform oxygen filling in this cubic ZrO2 grain (Supplementary Fig.\u00a018c). A cubic cutout of the 3D oxidation maps reveals that the degree of oxidation is strongly correlated to the atomic packing density of Zr; a highly oxidized region always has a lower Zr \u03c1N (Fig.\u00a02f). It\u2019s notable that some other Zr NPs are completely oxidized to cubic phase ZrO2 and/or amorphous ZrO2 (Supplementary Fig.\u00a019) even from the same batch of oxidation. These results indicate the oxidation process is kinetics controlled, in which we observed several intermediate states of oxidized Zr-ZrO2.\n\na, b Atomic concentration \u03c1N distribution (a) and the degree of oxidation (b) of all the atoms in Zr1. Each slice has a thickness of 5.3\u2009\u00c5. To increase the signal-to-noise ratio, we convolved the degree of oxidation with a 2-\u00c5-wide 3D Gaussian kernel, but this also reduces the 3D spatial resolution of oxidation map to \u2248 4\u2009\u00c5. c Distribution of \u03c1N in c-ZrO2 (blue), a-ZrO2 (red) and metal core (yellow) phase. c-ZrO2 has a slightly larger \u03c1N distribution by 1% (dashed lines) than a-ZrO2. The inset figure shows the magnified histogram of metal core. d The \u03c1N distribution of metal/c-ZrO2 as a function of the distance from the surface of metal core. The dashed lines show the standard \u03c1N in Zr metal (red) and cubic phase ZrO2 (blue). e A slice through the Zr1 NP as the red rectangle marked in (b), showing the degree of oxidation at different regions. f 3D surface rendering of local degree of oxidation and corresponding atomic concentration \u03c1N, showing the strong correlation. The cutout is 25\u2009\u00d7\u200925\u2009\u00d7\u200925 \u00c53. Source data are provided as a Source Data file.\n\nCoherency of the metal-oxide interface affects many properties, including strain, diffusion, and band structure26,45,46. It is difficult to identify the atomic arrangement of semi-coherent or incoherent metal-oxide interfaces from 2D projected images. To probe the 3D structure of metal-oxide interface at atomic level, we focus on the atomic Zr-Zr bonding of the interfaces with a range of \u2248 10\u2009\u00c5 based on the packing density between metal core and oxide phases (Fig.\u00a02d). Figure\u00a03a presents the 3D surface renderings of three major phase, showing the contour of metal core, c-ZrO2, and a-ZrO2 phase. Three slices with four atomic layers in thickness through the metal core show the Zr-Zr bonding of metal-oxide interfaces (Fig.\u00a03b\u2013d). We found several types of interfaces, including semi-coherent and incoherent interfaces between metal and c-ZrO2, and incoherent interfaces between metal and a-ZrO2. The white rectangles in Fig.\u00a03b\u2013d highlight three cutouts from the atomic structures of a semi-coherent (Fig.\u00a03e) and an incoherent interface (Fig.\u00a03k) between metal and c-ZrO2, and an incoherent interface (Fig.\u00a03l) between metal and a-ZrO2, respectively. The layer-by-layer slices of the raw reconstruction volume of these interfaces are shown in Supplementary Figs.\u00a020\u201322, indicating the consistency between the raw reconstruction and the traced atomic model.\n\na\u2013d 3D surface renderings of three major phases, showing the contour (a) of metal core (red), c-ZrO2 (green) and a-ZrO2 (blue) of Zr1. Three planes go through the Zr1 in different directions. The sliced atomic models (4-atom-layers thick) highlights three different types of interfaces, i.e., metal/c-ZrO2 semicoherent interface between (b; in blue frame), metal/c-ZrO2 incoherent interface (c; in green frame), and metal/a-ZrO2 incoherent interface (d; in orange frame). e\u2013g Experimental semicoherent interface structures specified by the rectangle region in (b). e The semicoherent interface viewing from metal [\\(1\\bar{1}0\\)] direction. There is a bending of \u2248 11\u00b0 between metal and interfacial layers in metal [112] direction (angle between red line and blue line), and a bending of \u2248 8\u00b0 between interfacial layers and c-ZrO2 in oxide [110] direction (angle in blue line and ivory line). The coordination tripods in red and ivory boxes shows the spatial crystal orientation of metal and oxide, respectively. f The semicoherent interface viewing from metal [101] direction (by rotating the cutout in (e) 120\u00b0 counter clockwise), showing a twisting of \u2248 4\u00b0 in metal [\\(1\\bar{1}0\\)] direction (angle between red line and ivory line). g One atomic plane extracted from the semicoherent interface (the highlighted area in red in e), viewing from metal [\\(\\bar{1}\\bar{1}1\\)] direction. In this direction, the oxide shows the (002) plane. The color of the atomic bonding shows the Zr-Zr bond length. h The ideal model of an interface structure between ideal FCC Zr metal and ideal cubic ZrO2, showing a 15\u00b0 of wedge if no bending exists. To minimize the interfacial energy and maintain the coherency, a bending of 15\u00b0 (i) is needed. The structure changed from metal to oxide shows in (j). The oxygen atoms are colored in red. k, l Incoherent interface structures specified by the rectangle region in (c, d), showing the metal/c-ZrO2 (k) and metal/a-ZrO2 interface (l). In (e\u2013l), the metal atoms, interface atoms and oxide atoms are colored in deep red, blue and ivory, respectively. The Zr atoms are bonded with their first-nearest Zr neighbors and linked with lines (Methods).\n\nIn the semi-coherent interface, four layers of metal Zr atoms (marked in deep red) from the metal [\\(1\\bar{1}0\\)] direction correspond to four layers of Zr atoms (marked as ivory) in the oxide (Fig.\u00a03e). To see the atomic connections in a single corresponding layer, one plane in the cutout is extracted and viewed from [\\(\\bar{1}\\bar{1}1\\)] direction of metal (Fig.\u00a03g, Supplementary Fig.\u00a023). Metal (\\(\\bar{1}\\bar{1}1\\)) plane is almost coplanar with oxide (002) plane; and the interface is about two atomic layers in thickness (blue atoms in Fig.\u00a03g) and primarily connects metal (111) face with oxide (\\(11\\bar{1}\\)) face. The Zr-Zr bond lengths increase from the metal side (\u2248 3.3\u2009\u00c5) to the oxide side (\u2248 3.6\u2009\u00c5). The interface has a long Zr-Zr distance, which is due to partial oxidation. Moreover, there is an angular mismatch of \u2248 11\u00b0 between metal planes and the interfacial planes in metal [112] direction (oxide [110] direction), making the interface bending towards the oxide (Fig.\u00a03e). To better illustrate the origin of the angular mismatch, we build an ideal model of Zr crystal grain and connect it to a cubic phase ZrO2 from the same crystal orientation (Fig.\u00a03h). Since the metal and oxide grains have different crystal orientations, there is a 15\u00b0 of wedge through direct connection (angular mismatch in Fig.\u00a03h). To minimize the interfacial energy while maintaining the coherency, the oxide has to adopt a bending of 15\u00b0 to fill the wedge (Fig.\u00a03i). At the interface, the maximum numbers of filling oxygen are four instead of eight (Fig.\u00a03j), which means the interface is partially oxidized and the maximum stoichiometric ratio is ZrO. Besides, it is notable that there is a gap angle of \u2248 8\u00b0 between the Zr (100) planes in the oxide and those in the interface (Fig.\u00a03e), alleviating the overall strain in the whole NPs. By rotating this cutout 120\u00b0 counterclockwise, we observed another angular mismatch of \u2248 4\u00b0 between the metal (\\(\\bar{1}\\bar{1}1\\)) planes and oxide (002) planes in metal [\\(1\\bar{1}0\\)] direction (oxide [\\(1\\bar{1}0\\)] direction; Fig.\u00a03f), which is perpendicular to metal [112] direction. It is considerable to have an angular mismatch when two adjacent crystal grains have different crystal plane spacing. The (111) spacing of Zr metal is 2.694\u2009\u00c5, while the (200) spacing of Zr oxide is 2.546\u2009\u00c5. To compensate for the spacing mismatch and to maintain the coherency, a certain degree (\u2248 4\u00b0) of twisting between metal and oxide is preferred (Supplementary Fig.\u00a024)47.\n\nMost of the metal-oxide interfaces are incoherent in the whole particle. Figure\u00a03k, l shows the incoherent interfaces of metal/c-ZrO2 and metal/a-ZrO2, respectively. Although the atomic bonding becomes more distorted and disordered in the incoherent interfaces between metal and c-ZrO2, most of the metal core {111} faces still correspond to oxide {111} faces (Fig.\u00a03k and Supplementary Fig.\u00a025). Zr atoms form an incoherent boundary with lower coordination number and longer bond length than crystalline region (Supplementary Figs.\u00a026, 27). Those metal-oxide incoherent interfaces introduce a number of defects which are distributed around the metal core. Many Zr defects are found in those incoherent interfaces. These observations indicate that when a semi-coherent interface forms, a significant amount of strain could occur due to lattice and/or angular mismatch during oxidation. Once the strain caused by bending or twisting is too large, some of the semi-coherent interfaces could possibly turn to disordered structures through amorphization48, where the coherency of the interface is completely broken.\n\nPorous structures of the oxide film formed on the surface of metal are usually associated with metal corrosion11,17,27,28,29. We observed numbers of porous structures in the Zr-ZrO2 particles. Figure\u00a04a shows a 2.4\u2009\u00c5-thick slice from the reconstruction volume of Zr1; in which a significant number of voids, such as Zr vacancies (triangle), nano-pores (rectangle), and the largest pore (circle), are observed in the particle. From the 3D intensity and surface renderings of three consecutive atomic layers, a single Zr vacancy defect can be clearly located (Supplementary Fig.\u00a028). To determine all the voids and evaluate their occupied volume, we employed Voronoi analysis by measuring the distance of Voronoi vertices to atoms (Methods). Figure\u00a04b shows the histogram of volume distribution of all the voids, which we define as Zr vacancies, nano-pores, and a significantly large nanoscale pore throughout the particle. The porosity is 17% and 14% in Zr1 and Zr2, respectively. Figure\u00a04c and Supplementary Movie\u00a05 show the distribution of all Zr vacancies in Zr1. No vacancy is found in the metal core. More than 110 vacancies are distributed in the particle, and all the Zr vacancies contribute 8.4% of the total porosity. Slightly more vacancies are found in a-ZrO2 than in c-ZrO2 (Fig.\u00a04d). We plot the density of Zr vacancies from the boundary of the metal core to the surface of the particle (Fig.\u00a04e). Most of the vacancies are distributed in the range of 15\u2009\u00c5 between metal core and oxide, which corresponds to the region where Zr packing density exponentially decreases (Fig.\u00a02d). It\u2019s notable that we exclude the vacancies from calculating the Zr packing density, the lower \u03c1N of interface is independent with the rich vacancies surrounding the metal core. We found 41 nano-pores in the volume range between 125 and 4500 \u00c53. They are mostly irregular and with a relatively large length-to-radius ratio. Figure\u00a04f and Supplementary Movie\u00a05 show the distribution of all nano-pores; they mostly sit at the boundaries between c-ZrO2 and a-ZrO2 regions. The largest pore is more than 34000 \u00c53 and penetrates throughout the whole particle, providing a possible pathway for further oxidation (Fig.\u00a04g and Supplementary Movie\u00a05). This pore predominantly sits in the a-ZrO2 regions, connecting and separating all three phases; it terminates at the c-ZrO2 region, releasing a large amount of strain. It\u2019s interesting that the Zr-Zr bonds are significantly distorted at the boundary between two c-ZrO2 domains (Fig.\u00a04h, i), where some of the Zr atoms turn to be completely amorphous to release strain. Several nano-pores are coincidentally observed at this region near the small amorphous ZrO2 domain. These findings indicate that when the strain reaches a certain point, possibly higher than the fracture point, the Zr-Zr crystal bonding could turn distorted and amorphous first, and then rupture to form defects to release the strain. It is generally believed that a compact layer of amorphous oxide at the micrometer scale can protect the interior of metal from further oxidation in aluminum49,50. While our results reveal that in zirconium oxide, the amorphous oxide regions are substantially more porous than those in the crystalline regions, the voids would further advance the oxidation of Zr metal. We observed a variety of voids, which are highly related to the structure of the incoherent interface in Zr NPs from the atomic scale to the nanometer scale. The rearrangements of all the atom positions, including distortion, amorphization, and the rupture of bonding, are possibly due to the massive mass transportation during oxidation at the metal-oxide interfaces facilitated by these voids.\n\na A 2.4\u2009\u00c5-thick slice from the reconstructed volume of Zr1, with vacancy (triangle), nano-pores (rectangle) and the largest pore (circle) highlight. b Volume distribution of all the voids. We define the voids with volume no larger than filling two Zr atoms (125\u2009\u00c53, Methods) as vacancies, the voids with volume between 125 and 4500\u2009\u00c53 as nano-pores. We consider the largest pore with volume of 34,000\u2009\u00c53 independently as it touches and separates all three phases. Dashed lines show the boundaries between three types of voids we define. c The surface renderings of all vacancies in c-ZrO2 (in green) and a-ZrO2 (in blue). The outline of whole NP is plotted with gray contour. d, e Statistics of vacancies. The fractions of vacancies in c-ZrO2 and a-ZrO2 show in (d). The radially normalized density distributions of vacancies as a function of distance from the surface core to the surface show in (e). f The surface renderings of all nano-pores in c-ZrO2 (in green), in a-ZrO2 (in blue) and in between c-ZrO2 and a-ZrO2 (in orange). g The surface rendering of the largest pore. The boundary atoms composed of amorphous and crystalline atoms are colored by blue and green, respectively. h One interface between two c-ZrO2 regions with distorted interfacial Zr-Zr bonds, amorphous region and nano-pores. The crystal and amorphous atoms distinguished by BOO analysis are colored as green and blue, respectively. The contour of the nano-pore is colored as orange. i One representative slice shows a 7.8\u2009\u00c5-thick (\u2248 five atomic layers) cross section of the nano-pores and surrounding atoms. Source data are provided as a Source Data file.",
+            "section_image": [
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+            ]
+        },
+        {
+            "section_name": "Discussion",
+            "section_text": "In conclusion, we determined the 3D atomic structure of metal-oxide interfaces in Zr-ZrO2 NP using atomic-resolution electron tomography. We quantitatively measured the atomic packing density and the degree of oxidation from our experimental model of the metal-oxide interface. The degree of oxidation from metal to oxide increases gradually, resulting in a diffuse interface between FCC Zr core and ZrO2. The Zr metal connects with its oxide via {111} planes; and the semi-coherent interface has severe distortion, including bending and twisting. The significant stress in the interface is relieved through low coordination and defects. Numbers of defects, including vacancies and nano-pores, together leverage the mass transportation during oxidation. We anticipate that our findings will fulfill the dearth of 3D atomic structure of metal-oxide interface and advance the study of fundamental problems of metal-oxide interfaces such as oxidation kinetics, diffusion, and defect evolution in variety of materials.",
+            "section_image": []
+        },
+        {
+            "section_name": "Methods",
+            "section_text": "The Zr NPs were synthesized in liquid using laser ablation methods. An all-solid-state ultraviolet laser with a wavelength of 355\u2009nm was employed for laser ablation in ethanol, with a pulse width of 7\u2009ps, a max pulse energy of 18\u2009\u03bcJ, a repetition frequency of 800\u2009kHz, and a beam spot diameter of 20\u2009\u03bcm. Before being placed in a clean beaker, the bulk Zr target (purity >\u200999.95%) was washed by acetone (99.5%) and ethanol (99.9%). The dissolved oxygen in liquid is eliminated to the minimization by nitrogen flow for 60\u2009min with a flow rate of 4\u2009L\u2009min\u22121. Then, the Zr target was submerged into ethanol and the laser beam was accurately focused vertically on the surface of the bulk Zr through the ethanol in a closed chamber. The laser ablation was continued for 1\u2009min, and the produced Zr NPs were dispersed using ultrasonic agitation and subsequently isolated via centrifugation to be collected in the ethanol solution. The freshly prepared Zr NPs were then placed in air for one month to obtain a naturally oxidized layer several nanometers thick. The detailed methods of synthesis are described in ref. 39. The final Zr-ZrO2 NPs were drop cast onto 7-nm-thick Si3N4 membranes using an atomizer for TEM experiment.\n\nEDS maps were collected on an aberration-corrected Thermo Fisher Scientific Themis Z microscope at 300\u2009kV in Analytical Instrumentation Center at Peking University. The iDPC-STEM imaging was conducted using aberration-corrected TEM (Thermo Fisher Themis Z) operated at 300\u2009kV. The convergence semi-angle is 15\u2009mrad. The collection angle is 6.3\u201324.7\u2009mrad. The last measured current is 19\u2009pA. The dwell time for each pixel is 10\u2009\u03bcs. The pixel size is 0.088\u2009\u00d7\u20090.088\u2009\u00c52. The iDPC-STEM images were filtered by a Gaussian filter with a sigma of 20 pixels, which is a common image-processing step directly conducted in Velox software.\n\nTomographic tilt series were acquired by an aberration-corrected Thermo Fisher Scientific Titan microscope at 300\u2009kV at the Electron Microscopy Laboratory of Peking University. The acceleration voltage was 300\u2009kV and the imaging mode was ADF-STEM mode. Detailed parameters for data acquisition are listed in Supplementary Table\u00a01. Each tomographic tilt series was acquired at the dose rate of <\u20095\u2009\u00d7\u2009105\u2009e \u00c5\u22122. For each tilt angle, three sequential images with a dwell time of 2 to 4\u2009\u03bcs were acquired and registered using normalized cross-correlation, and then averaged to enhance the signal-to-noise ratio.\n\nAcquired images were drift-corrected, denoised, and aligned before reconstruction. Linear drift from the sample or stage was corrected during the image registration. Three sequential frames of images at each tilt angle were used to estimate and compensate for the drift due to thermal vibration or instability of the stage. We computed the cross-correlation coefficient between the images to estimate the drift direction and drift speed. Then, we recovered the images by interpolating the raw images with drift-corrected pixel positions. This drift correction method has been used in many other image processing35,51. Block-matching and 3D filtering (BM3D) is employed to denoise the images after drift correction52. And then, the background was estimated using the discrete Laplacian function of MATLAB and subtracted. In the direction perpendicular to the tilt axis, the images were aligned by maximizing the cross-correlation between the common lines. Along the tilt axis, the images were aligned using the center-of-mass method.\n\nAfter image processing, the 3D reconstruction was computed from experimental tilt series using RESIRE algorithm40.\n\nAfter reconstruction, atom tracing was performed to determine the 3D atomic coordinates. First, we interpolated reconstructed volume with spline method. All the local maxima in the reconstruction were identified as the rough atomic coordinates. Then, the coordinates were optimized according to the local volume of 1.7\u2009\u00c5\u2009\u00d7\u20091.7\u2009\u00c5\u2009\u00d7\u20091.7\u2009\u00c5 with a polynomial fitting method. To separate the non-atoms from the potential atoms, K-means clustering method was employed based on the integrated intensity of the local volume (1.7\u2009\u00c5\u2009\u00d7\u20091.7\u2009\u00c5\u2009\u00d7\u20091.7\u2009\u00c5). For every potential atom, a minimum distance of 2\u2009\u00c5 to its nearest atom should be satisfied. The value of the cutoff is chosen based on the measurement deviation of atom positions. The standard error (\u03c3) of the deviation is measured by the blurring width of reconstruction volume (that is, the standard deviation of the Gaussian-shaped volume of an atom) at the atom sites. The distribution of \u03c3 is 0.357\u2009\u00b1\u20090.004\u2009\u00c5, as Supplementary Fig.\u00a029 shows. So, the cutoff is determined according to the \u201c3\u03c3\u201d criterion (in statistics) to be 3.2\u2009\u00c5 \u2212 3\u2009\u00d7\u20090.357\u2009\u00c5 \u2248 2\u2009\u00c5. The 3.2\u2009\u00c5 is the standard Zr-Zr bond length in metal. By carefully comparing the individual atom in the potential atomic models with the reconstructed volume, we manually corrected the atomic coordinates of unidentified or misidentified atoms. The manual correction has been routinely applied during the atom tracing and refinement in protein crystallography53. Specifically, we have manually removed unphysically too close atoms, which are 112 (0.73%) atoms for Zr1, 168 (0.75%) atoms for Zr2, and 93 (0.7%) atoms for Zr3.\n\nThe pixel size calibration procedure is shown in Supplementary Fig.\u00a030. A FIB sample of silicon is rotated to the [110] zone axis. Calibration images are taken at the same magnification with the same pixel size as the tomography experiments use (normally \u2248 35.8\u2009pm). To correct any potential image distortion caused by sample drift, we take 20 to 50 frames for each image. The dwell time of one pixel in each frame is only 200 to 500\u2009ns, which significantly alleviates the image stretching due to the drift. For each image, all frames are aligned and then averaged. The brightest spots of the fast Fourier transform (FFT) are precisely located using 2D gaussian fit. The distances of these points to the center of FFT are the countdowns of the lattice spacing of the image in the real space. Thus, we can get the lattice constants measured in this image. By comparing it to the standard lattice constants of Si, we can calibrate the pixel size in this magnification. We take multiple Si images at different scan rotation angles and then determine the mean value of the real pixel size.\n\nWe calculated the PDF curve from experimental 3D atomic model by\n\nwhere N is the total number of atoms; \u03b4 is the Dirac delta function; \u3008\u22c5\u3009 is the notation for expectation value; |rij| is the distance between the i-th atom and the j-th atom. To get a smoother PDF curve, a Gaussian kernel function with a \u03c3 of 1.5\u2009\u00c5 was applied to convolute with original g(r). Finally, the PDF was scaled to approach one at the large pair distances. Using this procedure, we calculate the c-ZrO2 and a-ZrO2 separately in three NPs. From the PDF, we determined the first valley position as 4.5\u2009\u00c5, corresponding to the first-nearest-neighbor shell distance. The distance was used as a cutoff for BOO and alpha shape calculation (see the sections below).\n\nWe calculated the normalized local BOO parameters to distinguish the order and disorder of all the atoms. The normalized BOO parameter is defined as \\(\\sqrt{{\\bar{Q}}_{4}^{2}+{\\bar{Q}}_{6}^{2}}/\\sqrt{{\\bar{Q}}_{4{\\mbox{FCC}}}^{2}+{\\bar{Q}}_{6{\\mbox{FCC}}}^{2}}\\), where the \\({\\bar{Q}}_{4}\\) and \\({\\bar{Q}}_{6}\\) values were computed based on the procedure described in ref. 54, using 4.5\u2009\u00c5 (the first-nearest-neighbor shell distance) as a constraint. The \\({\\bar{Q}}_{4{\\mbox{FCC}}}\\) and \\({\\bar{Q}}_{6{\\mbox{FCC}}}\\) are the reference values of the standard FCC structure. We separated the amorphous part from crystalline part according to the criterion of the normalized BOO less than 0.534.\n\nDelaunay triangulation and Voronoi tessellation were performed to determine the voids. Delaunay triangulation, Voronoi tessellation, and alpha shape were performed with the built-in functions of MATLAB (namely, \u2018delaunayTriangulation\u2019, \u2018voronoin\u2019, and \u2018alphaShape\u2019). The initial spatial region of NP was calculated by alpha shape with \u03b1\u2009=\u20094.5\u2009\u00c5 (the first-nearest-neighbor shell distance). Then, we calculated the space that accommodates at least one Zr atom in the initial particle region with the following steps:\n\nThe initial particle region was divided into tetrahedra by Delaunay triangulation.\n\nWe determined whether a tetrahedron is void. We calculated the radius of the circumscribed sphere for each tetrahedron. The radius represents the maximized sphere that can fit within the NP without intersecting with the center of any atom. Tetrahedra with a radius larger than 3.19\u2009\u00c5 were classified as voids. This criterion of radius was obtained based on the standard cubic phase of ZrO2 with one vacancy.\n\nWe grouped neighboring voids together to form larger voids. Two voids that share a common face are considered neighboring and thus combined into a single, larger void. The volume of these larger voids was calculated by summing the volumes of each void component.\n\nWe classified the voids into vacancies, nano-pores and the largest pore based on volume. We define the voids with volume filling one or two Zr atoms (45\u2013125\u2009\u00c53) as vacancies, the voids with volume between 125 and 4500 \u00c53 as nano-pores. The largest pore with volume of 34000\u2009\u00c53 was considered independently.\n\nFinally, the contours of voids were displayed with Laplacian smoothing conducted by GIBBON55.\n\nTopological bonds were determined based on the Voronoi tessellation. Two atoms are considered topologically bonded if their corresponding Voronoi polygons share a common face. In constructing the Voronoi polygons, we removed those surfaces with area less than 1% of the total area of the polygon surfaces56. Additionally, this bond must also be shorter than 4.5 \u00c5, corresponding to the first-nearest-neighbor shell distance. The atomic concentration was calculated by \u03c1N\u2009=\u20091/V, where V is the volume of Voronoi cell of an atom.\n\nOur current oxygen filling is based on geometric frustration of the tetrahedra sites formed by Zr atoms. One prior assumption for this geometric frustration is as long as the volume of any tetrahedra site is large enough (4.68\u2009\u00c53), it would be filled with oxygen atoms. This assumption is based on a fact that Zr is a highly oxygenophilic metal, it is relatively easy to form Zr-O bonds to oxidize Zr metal. Although it cannot give us the precise information about where all the oxygen atoms exactly are, we believe it could still give us a fairly good estimation of the degree of oxidation based on the reasonable Zr-specific knowledge. The oxidation state was then determined using Delaunay triangulation. First, the distortion of Delaunay tetrahedra was considered. The distortion parameter was calculated by \\(\\delta=({e}_{\\max }/{e}_{{\\mbox{avg}}})-1\\), where \\({e}_{\\max }\\) and \\({e}_{{\\mbox{avg}}}\\) are the maximum and average edge lengths of tetrahedron33. We removed the tetrahedron with a distortion parameter larger than 0.255. Then, the volume of the remaining Delaunay tetrahedra was calculated. If the volume of a tetrahedron is larger than 4.68 \u00c53 (the averaged tetrahedron volume of FCC Zr lattice and c-ZrO2 lattice), an oxygen atom was placed inside. Finally, the degree of oxidation for each Zr atom was calculated by the fraction of its surrounding tetrahedra that accommodated one oxygen atom.",
+            "section_image": []
+        },
+        {
+            "section_name": "Data availability",
+            "section_text": "The data that support the findings of this study, including the raw tilt series, raw reconstructions, and traced atom positions, are available from Zenodo57 and from the corresponding authors upon request.\u00a0Source data are provided with this paper.",
+            "section_image": []
+        },
+        {
+            "section_name": "Code availability",
+            "section_text": "The codes used in this study are available from Zenodo57 and from the corresponding authors upon request.",
+            "section_image": []
+        },
+        {
+            "section_name": "References",
+            "section_text": "Lee, S. W. et al. Controlling hot electron flux and catalytic selectivity with nanoscale metal-oxide interfaces. Nat. Commun. 12, 40 (2021).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nHan, Z., Yang, F. & Li, Y. Dynamics of metal-support interface revealed by environmental transmission electron microscopy. Matter 5, 2531\u20132533 (2022).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLowe, J. S. & Siegel, D. J. Modeling the interface between lithium metal and its native oxide. ACS Appl. Mater. Interfaces 12, 46015\u201346026 (2020).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLi, Q. et al. Extra storage capacity in transition metal oxide lithium-ion batteries revealed by in situ magnetometry. Nat. Mater. 20, 76\u201383 (2021).\n\nArticle\u00a0\n    ADS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nFoerster, B. et al. Interfacial states cause equal decay of plasmons and hot electrons at gold\u2013metal oxide interfaces. Nano Lett. 20, 3338\u20133343 (2020).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nTang, W. et al. The roles of metal oxidation states in perovskite semiconductors. Matter 6, 3782\u20133802 (2023).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nSmialek, J. L. Invited review paper in commemoration of over 50 years of oxidation of metals: alumina scale adhesion mechanisms: a retrospective assessment. Oxid. Met. 97, 1\u201350 (2022).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nHu, J. et al. Microstructure and oxidation behavior of the Y/Ta/Hf co-doped AlCoCrFeNi high-entropy alloys in air at 1100\u2009\u00b0C. Corros. Sci. 212, 110930 (2023).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBackman, L., Gild, J., Luo, J., Opila, E. J. & Part, I. Theoretical predictions of preferential oxidation in refractory high entropy materials. Acta Mater. 197, 20\u201327 (2020).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nJeurgens, L. P. H., Lyapin, A. & Mittemeijer, E. J. The mechanism of low-temperature oxidation of zirconium. Acta Mater. 53, 4871\u20134879 (2005).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBirks, N., Meier, G. H. & Pettit, F. S. Introduction to the High-Temperature Oxidation of Metals, 2nd Edition. (Cambridge University Press, 2006).\n\nSun, X. et al. Dislocation-induced stop-and-go kinetics of interfacial transformations. Nature 607, 708\u2013713 (2022).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nZhu, L. et al. Visualizing anisotropic oxygen diffusion in ceria under activated conditions. Phys. Rev. Lett. 124, 056002 (2020).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMorin, F., Beranger, G. & Lacombe, P. Limits of application for Wagner\u2019s oxidation theory. Oxid. Met. 4, 51\u201362 (1972).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nRailsback, J. G., Johnston-Peck, A. C., Wang, J. & Tracy, J. B. Size-dependent nanoscale Kirkendall effect during the oxidation of nickel nanoparticles. ACS Nano 4, 1913\u20131920 (2010).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nYou, R. et al. Revealing temperature-dependent oxidation dynamics of Ni nanoparticles via ambient pressure transmission electron microscopy. Nano Lett. 23, 7260\u20137266 (2023).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nVijayakumar, J. et al. Absence of a pressure gap and atomistic mechanism of the oxidation of pure Co nanoparticles. Nat. Commun. 14, 174 (2023).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nGesmundo, F. & Viani, F. Application of Wagner\u2019s theory to the parabolic growth of oxides containing different kinds of defects: I. pure oxides. J. Electrochem. Soc. 128, 460\u2013469 (1981).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nNeyman, K. M. & Kozlov, S. M. Quantifying interactions on interfaces between metal particles and oxide supports in catalytic nanomaterials. NPG Asia Mater. 14, 59 (2022).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nTea, E., Huang, J., Li, G. & Hin, C. Atomic bonding and electrical potential at metal/oxide interfaces, a first principle study. J. Chem. Phys. 146, 124706 (2017).\n\nArticle\u00a0\n    ADS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nZou, S. et al. Grafting nanometer metal/oxide interface towards enhanced low-temperature acetylene semi-hydrogenation. Nat. Commun. 12, 5770 (2021).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nPacchioni, G. Electronic interactions and charge transfers of metal atoms and clusters on oxide surfaces. Phys. Chem. Chem. Phys. 15, 1737 (2013).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWilson, R. B., Apgar, B. A., Hsieh, W.-P., Martin, L. W. & Cahill, D. G. Thermal conductance of strongly bonded metal-oxide interfaces. Phys. Rev. B 91, 115414 (2015).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nGreiner, M. T., Chai, L., Helander, M. G., Tang, W. & Lu, Z. Metal/metal\u2010oxide interfaces: How metal contacts affect the work function and band structure of MoO3. Adv. Funct. Mater. 23, 215\u2013226 (2013).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nNian, Y. et al. Atomic-scale dynamic interaction of H2O molecules with Cu surface. Phys. Rev. Lett. 125, 156101 (2020).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDong, Z., Ren, Q., Wang, S., Zhang, L. & Luo, L. Atomic-scale interfacial phase transformation governed Cu oxidation in water vapor. J. Phys. Chem. Lett. 12, 6996\u20137001 (2021).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nZhu, Q. et al. Defect-driven selective metal oxidation at atomic scale. Nat. Commun. 12, 558 (2021).\n\nArticle\u00a0\n    ADS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nSainju, R. et al. In situ studies of single-nanoparticle-level nickel thermal oxidation: from early oxide nucleation to diffusion-balanced oxide thickening. ACS Nano 16, 6468\u20136479 (2022).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nXia, W. et al. Bimetallic nanoparticle oxidation in three dimensions by chemically sensitive electron tomography and in situ transmission electron microscopy. ACS Nano 12, 7866\u20137874 (2018).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nNi, N. et al. How the crystallography and nanoscale chemistry of the metal/oxide interface develops during the aqueous oxidation of zirconium cladding alloys. Acta Mater. 60, 7132\u20137149 (2012).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDong, Y., Motta, A. T. & Marquis, E. A. Atom probe tomography study of alloying element distributions in Zr alloys and their oxides. J. Nucl. Mater. 442, 270\u2013281 (2013).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nZhou, J. et al. Observing crystal nucleation in four dimensions using atomic electron tomography. Nature 570, 500\u2013503 (2019).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nYuan, Y. et al. Three-dimensional atomic packing in amorphous solids with liquid-like structure. Nat. Mater. 21, 95\u2013102 (2022).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nYang, Y. et al. Determining the three-dimensional atomic structure of an amorphous solid. Nature 592, 60\u201364 (2021).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLi, Z. et al. Probing the atomically diffuse interfaces in Pd@Pt core-shell nanoparticles in three dimensions. Nat. Commun. 14, 2934 (2023).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nIshikawa, R., Shibata, N., Taniguchi, T. & Ikuhara, Y. Three-dimensional imaging of a single dopant in a crystal. Phys. Rev. Appl. 13, 034064 (2020).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nIshikawa, R. et al. High spatiotemporal-resolution imaging in the scanning transmission electron microscope. Microscopy 69, 240\u2013247 (2020).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nTong, X. et al. Breaking the vitrification limitation of monatomic metals. Nat. Mater. 23, 1193\u20131199 (2024).\n\nLiu, Y. et al. Fabrication of amorphous PdNiCuP nanoparticles as efficient bifunctional and highly durable electrocatalyst for methanol and formic acid oxidation. J. Mater. Sci. Technol. 122, 148\u2013155 (2022).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nPham, M., Yuan, Y., Rana, A., Osher, S. & Miao, J. Accurate real space iterative reconstruction (RESIRE) algorithm for tomography. Sci. Rep. 13, 5624 (2023).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nZhang, F. et al. In situ study of the crystallization from amorphous to cubic zirconium oxide: rietveld and reverse Monte Carlo analyses. Chem. Mater. 19, 3118\u20133126 (2007).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLarsen, P. M., Schmidt, S. & Schi\u00f8tz, J. Robust structural identification via polyhedral template matching. Model. Simul. Mater. Sci. Eng. 24, 055007 (2016).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nNicholls, R. J. et al. Crystal structure of the ZrO phase at zirconium/zirconium oxide interfaces. Adv. Eng. Mater. 17, 211\u2013215 (2015).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLi, X. et al. Polarization Switching and Correlated Phase Transitions in Fluorite\u2010Structure ZrO2 Nanocrystals. Adv. Mater. 35, 2207736 (2023).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDholabhai, P. P., Mart\u00ednez, E., Brown, N. T. & Uberuaga, B. P. On the mobility of carriers at semicoherent oxide heterointerfaces. Phys. Chem. Chem. Phys. 19, 23122\u201323130 (2017).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nPilania, G., Dholabhai, P. P. & Uberuaga, B. P. Role of symmetry, geometry, and termination chemistry on misfit dislocation patterns at semicoherent heterointerfaces. Matter 2, 1324\u20131337 (2020).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nShao, S., Wang, J. & Misra, A. Energy minimization mechanisms of semicoherent interfaces. J. Appl. Phys. 116, 023508 (2014).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nSun, Z. et al. Janus Icosahedral Particles: Amorphization Driven by Three-Dimensional Atomic Misfit and Edge Dislocation Compensation. http://arxiv.org/abs/2310.16474 (2023).\n\nMcGowan, J. C. Estimation of the approximate ionization constants of inorganic bases. Nature 168, 601\u2013602 (1951).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nNguyen, L. et al. Atomic-scale insights into the oxidation of aluminum. ACS Appl. Mater. Interfaces 10, 2230\u20132235 (2018).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nOphus, C., Ciston, J. & Nelson, C. T. Correcting nonlinear drift distortion of scanning probe and scanning transmission electron microscopies from image pairs with orthogonal scan directions. Ultramicroscopy 162, 1\u20139 (2016).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMakinen, Y., Azzari, L. & Foi, A. Collaborative filtering of correlated noise: Exact transform-domain variance for improved shrinkage and patch matching. IEEE Trans. Image Process. 29, 8339\u20138354 (2020).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBr\u00fcnger, A. T. et al. Crystallography & NMR System: A New Software Suite for Macromolecular Structure Determination. Acta Crystallogr. D. Biol. Crystallogr. 54, 905\u2013921 (1998).\n\nArticle\u00a0\n    ADS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLechner, W. & Dellago, C. Accurate determination of crystal structures based on averaged local bond order parameters. J. Chem. Phys. 129, 114707 (2008).\n\nArticle\u00a0\n    ADS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nM Moerman, K. GIBBON: The geometry and image-based bioengineering add-on. JOSS 3, 506 (2018).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nSheng, H. W., Luo, W. K., Alamgir, F. M., Bai, J. M. & Ma, E. Atomic packing and short-to-medium-range order in metallic glasses. Nature 439, 419\u2013425 (2006).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nZhang, Y. et al. Three-dimensional atomic interface between metal and oxide in Zr-ZrO2 nanoparticles. Zenodo. https://zenodo.org/doi/10.5281/zenodo.12724136 (2024).\n\nDownload references",
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+        },
+        {
+            "section_name": "Acknowledgements",
+            "section_text": "We thank the support of High-performance Computing Platform of Peking University. We thank the Electron Microscopy Laboratory at Peking University, Bay Area Centre for Electron Microscopy at Songshan Lake Materials Laboratory and Analytical Instrumentation Center at Peking University for the use of the aberration-corrected electron microscope. This work was supported by the National Natural Science Foundation of China (Grant No. 22172003, 52071222) and Guangdong Major Project of Basic and Applied Basic Research, China (Grant No. 2019B030302010).",
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+        },
+        {
+            "section_name": "Author information",
+            "section_text": "These authors contributed equally: Yao Zhang, Zezhou Li, Xing Tong.\n\nBeijing National Laboratory for Molecular Sciences, Center for Integrated Spectroscopy, College of Chemistry and Molecular Engineering, Peking University, Beijing, 100871, China\n\nYao Zhang,\u00a0Zezhou Li,\u00a0Zhiheng Xie,\u00a0Siwei Huang\u00a0&\u00a0Jihan Zhou\n\nSongshan Lake Materials Laboratory, Dongguan, 523808, China\n\nXing Tong,\u00a0Yue-E Zhang,\u00a0Hai-Bo Ke\u00a0&\u00a0Wei-Hua Wang\n\nCollege of Physics, Liaoning University, Shenyang, 110036, China\n\nYue-E Zhang\n\nInstitute of Physics, Chinese Academy of Sciences, Beijing, 100190, China\n\nWei-Hua Wang\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nJ.Z. conceived the idea and directed the study. Z.L., Z.X., and Y.Z. performed TEM experiment and acquired the data. Y.Z. and S.H. performed the imaging processing, reconstructions, and atom tracing. Y.Z., Z.L., S.H. conducted/discussed data analysis under the direction of J.Z.; T.X. and Y.-E.Z. synthesized Zr NPs under the direction of H.-B.K. and W.-H.W.; Y.Z., Z.L., and J.Z. wrote the manuscript. All authors commented on the manuscript.\n\nCorrespondence to\n                Hai-Bo Ke or Jihan Zhou.",
+            "section_image": []
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+        },
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+            "section_text": "Nature Communications thanks Robert Hovden, Ryo Ishikawa, and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. A peer review file is available.",
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+            "section_image": []
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+            "section_name": "About this article",
+            "section_text": "Zhang, Y., Li, Z., Tong, X. et al. Three-dimensional atomic insights into the metal-oxide interface in Zr-ZrO2 nanoparticles.\n                    Nat Commun 15, 7624 (2024). https://doi.org/10.1038/s41467-024-52026-w\n\nDownload citation\n\nReceived: 28 February 2024\n\nAccepted: 23 August 2024\n\nPublished: 02 September 2024\n\nVersion of record: 02 September 2024\n\nDOI: https://doi.org/10.1038/s41467-024-52026-w\n\nAnyone you share the following link with will be able to read this content:\n\nSorry, a shareable link is not currently available for this article.\n\n\n\n\n                            Provided by the Springer Nature SharedIt content-sharing initiative\n                        ",
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+            ]
+        },
+        {
+            "section_name": "This article is cited by",
+            "section_text": "Applied Microscopy (2025)",
+            "section_image": []
+        }
+    ]
+}

2be28d29fac1837acb16f3a122ee991594a1cc474dcaae29e51328cc54c6d461/metadata.json

@@ -0,0 +1,149 @@
+{
+    "title": "Evaluating large language model agents for automation of atomic force microscopy",
+    "pre_title": "Autonomous Microscopy Experiments through Large Language Model Agents",
+    "journal": "Nature Communications",
+    "published": "14 October 2025",
+    "supplementary_0": [
+        {
+            "label": "Supplementary Information",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-64105-7/MediaObjects/41467_2025_64105_MOESM1_ESM.docx"
+        },
+        {
+            "label": "Transparent Peer Review file",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-64105-7/MediaObjects/41467_2025_64105_MOESM2_ESM.pdf"
+        }
+    ],
+    "supplementary_1": [
+        {
+            "label": "Source Data",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-64105-7/MediaObjects/41467_2025_64105_MOESM3_ESM.xlsx"
+        }
+    ],
+    "supplementary_2": NaN,
+    "source_data": [
+        "/articles/s41467-025-64105-7#ref-CR37",
+        "https://github.com/M3RG-IITD/AILA",
+        "/articles/s41467-025-64105-7#Sec30"
+    ],
+    "code": [
+        "/articles/s41467-025-64105-7#ref-CR37",
+        "https://github.com/M3RG-IITD/AILA"
+    ],
+    "subject": [
+        "Atomic force microscopy",
+        "Computer science"
+    ],
+    "license": "http://creativecommons.org/licenses/by/4.0/",
+    "preprint_pdf": "https://www.researchsquare.com/article/rs-5600537/v1.pdf?c=1760526560000",
+    "research_square_link": "https://www.researchsquare.com//article/rs-5600537/v1",
+    "nature_pdf": "https://www.nature.com/articles/s41467-025-64105-7.pdf",
+    "preprint_posted": "18 Dec, 2024",
+    "research_square_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "The emergence of large language models (LLMs) has accelerated the development of self-driving laboratories (SDLs) for materials research. Despite their transformative potential, current SDL implementations rely on rigid, predefined protocols that limit their adaptability to dynamic experimental scenarios across different labs. A significant challenge persists in measuring how effectively AI agents can replicate the adaptive decision-making and experimental intuition of expert scientists. Here, we introduce AILA (Artificially Intelligent Lab Assistant), a framework that automates atomic force microscopy (AFM) through LLM-driven agents. Using AFM as an experimental testbed, we develop AFMBench\u2014a comprehensive evaluation suite that challenges AI agents based on language models like GPT-4o and GPT-3.5 to perform tasks spanning the scientific workflow: from experimental design to results analysis. Our systematic assessment shows that state-of-the-art language models struggle even with basic tasks such as documentation retrieval, leading to a significant decline in performance in multi-agent coordination scenarios.Further, we observe that LLMs exhibit a tendency to not adhere to instructions or even divagate to additional tasks beyond the original request, raising serious concerns regarding safety alignment aspects of AI agents for SDLs. Finally, we demonstrate the application of AILA on increasingly complex experiments open-ended experiments: automated AFM calibration, high-resolution feature detection, and mechanical property measurement. Our findings emphasize the necessity for stringent benchmarking protocols before deploying AI agents as laboratory assistants across scientific disciplines.Physical sciences/Materials science/Techniques and instrumentation/Imaging techniquesPhysical sciences/Materials science/Theory and computation/Computational methodsself-driving laboratoryatomic force microscopybenchmarkingAI agents",
+            "section_image": []
+        },
+        {
+            "section_name": "Additional Declarations",
+            "section_text": "There is NO Competing Interest.",
+            "section_image": []
+        },
+        {
+            "section_name": "Supplementary Files",
+            "section_text": "SupplementaryMaterials.pdfSUPPLEMENTARY INFORMATION",
+            "section_image": []
+        }
+    ],
+    "nature_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Large language models (LLMs) are transforming laboratory automation by enabling self-driving laboratories (SDLs) that could accelerate materials research. However, current SDL implementations rely on rigid protocols that fail to capture the adaptability and intuition of expert scientists in dynamic experimental settings. Here, we show that LLM agents can automate atomic force microscopy\u00a0(AFM) through our Artificially Intelligent Lab Assistant (AILA) framework. Further, we develop AFMBench\u2014a comprehensive evaluation suite challenging LLM agents across the complete scientific workflow from experimental design to results analysis. We find that state-of-the-art LLMs struggle with basic tasks and coordination scenarios. Notably, models excelling at materials science question-answering perform poorly in laboratory settings, showing that domain knowledge does not translate to experimental capabilities. Additionally, we observe that LLM agents can deviate from instructions, a phenomenon referred to as\u00a0sleepwalking, raising safety alignment concerns for SDL applications. Our ablations reveal that multi-agent frameworks significantly outperform single-agent approaches, though both remain sensitive to minor changes in instruction formatting or prompting. Finally, we evaluate AILA\u2019s effectiveness in increasingly advanced experiments\u2014AFM calibration, feature detection, mechanical property measurement, graphene layer counting, and indenter detection. These findings establish the necessity for benchmarking and robust safety protocols before deploying LLM agents as autonomous laboratory assistants across scientific disciplines.",
+            "section_image": []
+        },
+        {
+            "section_name": "Introduction",
+            "section_text": "Scientific experimentation demands exceptional domain expertise, from exploration or hypothesis-driven experimental design to precision execution and rigorous data analysis. This complexity creates bottlenecks in scientific discovery, particularly as experimental techniques grow increasingly sophisticated. The advent of large language models (LLMs) has propelled the development of self-driving laboratories (SDLs) that integrate diverse information sources for automated planning1 and experimentation. Artificial Intelligence (AI)-agents2,3 and SDLs have already achieved several feats in materials or molecular discovery4,5,6, chemistry research7, and inorganic materials synthesis. The promise of SDLs toward achieving sustainable development8 has resulted in enormous efforts to harness their potential in high-throughput experimentation and discovery9. Efforts to streamline SDLs have resulted in orchestration architectures such as ChemOS10. Additionally, it has been demonstrated that the capability of SDLs can be enhanced by a human-in-the-loop framework that handles disambiguation, thereby enabling better planning and execution11,12. While early demonstrations of LLM-based lab assistants showed promise in chemistry and materials science1,2,3, their operational reliability remains largely uncharacterized beyond specific applications or repetitive use cases with predetermined protocols13,14,15,16,17.\n\nCurrent research predominantly addresses well-documented or predefined protocols and single-objective tasks, failing to capture the intricate interplay between experimental planning, multi-tool coordination, and result interpretation or online intervention10. While recent investigations incorporating planning elements have demonstrated success in achieving specific experimental objectives, they have not systematically evaluated SDL reliability across the broader spectrum of laboratory automation tasks13,14. Although several studies have benchmarked LLMs15,16,17,18,19,20,21,22,23 and vision language models13,14,24,25 through question-answer protocols to assess their potential as materials research co-pilots, a crucial knowledge gap persists: understanding how these AI systems handle novel experimental scenarios and their fundamental limitations.\n\nTo address this challenge, we here introduce AILA (Artificially Intelligent Lab Assistant), an LLM-powered framework augmented with specialized tools. We selected scanning probe microscopy18, specifically atomic force microscopy (AFM), as our experimental testbed, given its inherent complexity and broad applicability in materials research. There have been several efforts to automate microscopy techniques using AI and human-in-the-loop approaches due to their extensive applications in materials characterization26,27,28,29,30,31,32,33,34,35. These efforts focus exclusively on advancing specific operational aspects, such as analysing moving objects or optimizing illumination conditions, with an emphasis on improving individual steps within the broader experimental protocol. In addition to these targeted advancements, Liu et al.36 explores the integration of LLMs\u00a0with Application Programming Interface\u00a0(API) to enhance workflow preparation, instrument operation, and data reproducibility in scanning probe microscopy research. AFM operation demands expertise across multiple domains\u2014from probe calibration to parameter optimization and data interpretation\u2014making it an ideal platform for evaluating AI agents\u2019 ability to manage sophisticated experimental workflows.\n\nUsing AFM as the model system, we probe AILA\u2019s capabilities through AFMBench on five critical aspects of scientific automation: experimental workflow design, multi-tool coordination, decision-making, execution of open-ended experiments, and data analysis. Our systematic evaluation reveals key failure modes and areas requiring enhancement. We demonstrate AILA\u2019s practical utility through five real-world experiments: (1) identification and analysis of an indentation mark on a glass sample, including inference of the indenter type used; (2) detection of graphene flakes on a silicon wafer and determination of the number of graphene layers present; (3) automated microscope calibration; (4) high-resolution imaging of graphene step edges; and (5) load-dependent friction characterization on highly oriented pyrolytic graphite (HOPG).",
+            "section_image": []
+        },
+        {
+            "section_name": "Results",
+            "section_text": "AILA\u2019s architecture prioritizes modularity, enabling seamless integration with diverse experimental and analytical platforms. At its core lies an LLM-powered planner\u2014the framework\u2019s cognitive centre\u2014which orchestrates user interactions and coordinates specialized agents (Fig.\u00a01a). This planner directly takes query from a user and identifies the appropriate agent to handle the task. The agent makes tool calls to carry out the necessary steps to complete the experiment. The agent-to-agent coordination is invoked by two keywords, namely, \u201cNEED HELP\u201d and \u201cFINAL ANSWER\u201d. While the former flag invokes a routing function that transfers the unresolved task to the next appropriate agent, the latter flag results in the termination of the experiment. Thus, AILA employs a dynamic routing, exploiting available agents and tools, for completing the task given by the user (see S2.4 in Supplementary Information for additional details).\n\nAILA a System architecture of the Artificially Intelligent Laboratory Assistant (AILA). Dotted lines indicate adaptive information flow governed by AILA\u2019s decision-making, and solid lines represent deterministic information pathways with predefined routing protocols. b Image of the atomic force microscope (AFM) experimental setup showing key hardware components and control interfaces. c Representative demonstration of AILA\u2019s operation: raw transcript of a user query and AILA\u2019s unedited response sequence, showing the system\u2019s query interpretation, task planning, and execution capabilities.\n\nFor AFM operations, AILA deploys two agents: the AFM Handler Agent (AFM-HA) for experimental control and the Data Handler Agent (DHA) for analysis. The AFM-HA interfaces with a document retrieval system comprising AFM software documentation and a code execution engine that translates Python commands into experimental actions. A Python-based API establishes the hardware-software interface, enabling direct control of the AFM system through vendor-specific protocols (Fig.\u00a01b). The DHA manages image optimization and analysis through dedicated tools: an Image Optimizer that fine-tunes Proportional-integral-derivative (PID) parameters for high-fidelity imaging and an Image Analyzer that extracts targeted features from experimental data. For queries beyond agent capabilities, the planner generates alternative approaches or recommended actions.\n\nIn an AFM experiment, the workflow usually involves two key steps: capturing the image and analysing the results. The imaging part starts with choosing the right cantilever, then setting the imaging parameters. Afterwards, the tip is gently moved toward the sample surface, and the scan is carried out. For every stage, AILA creates a specific Python script and executes it, controlling the AFM instrument in real-time through an API. This connection allows the digital commands to directly translate into physical movements on the instrument. Once the scan is complete, the image is saved automatically and opened for analysis. The technical specifications and implementation details of each module are explained in the Methodology section.\n\nTo demonstrate AILA\u2019s operational workflow, we present a multi-step experiment: acquiring an AFM image of HOPG and extracting its friction and roughness parameters (Fig.\u00a01c). This open-ended task exemplifies real-world complexity, offering multiple solution pathways. Upon receiving the query, AILA dissects it into sequential objectives: image acquisition via AFM-HA followed by DHA-led analysis. AFM-HA retrieves relevant documentation, generates executable code, and captures the image. Following successful acquisition, AILA transitions control to DHA, which directs the Image Analyzer to compute the specified parameters. This orchestrated sequence exemplifies AILA\u2019s core strengths: the ability to parse complex natural language queries, develop strategic workflows, and coordinate multiple agents toward achieving experimental objectives.\n\nAFMBench comprises 100 expertly curated experimental tasks (see S3.1 in Supplementary Information for a few examples of tasks; all the tasks are available in the GitHub repo37), manually designed to rigorously evaluate autonomous AFM operations across multiple dimensions of complexity. Unlike conventional LLM benchmarks or simulation-based evaluations, AFMBench task demands physical execution on AFM hardware, introducing real-world temporal constraints and experimental variability. Analysis of the tasks reveal distinct patterns in resource utilization and operational complexity. In Fig.\u00a02a, tool coordination requirements highlight a systematic preference for sophisticated workflows, with 69% of tasks demanding multi-tool integration, while 31% operate through single-tool protocols. Agent deployment analysis reveals a distribution: 83% of operations utilize single-agent protocols, while 17% require multi-agent coordination\u2014enabling evaluation of both targeted expertise and system-wide integration capabilities.\n\na Pie charts showing the distribution of tool requirements (left, single vs. multiple) and agent requirements (right, single vs. multiple) across benchmark tasks. b Operation complexity categorization showing the proportion of basic versus advanced tasks. c Horizontal bar chart quantifying module engagement frequency across all tasks, demonstrating utilization patterns of each tool and agent. d Venn diagram illustrating the overlap between documentation, analysis, and calculation tasks. e Representative examples of basic (left) and advanced (right) tasks, demonstrating increasing complexity in experimental workflows. Source data are provided as a Source data file.\n\nIn Fig.\u00a02b, the operational landscape is divided into two primary complexity tiers: basic operations (56%) encompassing fundamental microscopy tasks and advanced procedures (44%) requiring more sophisticated experimental workflows (for example questions see Fig.\u00a02e). Core system components\u2014the AFM Handler, Document Retriever tool, and Code Executor tool\u2014demonstrate maximum engagement, each activating in 66 distinct tasks\u00a0(see Fig. 2c). The Data Handler Agent and Image Analyzer tool exhibit selective activation patterns (52 and 48 tasks, respectively), while the Image Optimizer tool engages exclusively in critical parameter optimization scenarios (4 tasks).\n\nTask distribution across functional domains reveals three primary clusters: documentation (50 standalone tasks), analysis (14 tasks), and calculation (10 tasks) (see Fig.\u00a02d). A significant overlap between these domains emerges through integrated tasks that combine multiple functional requirements, reflecting the interconnected nature of experimental workflows. This carefully constructed distribution enables systematic evaluation of AI systems across a spectrum of experimental complexity\u2014from basic instrument control to advanced multi-step procedures requiring mathematical reasoning and dynamic decision-making\u2014effectively mirroring the cognitive hierarchy of expert atomic force microscopists.\n\nSystematic evaluation of AILA using three advanced closed-source and one open-source language models\u2014GPT-4o, GPT-3.5-turbo-0125, Claude-3.5-sonnet-20241022, and Llama-3.3-70B-versatile\u2014unveils distinctive execution patterns and operational efficacies. GPT-4o exhibits exceptional proficiency in documentation-centric operations, achieving an 88.3% success rate, complemented by robust execution in analysis (33.3%) and computational tasks (56.7%)\u00a0(see Fig. 3a). The model\u2019s strength lies in its ability to navigate interconnected workflows: 23.3% success in merged documentation-analysis procedures and 36.7% in documentation-calculation sequences. These metrics highlight GPT-4o\u2019s capacity to replicate the integrative reasoning characteristic of expert microscopists.\n\nClaude-3.5-sonnet-20241022 model exhibits significantly lower performance than GPT-4o except in tasks involving standalone documentation (85.3%). While it is able to perform some cross domain tasks, we observe that the performance is notably lower than GPT-4o. These findings stand in stark contrast to previous benchmarking results in the materials domain17,20, where Claude consistently outperformed other models, suggesting that the performance advantages may not transfer across different types of scientific tasks and interaction formats. In marked contrast, GPT-3.5-turbo-0125 displays poor performance even in standalone tasks: 63.7% accuracy in documentation, and 3.3% in mathematical operations. However, its performance degrades significantly when confronted with multi-domain challenges, registering null success rates in tasks demanding simultaneous expertise across domains. This limitation suggests insufficient development of cross-functional reasoning capabilities essential for autonomous experimentation. The open-source Llama-3.3-70B-versatile model demonstrates accuracy superior to GPT-3.5 in all standalone tasks. However, it completely fails in tasks requiring cross-domain analysis or expertise.\n\nTo further investigate whether the poor performance originates from the LangGraph framework, we implemented the Model Context Protocol (MCP) to assess the performance of Claude (see Section S3.4 in the Supplementary Information for detailed results). We observe\u00a0that the results from both the frameworks are consistent, confirming that the diminished performance is inherent to the model and not a result of the framework.\n\nFor evaluation of our multi-agent\u00a0AILA framework, all successful trials were assessed across operational, token efficiency, and performance metrics (see Methodology\u00a0and Fig. 3b for details). Operational analysis revealed significant disparities in agent coordination capabilities: Llama-3.3-70B exhibited substantial tool-agent confusion, requiring an average of 10 steps per task, whereas GPT-4o demonstrated superior contextual grounding and agent selection efficiency with only 6 average steps per task. Token utilization patterns correlated directly with these operational inefficiencies, where Llama-3.3-70B consumed the highest average prompt tokens, indicating verbose or redundant intermediate reasoning processes, while GPT-4o achieved task objectives with minimal token usage, suggesting focused and deliberate reasoning pathways. Critical deficiencies in agent disambiguation and task-instruction alignment were observed in GPT-3.5 and Claude-3.5, which failed all three trials involving the Data Handler agent. For AFM Handler operations, GPT-4o demonstrated optimal efficiency with approximately 2.5 agent calls per task, contrasting with Claude-3.5, which generated the highest completion token counts and tokens-per-step ratios, indicating excessively elaborate intermediate outputs. Performance metrics revealed substantial variation in task completion success rates: GPT-4o achieved 65% success while GPT-3.5 performed inconsistently at 32.8%. Latency analysis showed Claude-3.5 suffered the highest mean response time (17.31\u2009s), whereas Llama-3.3-70B demonstrated the lowest latency (7\u2009seconds). These comprehensive metrics indicate that while Llama-3.3-70B offers reduced latency, GPT-4o provides the optimal balance between operational efficiency and execution precision, establishing it as the most suitable model for complex multi-agent coordination in autonomous laboratory environments.\n\nComponent utilization analysis reinforces these observations. GPT-4o achieves consistently elevated engagement across system modules (see Fig.\u00a03c, d). For tasks of varying complexity, GPT-4o demonstrates the highest accuracy, while GPT-3.5 performs the worst on advanced and basic tasks. Across all models, performance is generally higher for basic tasks compared to advanced ones. In multi-agent and multi-tool collaborative tasks, GPT-4o achieves the highest accuracy, whereas GPT-3.5 has the lowest. GPT-3.5 performance, in both single-agent and multi-agent collaborative task settings, is lower than that of the other models. These results highlight the fundamental importance of model architecture in autonomous experimental platforms, with GPT-4o\u2019s advanced integrative capabilities positioning it as the superior choice for sophisticated experimental automation.\n\na Venn diagrams showing accuracy metrics for GPT-4o, GPT-3.5-turbo-0125, Llama-3.3-70B-versatile and Claude-3.5-sonnet-20241022 across documentation, analysis, and calculation tasks. Numbers indicate percentage accuracy. b Evaluation metrics are grouped into three categories\u2014Operational\u00a0(left), Token Usage\u00a0(center), and Performance\u00a0(right) Metrics\u2014to assess the performance of four LLM models. c A horizontal bar chart comparing tool and agent utilization efficiency between models is expressed as a percentage of successful engagements. d Performance comparison of different models across tasks of varying complexity (Advanced/Basic) and requiring different tools (Single/Multiple) and agents (Single/Multiple). Source data are provided as a Source data file.\n\nTo assess whether direct tool integration with AILA yields equivalent performance to the multi-agent framework, we conducted a comparative analysis. A representative subset of 10 questions from the AFMBench dataset was systematically evaluated across both single-agent and multi-agent architectures, with each question assessed through three independent trials to ensure statistical reliability and account for inherent variability. The comparative analysis revealed framework-dependent performance variations: GPT-4o demonstrated superior performance in the multi-agent configuration (70% success rate) compared to direct tool integration (58% success rate). For alternative models, performance differences were minimal, as most architectures exhibited fundamental limitations in cross-domain tasks that inherently require multi-agent coordination, regardless of framework structure (see Section S6 of the supplementary material for detailed results). These findings indicate that while computational efficiency favors single-agent architecture implementations, the enhanced coordination capabilities of multi-agent architecture provide measurable performance gains for advanced models capable of complex reasoning.\n\nDetailed examination of failure cases revealed distinctive error patterns between all the language models (see Fig.\u00a04), offering insights into their operational limitations. Note that for computing\u00a0evaluation metrics,\u00a0successful tasks\u00a0are defined as those\u00a0where all three trials for a given task\u00a0are successful. Whereas, for error mode distribution, all the trials for each task are counted\u00a0individually, totalling to 300 task instances.\u00a0GPT-4o exhibits a total error rate of 29%, with errors distributed across three primary categories: code generation (21.7%), agent selection (1.3%), tool selection (0.3%), and instruction adherence (5.7%). The predominance of code generation errors suggests challenges in translating conceptual understanding into executable commands despite the model\u2019s strong performance in task comprehension.\n\nError patterns among different models: GPT-4o (top left), GPT-3.5-turbo-0125 (top right), Llama-3.3-70B-versatile (bottom left) and Claude-3.5-sonnet-20241022 (bottom right). Segments represent a proportional distribution of error types: Instruction adherence (blue), agent selection (pink), tool selection (green) and code generation (gray). Source data are provided as a Source data file.\n\nGPT-3.5-turbo-0125 demonstrates a markedly higher total error rate of 66.6%, with errors concentrated in four categories: code generation (32%) and agent selection (27.3%), tool selection (0.3%). Notably, the model shows less fundamental query interpretation errors (7.0%), indicating robust natural language processing capabilities. However, the elevated frequency of code generation errors, coupled with significant agent or tool selection failures, points to underlying deficiencies in translating comprehension into actionable experimental protocols.\n\nLlama-3.3-70B-versatile and Claude-3.5-sonnet-20241022 demonstrate substantial error rates of 60.6% and 51.6%, respectively, with distinct failure patterns. Llama-3.3-70B-versatile exhibits a notably high frequency of code generation errors (32.0%), manifesting as incorrect argument formulation for tool execution and non-functional code production. Specifically, it struggles to construct appropriate argument structures required for successful tool invocation. In contrast, Claude-3.5-sonnet\u2019s deficiencies primarily stem from agent selection errors (28.3%), where it consistently misattributes tasks between AFM-HA and DHA, resulting in the delegation of experimental procedures to inappropriate agents.\n\nA critical finding emerged regarding LLM\u2019s instruction adherence. In one of the four recorded errors, GPT-4o exceeded its designated operational limits, performing actions that were not authorized by the provided guidelines. For instance, it carried out potentially risky tip movements while it was only instructed to change the cantilever (see S3.2 in the Supplementary Information). In another case, GPT-4o was instructed to capture an image and calculate surface friction. Instead of staying within the scope of the task, it performed additional actions. This behavior was not restricted to GPT4o but was observed in other LLMs as well. Although sometimes the final\u00a0result may have been correct, the failure to follow instructions highlights concerns about AI-agent behavior and raises safety risks in automated lab environments. Similar to the observation of hallucination in LLMs38, these results present a unique challenge\u2014SDLs tend to take arbitrary actions, potentially based on memory rather than following the instructions, referred to hereafter as sleepwalking. These issues are especially critical in sensitive experimental settings, where strict protocol adherence is essential to ensure both equipment safety and the validity of results.\n\nThe AILA framework incorporates iterative debugging protocols to address code generation failures through systematic error resolution. Upon error detection, AILA captures comprehensive error logs and initiates iterative correction cycles, with a maximum threshold of 20 iterations established to optimize the balance between thoroughness and computational efficiency. Analysis of debugging outcomes reveals two distinct failure modes: (1) Iteration Limit Exhaustion, where the system terminates after 20 unsuccessful correction attempts, with persistent errors classified as code generation failures; and (2) Sleepwalking, where AILA generates functional code that exceeds the specified requirements, demonstrating functionality beyond the original instructions\u2014a phenomenon indicating instruction drift or algorithmic overfitting, categorized as instruction adherence errors. This binary classification system enables systematic characterization of failure modes while the iteration threshold ensures computational tractability without compromising debugging efficacy in autonomous laboratory operations.\n\nThis error distribution illuminates critical areas for framework enhancement. While GPT-4o\u2019s balanced error profile suggests the need for targeted improvements across multiple domains, GPT-3.5-turbo-0125\u2019s concentrated error patterns indicate fundamental limitations in experimental execution capabilities. These findings underscore the necessity for specialized training in automated experimental systems, particularly focusing on the translation of scientific protocols into executable code sequences.\n\nTo understand the safety challenges39 of AI agents, we evaluate the effectiveness of implementing a safety framework in AILA. First, we establish restricted access protocols for critical AFM functions, coupled with ethical system prompts (see S2.1 in Supplementary Information) that constrain code generation to predefined documentation40. To implement this, we classified all the operations that could be performed on an AFM as per the instrument\u2019s documentation into two categories. (i) General operations\u2014these include setting imaging parameters, controlling the tip, selecting the scanning area, and other standard tasks. (ii) Critical operations\u2014these involve sensitive adjustments such as factory calibrations, laser alignment, piezo calibration, and thermal calibration. Even a minor coding error in critical operations could seriously damage the instrument.\n\nWe restricted the access to the documentation of critical operations in AILA, while allowing complete access to the documentation of general operations. The critical functions are limited to trained human experts. Note that general operations were selected in such a fashion that any experiment that could potentially be performed on an AFM could be carried out using some combination of these operations. Thus, the predefined documentation in AILA does not restrict any new experiment to be performed on the AFM instrument. Note that an alternate approach to implement safety is to identify risky actions and involve a human-in-the-loop mechanism to review the actions. This could also enhance the robustness and overall performance of the framework. However, such a framework requires human supervision, limiting the high-throughput nature that an autonomous system can otherwise achieve, with human response becoming the bottleneck. Hence, this approach was not implemented in AILA and could be explored as part of future work.\n\nSecond, we develop strict operational boundaries that permit dynamic code generation solely for image analysis while preventing external software installation or system modifications. Evaluation of the improved protocol demonstrates the effectiveness of these safeguards\u2014AILA appropriately failed when prompted to install external Python libraries. (see S3.3 in Supplementary Information for complete validation logs). These findings underscore the critical importance of robust safety protocols in SDLs, emphasizing the necessity of comprehensive benchmarking and operational guardrails.\n\nFinally, to demonstrate AILA\u2019s capabilities in real-world scenarios, we demonstrate five experimental tasks that typically require expert intervention: automated AFM calibration, high-resolution feature detection, load-dependent friction measurement, graphene layer analysis, and indenter profiling.\n\nAFM imaging requires precise calibration of Proportional-Integral-Derivative (PID) gain values, which traditionally demand expert intervention due to the continuous nature of these parameters. This dependency on skilled operators presents a significant barrier to broader AFM adoption. We demonstrate AILA\u2019s capability to autonomously optimize these parameters by minimizing the forward-backward scan differential on standard calibration grids. To this end, after loading the calibration sample, AILA was prompted to optimize the imaging parameters (see S4 in Supplementary Information for the complete prompt and output log). A total of 45 images are generated, with 3 images produced in each of the 15 generations. Figure\u00a05a presents experimental AFM data acquired by AILA for the 1st and 15th generation of variable PID configurations, with corresponding line scan analyses that quantify trace-retrace symmetry. Initial scans with suboptimal parameters (P: 93\u2013208, I: 1747\u20136623, D: 0\u201339) exhibit poor SSIM scores (0.392\u20130.768), manifesting as visible distortions in topographic data. Note that a higher SSIM value, closer to 1, indicates a perfect match, while a value of 0 represents no similarity. Through iterative optimization, AILA achieves superior scan quality (SSIM\u2009>\u20090.81) with optimized parameters (P: 246\u2013249, I: 8676\u20138957, D: 17\u201330; see Fig.\u00a05a).\n\na Evolution of AFM image quality under varying PID parameters. The left panels show topographic images of the calibration grid; the right panels display corresponding line scan profiles (solid: trace, dashed: retrace). Structural Similarity Index (SSIM) scores quantify trace-retrace correlation, with higher values indicating superior imaging quality. Optimal parameters (Proportional (P) gain: 249, Integral (I) gain: 8957, Derivative (D) gain: 26) achieve SSIM\u2009=\u20090.818. b Large-area scan demonstrating consistent imaging quality using optimized parameters across multiple grid features. c Convergence plot showing genetic algorithm optimization efficiency. Red circles: maximum SSIM; black circles: mean SSIM per generation. d High-resolution Highly Oriented Pyrolytic Graphite (HOPG) imaging demonstrating baseline artifact challenges. Top panels: topographic images at different height (Z) ranges; bottom panels: corresponding line profiles revealing surface features. Source data are provided as a Source data file.\n\nThe genetic algorithm\u2019s convergence efficiency is demonstrated in Fig.\u00a05c, where optimal PID configurations are achieved within 15 generations. Both maximum and mean SSIM values show rapid improvement, stabilizing above 0.8, indicating robust parameter optimization. Figure\u00a05b validates the optimized parameters (P:249, I:8957, D:26) across a larger scan area, maintaining high-quality imaging across multiple grid features.\n\nSurface characterization through AFM is challenged by noise sources such as thermal drift, mechanical vibrations, and electronic interference41,42,43, which can obscure subtle topographic features like graphene step edges. In this study, we leverage the advanced analytical capabilities of AILA to address these challenges using HOPG as a model system. AILA autonomously determines the necessity for baseline correction based on feature size, recognizing that baseline artifacts predominantly affect smaller features. To further demonstrate this, we tested two different prompts with samples of distinct morphologies (see Fig.\u00a0S3 in Supplementary Information). In both cases, AILA correctly selected the appropriate baseline correction. For instance, in the raw image (Fig.\u00a05d), the graphene step edge remains indiscernible due to baseline distortions. AILA applies a fifth-order polynomial baseline correction to generate the 1st generation image (Fig.\u00a05d), which serves as the foundation for PID gain optimization. Following a process similar to the calibration grid optimization, the image is refined through iterative PID adjustments, resulting in the final optimized image in the 10th generation, where atomic steps become distinctly visible. The automated optimization process surpasses conventional manual adjustments, offering an enhanced resolution of nanoscale features. Additionally, further analysis of the processed data, including the determination of graphene step height, was facilitated through specific prompts, with the prompts and results detailed in the Supplementary Information\u00a0S5. Note that in the AILA framework, edge detection is not based on a fixed algorithm. Instead, the system generates custom code to solve the problem, whereas, for feature detection, AILA uses the built-in Image Segment tool (see Methodology) that applies Otsu\u2019s thresholding to automatically segment images by finding the most effective intensity-based thresholds.\n\nThe experiments discussed thus far are routine, with limited number of steps and hence, complexity. Now, we conduct a comprehensive load-dependent friction analysis of HOPG (see Fig.\u00a06a). The experiment requires iterative adjustments of AFM parameters, including setting a range of setpoints, capturing images, and analyzing the corresponding friction data. Manually performing this procedure is time-intensive, involving parameter modifications, image acquisition, data extraction, and result plotting, making a case for automation.\n\na Left: Highly Oriented Pyrolytic Graphite (HOPG) images obtained using setpoints of 0.2\u2009V and 0.4\u2009V, both manually captured and taken by Artificially Intelligent Lab Assistant (AILA) with GPT-4o. Right: Raw, unedited plot generated by AILA showing the relationship between setpoint and average friction. b Demonstration of AILA\u2019s workflow for real-world experimentation on graphene-coated Si sample, displaying the user\u2019s transcribed query, AILA\u2019s unedited final response, intermediate analyses, and exported images. This showcases AILA\u2019s capability to autonomously conduct real-world experimental tasks. c Demonstration of how AILA identifies an indentation mark on a glass substrate, analyses the indenter type using a horizontal line profile, and provides a final interpretation with supporting explanation. Source data are provided as a Source data file.\n\nHowever, based on the experiments conducted above and this experiment, we observed that the performance of the LLMs could be directly affected by the prompts. To evaluate this effect, we analyzed the effect of prompting (see Methodology and Table\u00a0S3) by systematically varying the prompts from simple to complex, from compact to descriptive. Our findings revealed that GPT-4o demonstrated variable task completion rates across different prompt structures, ranging from partial execution to complete fulfillment. Significantly, more elaborate and detailed prompts consistently enhanced the model\u2019s performance reliability and execution accuracy, suggesting that comprehensive contextual information improves complex task handling. Based on these experiments, we designed the prompts consistently across the experiments and ensured that prompt optimization was not carried out to arrive at desirable results.\n\nAILA was instructed (see S5 in Supplementary Information for the complete prompt and output log) to vary the setpoint voltage from 0.2\u2009V to 1.2\u2009V in increments of 0.2\u2009V. At each setpoint, AILA independently captured the AFM image, calculated the average friction value, and generated the corresponding plot. Figure\u00a06a presents the graph of average friction versus setpoint voltage for both manually obtained and AILA-captured images using the GPT-4o model. The raw image generated by AILA can be found in the Supplementary Information Fig.\u00a0S2. The entire process was conducted without additional user input regarding figure formatting or parameter settings. Remarkably, AILA autonomously develops the required Python script, executes the experimental protocol, and generates the output, including raw, unedited plots. This automation significantly reduces the time and effort compared to manual execution. The results not only validate the capability of AILA in handling AFM experiments but also demonstrate its efficiency in generating reproducible and high-quality outputs for scientific analyses.\n\nTo evaluate the performance of AILA in a real-world experimental setting, we designed two distinct experiments. In both cases, an experimentalist is required to identify a specific feature of interest, capture it, and then carry out the experiment. Further, the results need to be analyzed to draw meaningful conclusions. In the first experiment (see Fig.\u00a06b), the objective is to locate a graphene flake and determine the number of atomic layers in it. To accomplish this, AILA performs image segmentation using Image Segment tool within a user-specified region, identifies the largest visible flake, and extracts it for further analysis. Through a sequence of intermediate processing steps, AILA autonomously generates code, processes the image, and ultimately provides an estimate of the number of graphene layers present in the selected flake. The second experiment (see Fig. 6c)\u00a0involves identifying the type of indenter used to create an impression on a sample surface. The intended image is analyzed by AILA, including an inspection of the indentation line profile. Based on this analysis, it infers and concludes, along with a detailed explanation, that the indenter used was most likely of Vickers-type geometry. Thus, in both the cases, AILA performs the experiment successfully and provides analysis and conclusions similar to human experts. Specifically, in the first case, it uses the knowledge of the thickness of graphene along with numerical computation to identify the number of layers, whereas in the second, it uses the knowledge on the characteristics of Vickers and conospherical indenters along with reason to identify the appropriate indenter. The complete set of raw user inputs and unprocessed outputs is presented in (Fig.\u00a06b, c). The log files of both the\u00a0experiments are available in our GitHub repository37.",
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+        {
+            "section_name": "Discussion",
+            "section_text": "AILA\u2019s modular design, along with AFMBench, establishes quantifiable metrics in experimental automation through systematic benchmarking. The framework\u2019s comprehensive performance metrics in AFM operations establish standards for autonomous laboratory evaluation, while AFMBench introduces reproducible protocols for systematic assessment across experimental domains. Successful execution of tasks\u2014from automated image optimization to nanomechanical measurements\u2014validates the framework\u2019s capabilities for sophisticated materials characterization.\n\nSeveral outcomes merit detailed examination. The measured limitations in tool coordination across different LLMs establish quantifiable thresholds for improving inter-module communication protocols. Our results demonstrate that multi-agent architectures systematically outperform single-agent configurations, with the primary advantage extending beyond mere instruction execution to encompass task modularization, specialized agent collaboration, independent reasoning, and dynamic decision-making regarding subtask sequencing and tool selection. These findings align with established literature demonstrating the superiority of multi-agent architecture over single-agent implementations across diverse computational domains44,45,46. These observations also establish an empirical baseline for balancing specialized and integrated operations\u2014a metric applicable to automation across analytical platforms, from mass spectrometers to X-ray diffractometers.\n\nHowever, the observed tendency of LLM agents to exceed operational boundaries through sleepwalking phenomenon during experimental execution presents critical safety concerns for autonomous laboratory deployment. This phenomenon, documented here for the first time in autonomous experimental systems, highlights urgent development priorities in instruction alignment and operational safety protocols. Additionally, despite providing direct access to comprehensive documentation and code snippets, persistent code generation errors indicate fundamental limitations in current retrieval-augmented generation frameworks. These findings necessitate the development of enhanced code generation architectures that incorporate domain-specific constraint validation and formal verification protocols to minimize coding errors\u2014representing an immediate opportunity for systematic improvement in autonomous laboratory reliability.\n\nThese findings suggest specific architectural improvements for next-generation autonomous laboratories. Enhanced integration protocols between specialized agents could address the observed limitations in multi-tool coordination. Similarly, dedicated code generation modules might mitigate the predominant error mode, potentially incorporating specialized scientific programming frameworks.\n\nThe implications of this work extend beyond materials characterization. The unexpected underperformance of Claude-3.5-sonnet-20241022 compared to GPT-4o highlights a critical insight: question-answer proficiency in a specific domain does not necessarily predict effectiveness in agentic implementations. Rather tool coordination capabilities of LLMs prove to be an important aspect for effective agentic implementation. Furthermore, the observed prompt fragility emphasizes the necessity for developing rigorous evaluation frameworks prior to deployment in research environments. Specifically, developing systematic and principled approaches to generate prompts and make systems that are robust to minor variations in prompts plays a crucial role in the wider acceptance of agentic systems. To this end, quantitative benchmarks such as AFMBench provide concrete guidance for implementing LLM-driven systems in experimental research settings where precision and reliability are paramount.\n\nApplications span pharmaceutical screening, environmental monitoring, and process optimization. For instance, documented success in parameter optimization could translate directly to automated high-throughput drug screening or catalyst discovery platforms. While current limitations in code generation and tool coordination define immediate development targets, these metrics provide clear objectives for advancing autonomous scientific platforms. The path forward requires focused development in three key areas: enhanced cross-domain reasoning capabilities, robust code generation protocols, and sophisticated multi-agent coordination mechanisms. Success in these domains would enable truly autonomous scientific platforms capable of accelerating discovery across the scientific landscape.",
+            "section_image": []
+        },
+        {
+            "section_name": "Methods",
+            "section_text": "AILA is constructed utilizing the LangChain software framework, incorporating components such as prompts, LLMs, memory, agents, and tools. AILA uses two categories of prompts: system prompts (see S2.1 in Supplementary Information for the system prompts) and user prompts. System prompts define ethical rules for AILA\u2019s interactions and describe the responsibilities assigned to each agent, whereas user prompts are variable inputs provided by end-users. AILA\u2019s backbone consists of LLMs, namely GPT-4o, GPT-3.5-turbo-0125, Llama-3.3-70B-versatile, and Claude-3.5-sonnet-20241022, which process user input as strings and provide string-based outputs. We used API keys from the developers for GPT-4o, GPT-3.5-turbo-0125, and Claude-3.5-sonnet-20241022. Additionally, we used API keys from Groq AI Inference for Llama-3.3-70B-versatile model. We have used a temperature value of zero for all models, with the parameters set as max tokens 2024, and max retries two. These LLMs are stateless, indicating that they do not save conversational context. Here, all interactions and agent states are stored in a Python dictionary and can be accessed by other agents. AILA consists of two specialized agents: the AFM Handler Agent and the Data Handler Agent, both equipped with unique tools to do specific tasks. These agents possess individual prompts, LLMs, and tools; however, they utilize a shared memory to store and access states, facilitating smooth interaction. The system prompts within the agents offer instructions for tool utilization and ethical guidelines, whereas the outputs from other tools or agents serve as user prompts. The framework utilizes LangGraph, a library that allows the construction of an effective multi-agent workflow, integrating all agents and tools seamlessly. AILA uses two different approaches for selecting algorithms, depending on the task. When performing standard calculations like friction or roughness analysis, AILA relies on established algorithms with adjustable input parameters. This method produces consistent and reproducible results. For exploratory work and data visualization, AILA takes a different approach by creating the code on the fly. This method adapts better to varying data formats and specific user requirements; however, this may introduce variability in the results depending on the complexity of the task.\n\nThe architecture for AILA\u2019s decision-making process is carefully designed to ensure precise information routing. Where it uses two different routing mechanism: dynamic and static routing. A detailed discussion of both dynamic and static routing is provided in the Supplementary Information. AILA can dynamically select among three primary options: AFM Handler, Data Handler, or FINISH. When AILA identifies the appropriate agent to handle a query, it routes the information to the selected option. In cases where AILA determines that none of the available agents can sufficiently address the question, it generates a well-structured response and selects the FINISH option to conclude the session effectively. The agents within this system are equipped with three distinct operational choices: utilizing their respective tools, transferring information to the next agent, or terminating the session. A system prompt has been integrated to streamline these decisions. Agents append the prefix NEED HELP to their response when transferring information to another agent. Alternatively, if they believe the query has been adequately addressed, they use the prefix FINAL ANSWER to signal the session\u2019s conclusion. By analyzing the output for these keywords, the system seamlessly routes the response to the designated agent or tool or finalizes the session. This structured approach enables efficient multi-agent collaboration, ensuring clarity, accuracy, and optimal performance across tasks while maintaining a robust and adaptive framework.\n\nAFM demands precise sequential execution of multiple experimental stages. Image acquisition requires optimization across three critical parameters: imaging conditions, probe selection, and operational mode configuration (tapping/contact). The experimental sequence encompasses surface approach protocols, scanning procedures, and standardized data acquisition\u2014with procedural deviations potentially resulting in equipment damage or data corruption. Our implementation utilizes the DriveAFM instrument (Nanosurf), which is accessed through a Python-based API architecture and designed for universal compatibility with API-enabled AFM systems. To facilitate AFM imaging experiments, we have created the AFM Handler agent, which is integrated with two specialized tools: the Document Retrieval Tool and the Code Executor Tool. Every tool has an individual role, and the AFM Handler agent can dynamically assign tasks to these tools. The agent will assign the responsibility to the Data Handler agent if it finds that neither tool can handle the task.\n\nThe documentation for the instrument offers detailed instructions on how to handle and calibrate it. However, providing full access of the documentation to an LLM entails risks, such as inadvertent alterations to factory settings or calibration data, which could potentially result in damage or malfunction of the instrument. To address this concern, we manually extracted the essential information from the AFM documentation necessary for conducting experiments while safeguarding the instrument\u2019s integrity. We consolidated all the crucial codes for regulating each parameter of the instrument into a comprehensive Python script. Since Python code relies heavily on precise indentation and line structure, we utilized the Recursive Character Text Splitter from the LangChain library, specifically designed for Python, to divide the script into manageable chunks. The chunk size was set to a maximum of 1000 characters without overlap, adhering to the token limit for embedding models. Each code chunk comprises three sections: the first includes the necessary Python libraries, the second contains the code required to load the application, and the third section features unique Python code specific to the given task. The first two sections are consistent across all chunks (see S2.2 in the Supplementary Information file for more details). These chunks were then combined to generate a document, embedded using OpenAI\u2019s text-embedding-3-large model. This model, with the capability of producing embeddings of size up to 3072 dimensions, delivers exceptional performance compared to other OpenAI embedding models, especially in multi-language retrieval benchmarks like MIRACL47. To store the embeddings, we opted for Chroma, an open-source vector database known for its reliability and efficiency in managing large-scale embedding data. We use a vector store retriever to retrieve the data from the vector store.\n\nA code executor tool has been developed to execute Python scripts generated by the AFM Handler Agent to control the AFM software. This tool is intended to run Python code, provided as a text string, directly on the local system to allow for smooth integration with the workflow of the AFM Handler Agent. The utility executes the code and sends back a success message or a detailed description of the error that occurred. If there is an error, the error message is returned to the AFM Handler agent so it can correct the error and retry executing. Otherwise, if the script runs without errors, it is considered the final result. This iterative process ensures precise control of the AFM system while systematically addressing any issues in the script.\n\nSurface tracking optimization in AFM requires precise calibration of three fundamental parameters: Proportional (P), Integral (I), and Derivative (D) gains. Optimal calibration manifests as convergence between trace and retrace signals, indicating stable scanning conditions. The Data Handler agent interfaces with specialized optimization and analysis modules; these models can access AFM image data stored in local storage systems. The agent can optimize P, I, and D gains or calculate various surface properties, such as average friction and surface roughness, using the help of modules and image files stored locally. While many AFM software packages offer basic data analysis functionalities, they present several limitations in an automated workflow as follows. (i) Most of these software solutions primarily support Windows systems, limiting cross-platform compatibility with operating systems such as macOS and Linux platforms. (ii) Commercial packages require paid licenses, restricting accessibility. (iii) Finally, most packages are not flexible to include additional functionalities beyond what is already included, limiting their customizability. Thus, to ensure broader adaptability and maintain an adaptable, flexible, modular, and open framework, we developed the Data Handler agent within AILA, which has access to several tools\u2014new functionalities can be easily integrated to this agent and the tools based on user needs. Note that this does not restrict the usage of vendor software packages, as they could also be included as a tool in AILA. The agent offers a significantly expanded suite of advanced analytical capabilities, such as:\n\nCustomizable and automated image processing workflows tailored to specific experimental needs.\n\nStatistical analysis across multiple datasets, enabling robust comparison of parameters such as average friction, surface roughness, and topographic variations.\n\nPlatform independence, ensuring compatibility across Windows, macOS, and Linux, and eliminating reliance on proprietary or licensed software.\n\nDynamic code generation via LLM integration, allowing users to automatically generate and execute scripts for plotting and analysing images.\n\nTo demonstrate the adaptability of the agent, we developed a custom function to calculate indentation volume (see Fig.\u00a0S4 in the Supplementary Information). Instructions for integrating additional functions into the Data Handler Agent are provided in a step-by-step guide available on the accompanying GitHub repository37.\n\nThe feedback system in an AFM plays a crucial role in maintaining control over the interaction between the cantilever tip and the sample surface. During scanning, variations in surface features alter the interaction forces between the tip and the sample, leading to deflections in the cantilever. These deflections are detected by a photodetector. To ensure that these deflections stay within a specified range, the feedback mechanism continuously adjusts the height of either the tip or the sample stage in real-time. This process is managed by a PID controller, which regulates the position of the z-piezo actuator. By\u00a0controlling the Z position of the AFM probe, the controller maintains a steady interaction force or adheres to a predefined setpoint, depending on the chosen mode of operation.\n\nFine-tuning the P, I, and D gain values of the controller is vital for achieving accurate control of the setpoint in AFM imaging. The integral gain is especially important for enhancing image clarity by mitigating drift and reducing steady-state errors. Once the integral gain is optimized, adjusting the proportional gain can provide further refinement. The derivative gain, on the other hand, is particularly beneficial for imaging samples with pronounced edge features. If the gains are set too low, the PID loop may fail to maintain the setpoint effectively, while excessively high gain values can introduce electrical noise into the image due to amplified feedback or overcompensation for deviations. Properly optimized PID parameters ensure that the feedback loop remains stable and responsive, enabling the AFM to accurately track surface topography, even at higher scanning speeds. This balance is especially critical when imaging delicate, irregular, or soft materials, as it preserves the integrity of tip-sample interactions.\n\nA genetic algorithm (GA) was employed for PID gain optimization. The GA parameters included a fixed population size of three and a total of 15 generations, enabling efficient tuning of the gains. Although these parameters can be manually adjusted, but excessive image scanning may degrade the AFM tip. The optimized gains ensure effective feedback control, producing comparable forward and backward images. This can be achieved by calculating the mean squared error (MSE) between forward and backward z-axis images for various PID gain settings. However, this method is sensitive to drift during scanning, and this method also depends on previously acquired images. To address this, the structural similarity index (SSIM) was adopted as the fitness function in the genetic algorithm, providing a robust measure of image similarity between the z-axis forward and backward images, independent of prior image data.\n\nThis metric offers advantages over traditional Mean Square Error (MSE) approaches by (i) addressing tip degradation challenges in contact-mode AFM by minimizing required scan cycles and enabling optimization using low-resolution images, (ii) maintaining accuracy under drift conditions, (iii) incorporating structural, brightness, and contrast variations in optimization, and (iv) providing normalized scores between 0 and 1, where 1 indicates perfect similarity.\n\nThe SSIM is defined as:\n\nwhere, \\(l(x,y)\\) is the luminance comparison, \\(c(x,y)\\) is the contrast comparison, and \\(s(x,y)\\) is the structure comparison with \\(\\alpha\\), \\(\\beta\\), \\(\\gamma\\) being the weighting parameters. Note that the individual components are defined as:\n\nwhere, \\({\\mu }_{x},{\\mu }_{y}\\) represent the mean intensities of images \\(x\\) and \\(y\\), \\({\\sigma }_{x},{\\sigma }_{y}\\) is the standard deviations of images \\(x\\) and \\(y\\), \\({\\sigma }_{{xy}}\\) is the cross-covariance between images \\(x\\) and \\(y\\), and \\({C}_{1},{C}_{2},{C}_{3}\\) are constants to avoid instability with \\(({C}_{1}={({k}_{1}L)}^{2},{C}_{2}={({k}_{2}L)}^{2},{C}_{3}={C}_{2}/2)\\) and \\(L\\) being the dynamic range of pixel values and \\({k}_{1}=0.01\\) and \\({k}_{2}=0.03\\).\n\nBaseline correction. The adaptive baseline correction employed in the step-edge detection of graphene is given by\n\nwhere, \\(B(x,y)\\) is the baseline function, \\({a}_{{ij}}\\) are the polynomial coefficients, \\(i\\) and \\(j\\) are the polynomial degrees \\((0\\le i,j\\le n)\\) with \\(n\\) being the maximum polynomial degree.\n\nAFM instrument stores the image data as a *.nid file in the local system. This *.nid file contains deflection, friction force, and z-axis images for both backward and forward scans. To further process any image from the file, exact data must be extracted from the file. To conduct this, we have used the NSFopen Python library in the Image Analyzer tool, which takes the query from the data handler agent regarding the specific image data and its location and returns the image data in an array to the data handler agent. To conduct further processing of the images, any Python script generated by the data handler agent can be executed in the Image Analyzer tool, and the result can be returned to the data handler agent. Note that there is no database available to guide the LLM model in generating the Python script. It can generate the Python script by itself. There is a total of 6 input parameters for this tool:\n\npath (str): directory path to search for the latest file (default: None).\n\nFilename (str): specific image file to display (default: None).\n\nDynamic_code (str): Python code for processing image data (default: None).\n\nCalculate_friction (bool): option to compute average friction (default: False).\n\nCalculate_mean_roughness (bool): option to compute mean roughness (default: False).\n\nCalculate_rms_roughness (bool): option to compute RMS roughness (default: False).\n\nReturns: a dictionary with the status, image data, or error details.\n\nAverage friction was calculated using the following formula:\n\nwhere \\({f}_{{ij}}\\) and \\({b}_{{ij}}\\) are the element at position \\(\\left(i,j\\right)\\) in the array of the forward and backward friction image data. We have used the formula in this tool to calculate the mean roughness and RMS roughness values\n\nwhere \\({z}_{{ij}}\\) is the element at position \\((i,j)\\) in the array, \\(\\bar{z}\\) is the mean of all elements in the array, \\(M\\) is the number of rows in the array, N is the number of columns in the array of the z-axis forward image data.\n\nAn Image Segment and an Image Scanner tool have been created to analyse AFM-scanned images. The Segment tool use the Otsu algorithm to segment images according to the various features present in the sample. Upon detection of features, the tool produces bounding boxes and allocates distinct grain IDs to each feature. This bounding box information is subsequently utilized by LLMs for additional data processing. Note that we used text-based LLM models that cannot discern any features inside the sample, whether they pertain to the material or represent alien inclusions. Following its analysis, the LLM can transmit designated grain IDs to the Image Scanner tool, which instructs the AFM instrument to meticulously scan those particular characteristics.\n\nTo evaluate the performance of the AILA, we have manually created a set of 100 questions, carefully categorized into three distinct groups. The first classification is based on whether a question requires one or multiple tools and agents to be solved. The second category assesses the complexity of the questions, distinguishing between basic and advanced levels. Lastly, the questions are grouped by their requirements, such as documentation analysis or calculations. The complexity of each question is determined by the number of agents involved and the steps required to achieve the solution. For instance, modifying a parameter in an AFM system typically requires documentation review and the use of a single agent, categorizing it as a basic task. Conversely, capturing an AFM image and analyzing its surface roughness involves multiple agents, documentation analysis, and calculations, making it an advanced task. A comprehensive JSON file has been created, encapsulating detailed metadata about each question, including its respective category, for streamlined analysis and evaluation. This file serves as a structured resource for further investigations and testing. All questions, along with their relevant classifications and details, have been made accessible on GitHub37 (https://github.com/M3RG-IITD/AILA) to support transparency and reproducibility in research.\n\nWe developed a graphical user interface (GUI) using Streamlit, an open-source Python framework, to streamline user interaction with AILA. The GUI allows users to input text-based queries, select the desired LLM model, and specify a log file name. It then executes AILA in the backend, saving the output log file locally and enabling users to observe results directly within the AFM software. Any output images or figures generated by AILA are also stored in the local system for further analysis. To ensure robustness, we manually evaluated all questions using each model, verifying the output log files and AFM software results multiple times in collaboration with different researchers to eliminate potential human errors. The evaluation of AILA\u2019s performance was categorized into two metrics: accuracy and efficiency. For accuracy, questions were divided into categories based on complexity and tool or agent usage, with a percentage of correct answers calculated for each category. For efficiency, uniform parameters were maintained across models in the AFM software, including default settings of 0.1\u2009s as time per line and 128\u00a0as lines per frame, when not specified by the user. To ensure precise efficiency measurements, scanning time for images and the time taken by questions with incorrect answers were excluded from the analysis. Average response times were computed for each category to assess AILA\u2019s overall efficiency.\n\nTo assess the evaluation of questions in terms of accuracy, we classified the answers provided by AILA into three categories: fully correct answers, incorrect and partially correct answers. A fully correct answer was considered accurate and given a score of 1, while any partially correct response was given a score of 0.5. Given that some questions require manual inspection of the AFM software to verify whether specific parameters are set correctly and whether the AFM image is captured as intended, multiple researchers were involved in verifying the results. They carefully checked the outcomes to ensure error-free results. For measurements of different properties, such as average friction, roughness, and RMS value of roughness, we used the Gwyddion software to verify the accuracy of the results. Subsequently, the questions were clustered into appropriate groups, and the corresponding average percentage of correct answers was calculated. The detailed evaluation process is provided in the Supplementary Information.\n\nAdditional evaluation metrics are defined as following. Based on the scoring, Success rate is computed as the average score (out of 100) across three iterations for all the tasks. For all the successful runs, following metrics are employed.\n\nAFM handler calls: the average number of times the AFM Handler agent was called to resolve a task (calls per task). An elevated score may signify a greater dependence on the AFM Handler for coordination.\n\nData handler calls: the average number of times the Data Handler agent was called during task solving.\n\nNumber of steps: the average number of discrete actions (represented by tool or agent call) taken by the AILA to arrive at a solution.\n\nTotal tokens: total number of LLM model tokens is processed on an average for each task, considering both input (prompt) and output (complete) tokens.\n\nPrompt tokens: number of tokens utilized in the conversation\u2019s input or instruction segment for each task.\n\nCompletion tokens: the average number of tokens that the system\u2019s answers create for all assignments.\n\nTokens per stage: this tells how many tokens were utilized on average for each stage in the process of solving a task.\n\nLatency: the average amount of time (in seconds) it takes to complete a task from the first to the final step.\n\nTime per step: the average amount of time (in seconds) spent on each step, representing the pace with which the system can perform different tasks.\n\nLatency per 1000 tokens: the average amount of time (in seconds) taken to process 1000 tokens.\n\nWe systematically investigated how prompt structure and phrasing influence GPT-4o\u2019s ability to perform load-dependent friction measurements, one of our most challenging open-ended tasks. LLMs process information hierarchically based on input format and length, making them sensitive to prompt design. Even subtle modifications can activate different training exemplars, altering response patterns and reasoning pathways. To evaluate performance within the AILA framework, we constructed multiple input prompts to assess task completion efficacy. In AILA, inter-agent collaboration is triggered when the model outputs \u201cNEED HELP\u201d, while \u201cFINAL ANSWER\u201d signals task completion. We developed and tested four distinct prompt categories: (1) concise task descriptions, (2) comprehensive task elaborations, (3) sequential task decompositions, and (4) explicit inclusions of the signaling phrases with case variations. By systematically combining these elements, we designed five system prompts, with detailed performance metrics documented in the Supplementary Information (Table\u00a0S3).",
+            "section_image": []
+        },
+        {
+            "section_name": "Data availability",
+            "section_text": "All the data generated in this study have been deposited in the GitHub repository37 under accession code https://github.com/M3RG-IITD/AILA.\u00a0Source data are provided with this paper.",
+            "section_image": []
+        },
+        {
+            "section_name": "Code availability",
+            "section_text": "All the codes in AFMBench37, along with the complete log files of the responses for each of the tasks from all models are available at: https://github.com/M3RG-IITD/AILA.",
+            "section_image": []
+        },
+        {
+            "section_name": "References",
+            "section_text": "Zhao, Z., Lee, W. S. & Hsu, D. Large language models as commonsense knowledge for large-scale task planning. Adv. Neural Inform. Process. Syst. 36, 31967\u20133198 (2024).\n\nLiu, Y. et al. Machine learning-based reward-driven tuning of scanning probe microscopy: towards fully automated microscopy. ACS Nano 19, 19659\u201319669 (2025).\n\nL\u00e1la, J. et al. Paperqa: retrieval-augmented generative agent for scientific research. arXiv https://doi.org/10.48550/arXiv.2312.07559 (2023).\n\nKoscher, B. A. et al. Autonomous, multiproperty-driven molecular discovery: From predictions to measurements and back. Science 382, eadi1407 (2023).\n\nArticle\u00a0\n    PubMed\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nSzymanski, N. J. et al. An autonomous laboratory for the accelerated synthesis of novel materials. Nature 624, 86\u201391 (2023).\n\nArticle\u00a0\n    ADS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDai, T. et al. Autonomous mobile robots for exploratory synthetic chemistry. Nature 635, 890\u2013897 (2024).\n\nArticle\u00a0\n    ADS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBoiko, D. A., MacKnight, R., Kline, B. & Gomes, G. Autonomous chemical research with large language models. Nature 624, 570\u2013578 (2023).\n\nArticle\u00a0\n    ADS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nSadeghi, S. et al. Engineering a sustainable future: harnessing automation, robotics, and artificial intelligence with self-driving laboratories. ACS Sustain. Chem. Eng. 12, 12695\u201312707 (2024).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDelgado-Licona, F. & Abolhasani, M. Research acceleration in self-driving labs: Technological roadmap toward accelerated materials and molecular discovery. Adv. Intell. Syst. 5, 2200331 (2023).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nSim, M. et al. ChemOS 2.0: An orchestration architecture for chemical self-driving laboratories. Matter 7, 2959\u20132977 (2024).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDarvish, K. et al. ORGANA: a robotic assistant for automated chemistry experimentation and characterization. Matter https://doi.org/10.1016/j.matt.2024.10.015 (2025).\n\nAbolhasani, M. & Kumacheva, E. The rise of self-driving labs in chemical and materials sciences. Nat. Synth. 2, 483\u2013492 (2023).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nCanty, R. B. & Abolhasani, M. Reproducibility in automated chemistry laboratories using computer science abstractions. Nat. Synth. 1, 13 (2024).\n\n\n                    Google Scholar\u00a0\n                \n\nVolk, A. A. & Abolhasani, M. Performance metrics to unleash the power of self-driving labs in chemistry and materials science. Nat. Commun. 15, 1378 (2024).\n\nArticle\u00a0\n    ADS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMirza, A. et al. Are large language models superhuman chemists? Nat. Chem. 17, 984\u2013985 (2025).\n\nZaki, M., Jayadeva, M. & Krishnan, N. M. A. MaScQA: investigating materials science knowledge of large language models. Digital Discov. 3, 313\u2013327 (2024).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nAlampara, N. et al. Probing the limitations of multimodal language models for chemistry and materials research. Nat. Comput. Sci. https://doi.org/10.1038/s43588-025-00836-3 (2025).\n\nMiret, S. & Krishnan, N. M. A. Enabling large language models for real-world materials discovery. Nat. Mach. Intell. 7, 991\u2013998 (2025).\n\nKrishnan, N. M. A., Kodamana, H. & Bhattoo, R. Natural language processing. In Machine Learning for Materials Discovery: Numerical Recipes and Practical Applications (Springer International Publishing, 2024).\n\nMishra, V. et al. Foundational Large Language Models for Materials Research. Preprint at https://doi.org/10.48550/arXiv.2412.09560 (2025).\n\nLi, Z. et al. Mmsci: a multimodal multi-discipline dataset for PhD-level scientific comprehension. in AI for Accelerated Materials Design-Vienna https://doi.org/10.48550/arXiv.2407.04903 (2024).\n\nSkarlinski, M. D. et al. Language agents achieve superhuman synthesis of scientific knowledge. Preprint at https://doi.org/10.48550/arXiv.2409.13740 (2024).\n\nBian, K. et al. Scanning probe microscopy. Nat. Rev. Methods Prim. 1, 36 (2021).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBayley, O., Savino, E., Slattery, A. & No\u00ebl, T. Autonomous chemistry: Navigating self-driving labs in chemical and material sciences. Matter 7, 2382\u20132398 (2024).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nTom, G. et al. Self-driving laboratories for chemistry and materials science. Chem. Rev. 124, 9633\u20139732 (2024).\n\nArticle\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLiu, Y. et al. AEcroscopy: a software\u2013hardware framework empowering microscopy toward automated and autonomous experimentation. Small Methods https://doi.org/10.1002/smtd.202301740 (2024).\n\nKandel, S. et al. Demonstration of an AI-driven workflow for autonomous high-resolution scanning microscopy. Nat. Commun. 14, 5501 (2023).\n\nArticle\u00a0\n    ADS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nVasudevan, R. K. et al. Autonomous experiments in scanning probe microscopy and spectroscopy: choosing where to explore polarization dynamics in ferroelectrics. ACS Nano 15, 11253\u201311262 (2021).\n\nArticle\u00a0\n    PubMed\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKalinin, S. V. et al. Automated and autonomous experiments in electron and scanning probe microscopy. ACS Nano 15, 12604\u201312627 (2021).\n\nArticle\u00a0\n    PubMed\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nArias, S., Zhang, Y., Zahl, P. & Hollen, S. Autonomous molecular structure imaging with high-resolution atomic force microscopy for molecular mixture discovery. J. Phys. Chem. A 127, 6116\u20136122 (2023).\n\nArticle\u00a0\n    PubMed\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKang, S., Park, J. & Lee, M. Machine learning-enabled autonomous operation for atomic force microscopes. Rev. Sci. Instrum. 94, 123704 (2023).\n\nArticle\u00a0\n    ADS\u00a0\n    PubMed\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nZaki, M. et al. Interpretable machine learning approach for identifying the tip sharpness in atomic force microscopy. Scr. Materialia 221, 114965 (2022).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKalinin, S. V. et al. Probe microscopy is all you need. Mach. Learn. Sci. Technol. 4, 023001 (2023).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLiu, Y. et al. Disentangling electronic transport and hysteresis at individual grain boundaries in hybrid perovskites via automated scanning probe microscopy. ACS Nano 17, 9647\u20139657 (2023).\n\nArticle\u00a0\n    PubMed\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLiu, Y. et al. Learning the right channel in multimodal imaging: automated experiment in piezoresponse force microscopy. npj Comput. Mater. 9, 34 (2023).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLiu, Y., Checa, M. & Vasudevan, R. K. Synergizing human expertise and AI efficiency with language model for microscopy operation and automated experiment design*. Mach. Learn. Sci. Technol. 5, 02LT01 (2024).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMandal, I. et al. Automation of atomic force microscopy with LLM agents including end-to-end evaluation suite. https://doi.org/10.5281/zenodo.16793992 (2025).\n\nHuang, L. et al. A survey on hallucination in large language models: Principles, taxonomy, challenges, and open questions. ACM Transac. Inform. Syst. 43, 1-55(2023).\n\nAnwar, U. et al. Foundational challenges in assuring alignment and safety of large language models. arXiv https://doi.org/10.48550/arXiv.2404.09932 (2024).\n\nLiu, Y. et al. Trustworthy LLMs: a survey and guideline for evaluating large language models\u2019 alignment. arXiv https://doi.org/10.48550/arXiv.2308.05374 (2023).\n\nGrobelny, J. et al. Size measurement of nanoparticles using atomic force microscopy. in Characterization of Nanoparticles Intended for Drug Delivery (ed. McNeil, S. E.) 71\u201382 (Humana Press, Totowa, NJ, 2011). https://doi.org/10.1007/978-1-60327-198-1_7.\n\nMoreno-Flores, S. Baseline correction of AFM force curves in the force\u2013time representation. Microsc. Res. Tech. 79, 1045\u20131049 (2016).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBurnham, N. A., Lyu, L. & Poulikakos, L. Towards artefact-free AFM image presentation and interpretation. J. Microsc. 291, 163\u2013176 (2023).\n\nArticle\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nShu, R., Das, N., Yuan, M., Sunkara, M. & Zhang, Y. Towards effective genai multi-agent collaboration: design and evaluation for enterprise applications. Preprint at https://doi.org/10.48550/arXiv.2412.05449 (2024).\n\nGao, M. et al. Single-agent or Multi-agent Systems? Why Not Both? Preprint at https://doi.org/10.48550/arXiv.2505.18286 (2025).\n\nSreedhar, K. & Chilton, L. Simulating human strategic behavior: comparing single and multi-agent LLMs. Preprint at https://doi.org/10.48550/arXiv.2402.08189 (2024).\n\nZhang, X. et al. Making a MIRACL: multilingual information retrieval across a continuum of languages. Preprint at https://doi.org/10.48550/arXiv.2210.09984 (2022).\n\nDownload references",
+            "section_image": []
+        },
+        {
+            "section_name": "Acknowledgements",
+            "section_text": "N.M.A.K. acknowledges the funding support from Google Research Scholar Award and the Alexander von Humboldt Foundation. I.M. thanks University Grants Commission (UGC), Government of India for the NET-JRF fellowship (221610021768). J.S. acknowledge the funding received from the Ministry of Education, Government of India, in the form of research fellowship. M.Z. acknowledges the funding received from the PMRF award by the Government of India. M.M.S. acknowledges support from the European Union (ERC, NewGLASS, 101044664). L.W. acknowledges funding from the Carl Zeiss Foundation through its Breakthrough program. The authors thank the IIT Delhi HPC facility for computational and storage resources. We also thank Sushant Sinha for his assistance with the image segmentation.",
+            "section_image": []
+        },
+        {
+            "section_name": "Author information",
+            "section_text": "School of Interdisciplinary Research, Indian Institute of Technology Delhi, Hauz Khas, New Delhi, India\n\nIndrajeet Mandal,\u00a0Nitya Nand Gosvami\u00a0&\u00a0N. M. Anoop Krishnan\n\nDepartment of Materials Science and Engineering, Indian Institute of Technology Delhi, Hauz Khas, New Delhi, India\n\nJitendra Soni\u00a0&\u00a0Nitya Nand Gosvami\n\nDepartment of Civil Engineering, Indian Institute of Technology Delhi, Hauz Khas, New Delhi, India\n\nMohd Zaki\u00a0&\u00a0N. M. Anoop Krishnan\n\nDepartment of Chemistry and Bioscience, Aalborg University, Aalborg, Denmark\n\nMorten M. Smedskjaer\n\nLeibniz Institute of Photonic Technology, Jena, Germany\n\nKatrin Wondraczek\n\nOtto Schott Institute of Materials Research, University of Jena, Jena, Germany\n\nLothar Wondraczek\n\nYardi School of Artificial Intelligence, Indian Institute of Technology Delhi, Hauz Khas, New Delhi, India\n\nNitya Nand Gosvami\u00a0&\u00a0N. M. Anoop Krishnan\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nI.M. developed the AILA framework, generated the visualizations for the figures and tables, and conducted the experiments. J.S. prepared figures and performed experiments. M.Z. contributed to the code development. M.M.S., K.W., and L.W. edited the draft and validated the results. All authors contributed to the conceptualization of the project, the design of the methodology. I.M. and N.M.A.K. wrote the original draft of the manuscript. All authors contributed to reviewing and editing the manuscript. N.M.A.K. and N.N.G. were responsible for funding acquisition, project administration, resource provision, and overall supervision of the project.\n\nCorrespondence to\n                Nitya Nand Gosvami or N. M. Anoop Krishnan.",
+            "section_image": []
+        },
+        {
+            "section_name": "Ethics declarations",
+            "section_text": "The authors declare no competing interests.",
+            "section_image": []
+        },
+        {
+            "section_name": "Peer review",
+            "section_text": "Nature Communications thanks the anonymous reviewers for their contribution to the peer review of this work. A peer review file is available.",
+            "section_image": []
+        },
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+            "section_image": []
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+        {
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+            "section_text": "Open Access  This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.\n\nReprints and permissions",
+            "section_image": []
+        },
+        {
+            "section_name": "About this article",
+            "section_text": "Mandal, I., Soni, J., Zaki, M. et al. Evaluating large language model agents for automation of atomic force microscopy.\n                    Nat Commun 16, 9104 (2025). https://doi.org/10.1038/s41467-025-64105-7\n\nDownload citation\n\nReceived: 01 March 2025\n\nAccepted: 04 September 2025\n\nPublished: 14 October 2025\n\nVersion of record: 14 October 2025\n\nDOI: https://doi.org/10.1038/s41467-025-64105-7\n\nAnyone you share the following link with will be able to read this content:\n\nSorry, a shareable link is not currently available for this article.\n\n\n\n\n                            Provided by the Springer Nature SharedIt content-sharing initiative\n                        ",
+            "section_image": [
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@@ -0,0 +1,145 @@
+{
+    "title": "Short-range order controlled amphoteric behavior of the Si dopant in Al-rich AlGaN",
+    "pre_title": "Short-range order controlled amphoteric behavior of the Si dopant in Al-rich AlGaN",
+    "journal": "Nature Communications",
+    "published": "30 May 2025",
+    "supplementary_0": [
+        {
+            "label": "Supplementary Information",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-60312-4/MediaObjects/41467_2025_60312_MOESM1_ESM.pdf"
+        },
+        {
+            "label": "Transparent Peer Review file",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-60312-4/MediaObjects/41467_2025_60312_MOESM2_ESM.pdf"
+        }
+    ],
+    "supplementary_1": [
+        {
+            "label": "Source Data",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-60312-4/MediaObjects/41467_2025_60312_MOESM3_ESM.zip"
+        }
+    ],
+    "supplementary_2": NaN,
+    "source_data": [
+        "/articles/s41467-025-60312-4#Fig1",
+        "/articles/s41467-025-60312-4#Fig4",
+        "/articles/s41467-025-60312-4#Sec15"
+    ],
+    "code": [],
+    "subject": [
+        "Applied physics",
+        "Electronic devices",
+        "Semiconductors"
+    ],
+    "license": "http://creativecommons.org/licenses/by/4.0/",
+    "preprint_pdf": "https://www.researchsquare.com/article/rs-5580951/v1.pdf?c=1748603303000",
+    "research_square_link": "https://www.researchsquare.com//article/rs-5580951/v1",
+    "nature_pdf": "https://www.nature.com/articles/s41467-025-60312-4.pdf",
+    "preprint_posted": "07 Jan, 2025",
+    "research_square_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "AlGaN alloys with high Al content offer the possibility to create deep ultraviolet (UV) light sources emitting at wavelengths \u2264 240 nm with enhanced quantum efficiency. However, pushing the limits of the band gap energies towards higher values leads to problems with n-type doping of AlGaN alloys with the standard choice of Si donors when the Al content surpasses \u223c80 %. This is due to the formation of the so-called negative Si DX center where the Si-N bond is ruptured, followed by a displacement of the N atom. In this paper, we show that the amphoteric nature of the Si dopant in AlGaN alloys is fundamentally controlled by the local environment and the ordering of the Ga and Al atoms in the vicinity of the Si atom. Our conclusions are based on advanced characterization sensitive to the local environment of defects and impurities: positron annihilation spectroscopy and X-ray absorption spectroscopy. Electronic structure calculations complete the picture. As our experiments show that the presence of Ga in the vicinity of Si controls the donor character of the latter in high Al content AlGaN, we propose that spatial ordering of these atoms could allow efficient n-type doping at even higher Al contents, including AlN.Physical sciences/Materials science/Materials for devices/Electronic devicesPhysical sciences/Physics/Applied physicsPhysical sciences/Physics/Condensed-matter physics/Semiconductors",
+            "section_image": []
+        },
+        {
+            "section_name": "Additional Declarations",
+            "section_text": "There is NO Competing Interest.",
+            "section_image": []
+        },
+        {
+            "section_name": "Supplementary Files",
+            "section_text": "AlGaNmanuscriptSI.pdfShort-range order controlled amphoteric behavior of the Si dopant in Al-rich AlGaN",
+            "section_image": []
+        }
+    ],
+    "nature_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "AlGaN alloys with high Al content offer the possibility to create deep ultraviolet light sources emitting at wavelengths \u2264 240\u2009nm with enhanced quantum efficiency. However, increasing the band gap when the Al content surpasses \u00a0~80% leads to problems with n-type doping of AlGaN alloys with the standard choice of Si donors, due to the formation of the so-called negative Si DX center. In this paper, we show that the amphoteric nature of the Si dopant in AlGaN alloys is fundamentally controlled by the local environment and the ordering of the Ga and Al atoms in the vicinity of the Si atom. Our conclusions are based on advanced characterization sensitive to the local environment of defects and impurities, complemented by electronic structure calculations. We propose that spatial ordering of Ga and Si atoms could allow efficient n-type doping at even higher Al contents, including AlN.",
+            "section_image": []
+        },
+        {
+            "section_name": "Introduction",
+            "section_text": "Discovery and technological realization of alloying of III\u2013V compound semiconductors with different band gaps (Eg) and stacking thin films thereof opened up the field of semiconductor optoelectronics several decades ago. The family of III-nitride semiconductors AlN (Eg\u2009=\u20096.2\u2009eV), GaN (Eg\u2009=\u20093.4\u2009eV) and InN (Eg\u2009=\u20090.7\u2009eV) extends the spectrum across the whole visible range and is at present the core technology in, for example, solid-state lighting. This technology is based mainly on InGaN alloy systems, while the device heterostructures typically include also thin layers of low Al content alloys. The ultra wide band gap of AlN allows band gap engineering for the development of short wavelength opto-electronic as well as power-electronic devices, such as displays with high luminosity, lasers and high-power high-frequency chips with improved stability and energy efficiency1,2. Moreover, synthesizing AlGaN alloys with high Al content creates the possibility to fabricate deep ultraviolet (UV) light sources emitting at wavelengths \u2264240 nm with enhanced quantum efficiency3,4,5,6. Such UV light emitting devices can be applied, for example, in sanitizing systems against viruses and bacteria, which possibly can help to inhibit infectious diseases or provide more people with drinking water7.\n\nControlling the conductivity of semiconductors is key to their functionality8. Already early on with conventional III\u2013V semiconductor AlGaAs alloys, it was discovered that pushing the limits of the band gap towards higher values led to problems with n-type doping with the standard choice of Si as a dopant. The root cause for the inability to obtain highly conductive material was found to be the formation of the so-called negative Si DX center when the Al content surpassed \u00a0~\u00a020% in the AlxGa1-xAs alloy9. In this defect the Si atom normally substituting for the cation lattice site displaces strongly and undergoes a donor-to-acceptor transition10,11. A similar phenomenon occurs in Si-doped AlGaN alloys, albeit at much higher Al content: in AlGaN with Al content higher than 80%, the negatively charged Si DX state is formed by the axial Si-N bond rupturing along the c-axis followed by the displacement of the N atom12,13,14,15. Electrical compensation by the formation of cation vacancy complexes with silicon has also been suggested as the doping limiting process in high Al content AlGaN16. Interestingly, the DX center formation appears universal to compound semiconductor alloys with Ga/Al cations, as also in the \u03b2-(Al,Ga)2O3 alloys Si is an efficient donor up to a certain Al content, above which the material becomes semi-insulating irrespective of the Si doping17. In these oxide alloys, the bond-breaking associated with the Si DX formation depends on the site of the Si atom as the lattice hosts two inequivalent cation sites: either the Si atom or the adjacent O atoms are strongly displaced 18.\n\nIn this paper, we show that the amphoteric nature of the Si dopant in AlGaN alloys is fundamentally controlled by the local environment and the ordering of the Ga and Al atoms in the immediate surroundings of the Si atom. This is in contrast to the common observation in conventional III-V semiconductors, where the Si DX transformation is generally interpreted in terms of a non-local average characteristic of the material, resulting in a threshold average alloy composition as a determining factor for the phenomenon. Our conclusions are based on advanced experimental characterization sensitive to the local environment of defects and impurities on an extended set of Al0.90Ga0.10N epitaxial thin films doped with Si in the range from 1\u2009\u00d7\u20091018 cm\u22123 to 2\u2009\u00d7\u20091019 cm\u22123. Positron annihilation spectroscopy19 reveals that negatively charged acceptor ions emerge at concentrations comparable only to the Si concentration, simultaneously with the onset of the compensating character of further increase in Si doping. X-ray absorption near edge structure spectroscopy (XANES)20 shows that the local environment of the Si atoms changes from GaN-like to AlN-like at the same threshold concentration. We also perform electronic structure calculations21 that show that Si is drawn to the locally Ga-rich lattice sites, retaining its donor character when these are available. As our experiments show that the presence of Ga in the vicinity of Si controls the donor character of the latter in high Al content AlGaN, we propose that spatial ordering of these atoms could allow efficient n-type doping at even higher Al contents, including AlN.",
+            "section_image": []
+        },
+        {
+            "section_name": "Results",
+            "section_text": "The basic characteristics of the Si-doped Al0.90Ga0.10N epitaxial thin films discussed in this paper are shown in Fig.\u00a01a. The samples were synthesized by metal-organic vapor phase epitaxy (MOVPE) on epitaxially laterally overgrown (ELO) AlN/sapphire, with the top layer as the material of interest22. The thin films were grown in two types of conditions resulting in either a relatively high carbon content (2\u00a0\u00d7\u00a01018 cm\u22123, samples H1 \u2013 H13), or in a relatively low carbon content (2\u00a0\u00d7\u00a01017 cm\u22123, samples L1 \u2013 L5), similar to ref. 23. In set H1-H5, the highest [Si] reached 7\u00a0\u00d7\u00a01018 cm\u22123 resulting in the lowest resistivity near the possible threshold [Si] changing to the upward trend in resistivity. The set H6-H13 covers broader range of [Si] and demonstrates the predicted knee behavior of resistivity similar to samples L1-L5. We include here data on previously reported samples H1-H523 to highlight the consistency in both the resistivity and positron data across these two sets of samples. The growth conditions of H1-H5 are similar to H6-H13 with minor fluctuations in precursors flow. The Si doping was controlled by adjusting the SiH4 flow during synthesis, resulting in the Si content ranging from 1\u00a0\u00d7\u00a01018 cm\u22123 to 2\u00a0\u00d7\u00a01019 cm\u22123 in the samples. The concentrations of other impurities are all below 5\u00a0\u00d7\u00a01017 cm\u22123.\n\na The basic structure (not in scale) of the samples studied is shown in the upper panel, together with the O and H concentrations. b Resistivity as a function of Si doping concentration, with respective C concentrations in the various sample series. The curves are drawn to guide the eye.\n\nThe resistivity of the AlGaN samples as a function of Si doping, shown in Fig.\u00a01b, exhibits a similar trend in both types of synthesis conditions. First, the resistivity decreases with the increase of Si content, as expected for a dopant that should increase the free carrier concentration. Above a certain threshold, this decrease levels off and at sufficiently high Si doping concentrations the resistivity increases with further increase of Si content. This behavior where the doping efficiency is severely reduced\u2014and even excess compensation observed\u2014above a certain threshold Si concentration is a well known problem in n-type doping of AlGaN alloys15. With increasing Al mole fraction in AlGaN, both the Si doping efficiency and threshold Si concentration decrease, strongly limiting the achievable conductivity in high Al content AlGaN. The reduced doping efficiency with high Al contents is likely due to the higher donor activation energies and formation of Si DX centers that exist in AlN but not in GaN14,15. However, the reason for the vanishing and even negative doping efficiency with increasing Si concentration is not clear.\n\nFigure\u00a02 shows the normalized (S,\u00a0W) parameters measured in the Si-doped AlGaN samples at room temperature. All the measured (S,\u00a0W) data are located within the area defined by the points characterizing the GaN and AlN lattices, the typical in-grown Ga vacancies in GaN (denoted by VGa-X), and the Al vacancy in AlN23,24,25,26. Our earlier work on a subset of these samples, where we performed also temperature-dependent experiments, allowed us to conclude that the data obtained in sample H1 represents the Al0.90Ga0.10N lattice, while the average VIII found in Al0.90Ga0.10N is characterized by the data obtained in samples L1-L323. The gradual shift in (S,\u00a0W) parameters obtained in the samples H1 - H9 (red markers) with increasing Si content from the AlGaN lattice point towards the VIII point indicates that the VIII concentration in these samples increases with increasing Si concentration. The VIII concentrations\u00a0can be estimated from the positron data and are shown in Fig.\u00a02\u2013 see the\u00a0Supplementary Information (SI) for detailed analysis. It is important to note that the VIII concentrations are an order of magnitude lower than the Si concentrations, and hence too low to account for the electrical compensation in these samples.\n\nThe light green circles mark the values for the GaN lattice, AlN lattice and VAl in AlN, and the light green dashed ellipse shows those for in-grown VGa complexed with H and O impurities or VN in GaN, as shown in earlier work23. The values given above the data markers show the evolution of the cation vacancy concentration with the (S,\u00a0W) parameters. The data points in red/blue are from samples where the resistivity decreases/increases with increasing Si content. The arrows show the direction of increasing Si content. The dashed blue star shows where the data point for sample H13 shifts if the carbon effect is removed.\n\nInterestingly, the (S,\u00a0W) parameters behave very differently in samples H10\u2013H13 and L1\u2013L5 (blue markers). Instead of saturating at the point characteristic of VIII that would result from further increase of the VIII concentration with the increase of the Si content, the (S,\u00a0W) parameters shift towards the left side of Fig.\u00a02. In the L series, the endpoint of this shift is very close to the point characteristic of the AlN lattice. In the H series the end-point W parameter is close to the original AlGaN - VIII line, but still clearly below, towards the AlN-like data of the L series. As seen in the temperature-dependent data in sample L523, this dramatic shift is due to the emergence of a high concentration of negative ion type defects in the samples. Detailed analysis (see\u00a0SI) shows that the concentrations required for this magnitude of effect are very close to the Si concentration in these samples, and significantly higher than the concentration of carbon that also acts as a negative ion type defect for positrons, or of any other impurity. The less dramatic vertical effect in samples H10-H13 is indeed due to the higher C concentration in these samples compared to L1\u2013L5: removing the carbon effect from the (S,\u00a0W) data for sample H13 moves the endpoint to the location shown by the dashed star in Fig.\u00a02. The most dramatic shift of the (S,\u00a0W) parameters and hence the emergence of a high concentration of negatively charged non-open volume defects coincides with the total loss and reversal of the Si doping efficiency in Fig.\u00a01b. It is also important to note that when the positron data are dominated by VIII, there is a clear over-representation of GaN-like behavior as the VIII point is much closer to the Ga vacancies in GaN than to the Al vacancies in AlN. In contrast, when the negative ion type defects dominate the positron data the situation is reversed and the AlN-like behavior is stronger.\n\nFigure\u00a03a\u2013c shows the XANES spectra obtained at the Si K-edge in selected AlGaN samples. We identify 12 characteristic features in the experimental spectra, as denoted in the figure. Features #1, #3 and #7 are so-called isosbestic points where all the spectra coincide. The H series samples are shown in Fig.\u00a03a, and there is a clear distinction between the samples H6\u2013H9 and H10\u2013H13. First, we note that the position of the whiteline (feature #2) is the same in all samples, but its intensity is clearly higher in samples H10\u2013H13 compared to H6\u2013H9. Second, the two peaks at 1846\u20131848\u2009eV (features #4 and #5) are divided between the two sets: the #4 is clearly stronger in samples H6\u2013H9, while #5 is clearly stronger in samples H10\u2013H13. Additionally, sample H9 contains a small shoulder in the vicinity of feature #5, denoted as feature #6. Third, the samples H6\u2013H9 exhibit a relatively high intensity plateau between features #8 and #9, while the samples H10\u2013H13 exhibit two separated peaks (features #8 and #10). Fourth, and finally, the samples H6\u2013H9 exhibit a shoulder above 1860\u2009eV (feature #11), while samples H10\u2013H13 show a peak at 1868 eV (feature #12). Figure\u00a03b shows the comparison of the experimental spectra obtained in samples H13 and L2\u2013L5. It is clear that the above-discussed features are very similar in these two sets of samples.\n\na XANES spectra at the Si K-edge in H series Si doped AlGaN samples. b XANES spectra in selected H and L series Si doped AlGaN samples. Numbers 1\u201312 indicate characteristic isosbestic points and features. Simulated unconvoluted XANES spectra at the Si K-edge for SiGa in GaN and SiAl in AlN are shown for comparison. c Simulated unconvoluted XANES spectra of at the Si K-edge for various Si configurations in AlN.\n\nThe experimental XANES spectra in Fig.\u00a03b show that the local environment of Si is clearly different in samples H6\u2013H9 compared to samples H10\u2013H13 and L2\u2013L5. This difference in local environment coincides with the different behavior in resistivity. Simultaneously, it coincides with the positron annihilation data resembling either GaN-rich (H6\u2013H9) or AlN-rich environments in the AlGaN alloy.\n\nFor a quantitative assessment of the XANES spectra, we performed finite difference method near edge structure (FDMNES) simulations of Si in various environments27: SiGa in GaN, SiAl in AlN, and several SiAl in AlN complexed with substitutional C, interstitial H, interstitial Si, and the Al vacancy with and without additional H. The simulated XANES spectra at the K-edge are shown as the total density of states vs. energy in Fig.\u00a03c, and SiGa and SiAl are included for comparison in Fig.\u00a03a, b. We note that most of simulated XANES spectra show similar behavior, except for SiAl-Hi and SiAl-Sii.\n\nIn the simulated XANES spectra, interstitials near the Si atom and substitutional impurities occupying the nearest N sites contribute most significantly to the appearance of spectral features #4 and #5. Around 1847\u2009eV, most simulated systems demonstrate common behavior, characterized by the presence of two peaks with variations in intensity and slightly also in energy. However, systems containing SiAl-Hi and SiAl-Sii pairs deviate from this general trend. In SiAl-Hi complexes, a high-intensity peak (#4) appears below 1847\u2009eV, followed by a smaller peak (#5) above 1847\u2009eV, with less than one-third of the intensity of feature #4. In contrast, in the SiAl-Sii system, feature #4 is less than 70% of the intensity of feature #5, and the latter is shifted approximately 1\u2009eV to lower energies compared to all other samples. All simulated spectra exhibit a small peak at 1852\u2009eV (features #7 and #8), with slight variations in centroid position and intensity.\n\nThe spectral features #9 and #10 are primarily influenced by the atomic species occupying the cation site nearest to the absorbing Si atom. For Si-complexes in AlN, all simulated spectra display a similar trend, with a peak appearing around 1860\u2009eV, whose intensity varies depending on the composition of the system. Once again, SiAl-Hi and SiAl-Sii systems appear as outliers. In the SiAl-Hi system, the peak shifts slightly to 1859\u2009eV. In the\u00a0SiAl-Sii system, there are three peaks at 1859, 1861, and 1863\u2009eV characteristic to the introduction of a Si atom. This unique behavior is exclusive to the SiAl-Sii system, with the third peak corresponding to feature #11. For feature #12, all simulated spectra exhibit a low-intensity peak near 1867\u2009eV. However, in the experimental spectra of H6-H9, where Si is predominantly in a Ga-rich environment, feature #12 is absent, and the spectra instead show a smooth transition to the continuum. We conclude that the slight differences between the various Si-related complexes in AlN are likely to induce broadening of the various features as observed in experiments, but they cannot account for the spectral differences between H6-H9 and each of the other groups, H10-H13 and L2-L5. We also note that the concentrations of O, H and C in the samples are significantly lower than the Si doping.\n\nThe comparison between experiments and the two simulated spectra reveals that the whiteline has higher intensity for SiAl than for SiGa. In addition, the intensity of feature #5 is clearly stronger than that of feature #4 for SiGa, while there difference is not significant for SiAl. SiGa exhibits a lower intensity of the feature #8 than SiAl, and the SiGa peak at feature #9 is broad, while SiAl exhibits a narrower peak at feature #10 instead of #9. Finally, SiAl exhibits a clear peak at feature #12, while SiGa shows no higher-energy peaks at this energy range, resembling feature #11. Comparing the simulations and experiments, three out of the four main observations above are in favor of the experimental XANES spectra of samples H6\u2013H9 being dominated by cation-substituting Si in GaN-resembling local environment, and the samples H10\u2013H13 and L2\u2013L5 dominated by cation-substituting SiAl in AlN-resembling local environment. We conclude that the local environment of Si atoms is Ga-rich in samples H6\u2013H9, and Al-rich in samples H10\u2013H13 and L2\u2013L5. The observed spatial correlation of Si and Ga atoms in samples H6\u2013H9 indicates that there is a force driving Si and Ga atoms together during synthesis.\n\nState-of-the-art electronic structure calculations provide valuable insight into the electronic behavior of Si in various environments and also into the driving force behind the spatial correlation of Si and Ga atoms in the AlGaN alloys found in experiments. In binary AlN and GaN, our results on the formation of Si in the positive, neutral and stable negative DX configurations are in excellent agreement, within 0.1\u2009eV, with previous work (see\u00a0SI)14,28. In short, we calculate the (\u00b1) transition for the Si in AlN to be located at 0.17\u2009eV below the conduction band minimum (CBM) that is at 6.17\u2009eV above the valence band maximum (VBM). In GaN, the negative Si DX configuration also exists, but the (\u00b1) transition occurs 1.68\u2009eV above the CBM.\n\nFigure\u00a04 shows the results of our calculations in 6 different atomic configurations of Si in AlGaN that we investigate in more detail. In all structures, we have placed 1 Si atom, 12 Ga atoms, 131 Al atoms and 144 N atoms in a 288 atom supercell, corresponding to an atomic fraction of 8.3% of Ga (and 91.7% of Al). In the first system (Fig.\u00a04a), the 12 Ga atoms fill the second-nearest-neighbor (SNN) shell of an Al site, forming an effective Ga cluster. Two different Si configurations are considered: (1) Si substituting for the central Al atom and (2) Si substituting for an Al atom next to the Ga cluster. In the second system (Fig.\u00a04b), the SNN shell of an Al site is half-filled with 6 randomly placed Ga atoms, and the other 6 Ga atoms are distributed randomly in the rest of the supercell. Two different configurations are Si considered: (1) Si substituting for the central Al atom and (2) Si substituting for an Al atom next to the Ga half-cluster. In the third system (Fig.\u00a04c), the 12 Ga atoms are distributed randomly in the supercell. Again, two different Si configurations are considered: (1) Si substituting for an Al atom with 2 Ga atoms as SNN and (2) Si substituting for an Al atom with 1 Ga atom as SNN. We show the formation energy of Si in these configurations that correspond to the localized Kohn-Sham states within the gap for q\u00a0=\u00a0+\u00a01 and the negatively charged Si DX configuration with a broken Si-N* bond along the c-axis.\n\nThree different supercells are considered: (a) cluster of 12 Ga atoms surrounding the Al site as the second-nearest neighbor (SNN) shell, (b) half-cluster of 6 Ga atoms as SNN and 6\u2009Ga atoms distributed randomly in the supercell, and (c) 12\u2009Ga atoms distributed randomly in the supercell. In the formation energy plot, the solid vertical line followed by the blue shaded area at higher energies indicates the corresponding band gap calculated in each system without the Si atom. The dotted vertical line inside the blue shaded area indicates the band gap estimated for the alloy containing 90% Al. It is added to provide an idea on the variation of the calculated band gap value between different atomic configurations in the model, and it should not be interpreted as the absolute band edge position of the macroscopic alloy.\n\nSeveral observations are evident from the formation energies. First, the more there is Ga next to the Si atom in any of the configurations, the lower is the formation energy. Second, a lower number of Ga atoms in the SNN of Si results in the shift of the (\u00b1) transition level to the lower Fermi level energies within the gap, making it thermodynamically possible to form in highly n-type doped samples. Third, the two different Si atomic configurations in the supercell with random Ga distribution result in very similar formation energies for both charge states (Fig 4c). Fourth, the (\u00b1) transition occurs very close to the calculated CBM in all cases.",
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+            ]
+        },
+        {
+            "section_name": "Discussion",
+            "section_text": "Doping high Al-content AlGaN with increasing concentrations of Si, as shown in Fig.\u00a01b, decreases the resistivity as expected up to a certain threshold concentration. Above this threshold, the resistivity increases with further increase of Si concentration. Positron annihilation results show that the concentration of compensating cation vacancy defects VIII increases with increasing Si content (Fig.\u00a02 and ref. 23), but the concentrations of these vacancy defects are an order of magnitude too low to efficiently compensate for the Si doping. Instead, at the highest Si doping concentrations where the resistivity increases with increasing Si content, the emergence of negatively charged acceptor-type defects with no associated open volume is evident, at concentrations comparable to the Si content. Importantly, the concentrations of the other impurities in the material, including carbon, are at least an order of magnitude lower. Hence the strong over-compensation is either due to a donor-to-acceptor transition of Si at high Si concentrations, or due to a so far unidentified intrinsic acceptor-type defect. We note that N vacancies have considerably higher formation energies than substitutional Si throughout the band gap of AlN, and hence are not likely to play a role, even if they also exhibit a negative charge state\u00a0when the Fermi level is close to the CBM14,29.\n\nThe details of the positron annihilation data (Fig.\u00a02) reveal that the VIII defects that are formed at increasing concentrations with increasing Si content are characterized by a strong over-representation of a GaN-like environment. In-grown cation vacancies are typically complexed with donor-like impurities and native defects. In heavily Si doped material, it is hence likely that the VIII defects observed by positrons are VIII\u2013Si complexes as the concentrations of the other impurities are not high enough. As a consequence, the Si dopants that raise the Fermi level and generate the VIII with which they are complexed are mostly in Ga-rich environments of the AlGaN alloy. In contrast, the negative acceptor defects that emerge at high Si concentrations exhibit a strong over-representation of AlN-like environments compared to the AlGaN lattice. The concentration of these negative acceptors is comparable to the Si concentration, and an order of magnitude higher than that of any other impurity. Further, the XANES spectra (Fig.\u00a03a) show that the local environment of Si is GaN-like up to a threshold Si content, and AlN-like above that threshold. The threshold concentration depends on the carbon content and the level of pre-existing compensation that dictates the Fermi level position: lower carbon content and less compensation lead to a somewhat lower Si concentration threshold. Importantly, the threshold is the same as that observed in the positron annihilation experiments and in the electrical characteristics. In short, the experimental evidence indicates that Si is predominantly incorporated in Ga-rich environments up to a threshold Si concentration and acts as a donor. Above that concentration, Si is predominantly incorporated in AlN-like environments, and acts as a negatively charged acceptor.\n\nThe experimentally observed preferential incorporation of Si in Ga-rich environments can be understood on the basis of the results of ab initio theoretical calculations presented in Fig.\u00a04a\u2013c. The formation energy of Si substituting for the cation in the AlGaN lattice is lowered by the presence of Ga atoms as second nearest neighbors (SNN), and this effect is stronger the more there are Ga atoms in the 12-atom SNN shell surrounding the Si site. While the lowering is not very large, its existence provides a driving force for the local ordering of Si and Ga atoms in AlGaN. The high growth temperature, above 1000\u2009\u2218C, allows Si to diffuse efficiently not only on the growth surface but also when buried in the film, to get stabilized at the lowest-energy lattice sites30. Assuming a random alloy with no clustering or other kind of ordering, the binomial distribution of Al/Ga atoms in Al0.90Ga0.10N leads to 2.6\u2009\u00d7\u20091019\u2009cm\u22123 cation sites with at least 50% of Ga atoms (6 out of 12) in the SNN shell. The average distance between such sites is 10\u201315 atomic jumps. Hence the Si diffusion that in AlN proceeds via the vacancy mechanism with an activation energy of about 3.5\u2009eV (ref. 30) easily allows finding the Ga-rich sites. Even if the energetic difference between Ga-rich and Al-rich cation sites for Si is relatively small\u2014roughly 0.25\u2009eV in our calculations\u2014this difference appears to be sufficient as seen in the experiments. We note that these observations are also in excellent agreement with the positron data showing that the cation vacancies that are most likely complexed with the Si dopants are in Ga-rich environments. Interestingly, this simple theoretical estimate of Ga-rich\u2014defined here as at least 50% Ga atoms as SNN\u2014lattice sites available for Si is close to the experimentally observed threshold concentration where the behavior of Si changes from donor to acceptor.\n\nThe nature of the local compositional fluctuations in a random binary alloy can be analyzed by examining the properties of the binomial distribution (see\u00a0SI for details), and this provides an additional observation. We consider 200 atoms surrounding a Si atom on the cation site, similar to the size of a typical supercell in state-of-the-art electronic structure calculations. In such a case, there are 100 Al/Ga atoms surrounding the Si atom. In Al0.90Ga0.10N, the probability of finding only 0 or 1 Ga atoms among the 100 Al/Ga atoms surrounding the Si atom on the cation site is similar to the probability of having 6 or more Ga atoms in the 12-atom SNN shell surrounding that site. It is hence possible, and even probable, that once the Ga-rich surroundings are \u201cfilled\" with Si when increasing the Si concentration, a significant fraction of the \u201coverflow\" Si atoms are incorporated in surroundings that are purely AlN-like on the scale of a few nm, the size of the supercell. On this scale31, the band structure in the vicinity of the Si atom is that of pure AlN, and the electronic behavior of Si is that found in AlN with the DX transition in the band gap. This is in good agreement with the donor activation energy being very similar in highly Si-doped AlGaN alloys with 90\u221295% Al content and in AlN, while for lower Al contents the Si donors are much more easily activated as the probability of having pure AlN on the few nm scale decreases very rapidly with Al content decreasing below 90%15. It is also important to note that these relatively large compositional fluctuations are inherent to the atomic scale, and are rapidly homogenized when the number of atoms is increased: in a 2000 atom cell that is only twice as large in diameter than the 200 atom cell, even the probability of finding a region with 95% of Al in Al0.90Ga0.10N is vanishing (see\u00a0SI).\n\nWhile the lowering of Si formation energy on the cation lattice site by the addition of Ga atoms as SNN provides the driving force for the local ordering of Si and Ga atoms in AlGaN, the ordering effects on the electronic transition levels are more subtle as shown in Fig 4. It is evident that the balance between the formation energies of various charged states is delicately influenced by the surrounding Ga atoms. Also the exact position of the CBM depends on the Ga distribution in the supercell used in the calculation. It is hence extremely important to take into account local compositional fluctuations when analyzing carrier localization phenomena in AlGaN32, similarly as recently demonstrated for InGaN alloys31. This is an important difference between the III-nitrides and the more conventional III\u2013V semiconductors where the virtual crystal approximation is a reasonable approach. Our calculations show that in each of the considered Ga configurations, the (\u00b1) transition level of Si is shallower with more Ga atoms surrounding the Si site. This supports the picture obtained from experiments: the donor character of Si is the strongest when there is a maximum amount of Ga atoms surrounding it, while the probability of Si being in a negative charge state increases when the immediate surroundings are AlN-like.\n\nCombining advanced experimental characterization and state-of-the-art electronic structure calculations allows us to show that the amphoteric behavior of Si in high Al content AlGaN alloys is controlled by short-range order with multiple Ga atoms. In addition to explaining the over-compensation at high Si doping levels, our results suggest an avenue for efficient doping by Si not only in high Al content AlGaN, but possibly also in AlN. Spatially correlating Si with multiple Ga atoms in a co-doping scheme could allow for efficient n-type doping up to much higher Si contents and carrier concentrations than so far. This could be achieved via enhanced clustering of Ga atoms in the 3D matrix, or by introducing digital superlattice structures where the Si dopants could be incorporated in the GaN or Ga-rich monolayers. Interestingly, a recent report on efficient Si doping of AlN highlights that there is excess Ga in their material33.",
+            "section_image": []
+        },
+        {
+            "section_name": "Methods",
+            "section_text": "The samples were grown by metal organic vapor phase epitaxy (MOVPE) in a 3\u00a0\u00d7\u00a02\" close-coupled showerhead (CCS) Aixtron reactor. Epitaxially laterally overgrown (ELO) AlN layers were grown on (0001) c-plane sapphire substrates with a miscut of 0.1\u2218 towards the [1-100] sapphire direction23. The threading dislocation density in the ELO AlN/sapphire templates was 1.5\u2009\u00d7\u2009109\u2009cm-2 22,34. The layer structure from bottom to top consists of a AlN buffer layer (400 nm), a graded transition layer from AlN to Al0.90Ga0.10N (25 nm), undoped Al0.90Ga0.10N (100 nm), and a Si-doped layer of Al0.90Ga0.10N (900\u20131400\u2009nm)35. The composition of the samples was determined by high resolution X-ray diffractometry measuring reciprocal space maps near the (10\u201315) AlN reflex under consideration of the layer strain state4,36. The resistivity of the samples was determined by contactless (eddy current) resistivity measurements in a Delcom system. Impurity concentrations (Si, C, O, H) were determined by secondary ion mass spectrometry by Evans Analytical group. In H series, the impurities contents were [H]\u2009=\u20095\u2009\u00d7\u20091017\u2009cm\u22123, [O]\u2009=\u20093\u2009\u00d7\u20091017\u2009cm\u22123 and [C]\u00a0=\u00a02\u2009\u00d7\u20091018\u2009cm\u22123. In L series, the impurities contents were [H]\u2009=\u20092\u2009\u00d7\u20091017 cm\u22123, [O]\u2009=\u20092\u2009\u00d7\u20091017\u2009cm\u22123 and [C]\u2009=\u20092\u2009\u00d7\u20091017 cm\u22123.\n\nThe Doppler broadening of the positron-electron annihilation radiation was recorded with a slow positron beam at varied energies in the range of 0.5\u201325\u2009keV at room temperature in all samples19,37. A high purity germanium detector with energy resolution of 1.27\u2009keV at the 511\u2009keV annihilation line was used to collect 106 counts in the annihilation spectra. Conventional S and W parameters determined at positron implantation energies corresponding to the layer of interest were used to estimate the concentrations of negative and neutral cation vacancies in the Si-doped AlGaN samples. The S parameter is defined as the fraction of counts around the \u22640.96 keV (0.4 a.u.) central region of the peak, and the W parameter is defined in the tail of the peak in the energy range of (3.00\u22127.60\u2009keV) (1.6\u22124.0 a.u.) from the center. The measured (S,\u00a0W) parameters are shown in this paper as normalized to those obtained in a p-type GaN reference sample, representing the GaN lattice24.\n\nThe concentrations cV of the cation vacancies are determined from the trapping rate \u03baV\u00a0=\u00a0\u03bcVcV estimated by analyzing the S (W) parameter data, where \u03bcV\u2009=\u20093\u2009\u00d7\u20091015\u2009s\u22121 is the trapping coefficient at the vacancy. Importantly, we take into account the effect of negative ion defects that act as shallow traps for positrons and are efficient in positron trapping even at room temperature in AlN and Al-rich AlGaN23. When this is the case, the measured S parameter depends on the parameters of the lattice (SB) and the vacancy (SV) in the following way (a similar equation holds for the W parameter):\n\nThe negative ions whose trapping rate is denoted with \u03baion produce the same annihilation parameters as the lattice. Here, \u03bbB is the annihilation rate in the lattice, and it is the inverse of the positron lifetime in the lattice \\({\\tau }_{B}={\\lambda }_{B}^{-1}=160\\) ps in GaN/AlN23. The trapping coefficient of the negative ions is the same as that of the cation vacancies19,37,38.\n\nWe acquired fluorescence yield spectra in X-ray absorption near-edge structure region at Si K-edge (~1839\u2009eV) in the selected samples (L2\u2212L5 and H6\u2212H13) on the LUCIA beamline at the SOLEIL synchrotron facility39. The 2.75 GeV beam was operating in a hybrid refill mode at 450\u2009mA. The energy calibration was performed with a InSb(111) monochromator using the first inflection point of a Si reference spectrum, and fixed at 1841\u2009eV. Acquisitions were made in the continuous scan mode from 40\u2009eV below the silicon absorption edge (~1839\u2009eV) up to 60\u2009eV above. The varying energy steps were 1\u2009eV, 0.2\u2009eV, 0.5\u2009eV and 1\u2009eV in the corresponding energy regions 1800\u22121836\u2009eV, 1836.2\u22121850\u2009eV, 1850.5\u22121880\u2009eV and 1881\u22121900\u2009eV, respectively. With the counting time of 10\u2009s on each point, one scan recording time sums up to 2280 s. We acquired at least 3 scans to obtain a suitable signal to noise ratio.\n\nWe used Finite Difference Method Near Edge Structure (FDMNES) software to obtain total electron density of state of 9 GaN:Si and 10 AlN:Si systems27,40. The self-consistent calculations were performed with Finite Difference Method in the range 30 eV below and 80 eV above the Si K-edge with a step of 0.1 eV. We put from one to three absorbing Si atoms on metal and interstitial sites in the center of wurtzite AlN or GaN supercells and varied the first nearest neighbors of Si absorbers with different interstitial impurities. Prior to\u00a0simulations we performed ionic relaxation of all systems with conjugate gradient algorithm and Projector Augmented Wave Perdew-Burke-Ernzerhof (PAW PBE) functional on VASP 5.441,42,43,44,45. The final state and potential calculations were performed with radius values of 7 and 8 \u00c5, respectively.\n\nDefect formation energy calculations were performed with density functional theory (DFT) using VASP 5.4 code. In the calculations, we applied the projector augmented-wave (PAW) method to Perdew-Burke-Ernzerhorf (PBE) potentials from 04 January 2001, 08 April 2002, 08 April 2002, and 05 January 2001 for Al, N, Ga, and Si, respectively. The 10 3d electrons of Ga were included in the core shell. All the calculations were spin-polarized. We used lattice parameters corresponding to the wurtzite phases of AlN (a = b = 3.11 \u00c5, c/a = 1.60) and GaN (a = b = 3.20 \u00c5, c/a = 1.62)14, and cut-off energy of 400\u2009eV. The orthorhombic primitive cell contained 8 atoms, which was further scaled up to super cells containing 96 and 288 atoms. We performed optimization for lattice parameters a and c, plane wave cut-off energy and k-points meshes, and full ionic relaxation for the reference cells. We used the range-separated hybrid functional HSE06 which mixes the Hartree-Fock (HF) and generalized gradient approximation (GGA) parametrized by PBE. The fraction of exchange in a Hartree-Fock-type calculations was set to \u03b1 = 0.33 for AlN and AlGaN alloys, and \u03b1\u2009=\u20090.31 for GaN. We used the default HF screening factor. We obtained band gap values of 6.17 and 3.58 eV for AlN:SiAl and GaN:SiGa systems containing 96 atoms and calculated with 3\u2009\u00d7\u20093\u2009\u00d7\u20093 Gamma-centered k-points mesh. While our results agree with the previously reported values28,46, minor variations are due to the use of different k-point meshes and potentials. The use of k-points mesh containing Gamma point was tested for convergence against denser Gamma-centered k-points meshes in 288 atoms systems. We further used 1\u2009\u00d7\u20091\u2009\u00d7\u20091 Gamma-centered k-point mesh to reduce the computational cost for larger systems. We calculated the formation energy of a charged defect as the energy difference between the investigated system and the components in their reference states following the procedure outlined in the reviews by Van de Walle and Neugebauer47, and Freysoldt et al.21, originally formulated by Zhang and Northrup48. For \\({{{{\\rm{Si}}}}}_{{{{\\rm{III}}}}}^{0}\\) and \\({{{{\\rm{Si}}}}}_{{{{\\rm{III}}}}}^{+}\\), Si occupies the metallic cation site of the corresponding lattice, with relaxations of the nearest-neighbor nitrogen atoms. For \\({{{{\\rm{Si}}}}}_{{{{\\rm{III}}}}}^{-}\\), the lowest energy DX configuration was achieved with the broken Si-N axial bond along the c axis and large N atom displacement14. The charged states of the studied defects were modeled by changing the corresponding amount of electrons in the system. The partial density of states of introduced levels was calculated in order to determine whether the electron is localized. We determine the electrostatic local potential and dielectric constant tensors for AlN and GaN to apply finite size corrections for charged-defects49. The DFT results shown in Fig.\u00a04a\u2013c are aligned on a relative scale for direct comparison within the same atomic configuration by aligning the electrostatic potentials between the cells with and without a defect. We neglected the growth conditions (metal- or nitrogen-rich) of the systems and left the formation energy in the relative scale. Taking the chemical potentials into account will move all the lines at the same time along the vertical axis to the absolute values in relation to the specified growth condition. We note that the Si DX is metastable in all the studied cases, with the simple \\({{{{\\rm{Si}}}}}_{{{{\\rm{III}}}}}^{-}\\) configuration having a total energy lower by 0.15\u22120.50\u2009eV, but the electron is not localized in this configuration and we present the Si DX data in the figures. We also checked the effect of the Ga atoms as nearest-neighbors of the displaced N atom in the Si DX configuration in the random supercell50, and found no difference to the other configurations in this supercell (the data are not shown for the sake of clarity).",
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+            "section_name": "Data availability",
+            "section_text": "Source data for Figs.\u00a01\u20134 in this study are provided with the paper.\u00a0Source data are provided with this paper.",
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+            "section_name": "Code availability",
+            "section_text": "All DFT calculations were performed with VASP, which is proprietary software for which the Tuomisto lab owns a license.",
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+            "section_text": "Amano, H. et al. The 2018 GaN power electronics roadmap. J. Phys. D: Appl. Phys. 51, 163001 (2018).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nAmano, H. et al. The 2020 UV emitter roadmap. J. Phys. D: Appl. Phys. 53, 503001 (2020).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBrunner, D. et al. Optical constants of epitaxial AlGaN films and their temperature dependence. J. Appl. Phys. 82, 5090\u20135096 (1997).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMehnke, F. et al. Highly conductive n-AlxGa1- xN layers with aluminum mole fractions above 80%. Appl. Phys. Lett. 103 (2013).\n\nKneissl, M. & Rass, J. (eds.) III-Nitride Ultraviolet Emitters. Technology and Applications (Springer Cham, 2016).\n\nKneissl, M., Seong, T.-Y., Han, J. & Amano, H. The emergence and prospects of deep-ultraviolet light-emitting diode technologies. Nat. Photonics 13, 233 (2019).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBuonanno, M., Welch, D., Shuryak, I. & Brenner, D. J. Far-UVC light (222 nm) efficiently and safely inactivates airborne human coronaviruses. Sci. Rep. 10, 1\u20138 (2020).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMcCluskey, M. & Haller, E. Dopants and defect in semiconductors (CRC Press, 2012).\n\nLang, D. V. & Logan, R. A. Large-lattice-relaxation model for persistent photoconductivity in compound semiconductors. Phys. Rev. Lett. 39, 635\u2013639 (1977).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nChadi, D. J. & Chang, K. J. Theory of the atomic and electronic structure of DX centers in GaAs and AlxGa1\u2212xAs alloys. Phys. Rev. Lett. 61, 873\u2013876 (1988).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nM\u00e4kinen, J. et al. Observation of a vacancy at the DX center in Si- and Sn-doped AlGaAs. Phys. Rev. Lett. 71, 3154\u20133157 (1993).\n\nArticle\u00a0\n    ADS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBrandt, M. S., Zeisel, R., G\u00f6nnenwein, S. T. B., Bayerl, M. W. & Stutzmann, M. DX behaviour of Si donors in AlGaN alloys. Phys. Status Solidi (b) 235, 13 (2003).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nTrinh, X. T. et al. Stable and metastable Si negative-U centers in AlGaN and AlN. Appl. Phys. Lett. 105, 162106 (2014).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nGordon, L., Lyons, J. L., Janotti, A. & Van de Walle, C. G. Hybrid functional calculations of DX centers in AlN and GaN. Phys. Rev. B 89, 085204 (2014).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMehnke, F. et al. Electronic properties of Si-doped AlxGa1-xN with aluminum mole fractions above 80%. J. Appl. Phys. 120, 145702 (2016).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBryan, I. et al. Doping and compensation in Al-rich AlGaN grown on single crystal AlN and sapphire by MOCVD. Appl. Phys. Lett. 112, 062102 (2018).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nGalazka, Z. et al. Bulk single crystals and physical properties of \u03b2-(AlxGa1-x)2O3 (x=0-0.35) grown by the Czochralski method. J. Appl. Phys. 133, 035702 (2023).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMu, S. et al. Role of carbon and hydrogen in limiting n-type doping of monoclinic \\({({{{{\\rm{Al}}}}}_{x}{{{{\\rm{Ga}}}}}_{1-x})}_{2}{{{{\\rm{O}}}}}_{3}\\). Phys. Rev. B 105, 155201 (2022).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nTuomisto, F. & Makkonen, I. Defect identification in semiconductors with positron annihilation: experiment and theory. Rev. Mod. Phys. 85, 1583 (2013).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nHenderson, G. S., de Groot, F. M. & Moulton, B. J. X-ray Absorption Near-Edge Structure (XANES) Spectroscopy. Rev. Mineral. Geochem. 78, 75\u2013138 (2014).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nFreysoldt, C. et al. First-principles calculations for point defects in solids. Rev. Mod. Phys. 86, 253\u2013305 (2014).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nEnslin, J. et al. Determination of Sapphire Off-Cut and Its Influence on the Morphology and Local Defect Distribution in Epitaxially Laterally Overgrown AlN for Optically Pumped UVC Lasers. Phys. Status Solidi A 216, 1900682 (2019).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nProzheev, I., Mehnke, F., Wernicke, T., Kneissl, M. & Tuomisto, F. Electrical compensation and cation vacancies in Al rich Si-doped AlGaN. Appl. Phys. Lett. 117, 142103 (2020).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nOila, J. et al. Influence of dopants and substrate material on the formation of Ga vacancies in epitaxial GaN layers. Phys. Rev. B 63, 045205 (2001).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nM\u00e4ki, J.-M. et al. Identification of the VAl-ON defect complex in AlN single crystals. Phys. Rev. B 84, 081204 (2011).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nTuomisto, F. et al. Amphoteric Be in GaN: Experimental evidence for switching between substitutional and interstitial lattice sites. Phys. Rev. Lett. 119, 196404 (2017).\n\nArticle\u00a0\n    ADS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBun\u0103u, O., Ramos, A. & Joly, Y. The FDMNES code (2021).\n\nSilvestri, L., Dunn, K., Prawer, S. & Ladouceur, F. Hybrid functional study of Si and O donors in wurtzite AlN. Appl. Phys. Lett. 99 (2011).\n\nYan, Q., Janotti, A., Scheffler, M. & Van de Walle, C. G. Appl. Phys. Lett. 105, 111104 (2014).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBonito Oliva, V. et al. Silicon diffusion in AlN. J. Appl. Phys. 134, 095103 (2023).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nTsai, T.-Y. et al. Carrier localization in III-nitride versus conventional III-V semiconductors: a study on the effects of alloy disorder using landscape theory and the Schr\u00f6dinger equation. Phys. Rev. Appl. 20, 044069 (2023).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nRoble, A. A. et al. Impact of alloy fluctuations and Coulomb effects on the electronic and optical properties of c-plane GaN/AlGaN quantum wells. Sci. Rep. 9, 18862 (2019).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKhan, M. I., Lee, C. & Ahmadi, E. Demonstration of controllable Si doping in N-polar AlN using plasma-assisted molecular beam epitaxy. Appl. Phys. Lett. 124, 062107 (2024).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKusch, G. et al. Spatial clustering of defect luminescence centers in Si-doped low resistivity Al0.82Ga0.18N. Appl. Phys. Lett. 107, 072103 (2015).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nSusilo, N. et al. Improved performance of UVC-LEDs by combination of high-temperature annealing and epitaxially laterally overgrown AlN/sapphire. Photonics Res. 8, 589 (2020).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKusch, G. et al. Analysis of doping concentration and composition in wide bandgap AlGaN:Si by wavelength dispersive x-ray spectroscopy. Semiconductor Sci. Technol. 32, 035020 (2017).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKrause-Rehberg, R. & Leipner, H. S.Positron Annihilation in Semiconductors: Defect Studies, vol. 127 (Springer, 1999).\n\nSaarinen, K., Hautoj\u00e4rvi, P. & Corbel, C. Chapter 5. Positron Annihilation Spectroscopy of Defects in Semiconductors. In Stavola, M. (ed.) Identification of Defects in Semiconductors, vol. 51 of Semiconductors and Semimetals, 209\u2013285 (Elsevier, 1998).\n\nVantelon, D. et al. The LUCIA beamline at SOLEIL. J. Synchrotron Radiat. 23, 635\u2013640 (2016).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBun\u0103u, O. & Joly, Y. Self-consistent aspects of x-ray absorption calculations. J. Phys.: Condens. Matter 21, 345501 (2009).\n\nPubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKresse, G. & Hafner, J. Abinitio molecular dynamics for liquid metals. Phys. Rev. B 47, 558 (1993).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBl\u00f6chl, P. E. Projector augmented-wave method. Phys. Rev. B 50, 17953\u201317979 (1994).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKresse, G. & Furthm\u00fcller, J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput. Mater. Sci. 6, 15\u201350 (1996).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKresse, G. & Furthm\u00fcller, J. Efficient iterative schemes for abinitio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169 (1996).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 59, 1758 (1999).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLyons, J. L. & Van de Walle, C. G. Computationally predicted energies and properties of defects in GaN. npj Comput. Mater. 3, 1 (2017).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nVan de Walle, C. G. & Neugebauer, J. First-principles calculations for defects and impurities: applications to III-nitrides. J. Appl. Phys. 95, 3851\u20133879 (2004).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nZhang, S. B. & Northrup, J. E. Chemical potential dependence of defect formation energies in GaAs: application to Ga self-diffusion. Phys. Rev. Lett. 67, 2339\u20132342 (1991).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nFreysoldt, C., Neugebauer, J. & Van de Walle, C. G. Fully ab initio finite-size corrections for charged-defect supercell calculations. Phys. Rev. Lett. 102, 016402 (2009).\n\nArticle\u00a0\n    ADS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBogus\u0142awski, P. & Bernholc, J. Doping properties of C, Si, and Ge impurities in GaN and AlN. Phys. Rev. B 56, 9496\u20139505 (1997).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDownload references",
+            "section_image": []
+        },
+        {
+            "section_name": "Acknowledgements",
+            "section_text": "This material is based upon work supported by the Air Force Office of Scientific Research under award number FA8655-23-1-7057 (F.T.). This work has been partially supported by Finnish Cultural Foundation through a personal grant (I.P.), through the Additional Million-euro Funding to Science programme grant 00231172 (F.T.), and supported by the German Federal Ministry of Education and Research (BMBF) within the \u201cAdvanced UV for Life\u201d consortium (M.K.). We acknowledge the Proposal Review Committee of SOLEIL for provision of their synchrotron radiation facilities (proposal no. 20210395) and beamtime allocation on the LUCIA beamline (R.B.). The authors wish to acknowledge CSC - IT Center for Science, Finland, for generous computational resources (project 2000028) (I.M.). The authors wish to thank S. Hagedorn, Ferdinand-Braun-Institut (FBH), Berlin, for providing the ELO AlN/sapphire templates, P. Desgardin, Universit\u00e9 Orl\u00e9ans, Orl\u00e9ans, France, for help with Doppler experiments, beamline scientist N. Trcera, LUCIA beamline, SOLEIL Synchrotron, Saint-Aubin, France, for technical assistance, and Y. Joly, Institut N\u00e9el, CNRS, Grenoble, France, and J. L. Lyons, US Naval Research Laboratory, Washington DC, USA, for fruitful discussions.",
+            "section_image": []
+        },
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+            "section_name": "Author information",
+            "section_text": "Department of Physics and Helsinki Institute of Physics, University of Helsinki, P.O. Box 43, FI-00014, Helsinki, Finland\n\nIgor Prozheev,\u00a0Ren\u00e9 B\u00e8s,\u00a0Ilja Makkonen\u00a0&\u00a0Filip Tuomisto\n\nInstitute of Solid State Physics, Technische Universit\u00e4t Berlin, Hardenbergstr. 36, EW 6-1, 10623, Berlin, Germany\n\nFrank Mehnke,\u00a0Marcel Schilling,\u00a0Tim Wernicke\u00a0&\u00a0Michael Kneissl\n\nFerdinand-Braun-Institut (FBH), Gustav-Kirchhoff-Str. 4, 12489, Berlin, Germany\n\nMichael Kneissl\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nI.P. with F.T. designed the study. F.M., M.S., T.W. and M.K. supplied samples and characterization with SIMS, XRD and resistivity measurements. I.P. performed the positron annihilation experiments. I.P. performed the X-ray absorption near edge structure experiments and FDMNES calculations with help of R.B. I.P. performed PAW-DFT calculations with help of I.M. I.P., R.B., I.M., and F.T. analyzed the results. All authors reviewed the manuscript.\n\nCorrespondence to\n                Filip Tuomisto.",
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+            "section_text": "Prozheev, I., B\u00e8s, R., Makkonen, I. et al. Short-range order controlled amphoteric behavior of the Si dopant in Al-rich AlGaN.\n                    Nat Commun 16, 5005 (2025). https://doi.org/10.1038/s41467-025-60312-4\n\nDownload citation\n\nReceived: 04 December 2024\n\nAccepted: 16 May 2025\n\nPublished: 30 May 2025\n\nVersion of record: 30 May 2025\n\nDOI: https://doi.org/10.1038/s41467-025-60312-4\n\nAnyone you share the following link with will be able to read this content:\n\nSorry, a shareable link is not currently available for this article.\n\n\n\n\n                            Provided by the Springer Nature SharedIt content-sharing initiative\n                        ",
+            "section_image": [
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2f238fc4de049b31c3ee1ae09e051f0ab53712d97e4910ca3de302bbe0df3052/metadata.json

@@ -0,0 +1,127 @@
+{
+    "title": "Uncovering a widely applicable empirical formula for field emission characteristics of metallic nanotips in nanogaps",
+    "pre_title": "Uncovering a Universal Scaling for the Field Emission Characteristics from Metallic Nanotips in Nanogap",
+    "journal": "Nature Communications",
+    "published": "01 July 2025",
+    "supplementary_0": [
+        {
+            "label": "Supplementary Information",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-60607-6/MediaObjects/41467_2025_60607_MOESM1_ESM.pdf"
+        },
+        {
+            "label": "Transparent Peer Review file",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-60607-6/MediaObjects/41467_2025_60607_MOESM2_ESM.pdf"
+        }
+    ],
+    "supplementary_1": [
+        {
+            "label": "Source Data",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-60607-6/MediaObjects/41467_2025_60607_MOESM3_ESM.rar"
+        }
+    ],
+    "supplementary_2": NaN,
+    "source_data": [
+        "/articles/s41467-025-60607-6#Sec11"
+    ],
+    "code": [],
+    "subject": [
+        "Applied physics",
+        "Electrical and electronic engineering"
+    ],
+    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
+    "preprint_pdf": "https://www.researchsquare.com/article/rs-5395439/v1.pdf?c=1751456284000",
+    "research_square_link": "https://www.researchsquare.com//article/rs-5395439/v1",
+    "nature_pdf": "https://www.nature.com/articles/s41467-025-60607-6.pdf",
+    "preprint_posted": "11 Dec, 2024",
+    "research_square_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Electron field emission is a key mechanism in nanoelectronics with nanogaps, offering advantages such as high electron velocity, fast switching speeds, operation at extreme temperatures, and exceptional radiation resilience. However, traditional field emission theory inadequately describes the electron emission and charge transport behaviors at the nanoscale, as it lacks consideration of geometric asymmetry effects, quantum effects and nanosize effects. Here, we carried out an in situ investigation on the intrinsic field emission characteristics of pure tungsten nanotips across vacuum nanogaps. For the first time, we revealed a universal scaling behaviour between field emission characteristics and the ratio R/d, and demonstrated that the nonlinear geometrical effect, rather than quantum effects, is predominant. We further proposed a modified Fowler-Nordheim (FN) equation considering geometric effects, where the electric field (F) in the FN equation is substituted by F=Vexp/(k\u00d7R) with k=f(R\u2044d)=1.680\u00d7 (R/d+0.468)(-1.066), which is valid for R/d\u2009=\u20090.04 to 48. The proposed FN equation for nanoscale field emission regime is validated by well matching with the reported experimental results. These findings, grounded in theoretical insights, are essential for refining the design and performance of nanoelectronics, driving advancements in next-generation technologies.Physical sciences/Physics/Applied physicsPhysical sciences/Engineering/Electrical and electronic engineering",
+            "section_image": []
+        },
+        {
+            "section_name": "Additional Declarations",
+            "section_text": "There is NO Competing Interest.",
+            "section_image": []
+        }
+    ],
+    "nature_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Field electron emission is a key mechanism in nanoelectronics with nanogaps, offering advantages such as high electron velocity and fast switching speeds. However, nanoscale field emission, affected by geometric asymmetry including quantum tunneling near to the emitter, and quantum space charge effects, remains largely unexplored in experimental studies. Here, we in situ investigated field emission characteristics of pure tungsten nanotips across vacuum nanogaps. We revealed a widely applicable scaling behavior between field emission characteristics and the ratio of apex radius to gap length (R/d), and demonstrated that the effects of quantum tunnelling due to emitter shape are the predominant influence. We further proposed a modified field emission equation, incorporating an empirical formula for the apex shape factor, kMG (kMG\u2009=\u2009f(R/d)\u2009=\u20091.680\u2009\u00d7\u2009(R/d\u2009+\u20090.468)\u22121.066), valid for R/d\u2009=\u20090.04 to 48. These findings provide fundamental insights into the optimization of nanoelectronic device design and the advancement of future technologies.",
+            "section_image": []
+        },
+        {
+            "section_name": "Introduction",
+            "section_text": "Tremendous efforts in development of novel nanomechanical fabrication techniques and devices have witnessed a variety of emerging nanoelectronics, including field emission diodes1,2,3, field effect transistors4,5,6,7,8,9,10,11,12, ultrafast switches13,14,15,16,17, biosensors18,19,20, and molecular transistors21,22. The typical device structure has a vacuum nanogap as an electron transport channel, which is expected to show extraordinary performances in terms of the high electron traveling velocity, fast switching rates, high operating temperatures, and exceptional radiation tolerance. Specially designed with asymmetric electrode structures and operating at low voltages, these devices rely heavily on field electron emission (FE)3,6,9,17,23,24,25. The state-of-the-art ultrafast nanoelectronic switches reported in Nature has successfully achieved picosecond-level switching speeds with lower power consumption by utilizing electron field emission induced nanoplasma13,14. However, 1950s type planar FE theory, based on the 1956 Murphy-Good (MG) FE equation (see Supplementary Note\u00a01)26,27,28, does not work well for nanodevices. This is because the traditional planar potential barrier, the so-called Schottky-Nordheim barrier (Supplementary Eq. (S1)), does not adequately describe the potential-energy variation near a significantly curved surface29,30. Further, when the gap distance is at the nanometer scale, quantum effects may occur, particularly if there is significant space-charge in the gap31,32,33. These quantum effects are, firstly that it may become necessary to describe the electron motion in the gap by using the Schr\u00f6dinger equation (rather than by using classical space-charge arguments), secondly that it may become necessary to consider exchange-and-correlation interactions between electrons in the space-charge. Both effects are difficult to clearly distinguish when the size of the emitter is comparable to the nanogap spacing.\n\nGenerally, for typical sharp emitters, it is common practice to assume that the average electrostatic field F0 is enhanced by a field enhancement factor (FEF) of \u03b3 in Supplementary Eq. (S2): F\u2009=\u2009\u03b3F0\u2009=\u2009\u03b3V/d, where F is the absolute magnitude of the electrostatic field at emitter surface, and \u03b3 depends on the definition of the distance d, either as the distance between planar plates (plate FEF), particularly for a post standing on one of a pair of parallel plates, or as the distance between the emitter apex and the anode plate (gap FEF)34,35. However, this approach by itself may fail to accurately predict the field emission behavior of emitter tips with apex radii R less than 50\u2009nm, as the width of tunneling barrier is getting very sensitive to the physical dimension36,37,38,39,40,41,42,43. Previous studies have reported that during field emission from nanotips, the electron total-energy distributions sometimes display multiple well-separated peaks rather than one strong peak at Femi level, indicating a considerable variation of the structure of electron states inside the nano-emitter44,45. Currently, most FE models proposed in the literatures for nano-emitters either are focused on the corrections of the supply function and transmission coefficient due to probable quantum confinement effects of emitter with a non-planar geometry or are mainly aimed to calculate the image charge potential of space charges with cathode alone more accurately by including the geometric effects in the related mathematical formulation42,46,47,48,49. It is important to note that the supply function and transmission coefficient can be strongly geometrically dependent. This complexity suggests that it is nearly impossible to have an analytical multi-dimensional field emission model for a given emitter. This has prompted this experimental attempt to obtain an empirical scaling.\n\nMoreover, when developing a FE model for nanogaps, a sophisticated approach has been to obtain space charge limited field emitted current density by solving the coupled Schr\u00f6dinger and Poisson equations self-consistently50,51,52,53,54. Therefore, the question of whether quantum effects of this kind need to be considered turns out to be a very fundamental issue for further elucidating the intrinsic and experimental field emission characteristics at the nanoscale.\n\nHere, we studied the experimental field emission characteristics of the pure tungsten nanoelectrodes across vacuum nanogaps by utilizing a home-built in situ electrical experiment system. We explored how the field emission characteristics vary as a function of the ratio of apex radius to gap length (R/d in the range of 0.04 to 48) and revealed a consistent scaling relationship between them. This scaling is shown to recover the accepted limits at R/d \u00ab 1 (ultrasharp tip) and R/d \u00bb 1 (planar gap). Furthermore, after excluding the space charge quantum effects, we successfully proposed a modified FE equation that accounts for geometric asymmetry effects and related R/d dependence. Finally, the I-F curves and corresponding FN plots based on this FE equation are compared with previous experimental results.",
+            "section_image": []
+        },
+        {
+            "section_name": "Results and discussion",
+            "section_text": "Experimental field emission characteristics from various nanoscopic emitters in nanogaps are tested using an in situ electrical experiment system, which comprises a transmission electron microscopy (JEOL-2100F TEM) and an in situ electrically biased TEM holder (ZepTools Technology)55,56. The electrode structure is tungsten nanotip (W, cathode)\u2014gold plate (Au, anode), and the pure tungsten nanotips with different apex radii of curvature are prepared by a two-step process: the ex-situ double\u2011electrolyte electrochemical etching method57,58 and the in situ Joule melting method59. Details of the in situ electrical measurement system and the preparation of tungsten nanotips are described in the \u201cMethods\u201d section. In this work, we investigated the field emission characteristics of tungsten nanotips with apex radii of curvature Rm (measured from TEM images) ranging from 2\u2009nm to 190\u2009nm across various nanogaps (5\u2009nm\u2009\u2264\u2009dm\u2009\u2264\u2009100\u2009nm), which covers a wide range of Rm/dm\u2009=\u20090.04 to 48. Notably, in our experiments, the gap distance dm refers to the distance between the emitter apex and the anode plate. The TEM images of these tungsten nanotips are shown in Fig.\u00a01.\n\na Rm\u2009=\u20092\u2009nm. b Rm\u2009=\u20093\u2009nm. c Rm\u2009=\u20094\u2009nm. d Rm\u2009=\u20095\u2009nm. e Rm\u2009=\u20096\u2009nm. f Rm\u2009=\u200917\u2009nm. g Rm\u2009=\u200920\u2009nm. h Rm\u2009=\u200943\u2009nm. i Rm\u2009=\u200955\u2009nm. j Rm\u2009=\u200960\u2009nm. k Rm\u2009=\u200970\u2009nm. l Rm\u2009=\u2009100\u2009nm. m Rm\u2009=\u2009170\u2009nm. n Rm\u2009=\u2009180\u2009nm. o Rm\u2009=\u2009190\u2009nm.\n\nFigure\u00a02a, b presents the experimental field emission Im-Vm curves (solid lines) and the corresponding Fowler-Nordheim (FN) plots (solid lines) of the tungsten nanotip with an apex radius of 4\u2009nm, across nanogaps dm ranging from 5\u2009nm to 80\u2009nm. As depicted, the current increases rapidly as the voltage reaches the turn-on threshold, and with increasing nanogap distance, the Im-Vm curves shift towards higher voltages. Notably, all FN plots exhibit a nearly linear relationship, indicating the typical field emission behavior. The dotted lines in Fig.\u00a02a, b represent theoretical IMG-VMG-eff data generated as described in the following Section. The experimental field emission Im-Vm curves of all tungsten nanotips offer valuable insights into how both the radius of curvature Rm of nanotips and the gap spacing dm affect their emission characteristics. Figure\u00a02c\u2013e illustrate the applied voltages Vm (measured at Im\u2009=\u20092\u2009nA), the FEFs \u03b3a, and the \u03b3a\u00b7Vm as functions of R/d in logarithmic coordinates (scatterplots). Here, \u03b3a is obtained from finite element method (FEM) simulations (see \u201cMethods\u201d section and Supplementary Fig.\u00a03), where the nanotips are modeled using the sphere-on-cone approach, based on the morphology of all the tungsten nanotips in Fig.\u00a01. Notably, although the nanotip models are constructed using parameters (Rm, dm) measured from TEM images, they may not perfectly match the experimental nanotips. Thus, the radius of curvature of nanotip models and the gap distance in FEM simulations are denoted by Rt and dt, to distinguish them from the experimental nanotips, even though Rt\u2009=\u2009Rm and dt\u2009=\u2009dm. From the FEM electrostatics simulations, \u03b3a can be obtained as \u03b3a\u2009=\u2009Fa/FG, where Fa represents the electrostatic surface-field magnitude at the emitter apex, and FG is the average field amplitude in the gap between the emitter apex and the anode plate, given by FG\u2009=\u2009Vm/dt. It\u2019s important to note that our experiments are conducted in a near anode configuration, where the total emitter height Hm \u00bb Rm and Hm \u00bb dm, meaning that \u03b3 is not sensitive to H. To minimize the effect of the simulated height on the electrostatic fields, we set the height of the simulation models to be sufficiently large (at Ht/Rt\u2009=\u2009400) as shown in the \u201cMethods\u201d section and Supplementary Fig.\u00a02. The relationships \\({V}_{{{{\\rm{m}}}}}\\propto {({R}_{{{{\\rm{m}}}}}/{d}_{{{{\\rm{m}}}}})}^{-{n}_{1}}\\), \\({\\gamma }_{{{{\\rm{a}}}}}\\propto {({R}_{{{{\\rm{t}}}}}/{d}_{{{{\\rm{t}}}}})}^{-{n}_{2}}\\), and \\({\\gamma }_{{{{\\rm{a}}}}}\\cdot {V}_{{{{\\rm{m}}}}}\\propto {(R/d)}^{-{n}_{3}}\\) are used to obtain the fitted values of n1, n2, and n3 based on R/d, respectively, as shown in Fig.\u00a02c\u2013e. As expected, the required applied voltages Vm (at a fixed current) and the \u03b3a decrease with higher values of R/d. Notably, the relationship between \u03b3a and Rt/dt is nearly identical for all tungsten nanotip sphere-on-cone models with different Rt at different gap spacing dt (Fig.\u00a02d). For Rm/dm values less than 0.1, n1 increases slowly to about 0.2, rises rapidly to 0.9 as Rm/dm approaches 10, and then increases more slowly towards 1 for Rm/dm greater than 10, reflecting a transition to planar geometry with the relationship approximated as Vm \u221d dm/Rm (Fig.\u00a02c). Similarly, for Rt/dt\u2009<\u20090.1, the electrostatic field distribution between the emitter apex and the anode plane is non-uniform with n2 decreasing slowly to about 0.8, becoming more uniform as Rt/dt increases to 10 (where n2 drops rapidly to about 0.1), and approaching a planar case for Rt/dt\u2009>\u200910 with \u03b3a nearing 1 or n2\u2009=\u20090 (Fig.\u00a02d). More importantly, for all nanotips in our experiments, n3 is approximately 1 (Fig.\u00a02e), with acceptable fluctuations due to the differences between the experimental nanotips and the sphere-on-cone models. Therefore, we disregard the subscript differences \u201cm\u201d and \u201ct\u201d for R and d, obtaining the following relationship: \u03b3a\u00b7Vm \u221d d/R, which further leads to Fa\u2009=\u2009\u03b3a\u00b7FG \u221d 1/R. This finding implies that the local electrostatic field strength at the emitter apex required to obtain the same field emission current remains largely unchanged across the range of R/d\u2009=\u20090.04 to 48, with values for different nanotips depending on their apex radii of curvature. Moreover, within this range of R/d, even with a minimum R of 2\u2009nm and d of 5\u2009nm, no significant deviations from this relationship \u03b3a\u00b7Vm \u221d d/R (Fa\u2009=\u2009\u03b3a\u00b7FG \u221d 1/R) are observed in Fig.\u00a02e. This suggests that the effects due to the non-planar shape of the emitter may play a critical role in nanoscale field emission process. Notably, these relationships hold across various field emission currents in the nanoampere (nA) range. Additional details, including the logarithmic relationship between applied voltages Vm and Rm/dm, as well as between \u03b3a\u00b7Vm and R/d at different field emission currents of (10, 50, and 100\u2009nA), are provided in Supplementary Fig.\u00a04.\n\na The experimental field emission current-voltage Im-Vm curves (solid lines) of the tungsten nanotip with an apex radius of 4\u2009nm across different nanogaps. The dotted lines represent the theoretical IMG-VMG-eff data based on the Murphy-Good (MG) FE equation (VMG-eff\u2009=\u2009VMG/CMG \u2248 Vm, where CMG is correction factor). b The corresponding experimental Fowler-Nordheim (FN) plots (solid lines) and the corresponding FN plots (dotted lines) based on the MG FE equation (VMG-eff\u2009=\u2009VMG/CMG \u2248 Vm) of the tungsten nanotip with an apex radius of 4\u2009nm. c The applied voltages Vm at a field emission current (Im) of 2\u2009nA as a function of the ratio of experimental apex radius to gap length (Rm/dm) in logarithmic coordinates (scatterplots), along with the corresponding negative exponent n1 (solid line). d The field enhancement factors \u03b3a obtained from simulation as a function of simulated apex radius to gap length (Rt/dt) in logarithmic coordinates (scatterplots), along with the corresponding negative exponent n2 (solid line). e The product \u03b3a\u00b7Vm of the field enhancement factors \u03b3a and the applied voltages Vm at Im\u2009=\u20092\u2009nA as a function of R/d in logarithmic coordinates (scatterplots), along with the corresponding negative exponent n3 (solid line).\n\nNotably, the aforementioned relationships are based on experimental data or simulated data, and the specific analytical scaling (i.e., the specific analytical relationship between \u03b3a\u00b7Vm and R/d has yet to be derived (which may not be possible). Generally, the electrostatic field at the emitter apex can be expressed as Fa\u2009=\u2009\u03b2a\u00b7Vm\u2009=\u2009Vm/(kaR), where \u03b2a is the conversion factor connecting the electrostatic surface-field magnitude at the emitter apex and the applied voltages, and ka is a shape factor to be determined either experimentally or numerically60. The previous theoretical analytical scaling60 at the apex of the microtip with the prolate-spheroidal shape (which also used the assumption in Supplementary Note\u00a01) shows ka\u2009=\u20090.5\u2009\u00d7\u2009ln(4\u2009d/R) and ka\u2009=\u2009d/R, respectively, for R/d \u00ab 1 (sharp tip) and R/d \u00bb 1 (planar limit). By writing Fa\u2009=\u2009\u03b2a\u00b7d\u00b7Vm/d\u2009=\u2009\u03b3a\u00b7FG, we have \u03b3a\u2009=\u2009\u03b2a\u00b7d\u2009=\u2009d/(kaR), which gives \u03b3a\u2009=\u20092/(R/d) and \u03b3a\u2009=\u20091 (see the derivation in Supplementary Note\u00a02), respectively, for R/d \u00ab 1 (sharp tip) and R/d \u00bb 1 (planar limit), which is consistent with results shown in Fig.\u00a02d. It is important to note that the geometrical shape of our experimental tip (in Fig.\u00a01) is not exact similar to the assumed in ref. 60, but the discussion above shows qualitative agreement.\n\nTo further determine whether the space charge quantum effects are significant in our experiment, we used a self-consistent quantum model, which has been reported in refs. 53,54, to obtain the field emission characteristics JQ for the tungsten (cathode)-gold (anode) parallel-plate electrode structure50,51,52,53,54. In this model, the one-dimensional modified Poisson-Schr\u00f6dinger equation combined with the Jeffreys-Wentzel-Kramers-Brillouin tunneling model is solved numerically for calculating electron field emission current density54. The local work function (\u03d5) and Fermi Energy (EF) used for tungsten are given as 4.5\u2009eV and 5.782\u2009eV, respectively, and for gold, they are 5.1\u2009eV and 5.535\u2009eV, respectively61. Figure\u00a03 shows the normalized electron current density \u03bcQC\u2009=\u2009JQ/JCL (black lines) compared to \u03bcMC\u2009=\u2009JMG/JCL (red lines) at different distances between well-separated parallel planar plates (dsep\u2009=\u20091\u2009nm, 5\u2009nm, and 10\u2009nm) based on theoretical calculations, where JCL is the classical Child-Langmuir (CL) law62,63, and the JMG is the MG FE equation without the space charge effects (see Supplementary Note\u00a01 and Supplementary Eq. (S2)). When the gap distance dsep is greater than 5\u2009nm and the electrostatic field FP (FP\u2009=\u2009VP/dsep, VP is the applied voltage between the plates) is less than 10\u2009V/nm, the field emission characteristics considering space charge quantum effects are consistent with those obtained by MG FE equation. This indicates that the space charge quantum effects can be ignored so that we can conclude the effects due to the non-planar shape of the emitter are more important for R/d\u2009=\u20090.04 to 48 as studied in our experiment. Moreover, it should be noted that when dsep is 1\u2009nm and FP is less than 4\u2009V/nm, the emission current density \u03bcQC is higher than \u03bcMC, due to direct tunneling (see Supplementary Note\u00a03 and Supplementary Fig.\u00a05)54.\n\na The normalized electron emission current density \u03bcQC\u2009=\u2009JQ/JCL (black lines) and \u03bcMC\u2009=\u2009JMG/JCL (red lines) as a function of electrostatic fields FP\u2009=\u20091 to 12\u2009V/nm (FP\u2009=\u2009VP/dsep, VP is the applied voltage between the plates, dsep is distance between well-separated parallel planar plates) at dsep\u2009=\u20091\u2009nm for the tungsten (cathode)-gold (anode) parallel-plate electrode structure, based on theoretical calculations. Here, JCL is the classical Child-Langmuir (CL) law, JMG is the MG FE equation, and JQ is obtained by a self-consistent quantum model53,54. b \u03bcQC\u2009=\u2009JQ/JCL (black lines) and \u03bcMC\u2009=\u2009JMG/JCL (red lines) at dsep\u2009=\u20095\u2009nm. c \u03bcQC\u2009=\u2009JQ/JCL (black lines) and \u03bcMC\u2009=\u2009JMG/JCL (red lines) at dsep\u2009=\u200910\u2009nm.\n\nSince the space charge quantum effects can be ignored in our experiment, we further compare the experimental current-voltage Im-Vm characteristics with theoretically predicted characteristics. The representative geometry models used are shown in Supplementary Fig.\u00a03. For a given voltage between the emitter and the anode plate, the electrostatic field distribution over the emitter-shape-model surface is first calculated by finite-element methods (FEM), where the FEFs \u03b3a can also be obtained. Then, the total predicted emission current is obtained by integration of local emission current density (LECD) over the shape-model surface, using the planar emission approximation and the MG FE equation (see Supplementary Note\u00a01 and Supplementary Eq. (S2)). The planar emission approximation assumes that the LECD JL at any particular location \u201cL\u201d on the emitter surface is given by some specified planar emission equation, using the values at \u201cL\u201d of the local work function and the surface electrostatic field magnitude34. For a specific model and emission current, we find that theoretically predicted voltage values VMG are less than those Vm found experimentally for the same gap spacing d. This suggests that (other things being equal) MG FE theory may be over-predicting LECDs. To quantify the discrepancy, we introduced a correction factor CMG\u2009<\u20091. Specifically, due to the consistent scaling relationship at different currents (Im\u2009=\u20092\u2009nA, 10\u2009nA, 50\u2009nA, and 100\u2009nA) as shown in Fig.\u00a01 and Supplementary Fig.\u00a04, we selected the voltage at I\u2009=\u20092\u2009nA to calculate CMG, (CMG\u2009=\u2009[VMG(IMG\u2009=\u20092\u2009nA)]/[Vm(Im\u2009=\u20092\u2009nA)]), then the effective voltage for all VMG values can be expressed as: VMG-eff\u2009=\u2009VMG/CMG \u2248 Vm. The theoretical IMG-VMG-eff curves and corresponding theoretical FN plots obtained are shown in Fig.\u00a02a, b (dotted lines), which are closely aligned with the experimental data. Figure\u00a04a illustrates the numerical values of correction factors CMG as a function of R/d in logarithmic coordinates. As R/d increases, CMG initially increases from approximately 0.4 and gradually approaches 0.7. This confirms experimentally the discrepancies between the actual field emission and theoretical predictions64.\n\na The correction factors CMG as a function of the ratio of apex radius to gap length R/d in logarithmic coordinates (scatterplots). b The effective field-voltage conversion factors \u03b2eff-MG as a function of R/d in logarithmic coordinates (scatterplots), along with the corresponding exponent n4 (solid line). c The shape factors kMG as a function of R/d in logarithmic coordinates (scatterplots), along with the corresponding negative exponent n5 (solid line). The black line shows the fitting curve by kMG\u2009=\u20091.680\u2009\u00d7\u2009(R/d\u2009+\u20090.468)\u22121.066. d The field emission Im-Feff-MG curves of the tungsten nanotip with an apex radius of 4\u2009nm across different nanogaps. e The corresponding Fowler-Nordheim (FN) plots of Im-Feff-MG curves. f The effective emission area Aeff-MG obtained by finite element method (FEM) simulation.\n\nFigure\u00a04b, c show the effective field-voltage conversion factors \u03b2eff-MG (\u03b2eff-MG\u2009=\u2009CMG\u03b2a\u2009=\u2009CMG\u03b3a/d) and shape factors kMG (\u03b2eff-MG\u2009=\u20091/(kMGR)) as functions of R/d in logarithmic coordinates. The relationships \\({\\beta }_{{{{\\rm{eff}}}}-{{{\\rm{MG}}}}}\\propto {(R/d)}^{{n}_{4}}\\) and \\({k}_{{{{\\rm{MG}}}}}\\propto {(R/d)}^{-{n}_{5}}\\) are used to fit n4 and n5. For R/d\u2009<\u20090.1, n4 increases slowly to about 0.2, rises rapidly to 0.9 as R/d approaches 10, and then increases more slowly towards 1 for R/d\u2009>\u200910, following \u03b2eff-MG \u221d R/d (Fig.\u00a04b). This is consistent with the n1 trend reported in Fig.\u00a02c. Surprisingly, the scaling of kMG is valid for all tungsten nanotips with different R, which converges onto a single line with R/d (Fig.\u00a04c). Analogously, for R/d values less than 0.1, n5 rises slowly to about 0.2, increases rapidly to 0.9 as R/d approaches 10, and then rises more slowly towards 1 for R/d\u2009>\u200910, following kMG \u221d d/R (for planar geometry) and indicating a nearly uniform electrostatic field distribution between the emitter apex and the anode plane. As we can see, the kMG values ranging from 0.02 to 4 provide a clear and detailed characterization of field emission of a nanotip in a nanogap. We believe that these scaling laws should be valid for any metallic nanotip of apex radius R in a nanogap of spacing d, in the range of R/d\u2009=\u20090.04 to 48 reported experimentally in this work. For the ease of applications, the values of kMG can be fitted into a simple analytical expression depending of R/d, which is kMG\u2009=\u20091.680\u2009\u00d7\u2009(R/d\u2009+\u20090.468)\u22121.066 (based on Fig.\u00a04c, with a R-squared fitting of 0.986). Thus, the electrostatic field F in the MG FE equation (Supplementary Eq. (S2)) should be substituted by the effective electrostatic field Feff-MG\n\nwhere Feff-MG is the effective apex-field. Then, the total field emission current can be estimated by\n\nwhere Jeff-MG is the effective apex emission current density, Aeff-MG is effective emission area, a (=\u20091.54\u2009\u00d7\u200910\u22126 [A eV V\u22122]) and b (=\u20096.83 [eV\u22123/2 V nm\u22121]) are constants, y is the Nordheim parameter (where y\u2009=\u2009(1.20\u2009eV\u2009V\u22121/2 nm1/2) F1/2/\u03d5, and F is in V/nm), and t(y) and v(y) are well-known mathematical functions26,27,28.\n\nBased on the proposed equation, the applied voltage Vm in field emission characteristics of the tungsten nanotip with a radius of curvature of 4\u2009nm shown in Fig.\u00a02a, b can be replaced by the effective apex-field, Feff-MG. Figure\u00a04d, e show the field emission Im-Feff-MG curves and their corresponding FN plots. Notably, as d increases, the Im-Feff-MG curves gradually converge for R/d\u2009\u2264\u20090.27. The observed differences in the curves at d\u2009=\u20095\u2009nm (R/d\u2009=\u20090.8) and d\u2009=\u200910\u2009nm (R/d\u2009=\u20090.4) can be explained by the effective emission area Aeff-MG in Fig.\u00a04f. As the gap increases with R/d\u2009\u2264\u20090.27, the effective emission area increases and converges gradually. However, for d\u2009=\u20095\u2009nm (R/d\u2009=\u20090.8), especially or d\u2009=\u200910\u2009nm (R/d\u2009=\u20090.4), the effective emission area remains below this convergent value, indicating that the nanotip requires a higher electrostatic field to maintain the same field emission current Im. This causes the deviations of the Im-Feff-MG curves and the corresponding FN plots when R/d\u2009>\u20090.27, differing from the reported collapsing log10(I/F2)\u2009~\u20091/F curves in ref. 65, where the change of emission area is not considered. Despite this difference at R/d\u2009>\u20090.27, the collapsing I-V curves and the FN plots reported in ref. 65 are consistent with our findings for R/d\u2009<\u20090.27. To be specific, the I-V curves can collapse onto one single I-VR(d) curve, with R(d) approximating a power law R(d) \u221d d\u2212\u03bb (where \u03bb\u2009\u2248\u20090.22 for d\u2009=\u20093\u2013300\u2009nm and R \u2248 5\u2009nm). Furthermore, they found that when d\u2009>\u200910\u2009nm, V \u221d d\u03bb with \u03bb\u2009\u2248\u20090.2\u20130.35, while \u03bb towards to a larger value for d\u2009<\u200910\u2009nm65. This well matches our universal scaling \\({V}_{{{{\\rm{m}}}}}\\propto {d}^{{n}_{1}}\\) for a nanotip with R as the radius of curvature, where n1 increases slowly at approximately 0.2 for R/d\u2009<\u20090.1, which proves the validity of our proposed models for field emission of nanotip in nanogap as studied in this work.\n\nBased on the above analysis, the effects of the emitter\u2019s non-planar shape are more important for R/d\u2009=\u20090.04 to 48 as studied in our experiment. Therefore, we utilize the Kyritsakis-Xanthakis (KX) FE equation42, including surface curvature corrections for local electrostatic potential and the image charge potential which is valid only along the emitter\u2019s axis (see Supplementary Note\u00a01 and Supplementary Eq. (S4)), to derive the correction factor CKX, effective field-voltage conversion factors \u03b2eff-KX and kKX as functions of R/d, along with the corresponding power exponents, as provided in Supplementary Note\u00a04 and Supplementary Fig.\u00a06. This approach, based on the planar emission approximation, is similar to the process used for deriving CMG, \u03b2eff-MG and kMG. As shown in Supplementary Fig.\u00a06, for R/d\u2009<\u20091, CKX is greater than CMG, increasing from 0.5 (whereas CMG increases from 0.4 in Fig.\u00a04a), due to the inclusion of the curvature correction effects. For R/d\u2009>\u20091, CKX is consistent with CMG, and approaches 0.7. Therefore, despite these corrections, the KX FE equation (ref. 42), which uses an Earthed-sphere model to assess surface curvature effects, still does not accurately predict the field emission current of nanotips.\n\nInterestingly, the investigation of electron tunneling process between the planar substrate and the non-planar tips (spherical or hyperboloidal geometry) decades ago has already concluded that electron field emission current density in a nanogap is significantly regulated by the two factors including the asymmetry in the geometries of cathode and anode, and the overall image charge potential of space charge with both electrodes. Those effects on the overall image charge potential have been carefully examined in refs. 29,30 for sphere-plane electrode configuration with nanogaps using the rigorous electrodynamic models under spherical and prolate spheroidal coordinates. It was found that the non-planar geometry of cathode could directly result in the anisotropic distribution of image charge potential spatially surrounding the cathode. Most importantly, the overall image charge potential of sphere-plane system in nanogap was predicted to be less negative near the cathode, compared to that of plane-plane configuration, indicating an increasing of electron transmission barrier height in the former case due to the anticipated geometric asymmetry in electrode pair. Furthermore, the increasing of geometric asymmetry further diminishes the lowering of electron emission barrier height, because the complete multiple-image potential goes to less negative, relative to that of plane-plane geometry. For example, using the exact image charge potential model given in ref. 30 for hyperboloidal tip model (tungsten electrode with R\u2009=\u200910 nm and d\u2009=\u20091, 2, and 3\u2009nm, respectively), for R/d\u2009=\u200910, 5.0, and 3.3, the absolute values are reduced by 1.0%, 1.9%, and 2.9%, compared to those of plane-plane system, respectively. The raising of electron transmission energy barrier height with the increasing of the geometric asymmetry in nanogap for anode-cathode system can reduce the emission current density in comparison with that of plane-plane configuration under the same electrostatic field. This may be the main reason for the presence of the correction factor VMG\u2009=\u2009CMGVm\u2009<\u2009Vm between experimental field emission curves and the MG FE equation, as shown in Fig.\u00a04a. These insight inspires further theoretical exploration to refine predictions for nanoscale field emission phenomena, where the three-dimensional image charge potential between space charges and the bulk charges in the both electrodes (anode and cathode) should be especially considered30.\n\nIn this study, we delved into the experimental relationship between field emission characteristics of nanotips in nanogaps and the ratio of apex radius to gap length (R/d). We demonstrated that space charge quantum effects are not considerable in the range of R/d\u2009=\u20090.04 to 48, while the effects of quantum tunnelling due to the emitter shape are predominant. Based on our experimental results, we proposed a modified field emission (FE) equation, where the effective electrostatic field at the emitter apex is given by Feff-MG\u2009=\u2009Vm/(kMGR), with a detailed analytical expression for the shape factor, kMG\u2009=\u20091.680\u2009\u00d7\u2009(R/d\u2009+\u20090.468)\u22121.066. These findings are believed to be valid for any metallic nanotip in the range of R/d\u2009=\u20090.04 to 48. It is important to note that despite the success and limitation of 1D field emission models (many different versions), all models require some approximation to derive some scaling laws or equations to compare with experimental results. Physics-consistent 3D model for arbitrary shape of emitter is likely to be impossible. In this paper, we performed a clear measurement of field emission from an emitter of radius R\u2009=\u20092 to 190\u2009nm in a nanogap of d\u2009=\u20095\u2009nm to 100\u2009nm and provide a first experimental-proved scaling that is valid over a wide range of R/d (4 order of magnitude). Discussion of this scaling to other models can be referred to Supplementary Note\u00a04. Our work underscores the importance of emitter shape effects in dictating the emission properties, and highlights the need for precise theoretical models to accurately predict and harness these effects in practical applications, which is crucial for understanding and improving the performance of nanoelectronic devices.",
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+            "section_name": "Methods",
+            "section_text": "The in situ electrical experiment system consists of the transmission electron microscopy (JEOL-2100F TEM) and an in situ electrically biased TEM holder (ZepTools Technology). This setup achieves a spatial resolution of 0.1\u2009nm and allows for nanogap adjustment with an accuracy of 0.04\u2009nm. During field emission measurements, the system can apply a direct current voltage of up to 150\u2009V across nanogaps, with a current measurement resolution of 0.1\u2009nA. The in situ electrically biased TEM holder and the schematic diagram of the field emission measurement are shown in Supplementary Fig.\u00a01a, b. All measurements are performed at room temperature and a vacuum level of ~10\u22125\u2009Pa.\n\nThe preparation of the tungsten nanotips involves two steps. The first step is an ex-situ double\u2011electrolyte electrochemical etching method57,58, and the schematic is shown in Supplementary Fig.\u00a01c. Specifically, a stepping motor (TSTA-1050, 7-star, Beijing) precisely controls the motion of a 99.97% pure tungsten wire with a diameter of 0.3\u2009mm. The tungsten wire passes through a 5\u2009M NaOH electrolyte lamella (flake, purity 97%, Aladdin) and is immersed perpendicularly in a saturated NaCl solution (AR, Aladdin). A DC power source (B2091A, Keysight, USA) supplies a voltage of 5\u2009V to a stainless-steel anode immersed in the saturated NaCl solution and a ring inert nickel-chromium cathode (diameter 10\u2009mm). The tungsten wire is etched only in the NaOH lamella, with the NaCl solution acting as a conducting element between the tungsten wire and the stainless-steel anode. Once the tungsten wire breaks, the electric circuit is automatically cut off as the lower fragment of the tungsten wire drops. However, although the apex radius of the prepared tungsten nanotip by first step is less than 50\u2009nm, there is an unavoidable oxide layer with a few nanometers thick on the tungsten nanoelectrode surface due to the ex-situ preparation, which significantly affects the field emission characteristics.\n\nThe second step is an in situ Joule melting method. Initially, the tungsten nanoelectrodes prepared by the first step and the gold plate (prepared by pressing and cutting) are mounted on the TEM electrical sample holder, as shown in Supplementary Fig.\u00a01a. Next, the interelectrode gap is adjusted in situ to less than 20\u2009nm under TEM. A ramped DC voltage is then applied across the nanogap to induce electrical breakdown, with the tungsten nanotip acting as the cathode and the gold plate as the anode. Following the breakdown, the tungsten nanotips with radii of curvature from 2\u2009nm to 200\u2009nm can be prepared in situ. The surfaces of the tungsten nanotips prepared by this method are very clean and free of contaminants such as oxide layer. This is demonstrated by the representative high-resolution TEM images and the selected area electron diffraction results of the pure tungsten nanotip with an apex radius of 5\u2009nm, as shown in Supplementary Fig.\u00a01d.\n\nThe FEFs are obtained using a commercial FEM tool (COMSOL Multiphysics). First, the sphere-on-cone nanotip models are established based on the morphology of all the tungsten nanotips shown in Fig.\u00a01. Material parameters are based on the default values provided by the COMSOL internal library. It\u2019s worth noting that the heights of practical tungsten nanotips are approximately 1\u2009cm, i.e., Hm \u00bb Rm and Hm \u00bb dm (in a near anode configuration), and in order to reduce the effect of the simulated heights on the simulated electrostatic fields, we set the height of the simulated models at Ht/Rt\u2009=\u2009400. The reason is that according to the Supplementary Fig.\u00a02, when Ht/Rt is greater than 400, the selected heights have little effect on the FEF, given that the minimum Rt/dt ratio in our experiments is 0.04. Next, the electrostatic fields are simulated using the electrostatics module. The FEF \u03b3a can be obtained as \u03b3a\u2009=\u2009Fa/FG, where Fa represents the electrostatic surface-field magnitude at the emitter apex, and FG is the average field amplitude in the gap between the emitter apex and the anode plate, given by FG\u2009=\u2009V/d. Then, the total predicted emission current is obtained by integration of LECD over the shape-model surface, using the planar emission approximation and the MG FE equation26,27,28 or KX FE equation42 (see Supplementary Note\u00a01 and Supplementary Eqs. (S2) and (S4)). The planar emission approximation assumes that the LECD JL at any particular location \u201cL\u201d on the emitter surface is given by some specified planar emission equation, using the values at \u201cL\u201d of the local work function and the surface electrostatic field magnitude34. Supplementary Fig.\u00a03 shows the electrostatic field distribution, as well as field emission current density JMG and JKX (two-dimensional linear current density) for the nanotip with an apex radius of 4\u2009nm at d\u2009=\u20095\u2009nm and V\u2009=\u200920\u2009V.",
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+            "section_name": "Data availability",
+            "section_text": "The authors declare that all relevant data supporting the findings of this work are included in the Article, with additional data provided in the Supplementary Information.\u00a0Source data are provided with this paper.",
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+            "section_name": "References",
+            "section_text": "Hernandez, N. et al. Field emission characteristics of AlGaN/GaN nanoscale lateral vacuum diodes. J. Appl. Phys. 135, 204305 (2024).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nXu, J. et al. High-quality and stable electron emission device with sub-30-nm aligned nanogap arrays. IEEE Trans. Electron Devices 64, 2364\u20132368 (2017).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBrimley, S., Miller, M. S. & Hagmann, M. J. Field emission in air and space-charge-limited currents from iridium-iridium oxide tips with gaps below 100 nm. J. Appl. Phys. 109, 094510 (2011).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nSrisonphan, S. Nanogaps mediated field effect-controlled field emission triode. Acs Appl. Electron. Mater. 4, 4857\u20134862 (2022).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nSrisonphan, S. Field effect-controlled space-charge limited emission triode with nanogap channels. IEEE Electron Device Lett. 42, 1540\u20131543 (2021).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nPescini, L. et al. Nanoscale lateral field-emission triode operating at atmospheric pressure. Adv. Mater. 13, 1780\u20131783 (2001).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nNguyen, H. D., Kang, J. S., Li, M. & Hu, Y. J. High-performance field emission based on nanostructured tin selenide for nanoscale vacuum transistors. Nanoscale 11, 3129\u20133137 (2019).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nSrisonphan, S., Jung, Y. S. & Kim, H. K. Metal-oxide-semiconductor field-effect transistor with a vacuum channel. Nat. Nanotechnol. 7, 504\u2013508 (2012).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nHan, J. W., Seol, M. L., Kim, J. & Meyyappan, M. Nanoscale complementary vacuum field emission transistor. ACS Appl. Nano Mater. 3, 11481\u201311488 (2020).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nHan, J. W., Seol, M. L., Moon, D. I., Hunter, G. & Meyyappan, M. Nanoscale vacuum channel transistors fabricated on silicon carbide wafers. Nat. Electron 2, 405\u2013411 (2019).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nNirantar, S. et al. Metal-air transistors: semiconductor-free field-emission air-channel nanoelectronics. Nano Lett. 18, 7478\u20137484 (2018).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nChang, W. T. & Pao, P. H. Field electrons intercepted by coplanar gates in nanoscale air channel. IEEE Trans. Electron Devices 66, 3961\u20133966 (2019).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nNikoo, M. S. & Matioli, E. Electronic metadevices for terahertz applications. Nature 614, 451\u2013455 (2023).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nNikoo, M. S. et al. Nanoplasma-enabled picosecond switches for ultrafast electronics. Nature 579, 534\u2013539 (2020).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nXu, J., Wang, Q. L., Qi, Z. Y., Zhai, Y. S. & Zhang, X. B. Study on the frequency characteristics of nanogap electron devices. J. Appl. Phys. 117, 204504 (2015).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLoganathan, K. et al. Rapid and up-scalable manufacturing of gigahertz nanogap diodes. Nat. Commun. 13, 3260 (2022).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLi, N. N., Zhang, B. L., He, Y. & Luo, Y. Sub-picosecond nanodiodes for low-power ultrafast electronics. Adv. Mater. 33, 2100874 (2021).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nZhang, H. J. et al. Polymer-protected sub-2-nm-nanogap fabrication for biological sensing in near-physiological conditions. Small 5, 2797\u20132801 (2009).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nIvanov, A. P. et al. DNA tunneling detector embedded in a nanopore. Nano Lett. 11, 279\u2013285 (2011).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nChen, X. et al. Electrical nanogap devices for biosensing. Mater. Today 13, 28\u201341 (2010).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nXiang, D., Jeong, H., Lee, T. & Mayer, D. Mechanically controllable break junctions for molecular electronics. Adv. Mater. 25, 4845\u20134867 (2013).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDurkan, C. & Zhang, Q. Towards reproducible, scalable lateral molecular electronic devices. Appl. Phys. Lett. 105, 083504 (2014).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nHan, J. W., Oh, J. S. & Meyyappan, M. Vacuum nanoelectronics: back to the future?-Gate insulated nanoscale vacuum channel transistor. Appl. Phys. Lett. 100, 213505 (2012).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nHan, J. W., Moon, D. I. & Meyyappan, M. Nanoscale vacuum channel transistor. Nano Lett. 17, 2146\u20132151 (2017).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLi, X. H. & Feng, J. J. Review of nanoscale vacuum devices. Electron.-Switz. 12, 802 (2023).\n\nCAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMurphy, E. L. & Good, R. H. Thermionic emission, field emission, and the transition region. Phys. Rev. 102, 1464\u20131473 (1956).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nEgorov, N. & Sheshin, E. Field Emission Electronics (Springer, Cham, 2017).\n\nFursey, G. N. Field Emission in Vacuum Microelectronics (Springer, New York, 2005).\n\nMorawitz, H., Batra, I. P., Reinisch, R. & Henry, G. R. Multiple image potential effects in a simple-model of the scanning tunneling microscope (STM). Surf. Sci. 180, 333\u2013352 (1987).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMiskovsky, N., Cutler, P., Feuchtwang, T. & Lucas, A. A Green\u2019s function solution to the image and multiple image interactions for hyperboloidal geometry: application to metallic pointcontact infrared detectors. Int. J. Infrared Millim. Waves 2, 739\u2013772 (1981).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nZhang, P., Valfells, A., Ang, L. K., Luginsland, J. W. & Lau, Y. Y. 100 years of the physics of diodes. Appl. Phys. Rev. 4, 011304 (2017).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLi, Y. M. et al. Review of electron emission and electrical breakdown in nanogaps. Phys. Plasmas 31, 040502 (2024).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nZhang, P. et al. Space-charge limited current in nanodiodes: ballistic, collisional, and dynamical effects. J. Appl. Phys. 129, 100902 (2021).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nde Assis, T. A., Dall\u2019Agnol, F. F. & Forbes, R. G. Field emitter electrostatics: a review with special emphasis on modern high-precision finite-element modelling. J. Phys.-Condens Mat. 34, 493001 (2022).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nGaertner, G., Knapp, W. & Forbes, R. G. Modern Developments in Vacuum Electron Sources Preface (Springer, Cham, 2020).\n\nCutler, P. H., He, J., Miskovsky, N. M., Sullivan, T. E. & Weiss, B. Theory of electron-emission in high fields from atomically sharp emitters - Validity of the Fowler-Nordheim equation. J. Vac. Sci. Technol. B 11, 387\u2013391 (1993).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nFursey, G. N. & Glazanov, D. V. Deviations from the Fowler-Nordheim theory and peculiarities of field electron emission from small-scale objects. J. Vac. Sci. Technol. B 16, 910\u2013915 (1998).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nHe, J. et al. Derivation of the image interaction for non-planar pointed emitter geometries: application to field emission I\u2013V characteristics. Surf. Sci. 246, 348\u2013364 (1991).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBiswas, D. & Ramachandran, R. The image-charge correction for curved field emitters (vol 24, 073107, 2017). Phys. Plasmas 24, 079901 (2017).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nJensen, K. L., Shiffler, D. A., Harris, J. R., Rittersdorf, I. M. & Petillo, J. J. 2D/3D image charge for modeling field emission. J. Vac. Sci. Technol. B 35, 02C101 (2017).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKyritsakis, A., Xanthakis, J. P. & Pescia, D. Scaling properties of a non-Fowler-Nordheim tunnelling junction. P. R. Soc. a-Math. Phy. 470, 20130795 (2014).\n\n\n                    Google Scholar\u00a0\n                \n\nKyritsakis, A. & Xanthakis, J. P. Derivation of a generalized Fowler-Nordheim equation for nanoscopic field-emitters. P. R. Soc. a-Math. Phy 471, 20140811 (2015).\n\nMathSciNet\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nJensen, K. L., Shiffler, D. A., Peckerar, M., Harris, J. R. & Petillo, J. J. Current from a nano-gap hyperbolic diode using shape-factors: theory. J. Appl Phys. 122, 064501 (2017).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBinh, V. T., Purcell, S., Garcia, N. & Doglioni, J. Field-emission electron spectroscopy of single-atom tips. Phys. Rev. Lett. 69, 2527 (1992).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nPurcell, S. T. et al. Field-emission from narrow bands above the Fermi-level of nanometer-scale objects. Phys. Rev. B 49, 17259\u201317263 (1994).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nPatterson, A. A. & Akinwande, A. I. Elementary framework for cold field emission: Incorporation of quantum-confinement effects. J. Appl. Phys. 114, 234303 (2013).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKleshch, V. I., Zestanakis, P. A. & Xanthakis, J. P. Breakdown of plane-wave-based theories of field emission from a subnanometer-radius tip. Appl. Surf. Sci. 623, 156990 (2023).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nChatziafratis, A. & Xanthakis, J. P. Field emission from a nanometric paraboloidal emitter. J. Electron Spectrosc. Relat. Phenom. 241, 146871 (2020).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nChatziafratis, A., Fikioris, G. & Xanthakis, J. P. Exact eigenstates of a nanometric paraboloidal emitter and field emission quantities. P. R. Soc. a-Math. Phy 474, 20170692 (2018).\n\nCAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBanerjee, S. & Zhang, P. A generalized self-consistent model for quantum tunneling current in dissimilar metal-insulator-metal junction. AIP Adv. 9, 085302 (2019).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nZhang, P. Scaling for quantum tunneling current in nano- and subnano-scale plasmonic junctions. Sci. Rep. 5, 09826 (2015).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nZhang, P. & Lau, Y. Y. Ultrafast and nanoscale diodes. J. Plasma Phys. 82, 595820505 (2016).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKoh, W. S. & Ang, L. K. Quantum model of space-charge-limited field emission in a nanogap. Nanotechnology 19, 235402 (2008).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLi, N., Wu, K., Cheng, Y. H. & Xiao, B. Self-consistent numerical solution of quantum regime with exchange-correlation effects of space charges for electron field emission in a nano-gap. Front. Phys. 11, 1223704 (2023).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMeng, G. et al. In situ Observation of Field-induced nanoprotrusion growth on a carbon-coated tungsten nanotip. Phys. Rev. Lett. 132, 176201 (2024).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLi, Y., Zhan, F., Tang, J., Cheng, Y. & Meng, G. Effect of cathode radius on the pre-breakdown characteristics in vacuum nanogaps. In 30th International Symposium on Discharges and Electrical Insulation in Vacuum (ISDEIV). (ed. Motoyoshi, T.) 1\u20134 (Institute of Electrical and Electronics Engineers (IEEE), 2023).\n\nLi, Y. Z. et al. A double-electrolyte etching method of high-quality tungsten probe for undergraduate scanning tunneling microscopy and atomic force microscopy experiments. Eur. J. Phys. 40, 025004 (2019).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLi, B. W. et al. Fabricating ultra-sharp tungsten STM tips with high yield: double-electrolyte etching method and machine learning. Sn Appl. Sci. 2, 1246 (2020).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMeng, G. D., Cheng, Y. H., Wu, K. & Chen, L. Electrical characteristics of nanometer gaps in vacuum under direct voltage. IEEE Trans. Dielectr. Electr. Insul. 21, 1950\u20131956 (2014).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nZuber, J. D., Jensen, K. L. & Sullivan, T. E. An analytical solution for microtip field emission current and effective emission area. J. Appl. Phys. 91, 9379\u20139384 (2002).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nJensen, K. L. Exchange-correlation, dipole, and image charge potentials for electron sources: Temperature and field variation of the barrier height. J. Appl. Phys. 85, 2667\u20132680 (1999).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nChild, C. D. Discharge from hot CaO. Phys. Rev. 32, 0492\u20130511 (1911).\n\nCAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLangmuir, I. The effect of space charge and residual gases on thermionic currents in high vacuum. Phys. Rev. 2, 450\u2013486 (1913).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nForbes, R. G. Development of a simple quantitative test for lack of field emission orthodoxy. Proc. R. Soc. A: Math., Phys. Eng. Sci. 469, 20130271 (2013).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nCabrera, H. et al. Scale invariance of a diodelike tunnel junction. Phys. Rev. B 87, 115436 (2013).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDownload references",
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+        },
+        {
+            "section_name": "Acknowledgements",
+            "section_text": "G.M. is supported by National Natural Science Foundation of China (51977169) and the Fundamental Research Funds for the Central Universities (xtr062023001). L.K.A. is supported by the A*STAR AME IRG (M23M6c0102). Y.L. is supported by the China Scholarship Council program (202406280230). G.M. and Y.L. are grateful to The Center for Advancing Materials Performance from the Nanoscale (CAMP-Nano) in Xi\u2019an Jiaotong University for the in situ TEM measurement.",
+            "section_image": []
+        },
+        {
+            "section_name": "Author information",
+            "section_text": "State Key Laboratory of Electrical Insulation and Power Equipment, Xi\u2019an Jiaotong University, Xi\u2019an, P.R. China\n\nYimeng Li,\u00a0Linghan Xia,\u00a0Nan Li,\u00a0Shilong Tang,\u00a0Yunsong Ge,\u00a0Jianyu Wang,\u00a0Bing Xiao,\u00a0Yonghong Cheng\u00a0&\u00a0Guodong Meng\n\nScience, Mathematics and Technology, Singapore University of Technology and Design, Singapore, Singapore\n\nLay Kee Ang\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nG.M., Y.C., and Y.L. conceived the project. L.K.A. contributed expertise and assistance in theoretical guidance. B.X. contributed expertise and assistance in simulation guidance. Y.L. carried out the experiments and simulations, analyzed the data, and wrote the original manuscript. L.X., S.T., Y.G., and J.W. assisted with experimentation. N.L. assisted with simulations. All authors contributed to the discussion of the data and to writing the manuscript. All authors have given approval to the final version of the manuscript.\n\nCorrespondence to\n                Lay Kee Ang or Guodong Meng.",
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+            "section_text": "Li, Y., Xia, L., Li, N. et al. Uncovering a widely applicable empirical formula for field emission characteristics of metallic nanotips in nanogaps.\n                    Nat Commun 16, 5583 (2025). https://doi.org/10.1038/s41467-025-60607-6\n\nDownload citation\n\nReceived: 05 November 2024\n\nAccepted: 22 May 2025\n\nPublished: 01 July 2025\n\nVersion of record: 01 July 2025\n\nDOI: https://doi.org/10.1038/s41467-025-60607-6\n\nAnyone you share the following link with will be able to read this content:\n\nSorry, a shareable link is not currently available for this article.\n\n\n\n\n                            Provided by the Springer Nature SharedIt content-sharing initiative\n                        ",
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+{
+    "title": "Decoupled charge and heat transport in Fe2VAl composite thermoelectrics with topological-insulating grain boundary networks",
+    "pre_title": "Topological-insulating grain boundary networks for high-performance Fe2VAl thermoelectrics",
+    "journal": "Nature Communications",
+    "published": "26 March 2025",
+    "supplementary_0": [
+        {
+            "label": "Supplementary Information",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-57250-6/MediaObjects/41467_2025_57250_MOESM1_ESM.pdf"
+        },
+        {
+            "label": "Transparent Peer Review file",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-57250-6/MediaObjects/41467_2025_57250_MOESM2_ESM.pdf"
+        }
+    ],
+    "supplementary_1": NaN,
+    "supplementary_2": NaN,
+    "source_data": [
+        "/articles/s41467-025-57250-6#MOESM1"
+    ],
+    "code": [],
+    "subject": [
+        "Composites",
+        "Electronic properties and materials",
+        "Thermoelectrics",
+        "Topological matter"
+    ],
+    "license": "http://creativecommons.org/licenses/by/4.0/",
+    "preprint_pdf": "https://www.researchsquare.com/article/rs-5271025/v1.pdf?c=1743073679000",
+    "research_square_link": "https://www.researchsquare.com//article/rs-5271025/v1",
+    "nature_pdf": "https://www.nature.com/articles/s41467-025-57250-6.pdf",
+    "preprint_posted": "14 Nov, 2024",
+    "research_square_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Decoupling charge and heat transport is essential for optimizing thermoelectric materials. Strategies to inhibit lattice-driven heat transport, however, also compromise carrier mobility, limiting the performance of most thermoelectrics, including Fe2VAl Heusler compounds. Here, we demonstrate an innovative approach, which bypasses this tradeoff: via liquid-phase sintering, we incorporate the archetypal topological insulator Bi1-xSbx between Fe2V0.95Ta0.1Al0.95 grains. Structural investigations alongside extensive thermoelectric and magneto-transport measurements reveal distinct modifications in the microstructure, a reduced lattice thermal conductivity and a simultaneously enhanced carrier mobility arising from topologically protected charge transport along the grain boundaries. This yields a huge performance boost - far beyond the effective-medium limit - and results in one of the highest figure of merits among both half- and full-Heusler compounds, z \u2248 1.6 x 10^-3 K^-1 (zT \u2248 0.5) at 295 K. Our findings highlight the potential of topological-insulating secondary phases to decouple charge and heat transport and call for more advanced theoretical studies of multiphase composites.Physical sciences/Materials science/Materials for energy and catalysis/ThermoelectricsPhysical sciences/Materials science/Condensed-matter physics/Topological matter/Topological insulatorsPhysical sciences/Materials science/Techniques and instrumentation/Design, synthesis and processingPhysical sciences/Materials science/Structural materials/Composites",
+            "section_image": []
+        },
+        {
+            "section_name": "Additional Declarations",
+            "section_text": "There is NO Competing Interest.",
+            "section_image": []
+        },
+        {
+            "section_name": "Supplementary Files",
+            "section_text": "MethodsSupplementalInformation.pdfSupplementary Information",
+            "section_image": []
+        }
+    ],
+    "nature_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Decoupling charge and heat transport is essential for optimizing thermoelectric materials. Strategies to inhibit lattice-driven heat transport, however, also compromise carrier mobility, limiting the performance of most thermoelectrics, including Fe2VAl Heusler compounds. Here, we demonstrate an innovative approach, which bypasses this tradeoff: via liquid-phase sintering, we incorporate the archetypal topological insulator Bi1\u2212xSbx between Fe2V0.95Ta0.1Al0.95 grains. Structural investigations alongside extensive thermoelectric and magneto-transport measurements reveal distinct modifications in the microstructure, a reduced lattice thermal conductivity and a simultaneously enhanced carrier mobility arising from topologically protected charge transport along the grain boundaries. This yields a huge performance boost, resulting in one of the highest figure of merits among both half- and full-Heusler compounds, z\u00a0\u2248\u00a01.6\u00a0\u00d7\u00a010\u22123 K\u22121 (zT\u00a0\u2248\u00a00.5) at 295 K. Our findings highlight the potential of topological-insulating secondary phases to decouple charge and heat transport and call for more advanced theoretical studies of multiphase composites.",
+            "section_image": []
+        },
+        {
+            "section_name": "Introduction",
+            "section_text": "Given the increasing global demand for efficient energy utilization, thermoelectrics (TEs) present a promising solution as they can harvest decentralized waste heat sources or function as Peltier coolers, e.g., for thermal management applications1,2. The conversion efficiency of TE devices depends on the hot- and cold-side temperatures and a material-dependent figure of merit, z \u221d \u03bcW/\u03baL. The highest achievable z in a semiconductor with optimized carrier concentration is determined by the weighted carrier mobility \u03bcW of electrons or holes, which should be maximized, and by the lattice thermal conductivity \u03baL, which should be minimized3,4. The inherent tradeoff between \u03bcW and \u03baL presents one of the most formidable challenges in the design and optimization of TE materials, requiring the decoupling of charge and heat transport, that is, the realization of a phonon-glass electron-crystal concept.\n\nSince the mid-20th century, Bi2Te3-based systems have been the gold standard for TEs operating near room temperature, and currently, they remain the only commercially available option5,6. However, the scarcity of tellurium, along with the brittle nature and poor mechanical properties of these materials limits their widespread use in everyday life and industrial applications. Therefore, it is crucial to explore alternatives that offer competitive performance and overcome the challenges related to Bi2Te3.\n\nFor n-type materials, cost-effective Mg3(Bi,Sb)2 Zintl compounds have been considered the hottest candidates as they exhibit very high z7,8,9. However, these materials, especially the Bi-rich alloys with attractive near-room temperature properties, suffer from poor chemical stability and degrade rapidly when exposed to air, presenting an ongoing challenge for practical applications.\n\nOn the other hand, Heusler compounds based on Fe2VAl, the focus of this study, exhibit excellent chemical and mechanical stability. These materials are also composed of earth-abundant, inexpensive elements with great recyclability10 \u2013 sustainability aspects that are becoming increasingly important worldwide, and particularly within the EU. Moreover, they display outstanding electronic transport properties, with weighted mobilities that are comparable to or even greater than those of other state-of-the-art TEs11. Yet, their intrinsically large \u03baL limits their potential as TE materials12. Consequently, previous studies have primarily focused on reducing \u03baL by substituting heavy elements13,14,15, lowering the dimensionality through thin-film deposition16,17,18, or reducing the grain size12,19,20. Although these strategies have resulted in enhancements of z, the overall performance remains a significant bottleneck and is too low for most practical applications.\n\nIn this study, we demonstrate that by incorporating chemically and structurally distinct Bi1\u2212xSbx at the grain boundaries, charge, and heat transport can be decoupled, resulting in a reduction of \u03baL, and simultaneously, in an unexpected increase of \u03bcW (Fig.\u00a01a). Consequently, the figure of merit is boosted by more than a factor of two, up to \\({z}_{\\max }\\approx 1.7\\times 1{0}^{-3}\\) K\u22121 at 240\u2013250\u2009K (z \u2248\u00a01.6\u2009\u00d7\u200910\u22123\u2009K\u22121 at room temperature), representing one of the largest values hitherto reported among n-type half- and full-Heusler compounds (Fig.\u00a01b).\n\na Tradeoff between weighted mobility and lattice thermal conductivity (plus bipolar term \u03baB) in Fe2VAl-based Heusler compounds at room temperature13,14,21,22,23. Data for state-of-the-art n-type Bi2Te3- and Mg3Bi2-based systems6,7 at 300\u2009K are shown for comparison. Composites in this work are found to bypass this tradeoff. b Temperature-dependent figure of merit of the best composite from this work (FVAB50), compared to other optimally doped, high-performance n-type thermoelectrics50,51,52,53,54,55, reaching one of the highest z among both half-Heusler (hH) and full-Heusler (fH) compounds. c Schematic synthesis of composites via liquid-phase sintering.",
+            "section_image": [
+                "https:////media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41467-025-57250-6/MediaObjects/41467_2025_57250_Fig1_HTML.png"
+            ]
+        },
+        {
+            "section_name": "Results",
+            "section_text": "The lattice thermal conductivity of Fe2VAl Heusler compounds is intrinsically large, \u03baL \u2248\u00a027\u2009W\u2009m\u22121\u2009K\u22121 at 300\u2009K21, which can be mainly attributed to a lack of structural and chemical bonding complexity as well as the absence of heavy elements, leading to high sound velocities. Upon alloying, \u03baL can be drastically reduced down to 10\u2009W\u2009m\u22121\u2009K\u22121 in Fe2VAl1\u2212xSix21, 7\u2009W\u2009m\u22121\u2009K\u22121 in Fe2VAl1\u2212xGex21, and by substituting heavy 5d elements, further down to 5\u2009W\u2009m\u22121\u2009K\u22121 in Fe2VTaxAl1\u2212x14 and 4\u2009W\u2009m\u22121\u2009K\u22121 in Fe2V1\u2212xWxAl15. As a downside, the very same point defects, which effectively inhibit heat transport by high-frequency phonons, also strongly scatter charge carriers. This is particularly true for the 5d elements like Ta and W, which are substituted for V atoms. Since V-d states dominate the electronic states of the conduction band, introducing substitutional disorder at the V site results in intense electronic scattering. We gathered TE property data from various substitution studies13,14,21,22,23 and calculated \u03bcW4. A strong tradeoff relationship between \u03bcW and \u03baL is obvious from Fig.\u00a01a (black symbols).\n\nAside from introducing point defects, \u03baL can be suppressed by reducing the grain size d and several studies attempted to enhance z by grain size reduction, e.g., via ball milling13,19 or high-pressure torsion (HPT)20,24, yielding d \u2248\u00a0100\u2009nm. Employing HPT, Fukuta et al. recently reported very low values of \u03baL down to 1.3\u2009W\u2009m\u22121\u2009K\u22121 in Fe2V0.98Ta0.1Al0.92 at 350\u2009K and zT up to 0.37 at 400 K (z \u2248\u00a00.9\u2009\u00d7\u200910\u22123\u2009K\u22121)24. These remarkable findings motivated us to (i) reproduce them and (ii) apply HPT to a variety of different samples with optimized compositions. The results of these endeavors are summarized in the\u00a0Supplementary Information (SI). While \u03baL could indeed be dramatically reduced down to \u00a0<2\u2009W\u2009m\u22121\u2009K\u22121, we concomitantly observed a huge deterioration of electronic transport in all cases (see Figs. S1 and S2 and blue symbols in Fig.\u00a01a), resulting in no enhancement of zT (Fig. S3). Similar observations have been made, e.g., for Mg3(Bi,Sb)225,26 and various half-Heuslers, where reducing grain size comes at a cost of reducing \u03bcW27,28. The discrepancy between our results and previous ones from ref. 29 suggests that setup-specific conditions during HPT are generally very important, complicating reproducibility and upscale production.\n\nInstead, we have devised a different approach wherein chemically and structurally distinct Bi1\u2212xSbx is incorporated as a secondary phase between the Heusler grains. Figure\u00a01c outlines the synthesis procedure. The starting materials were first synthesized using an induction melting furnace and then hand-ground into a fine powder. The powders were mixed in various ratios (5\u201350 vol.% Bi0.9Sb0.1), and sintered at 1373\u2009K. The much lower melting point of Bi0.9Sb0.1 causes excess liquid to be expelled during sintering. The retention of Bi1\u2212xSbx in the composite depends on the particle size of the Heusler phase and the amount of Bi0.9Sb0.1 used. Backscattered scanning electron microscopy (BS-SEM) shows that up to \u00a0\u224830 vol.%, Bi0.9Sb0.1 fills only the triple junctions of Heusler grains, while 50 vol.% Bi0.9Sb0.1 allows the liquid phase to wet and coat all grains as a grain boundary (GB) phase (Fig. S10). This produces highly dense (Fe2V0.95Ta0.1Al0.95\u2009+\u2009Bi0.9Sb0.1) composites, referred to as FVABX, with X indicating the Bi0.9Sb0.1 volume percentage added before sintering. The reference sample, without any Bi1\u2212xSbx, achieved a density of approximately 95% of its theoretical density. When about 10 vol.% Bi0.9Sb0.1 are added before sintering, the composite material shows minimal porosity. SEM micrographs confirm that any pores present in the initial sample are filled by the secondary Bi1\u2212xSbx phase, resulting in a density close to 100% for all composite samples.\n\nThe \u03bcW versus \u03baL trend (see Fig.\u00a01a) for the composite samples is unusual and cardinally different from other approaches, like alloying or grain size reduction via HPT. Moreover, the exceptionally high \u03bcW, in spite of the suppressed \u03baL, signifies a decoupling of charge and lattice-driven heat transport. In the following, we present investigations of the microstructure of these materials alongside local microscale probing of the Seebeck coefficient S. Finally, we show and discuss experimental results from extensive TE and magneto-transport measurements carried out in a broad range of temperatures and magnetic fields.\n\nThe structural properties of the sintered samples were investigated via scanning and transmission electron microscopy (TEM), energy-dispersive X-ray spectroscopy (EDX), and X-ray diffraction (XRD). Fig. S4 shows BS-SEM images of Fe2V0.95Ta0.1Al0.95 sintered at 1373\u2009K without the addition of Bi0.9Sb0.1. Throughout the whole sample, nanoscale precipitates of a secondary Ta-rich phase are clearly noticeable at the GBs. This is in agreement with the previously established low solubility limit of Ta, x\u2009=\u20090.07 in Fe2V1\u2212xTaxAl30. Apart from that, the microstructure displays a very homogeneous phase distribution without any variations in the composition.\n\nFigure\u00a02a shows a low-magnification image of the microstructure of the FVAB50 composite, with the best TE properties. A uniform distribution of Bi1\u2212xSbx along the GBs is obvious and confirmed by compositional mapping using EDX (Fig.\u00a02b) with an estimated volume fraction of around 5\u20137 vol. %. Additionally, we find that the segregation of Bi1\u2212xSbx along the GBs goes hand in hand with two changes in the microstructure: (i) strong suppression of nanoscale Ta-rich precipitates at the GBs, (ii) diffuse brightness variations within the grains. Both these structural changes suggest an enhanced solubility limit of heavy Ta atoms, when Bi1\u2212xSbx is incorporated as a GB network during the liquid-phase sintering, contributing to a reduction of the lattice thermal conductivity as shown later. This is confirmed by EDX line scans (Fig.\u00a02d) across the grain, revealing periodic fluctuations in the Ta and V concentration, and XRD, revealing an increase of the lattice parameter of the Heusler phase (Fig.\u00a02e and inset of Fig. S12c) as larger and heavier Ta atoms are substituted. In Fig.\u00a02f, g, we focus on Bi1\u2212xSbx. Since Fe2VAl and Bi1\u2212xSbx are chemically and structurally distinct, there exists a well-defined GB without apparent interdiffusion. We find that Bi1\u2212xSbx, when embedded between Heusler grains, displays a peculiar ladder-like nanostructure with arrays of stacking fault defects. Moreover, detailed EDX analyses of different samples indicate that the Bi:Sb ratio fluctuates and that the Sb concentration is above the nominal one (although remaining within the topological-insulating regime) in our high-performance FVAB50 composite (Figs. S9 and S11).\n\na Microstructure of FVAB50 composite, where the majority of GBs are filled with Bi-Sb. b EDX analyses reveal that Bi and Sb are found at the GBs, while Fe, V, Al, and Ta are almost exclusively distributed within the grains. c BS-SEM image of a Heusler grain with periodic contrast variations, surrounded by Bi-Sb. d EDX line scan along the Heusler grain shown in (c). e Comparison of normalized X-ray diffraction peaks of the (220) plane of Fe2V0.95Ta0.1Al0.95 and FVAB50 composite. f Bright-field TEM image of the GB with ladder-like nanostructure arrays of stacking faults and (g) high-magnification image near stacking-faults. Insets in (e and g) show Heusler and Bi-Sb unit cells, respectively.\n\nThe pivotal role of understanding and investigating TE transport across grain boundaries is increasingly recognized25,29,31,32. To draw a connection between microstructure and electronic transport we employed a transient potential Seebeck microprobe (TPSM), with local property investigations performed on the same rectangular area of the sample (Fig.\u00a03a). Figure\u00a03b shows a map of the locally determined S with a spatial resolution of 3\u20135 microns. The results obtained are in excellent agreement with structural investigations revealing a rich and complex microstructure consisting of Heusler grains and a Bi1\u2212xSbx GB network. Interestingly, TPSM measurements suggest that Bi1\u2212xSbx exhibits a larger S as a secondary phase compared to its bulk form. This is emphasized by looking at line scans across Heusler grains. The plateau in Fig.\u00a03c refers to the value of Bi1\u2212xSbx within the composite, which is significantly higher than its bulk value, especially considering that TPSM measurements typically underestimate S by at least 20\u201330% due to the cold finger effect. This enhancement, which exceeds the highest S at 300\u2009K in the entire composition range of polycrystalline Bi1\u2212xSbx33, is surprising, given the near-complete immiscibility between Bi1\u2212xSbx and the Heusler phase.\n\na Microstructure, composition, and local transport probing in the same area (orange square in Fig. 2a). b, c Transient potential Seebeck microprobe (TPSM) mapping of FVAB50 at room temperature. Ta-enriched regions inside the Heusler grains and Bi1\u2212xSbx at the GBs display a smaller S than the remaining part of the matrix. c TPSM line scans across distance marked in (b). d Histogram from TPSM mapping. Solid lines are normal distributions centered around S1\u2009=\u2009\u2212140\u2009\u03bcV\u22121\u2009K\u22121 and S2\u2009=\u2009\u221278\u2009\u03bcV\u22121\u2009K\u22121, the bulk values for Fe2V0.95Ta0.1Al0.95 and Bi0.9Sb0.1, respectively.\n\nFigure\u00a03d shows the distribution histogram of the measured Seebeck coefficient. For the Heusler phase, S1 \u2248\u00a0\u2212140\u2009\u03bcV\u2009K\u22121, and for Bi0.9Sb0.1, S2 \u2248\u00a0\u221278\u2009\u03bcV\u2009K\u22121 would be expected. However, instead of two normal distributions centered around those values, the observed distribution appears much more merged with S being significantly under(over)estimated with respect to S1(S2). While the underestimation is an artifact from the cold finger effect, inherent to the TPSM and basically all microprobe measurements34, the enhanced S of the secondary phase indicates a beneficial interplay between the two components and explains why the integral value of S remains large in the composite (Fig.\u00a04c), despite being short-circuited across the GBs. We note that a similar observation has been made already several years ago by Mikami and Kobayashi in (Fe2VAl0.9Si0.1\u2009+\u2009Bi) composites with \\(z{T}_{\\max }=0.11\\)35.\n\na Temperature-dependent thermal conductivity, b electrical resistivity, c Seebeck coefficient, and (d) dimensionless figure of merit zT of Fe2V0.95Ta0.1Al0.95 composites with 20 and 50 vol.% Bi0.9Sb0.1 added before sintering (FVAB20, FVAB50) compared to pristine Fe2V0.95Ta0.1Al0.95 and Bi0.9Sb0.1. The error bars in (c) indicate the statistical variation of the Bi-Sb phase corresponding to the area shown in Fig.\u00a03b. The red solid line in (d) represents a calculation based on effective-medium theory (EMT) for FVAB50, using a volume fraction of \u00a0\u22486 vol.% Bi0.9Sb0.1, determined by EDX.\n\nIn Fig.\u00a04, we compare the temperature-dependent bulk TE properties of our FVABX (X\u2009=\u20090,\u00a020,\u00a050) composites over a broad temperature range from 4 to 523\u2009K. Measurements were performed using different setups in various laboratories at the National Institute for Materials Science (NIMS) in Japan and at TU Wien (TUW) in Austria. Additionally, extensive measurements have also been conducted on a bulk sample of Bi0.9Sb0.1 synthesized during this study, and the data have been included for comparison. The latter are in excellent agreement with those reported previously (see Fig. S13).\n\nFigure\u00a04a displays the temperature-dependent thermal conductivity \u03ba(T). At 200\u2013300\u2009K, \u03ba(T) increases due to bipolar thermal transport, consistent with the S(T) curves. Most importantly, when Bi1\u2212xSbx is incorporated as a secondary phase, \u03ba(T) decreases significantly, which we attribute to the complex microstructural evolution involving microscale Bi1\u2212xSbx GBs with an extremely large acoustic mismatch (\u22489\u2009THz) with respect to the Heusler matrix, periodic composition fluctuations within the grains, and an enhanced solubility limit of heavy Ta atoms. Moreover, \u03ba(T) of the Bi1\u2212xSbx GB network is likely reduced as well compared to the bulk values owing to the ladder-like arrays of stacking fault defects (see Fig.\u00a02f, g) and microscale composition fluctuations (Fig. S9), likely inhibiting phonon-driven heat transport along the GBs36.\n\nFrom Fig.\u00a04b, it is evident that, despite the significant reduction in \u03ba(T), electronic transport remains excellent. The temperature-dependent resistivity \u03c1(T) flattens when Bi0.9Sb0.1 is incorporated, even resulting in a decrease of \u03c1(T) at elevated temperatures. The flattening of the resistivity curves and the increased residual resistivity at low temperatures both imply a weakening of the electron-phonon coupling and enhanced disorder, aligning with the notion of an enhanced Ta solubility limit. Previous work shows that V/Ta substitution results in a softening of the Heusler lattice and a reduction of the electron-phonon deformation potential, decreasing \u03c1(T) at elevated temperatures, where acoustic phonon scattering dominates. Moreover, V/Ta substitution can expand the band gap by pushing the V-eg conduction band toward higher energies, enhancing the maximum of the Seebeck coefficient37.\n\nThe temperature-dependent Seebeck coefficient S(T) only varies moderately in the composites with \\({S}_{\\max }\\) shifting to slightly lower temperatures. As mentioned in the previous section, a simple effective-medium theory (EMT) with parallel conduction along the GB network would result in a sizeable decrease of S(T). The fact that S retains large values, is surprising and unexpected, calling for more advanced theoretical studies of TE transport in composite materials. Although it is well known that the TE properties of nanocomposites can deviate strongly from those of the individual material components38,39, deviations from the EMT in microscale composites are much rarer.\n\nThe above-listed modifications result in an extreme boost of zT by more than a factor of two (see Fig.\u00a04d) up to a \\(z{T}_{\\max }\\) of almost 0.5 at 295\u2009K. Note that, like for almost all TE studies, error bars of \u00a0\u224820% should be considered40, which were omitted for better visibility of the data. This clearly exceeds the predictions of the EMT, which, as demonstrated by Bergman and Levy in their seminal work41, states that zT in composites needs to be always smaller than the largest zT of the individual components, irrespective of the geometry. We also note that this exceeds the largest room-temperature zT of the entire binary Bi-Sb system, with \\(z{T}_{\\max }\\approx 0.3\\)33. This implies that the TE properties of the individual components change dramatically in the composite or are subject to reciprocal action of both, allowing for a decoupling of charge and heat transport. To investigate the thermal stability of our composites, transport measurements were conducted for various thermal cycles (Fig. S22), which reveal excellent reproducibility and no degradation of the properties at least up to 500\u2009K \u2013 the most relevant temperature range for the potential application of these materials.\n\nTo further elucidate transport in the best-performing composite sample (FVAB50), we measured the Hall effect in a broad temperature and magnetic field range, 4\u2013400\u2009K and \u00a0\u22129\u2009T to 9\u2009T. These results are summarized in Fig.\u00a05. The field-dependent Hall resistivity \u03c1xy, plotted in Fig.\u00a05a for various temperatures displays an extremely large anomalous Hall effect, which even increases with rising temperature up to \u00a0\u2248300\u2009K, despite the absence of any sizeable magnetization in the sample. On the contrary, the sintered Heusler compound without Bi1\u2212xSbx at the GBs exhibits a simple linear magnetic field dependence. While the observation of a giant anomalous Hall effect in various topological materials is often ascribed to huge Berry curvatures, emerging from the respective topological band structure features42,43, we interpret the complex field-dependent curves in Fig.\u00a05a as a two-channel conduction mechanism, where charge carriers can move across the sample either through topologically trivial bulk states of the Heusler grains or through topologically protected surface states of the Bi1\u2212xSbx GB network (see inset Fig.\u00a05b). Figure\u00a05b shows that the field-dependent behavior of \u03c1xy from \u00a0\u22125\u2009T to 5\u2009T can be reasonably well described by a simple two-channel transport model (details of the modeling procedure and underlying theory is presented in the\u00a0SI). The mobilities obtained for the two distinct transport channels are presented in Fig.\u00a05c alongside the values of pristine Fe2V0.95Ta0.1Al0.95 without topological-insulating GBs. The bulk values of Fe2V0.95Ta0.1Al0.95 are of the order of 10\u2009cm2\u2009V\u22121\u2009s\u22121. The mobility of the bulk channel, \u03bc1, extracted from our transport modeling is comparable, especially at low temperatures. The mobility of the Dirac-like surface states, \u03bc2, associated with the Bi-Sb network, on the other hand, is several orders of magnitude higher up to 3\u2009\u00d7\u2009105\u2009cm2\u2009V\u22121\u2009s\u22121 and 2\u2009\u00d7\u2009104\u2009cm2\u2009V\u22121\u2009s\u22121 for the Dirac holes and electrons, respectively. As a consistency check, we calculated the temperature-dependent zero-field resistivity from the obtained carrier mobilities \u03bc1,2 and carrier densities n1,2 via \\({\\rho }_{xx}(0,T)={(e{n}_{1}{\\mu }_{1}+e{n}_{2}{\\mu }_{2})}^{-1}\\), which should match temperature-dependent measurements in Fig.\u00a04b. As shown in Fig. S19, there is excellent agreement across the entire temperature range, underscoring the robustness and reliability of the fits.\n\na Field-dependent Hall resistivity of FVAB50 at different temperatures 4\u00a0\u2264\u00a0T\u00a0\u2264\u00a0400 K. Room-temperature data of Fe2V0.95Ta0.1Al0.95 are shown for comparison as black open circles. b Two-channel transport modeling of field-dependent Hall resistivity. Solid lines are least squares fits. Inset shows a sketch of the Hall effect in FVABX composites. Highly mobile Dirac-like carriers along the Bi-Sb GB network have a much larger mean free path than the Heusler bulk electrons and are deflected much easier, even in small magnetic fields. c Temperature-dependent Hall mobility of FVAB50 obtained by modeling the complex field-dependent behavior. Error bars indicate uncertainties in the fit results. The inset shows a sketch of the two transport channels (1) the bulk conduction electrons of the Heusler main phase and (2) the Dirac-like surface states of the Bi-Sb GB network.\n\nIn summary, the field-dependent Hall effect reveals a significant contribution to electronic transport from the Dirac-like surface states of the Bi1\u2212xSbx GB network, leading to a pronounced anomalous Hall effect, which can be explained by a two-channel transport model. This aligns with the colossal mobilities expected from such topologically robust carriers and the higher surface-area-to-volume ratio in the composite.",
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+            ]
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+        {
+            "section_name": "Discussion",
+            "section_text": "Concluding, we demonstrated that incorporating Bi1\u2212xSbx in Fe2VAl Heusler compounds can boost the zT compared to both individual materials. This is particularly surprising considering the near-complete immiscibility of both components and their chemical distinctness, which should prevent sizeable interdiffusion and changes to the individual material properties. Decoupling charge and lattice-driven heat transport in such composites is an auspicious route toward high zT, even more so in systems where reducing grain size and alloying strongly compromise carrier mobility, although, a more profound theoretical understanding of charge and heat transport in composites is required to optimally design and choose the best candidates.\n\nIn this study, we achieved heavily reduced \u03baL, and simultaneously high \u03bcW. To provide a broad comparison with other material classes for the latter, we downloaded all available TE property data from the Starrydata2 open web database44, which, as of July 2024, contains TE data from 8961 different papers and 52,020 different samples. We then calculated \u03bcW for those samples, where both S(T) and \u03c1(T) are reported. Fig. S23 shows that, near room temperature, \u03bcW of the best composite sample from this work surpasses all other reported n-type semiconductors.\n\nTo further elevate the performance of Fe2VAl systems, broad screening of secondary phases needs to be done; especially other topological insulators like Bi2Se3 could be considered. Additionally, one has to think about strategies to increase and reliably tune the volume fraction. Lastly, it is crucial to identify promising p-type compounds with competitive z. Since p-type Fe2VAl compounds inherently show much smaller Seebeck coefficients, this can only be realized via band engineering of the valence band electronic structure45,46. Only then can competitive Fe2VAl-based modules be realized, which could substitute the long-reigning Bi2Te3 systems. The present study suggests that, by proper GB engineering, Fe2VAl Heusler alloys may indeed bear the potential to rival state-of-the-art Bi2Te3 and Mg3Bi2 semiconductors. High-performance modules entirely based upon Fe2VAl alloys could open a new era for near-ambient applications, as these systems excel in terms of cost-effectiveness, excellent recyclability, and simpler device structures. Moreover, they exhibit superior mechanical, thermal, and chemical long-term stability, factors that are becoming increasingly recognized as essential assets for realizing widespread thermoelectric technology.",
+            "section_image": []
+        },
+        {
+            "section_name": "Methods",
+            "section_text": "Bulk elements of high purity (Fe 99.99%, V 99.93%, Ta 99.95%, Al 99.999%, Bi 99.999%, Sb 99.999%) were stoichiometrically weighed and polycrystalline ingots of the starting materials (Fe2V0.95Ta0.1Al0.95 and Bi0.9Sb0.1) were synthesized by high-frequency induction melting under Ar atmosphere. The as-cast ingots were manually crushed and ground using a tungsten carbide pestle and mortar. The resulting powders from the individual starting materials were then mixed in various volume ratios. The volume percentage of Bi0.9Sb0.1 powder added was adjusted and calculated based on the theoretical densities of the respective starting materials. After the powders were thoroughly mixed, the mixture was filled into a graphite die and sintered at a temperature of 1373\u2009K, which is about 80% of the melting point of the full-Heusler phase and about 800\u2009K higher than the melting point of Bi0.9Sb0.1. Consequently, excess liquid was expelled during the sintering process. Additionally, we observed that the liquid-phase sintering led to a significant decrease in the sintering temperature of the Heusler material by up to almost 200\u2009K when Bi0.9Sb0.1 powder was added as compared to when only Fe2V0.95Ta0.1Al0.95 powder was sintered. Nonetheless, to ensure consistent and comparable processing conditions for the samples studied in this work, all specimens were sintered using exactly the same synthesis conditions, i.e., a compaction pressure of 50\u2009MPa, a maximum temperature of 1373\u2009K, and a holding time of 15\u2009min. No additional heat treatment has been applied to the samples after the sintering process.\n\nThe microstructure and elemental composition of the sintered samples were investigated using scanning electron microscopy in both secondary electron (SE) and backscattered electron (BSE) modes, complemented by energy-dispersive X-ray spectroscopy (EDX). These analyses were performed on an ultra-high-resolution field emission SEM (HRSEM SU8230, Hitachi, Japan), equipped with an X-MaxN EDS detector (Horiba, Japan). For HRSEM observations, the samples were mounted in electroconductive epoxy and polished meticulously. EDX analysis utilized an acceleration voltage of 25\u2009kV, gathering 10\u2009\u00d7\u2009106 counts per EDX map and 1\u2009\u00d7\u2009106 counts for point analysis.\n\nTo investigate the interface between the Fe2VAl matrix and the Bi0.9Sb0.1 secondary phase at the nanoscale, the sample was prepared using a conventional focused ion beam (FIB) technique. A thin section was extracted from the targeted area, attached to an Omnigrid, and thinned to approximately 90\u2009nm for electron transparency. Additionally, the FVAB50 sample was crushed into fine particles, dispersed in ethanol, and deposited on a grid to investigate the sample surface. Transmission electron microscopy (TEM) bright-field and lattice images were acquired using a JEOL JEM-3100FEF (JEOL, Japan) microscope operating at 300\u2009kV, which was also equipped with an EDS detector for detailed elemental mapping.\n\nThe X-ray powder diffraction measurements were conducted at the Institute of Solid State Physics, TU Wien, using an in-house diffractometer (AERIS by PANalytical). These measurements utilized standard Cu K-\u03b1 radiation, with data collected in the Bragg-Brentano geometry over the angular range 20\u2218\u2009<\u20092\u03b8\u2009<\u2009100\u2218. Rietveld refinements on the obtained powder patterns were performed using the program PowderCell.\n\nThermal conductivity measurements at high temperatures were performed in N2 atmosphere directly on the sintered pellets, in the direction parallel to the pressing (compaction) direction during sintering with a commercially available setup (LFA 467 by NETZSCH). The instrument makes use of a conventional laser flash method for the\u00a0diffusivity D and a differential scanning calorimeter for determining the specific heat cp. The density of the sample dm was determined via Archimedes principle and the thermal conductivity was calculated from \u03ba\u2009=\u2009D\u2009cp\u2009dm.\n\nAfter performing high-temperature thermal conductivity measurements, the samples were cut into strips 2\u22123\u2009mm in width and\u00a08\u221210\u2009mm in length using a high-speed aluminum oxide cutting wheel. The bar-shaped samples were then mounted in a commercial setup (ZEM3 by ADVANCE RIKO) and the electrical resistivity and Seebeck coefficient were measured as a function of temperature. For the best sample, the measurement was repeated to confirm reproducible and stable results.\n\nLow-temperature measurements provide valuable insights into lower-energy excited states and states near the Fermi energy. This is especially significant for samples with narrow energy gaps, such as Fe2VAl-based full-Heusler and binary Bi1\u2212xSbx systems, where the Seebeck coefficient often peaks below or near room temperature. Furthermore, when modeling temperature-dependent data (using a parabolic band model for example), it is crucial that the experimental data span a wide temperature range. The thermoelectric characterization at low temperatures was carried out at TU Wien (Austria) on the same rectangular bar-shaped sample pieces that were used for the high-temperature measurements at NIMS (Japan).\n\nThe temperature-dependent electrical resistivity was measured in a home-built bath cryostat at TU Wien. The sample was contacted in a four-probe geometry with thin gold wires, using a spot-welding device. The sample was then mounted on a sample puck using GE Varnish as an adhesive and directly inserted into the cryostat. The measurement was performed continuously every time the temperature changed by 1\u2009K.\n\nThe temperature-dependent Seebeck coefficient was also measured on the very same sample piece using a different home-built setup at TU Wien. Here, two chromel-constantan thermocouples are contacted to both ends of the sample to pick up the temperature difference and voltages. Since it is difficult to solder directly on the sample surface, a bundle of thick copper wires was first spot-welded onto the sample surface to which the thermocouples were then soldered. The high thermal conductivity of copper and the fact that the thermocouples are soldered in very close proximity to the sample surface ensures that the cold finger effect can be minimized. Furthermore, two strain gauges with a resistance of \u00a0\u2248120\u2009\u03a9 function as heaters and are fixed to the bottom of both sample ends via GE varnish. The two heaters allow switching the temperature difference (\"seesaw heating\"47) to cancel spurious voltage contributions. The measurement is carried out in an evacuated sample chamber with He exchange gas to ensure thermal coupling to the cryogen.\n\nThe thermal conductivity at low temperatures was measured by making use of a steady-state method using a home-built sample probe with a flow cryostat. Here, a heater is attached to the top surface of the sample employing a thermally conductive epoxy resin (STYCAST 2850FT). Similar to the Seebeck coefficient measurements, two bundles of copper wires are first fixed to the sample to each of which a thermocouple is then soldered. The bottom of the sample is mounted on a copper heat sink and the measurement is carried out in high vacuum (\u00a0\u224810\u22125\u2009mbar).\n\nIn a two-channel transport model for two types of charge carriers with charge q1,2, carrier density n1,2, and carrier mobility \u03bc1,2, the field-dependent longitudinal resistivity \u03c1xx(B) and Hall resistivity \u03c1xy(B) can be expressed as48\n\nand\n\nFrom the above equations, it becomes evident that non-linearities can occur in the field-dependent Hall resistivity if, for instance, there is a sizeable difference between \u03bc1 and \u03bc2. While previous models have employed four different fit parameters, i.e. the respective carrier densities and mobilities to model non-linear field dependencies, Eguchi and Paschen previously suggested a novel, more robust scheme for analyzing field-dependent magneto-transport properties49. We utilized this framework to model the non-linear field-dependent Hall effect of the FVAB50 composite. More details regarding the modeling procedure are presented in the\u00a0Supplementary Information.",
+            "section_image": []
+        },
+        {
+            "section_name": "Data availability",
+            "section_text": "All data supporting the findings of this study are available within the article and its\u00a0Supplementary Information file.",
+            "section_image": []
+        },
+        {
+            "section_name": "References",
+            "section_text": "Rowe, D. M. Thermoelectrics Handbook: Macro to Nano (CRC Press, 2018).\n\nHendricks, T., Caillat, T. & Mori, T. Keynote review of latest advances in thermoelectric generation materials, devices, and technologies 2022. Energies 15, 7307 (2022).\n\nArticle\u00a0\n    CAS\u00a0\n    MATH\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nZevalkink, A. et al. A practical field guide to thermoelectrics: fundamentals, synthesis, and characterization. Appl. Phys. Rev. 5, 021303 (2018).\n\nSnyder, G. J. et al. Weighted mobility. Adv. Mater. 32, 2001537 (2020).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nGoldsmid, H. J. The electrical conductivity and thermoelectric power of bismuth telluride. Proc. Phys. Soc. 71, 633\u2013646 (1958).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    MATH\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWitting, I. T. et al. The thermoelectric properties of bismuth telluride. Adv. Electron. Mater. 5, 1800904 (2019).\n\nArticle\u00a0\n    MATH\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMao, J. et al. High thermoelectric cooling performance of n-type Mg3Bi2-based materials. Science 365, 495\u2013498 (2019).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    MATH\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLiu, Z. et al. Demonstration of ultrahigh thermoelectric efficiency of ~7.3% in Mg3Sb2/MgAgSb module for low-temperature energy harvesting. Joule 5, 1196\u20131208 (2021).\n\nArticle\u00a0\n    CAS\u00a0\n    MATH\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLiu, Z. et al. Maximizing the performance of n-type Mg3Bi2 based materials for room-temperature power generation and thermoelectric cooling. Nat. Commun. 13, 1120 (2022).\n\nArticle\u00a0\n    ADS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    MATH\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nPecunia, V. et al. Roadmap on energy harvesting materials. J. Phys. Mater. 6, 042501 (2023).\n\nAnand, S. et al. Thermoelectric transport of semiconductor full-Heusler VFe2Al. J. Mater. Chem. C. 8, 10174\u201310184 (2020).\n\nArticle\u00a0\n    CAS\u00a0\n    MATH\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nAlleno, E. Review of the thermoelectric properties in nanostructured Fe2VAl. Metals 8, 864 (2018).\n\nArticle\u00a0\n    CAS\u00a0\n    MATH\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMikami, M., Kinemuchi, Y., Ozaki, K., Terazawa, Y. & Takeuchi, T. Thermoelectric properties of tungsten-substituted Heusler Fe2VAl alloy. J. Appl. Phys. 111, 093710 (2012).\n\nRenard, K. et al. Thermoelectric properties of the Heusler-type, Fe2VTaxAl1\u2212x alloys. J. Appl. Phys. 115, 033707 (2014).\n\nHinterleitner, B. et al. Stoichiometric and off-stoichiometric full Heusler Fe2V1\u2212xWxAl thermoelectric systems. Phys. Rev. B 102, 075117 (2020).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    MATH\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nFuruta, Y., Kato, K., Miyawaki, T., Asano, H. & Takeuchi, T. Fe2VAl-based thermoelectric thin films prepared by a sputtering technique. J. Electron. Mater. 43, 2157\u20132164 (2014).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    MATH\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nHiroi, S., Mikami, M., Kitahara, K. & Takeuchi, T. Thickness dependence of thermal conductivity and electron transport properties of Fe2VAl thin-films prepared by RF sputtering technique. Int. J. Nanotechnol. 13, 881\u2013890 (2016).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBourgault, D. et al. Improved power factor in self-substituted Fe2VAl thermoelectric thin films prepared by co-sputtering. ACS Appl. Energy Mater. 6, 1526\u20131532 (2023).\n\nArticle\u00a0\n    CAS\u00a0\n    MATH\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMikami, M., Matsumoto, A. & Kobayashi, K. Synthesis and thermoelectric properties of microstructural Heusler Fe2VAl alloy. J. Alloy. Compd. 461, 423\u2013426 (2008).\n\nArticle\u00a0\n    CAS\u00a0\n    MATH\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMasuda, S., Tsuchiya, K., Qiang, J., Miyazaki, H. & Nishino, Y. Effect of high-pressure torsion on the microstructure and thermoelectric properties of Fe2VAl-based compounds. J. Appl. Phys. 124, 035106 (2018).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nNishino, Y., Deguchi, S. & Mizutani, U. Thermal and transport properties of the Heusler-type Fe2VAl1\u2212xGex (0\u2264x\u22640.20) alloys: Effect of doping on lattice thermal conductivity, electrical resistivity, and Seebeck coefficient. Phys. Rev. B 74, 115115 (2006).\n\nArticle\u00a0\n    ADS\u00a0\n    MATH\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMiyazaki, H., Tanaka, S., Ide, N., Soda, K. & Nishino, Y. Thermoelectric properties of Heusler-type off-stoichiometric Fe2V1+xAl1\u2212x alloys. Mater. Res. Express 1, 015901 (2013).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nTakeuchi, T., Terazawa, Y., Furuta, Y., Yamamoto, A. & Mikami, M. Effect of heavy element substitution and off-stoichiometric composition on thermoelectric properties of Fe2VAl-based Heusler phase. J. Electron. Mater. 42, 2084\u20132090 (2013).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nFukuta, K., Tsuchiya, K., Miyazaki, H. & Nishino, Y. Improving thermoelectric performance of Fe2VAl-based Heusler compounds via high-pressure torsion. Appl. Phys. A 128, 184 (2022).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nWood, M., Kuo, J. J., Imasato, K. & Snyder, G. J. Improvement of low-temperature zT in a Mg3Sb2\u2013Mg3Bi2 solid solution via Mg-vapor annealing. Adv. Mater. 31, 1902337 (2019).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nLuo, T. et al. Nb-mediated grain growth and grain-boundary engineering in Mg3Sb2-based thermoelectric materials. Adv. Funct. Mater. 31, 2100258 (2021).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nQiu, Q. et al. Grain boundary scattering of charge transport in n-type (Hf,Zr)CoSb half-Heusler thermoelectric materials. Adv. Energy Mater. 9, 1803447 (2019).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBueno Villoro, R. et al. Grain boundary phases in NbFeSb half-heusler alloys: a new avenue to tune transport properties of thermoelectric materials. Adv. Energy Mater. 13, 2204321 (2023).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMori, T. & Hara, T. Hybrid effect to possibly overcome the trade-off between Seebeck coefficient and electrical conductivity. Scr. Mater. 111, 44\u201348 (2016).\n\nArticle\u00a0\n    CAS\u00a0\n    MATH\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nGarmroudi, F. et al. Solubility limit and annealing effects on the microstructure & thermoelectric properties of Fe2V1\u2212xTaxAl1\u2212ySiy Heusler compounds. Acta Mater. 212, 116867 (2021).\n\nArticle\u00a0\n    CAS\u00a0\n    MATH\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKuo, J. J. et al. Grain boundary dominated charge transport in Mg3Sb2-based compounds. Energy Environ. Sci. 11, 429\u2013434 (2018).\n\nArticle\u00a0\n    CAS\u00a0\n    MATH\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nGhosh, S. et al. Towards energy filtering in Mg2X-based composites: investigating local carrier concentration and band alignment via SEM/EDX and transient Seebeck microprobe analysis. Mater. Today Phys. 38, 101244 (2023).\n\nArticle\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDoroshenko, A., Rogacheva, E., Drozdova, A., Martynova, K. & Men\u2019shov, Y. V. Thermoelectric properties of polycrystalline Bi1\u2212xSbx solid solutions in the concentration range x\u00a0=\u00a00\u00a0\u2212\u00a00.25. J. Thermoelectr. 4, 23\u201336 (2016).\n\nZiolkowski, P., Karpinski, G., Dasgupta, T. & Mueller, E. Probing thermopower on the microscale. Physica Status Solidi A 210, 89\u2013105 (2013).\n\nMikami, M. & Kobayashi, K. Effect of Bi addition on microstructure and thermoelectric properties of Heusler Fe2VAl-sintered alloy. J. Alloy. Compd. 466, 530\u2013534 (2008).\n\nArticle\u00a0\n    CAS\u00a0\n    MATH\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nIsotta, E. et al. Heat Transport at silicon grain boundaries. Adv. Funct. Mater. 34, 2405413 (2024).\n\nGarmroudi, F. et al. Boosting the thermoelectric performance of Fe2VAl-type Heusler compounds by band engineering. Phys. Rev. B 103, 085202 (2021).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    MATH\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nZhao, W. et al. Magnetoelectric interaction and transport behaviours in magnetic nanocomposite thermoelectric materials. Nat. Nanotechnol. 12, 55\u201360 (2017).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    MATH\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nZhao, W. et al. Superparamagnetic enhancement of thermoelectric performance. Nature 549, 247\u2013251 (2017).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    MATH\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBorup, K. A. et al. Measuring thermoelectric transport properties of materials. Energy Environ. Sci. 8, 423\u2013435 (2015).\n\nArticle\u00a0\n    CAS\u00a0\n    MATH\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nBergman, D. J. & Levy, O. Thermoelectric properties of a composite medium. J. Appl. Phys. 70, 6821\u20136833 (1991).\n\nArticle\u00a0\n    ADS\u00a0\n    MATH\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nNayak, A. K. et al. Large anomalous Hall effect driven by a nonvanishing Berry curvature in the noncolinear antiferromagnet Mn3Ge. Sci. Adv. 2, e1501870 (2016).\n\nArticle\u00a0\n    ADS\u00a0\n    PubMed\u00a0\n    PubMed Central\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nManna, K. et al. From colossal to zero: controlling the anomalous Hall effect in magnetic Heusler compounds via Berry curvature design. Phys. Rev. X 8, 041045 (2018).\n\nCAS\u00a0\n    MATH\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nKatsura, Y. et al. Data-driven analysis of electron relaxation times in PbTe-type thermoelectric materials. Sci. Technol. Adv. Mater. 20, 511\u2013520 (2019).\n\nArticle\u00a0\n    CAS\u00a0\n    MATH\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nNishino, Y., Kamizono, S., Miyazaki, H. & Kimura, K. Effects of off-stoichiometry and Ti doping on thermoelectric performance of Fe2VAl Heusler compound. AIP Adv. 9, 125003 (2019).\n\nArticle\u00a0\n    ADS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nParzer, M. et al. High solubility of Al and enhanced thermoelectric performance due to resonant states in Fe2VAlx. Appl. Phys. Lett. 120, 071901 (2022).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    MATH\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nResel, R. et al. Thermopower measurements in magnetic fields up to 17 tesla using the toggled heating method. Rev. Sci. Instrum. 67, 1970\u20131975 (1996).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    MATH\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nAshcroft, N. W. & Mermin, N. D. Solid State Physics 1st edn (Harcourt College Publishers, 1976).\n\nEguchi, G. & Paschen, S. Robust scheme for magnetotransport analysis in topological insulators. Phys. Rev. B 99, 165128 (2019).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    MATH\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nRogl, G. et al. (V, Nb)-doped half Heusler alloys based on {Ti, Zr, Hf} NiSn with high ZT. Acta Mater. 131, 336\u2013348 (2017).\n\nArticle\u00a0\n    ADS\u00a0\n    CAS\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nChauhan, N. S. et al. Vanadium-doping-induced resonant energy levels for the enhancement of thermoelectric performance in Hf-free ZrNiSn half-Heusler alloys. ACS Appl. Energy Mater. 1, 757\u2013764 (2018).\n\nArticle\u00a0\n    CAS\u00a0\n    MATH\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nChauhan, N. S. et al. Compositional tailoring for realizing high thermoelectric performance in hafnium-free n-type ZrNiSn half-Heusler alloys. ACS Appl. Mater. interfaces 11, 47830\u201347836 (2019).\n\nArticle\u00a0\n    CAS\u00a0\n    PubMed\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nSankhla, A. et al. Mechanical alloying of optimized Mg2 (Si, Sn) solid solutions: understanding phase evolution and tuning synthesis parameters for thermoelectric applications. ACS Appl. Energy Mater. 1, 531\u2013542 (2018).\n\nArticle\u00a0\n    CAS\u00a0\n    MATH\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nMeng, X. et al. Grain boundary engineering for achieving high thermoelectric performance in n-type skutterudites. Adv. Energy Mater. 7, 1602582 (2017).\n\nArticle\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nZhang, Q. et al. Deep defect level engineering: a strategy of optimizing the carrier concentration for high thermoelectric performance. Energy Environ. Sci. 11, 933\u2013940 (2018).\n\nArticle\u00a0\n    CAS\u00a0\n    MATH\u00a0\n    \n                    Google Scholar\u00a0\n                \n\nDownload references",
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+            "section_name": "Acknowledgements",
+            "section_text": "Research in this paper was financially supported by the Japan Science and Technology Agency (JST) program MIRAI, JPMJMI19A1. Furthermore, F.G. acknowledges financial support by the Lions Club Wien St. Stephan and J.d.B. acknowledges funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation), project number 520487260\u00a0The authors also acknowledge\u00a0the TU Wien Bibliothek for financial support through its Open Access Funding Programme.",
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+            "section_name": "Author information",
+            "section_text": "Institute of Solid State Physics, TU Wien, Vienna, Austria\n\nFabian Garmroudi,\u00a0Michael Parzer,\u00a0Alexander Riss,\u00a0Sebastian Steyrer\u00a0&\u00a0Ernst Bauer\n\nInternational Center for Materials Nanoarchitectonics (WPI-MANA), National Institute for Materials Science (NIMS), Tsukuba, Japan\n\nFabian Garmroudi,\u00a0Illia Serhiienko,\u00a0C\u00e9dric Bourg\u00e8s,\u00a0Yuya Hattori\u00a0&\u00a0Takao Mori\n\nInstitute of Materials Research, German Aeropspace Center (DLR), Cologne, Germany\n\nSanyukta Ghosh,\u00a0Pawel Ziolkowski,\u00a0Gregor Oppitz,\u00a0Eckhard M\u00fcller\u00a0&\u00a0Johannes de Boor\n\nCenter for Basic Research on Materials (CBRM), National Institute for Materials Science (NIMS), Tsukuba, Japan\n\nHieu Duy Nguyen\u00a0&\u00a0Naoyuki Kawamoto\n\nInternational Center for Young Scientists, National Institute for Materials Science (NIMS), Tsukuba, Japan\n\nC\u00e9dric Bourg\u00e8s\n\nInstitute of Materials Chemistry, University of Vienna, Vienna, Austria\n\nGerda Rogl\u00a0&\u00a0Peter Rogl\n\nFaculty of Physics, University of Vienna, Vienna, Austria\n\nErhard Schafler\n\nInstitute of Inorganic and Analytical Chemistry, Justus Liebig University Giessen, Giessen, Germany\n\nEckhard M\u00fcller\n\nUniversity of Duisburg-Essen, Faculty of Engineering, Institute of Technology for Nanostructures (NST) and CENIDE, Duisburg, Germany\n\nJohannes de Boor\n\nGraduate School of Pure and Applied Sciences, University of Tsukuba, Tsukuba, Japan\n\nTakao Mori\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nF.G., M.P., and A.R. conceived the idea for the study. F.G. designed the work, and, with help from I.S., C.B., and Y.H., synthesized the samples and measured the thermoelectric properties. I.S., S.G., and H.D.N. investigated the micro- and nanostructure of the material via SEM and TEM techniques. S.G., P.Z., and G.O. performed TPSM measurements, and E.M. and J.d.B. analyzed and interpreted the data. C.B., S.S., G.R., and E.S. assisted in the synthesis and experimental investigations of the samples. P.R., N.K., E.M., and E.B. discussed and improved the contents of the paper. J.d.B. and T.M. supervised the work and assisted in outlining the initial draft of the manuscript. F.G. wrote the initial draft. All authors read, discussed, and edited the manuscript.\n\nCorrespondence to\n                Fabian Garmroudi, Johannes de Boor or Takao Mori.",
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+            "section_text": "Garmroudi, F., Serhiienko, I., Parzer, M. et al. Decoupled charge and heat transport in Fe2VAl composite thermoelectrics with topological-insulating grain boundary networks.\n                    Nat Commun 16, 2976 (2025). https://doi.org/10.1038/s41467-025-57250-6\n\nDownload citation\n\nReceived: 08 November 2024\n\nAccepted: 17 February 2025\n\nPublished: 26 March 2025\n\nVersion of record: 26 March 2025\n\nDOI: https://doi.org/10.1038/s41467-025-57250-6\n\nAnyone you share the following link with will be able to read this content:\n\nSorry, a shareable link is not currently available for this article.\n\n\n\n\n                            Provided by the Springer Nature SharedIt content-sharing initiative\n                        ",
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