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preprint/preprint__c8c579f466f81113c7b03509aa0dedea88775bd6d6ca33bb44b54e5cf9a0c632/images_list.json

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+[
+  {
+    "type": "image",
+    "img_path": "images/Figure_1.jpg",
+    "caption": "Figure 1. Validation of the COVA1-27-DFO tracer (a) Impact of the addition of DFO on COVA1-27 specificity: Change in binding of native COVA1-27 versus DFO-functionalized COVA1-27 to the spike proteins of the Wuhan and Delta variants, presented as the percentage of the ratio of their ECL signals. (b) Impact of the addition of DFO on COVA1-27 stability: evolution of the binding, expressed as the ratio of binding to that on D0, of COVA1-27-DFO to the Delta variant spike protein over a two-week incubation period in macaque serum at \\(37^{\\circ}\\mathrm{C}\\) . (c) In vivo \\([^{89}\\mathrm{Zr}]\\mathrm{COVA1 - 27 - DFO}\\) specificity: representative PET/CT image (maximum intensity projection) of the spike (left thigh) and PBS injection sites (right thigh) in the white dashed circles at two days post-injection (p.i.). (d) Associated quantification of PET uptake at 2 dpe: ratio of the maximum signal uptake (SUVmax) at the spike injection site to the that at the PBS injection site for the animals injected with \\([^{89}\\mathrm{Zr}]\\mathrm{COVA1 - 27 - DFO}\\) (black circles) and those injected with \\([^{89}\\mathrm{Zr}]\\mathrm{IgG - DFO}\\) (black squares), star: animal exhibiting edema for several days at the PBS injection site. Data are presented as individual values (a, d) with the mean (a, b, d) and standard deviation (a, b).",
+    "footnote": [],
+    "bbox": [
+      [
+        140,
+        120,
+        844,
+        664
+      ]
+    ],
+    "page_idx": 26
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_2.jpg",
+    "caption": "Figure 2: Experimental design",
+    "footnote": [],
+    "bbox": [
+      [
+        131,
+        87,
+        886,
+        212
+      ]
+    ],
+    "page_idx": 27
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_3.jpg",
+    "caption": "Figure 3. COVA1-27 uptake in convalescent animals",
+    "footnote": [],
+    "bbox": [
+      [
+        63,
+        85,
+        936,
+        600
+      ]
+    ],
+    "page_idx": 28
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_4.jpg",
+    "caption": "Figure 4. SARS-CoV-2 RNA titers in the nasopharyngeal and tracheal compartments Evaluation of the SARS-CoV-2 genomic RNA (gRNA) titers (Log10 copies/mL) over two weeks in the nasopharynx (a) and trachea (b). The individual follow-up is represented by the thin lines and the average (mean) of each group by the bold lines. Horizontal dotted line: limit of quantification (LoQ)/limit of detection (LoD), vertical dotted line: euthanasia (n = 2) during the acute phase of the infection. SARS-CoV-2 gRNA titers (log10 copies/mL) showing the individual peak values for each group in the nasopharynx (c) and trachea (d). Area under the curve (AUC) calculated for each group in the nasopharynx (e) and trachea (f). The Mock + COVA group is indicated in black, the exposed + COVA group in turquoise, and the exposed + IgG group in pink. (c-f) Data are presented as individual values (circles) with the mean and standard deviation.",
+    "footnote": [],
+    "bbox": [
+      [
+        130,
+        90,
+        856,
+        707
+      ]
+    ],
+    "page_idx": 29
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_5.jpg",
+    "caption": "Figure 5. COVA1-27 uptake in the nasal cavity (a) Representative image of CT-detected opacity in the left sinus on day 3 post-exposure (dpe) indicated by the yellow arrows. (b) Corresponding PET signal in the left sinus indicated by the white arrows, color scale: 0-3 SUV. (c) 3D representation of both CT opacity (in yellow) and the PET signal (in orange) in the left sinus of the nasal cavity (in green) at 3 dpe. (d) Longitudinal evaluation of the PET signal (SUVmax) normalized to that at D0 in the nasal cavity. The exposed + COVA group is indicated in turquoise (circles and squares), the mock + COVA group in black (triangles), and the exposed + IgG group in pink (circles and squares).",
+    "footnote": [],
+    "bbox": [
+      [
+        120,
+        83,
+        880,
+        475
+      ]
+    ],
+    "page_idx": 30
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_6.jpg",
+    "caption": "Figure 6. Nasopharyngeal swab sample radioactivity and associated viral RNA titers",
+    "footnote": [],
+    "bbox": [
+      [
+        120,
+        87,
+        870,
+        312
+      ]
+    ],
+    "page_idx": 31
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_7.jpg",
+    "caption": "Figure 7. COVA1-27 uptake in the trachea",
+    "footnote": [],
+    "bbox": [
+      [
+        130,
+        90,
+        870,
+        545
+      ]
+    ],
+    "page_idx": 32
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_8.jpg",
+    "caption": "Figure 8. COVA1-27 uptake in the lungs (a, c) Representative ground-glass opacity CT lung lesions indicated by the white arrow and (b, d) the associated PET signal (arrows) at 7 dpe. (e) CT score grading of lung lesion severity at 2 dpe. Data are presented as individual values with the mean and standard deviation. (f) Quantification of the maximum PET signal in the lesional (squares, gray background) and non-lesional areas (circles, white background) of the lungs of animals. Data are presented as individual ROI values with the mean and standard deviation. Mann Whitney t-tests, \\(^{*}\\mathrm{p}< 0.05\\) , \\(^{**}p< 0.01\\) , \\(^{***}p< 0.001\\) . The exposed + COVA group is indicated in turquoise, the exposed + IgG group in pink and, the mock + COVA group in black.",
+    "footnote": [],
+    "bbox": [
+      [
+        175,
+        95,
+        825,
+        812
+      ]
+    ],
+    "page_idx": 33
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_9.jpg",
+    "caption": "Figure 9. COVA1-27 tracer uptake in the kidneys Representative PET signal in the kidneys of CM4 (a), CM8 (b), and CM7 (c), color scale 0-4 SUV. (d) Longitudinal evaluation of the PET signal SUVmean normalized against that of 0 dpe in the kidneys of animals and (e) quantification of the mean \\([^{89}\\mathrm{Zr}]\\mathrm{COVA1 - 27 - DFO}\\) PET signal normalized to that of 0 dpe in the kidneys. The exposed \\(^+\\) COVA group is indicated in turquoise (circles, squares, hexagons, diamonds), the exposed \\(^+\\) IgG group in pink (circles, squares), and the mock \\(^+\\) COVA group in black (triangles). Data are presented as individual values the the mean and SD.",
+    "footnote": [],
+    "bbox": [
+      [
+        123,
+        85,
+        875,
+        430
+      ]
+    ],
+    "page_idx": 34
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_10.jpg",
+    "caption": "Figure 10. Postmortem analysis of the organs (a) PET/CT representative coronal slice of the isolated rinsed lung lobes and trachea postmortem. (b). Linear regression showing the correlation between the SARS-CoV-2 gRNA titers in all harvested organs and their associated radioactivity (expressed as %ID/g). (c) Tissue- and cell-scale evaluation of the distribution of the virus (brown signal) by in situ hybridization (ISH) in the lungs (caudal left lobe), with a zoom of a pulmonary bronchus (red square) and the corresponding histological characterization by hematoxylin eosin (HE) staining. Cp: capillary, B.L.: basal lamina, Nt.: neutrophil. 1. Prismatic ciliated bronchial epithelium, 2. Muscle layer, and 3. Cartilage. (d) CT of kidney stone indicated by the yellow arrow, (e) associated PET signal (white arrow) at 3 dpe, and (f) cellular-scale evaluation of the distribution of the virus (brown signal) by ISH in the left kidney of CM10 postmortem.",
+    "footnote": [],
+    "bbox": [
+      [
+        128,
+        90,
+        868,
+        568
+      ]
+    ],
+    "page_idx": 35
+  }
+]

preprint/preprint__c8d3aa6fde0f412eb02ef175def71078ccb36fa008e0ba5966220436913eb933/images_list.json

@@ -0,0 +1,18 @@
+[
+  {
+    "type": "image",
+    "img_path": "images/Figure_4.jpg",
+    "caption": "Figure 4",
+    "footnote": [],
+    "bbox": [],
+    "page_idx": 29
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_0.jpg",
+    "caption": "d",
+    "footnote": [],
+    "bbox": [],
+    "page_idx": 29
+  }
+]

preprint/preprint__c8ea0fd9793775451b1580cefcf4cd08c8dfd9b2baff1b29377d0ff48c5d5b10/images_list.json

@@ -0,0 +1,77 @@
+[
+  {
+    "type": "image",
+    "img_path": "images/Figure_1.jpg",
+    "caption": "Figure 1. Ejecta cone and impact cratering flow fields. The arrows in light blue show \\((x^{\\prime},y^{\\prime},z^{\\prime})\\) in J2000, while those in green \\((x,y,z)\\) are IAU_DIMORPHOS. The arrows in red give the local frame at the impact site. \\(z^{\\prime \\prime}\\) is the DART impact direction, \\(x^{\\prime \\prime}\\) is orthogonal to Dimorphos's north and \\(z^{\\prime \\prime}\\) , and \\(y^{\\prime \\prime}\\) is orthogonal to these axes. A and B. Cone geometry and Dimorphos. The cone's perimeter defines its edge. C. Slice in light red representing a plane used for the Maxwell Z-model. The red curve over Dimorphos represents the intersection between the body and the slicing plane. D. Illustrations of streamlines defined as \\(SL\\) . An example streamtube is a region between \\(SL1\\) and \\(SL2\\) .",
+    "footnote": [],
+    "bbox": [
+      [
+        85,
+        102,
+        912,
+        750
+      ]
+    ],
+    "page_idx": 9
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_2.jpg",
+    "caption": "Figure 2. Variations in Maxwell Z-model parameters and projected cone geometry onto Dimorphos's surface with azimuthal angle from Dimorphos's north. A. Variations in Z. B. Variations in \\(\\alpha\\) . C. Variations in excavation range, which plots \\(r_{E}^{*}\\) (Figure 1). D. Variations in geometric factor along each piece in an azimuthal direction. Uncertainties are provided in \\(1\\sigma\\) .",
+    "footnote": [],
+    "bbox": [
+      [
+        90,
+        210,
+        884,
+        701
+      ]
+    ],
+    "page_idx": 11
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_3.jpg",
+    "caption": "Figure 3. Geometric factor distributions of 103 small NEOs measured by the MANOS project<sup>30</sup>. A. Geometric factor of an impact along each target's semi-minor axis. B. Relative geometric factor of an impact along the semi-major axis to one along the semi-minor axis. Specifically, the relative geometric factor defines the geometric factor along the semi-major axis minus that along the semi-minor axis. All panels give the geometric factor distributions in percentile as a function of diameter and minimum strength. All negative outcomes in Panel A are truncated and noted as zero geometric factors. The curves in different colors show interpolations between the catastrophic disruption thresholds for a pumice-like target and a cohesionless target (red) and a basalt-like target and a cohesionless target (blue). For the cohesionless target, we assume a minimal strength of 0.01 Pa. The dashed, solid, and dotted lines give bulk densities of \\(1000\\mathrm{kg / m}^3\\) , \\(2000\\mathrm{kg / m}^3\\) , and \\(4000\\mathrm{kg / m}^3\\) . If target asteroids stay on the right side of those thresholds, they do not experience catastrophic disruption.",
+    "footnote": [],
+    "bbox": [
+      [
+        103,
+        82,
+        890,
+        323
+      ]
+    ],
+    "page_idx": 12
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_4.jpg",
+    "caption": "Figure 4. Schematics for kinetic impact-driven momentum transfer depending on different scenarios. Impactors with two kinetic energies add the same net kinetic energy to a target by performing multiple impacts. Net momentum transfer changes due to orientation and kinetic energy per impactor. The ID of the attached LICIACube image is liciacube_luke_10_1664234219_00112_01.fits.",
+    "footnote": [],
+    "bbox": [
+      [
+        90,
+        92,
+        905,
+        816
+      ]
+    ],
+    "page_idx": 14
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_5.jpg",
+    "caption": "Figure 5. Result comparison between Maxwell Z-model and iSALE-2D simulations. The \\(x\\) axis is the aspect ratio of the biaxial ellipsoid target with dimensions of \\(2a \\times 2b \\times 2c\\) , where \\(b = c\\) , and the \\(y\\) axis is the geometric factor relative to a spherical target, \\(P_{sp}\\) , in percentiles. The aspect ratio is defined as \\(b / a\\) . The black line resulted from Maxwell Z-model simulations, while the red line was from iSALE-2D simulations. The Maxwell Z-model's error bar gives \\(1\\sigma\\) uncertainties.",
+    "footnote": [],
+    "bbox": [
+      [
+        214,
+        99,
+        754,
+        432
+      ]
+    ],
+    "page_idx": 19
+  }
+]

preprint/preprint__c8ea0fd9793775451b1580cefcf4cd08c8dfd9b2baff1b29377d0ff48c5d5b10/preprint__c8ea0fd9793775451b1580cefcf4cd08c8dfd9b2baff1b29377d0ff48c5d5b10.mmd

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+
+# Kinetic deflection change due to target global curvature as revealed by NASA/DART  
+
+Masatoshi Hirabayashi  thirabayashi@gatech.edu  
+
+Georgia Institute of Technology https://orcid.org/0000- 0002- 1821- 5689  
+
+Sabina Raducan  University of Bern https://orcid.org/0000- 0002- 7478- 0148  
+
+Jessica Sunshine  University of Maryland  
+
+Tony Farnham  University of Maryland College Park https://orcid.org/0000- 0002- 4767- 9861  
+
+Prasanna Deshapriya  INAF  
+
+Jian- Yang Li  Planetary Science Institute https://orcid.org/0000- 0003- 3841- 9977  
+
+Gonzalo Tancredi  Facultad Ciencias https://orcid.org/0000- 0002- 4943- 8623  
+
+Steven Chesley  
+
+Jet Propulsion Laboratory, California Institute of Technology https://orcid.org/0000- 0003- 3240- 6497  
+
+Ronald Daly  
+
+Johns Hopkins University Applied Physics Laboratory https://orcid.org/0000- 0002- 1320- 2985  
+
+Carolyn Ernst  
+
+Johns Hopkins University Applied Physics Laboratory https://orcid.org/0000- 0002- 9434- 7886  
+
+Igor Gai  University of Bologna  
+
+Pedro Hasselmann  INAF- Osservatorio Astronomico di Roma  
+
+Shantanu Naidu  
+
+Jet Propulsion Laboratory, California Institute of Technology https://orcid.org/0000- 0003- 4439- 7014  
+
+Hari Nair  
+
+Johns Hopkins University Applied Physics Laboratory  
+
+Eric Palmer  
+
+PSI https://orcid.org/0000- 0001- 6755- 8736  
+
+C. Waller
+
+<--- Page Split --->
+
+Johns Hopkins University Applied Physics Laboratory  
+
+Angelo Zinzi ASI- SSDC https://orcid.org/0000- 0001- 5263- 5348  
+
+Harrison Agrusa Universite Cote d'Azur, Observatoire de la Cote d'Azur, CNRS, Laboratoire Lagrange  
+
+Brent Barbee NASA/GSFC https://orcid.org/0000- 0003- 3739- 3242  
+
+M. Bruck Syal Lawrence Livermore National Laboratory, Livermore, CA, USA  
+
+Gareth Collins Imperial College London https://orcid.org/0000- 0002- 6087- 6149  
+
+Thomas Davison Imperial College London https://orcid.org/0000- 0001- 8790- 873X  
+
+Mallory DeCoster Johns Hopkins University Applied Physics Laboratory https://orcid.org/0000- 0002- 1139- 9235  
+
+Martin Jutzi University of Bern  
+
+Kathryn Kumamoto Lawrence Livermore National Laboratory https://orcid.org/0000- 0002- 0400- 6333  
+
+Nicholas Moskovitz Lowell Observatory  
+
+Joshua Lyzhoft NASA GSFC https://orcid.org/0000- 0001- 6420- 8423  
+
+Stephen Schwartz Planetary Science Institute  
+
+Paul Abell NASA/Goddard Space Flight Center  
+
+Olivier Barnouin Johns Hopkins University Applied Physics Laboratory https://orcid.org/0000- 0002- 3578- 7750  
+
+Nancy Chabot Johns Hopkins University Applied Physics Laboratory https://orcid.org/0000- 0001- 8628- 3176  
+
+Andy Cheng Johns Hopkins University Applied Physics Laboratory https://orcid.org/0000- 0001- 5375- 4250  
+
+Elisabetta Dotto INAF- OAR https://orcid.org/0000- 0002- 9335- 1656  
+
+Eugene Fahnestock Jet Propulsion Laboratory, California Institute of Technology  
+
+Patrick Michel
+
+<--- Page Split --->
+
+Université Côte d'Azur, Observatoire de la Côte d'Azur, CNRS, Laboratoire Lagrange https://orcid.org/0000-0002-0884-1993 
+
+**Derek Richardson**
+Department of Astronomy, University of Maryland  https://orcid.org/0000-0002-0054-6850 
+
+**Andrew Rivkin**
+Johns Hopkins University Applied Physics Laboratory  https://orcid.org/0000-0002-9939-9976 
+
+**Angela Stickle**
+Johns Hopkins University Applied Physics Laboratory 
+
+**Cristina Thomas**
+Northern Arizona University  https://orcid.org/0000-0003-3091-5757 
+
+**Joel Beccarelli**
+INAF-Osservatorio Astronomico di Padova 
+
+**John Brucato**
+INAF  https://orcid.org/0000-0002-4738-5521 
+
+**Massimo Dallora**
+INAF 
+
+**Vincenzo Della Corte**
+INAF 
+
+**Elena Mazzotta Epifani**
+INAF-Osservatorio Astronomico di Roma 
+
+**Simone Ieva**
+INAF-Osservatorio Astronomico di Roma  https://orcid.org/0000-0001-8694-9038 
+
+**Gabriele Impresario**
+ASI  https://orcid.org/0000-0001-8984-4231 
+
+**Stavro Ivanovski**
+INAF - Osservatorio Astronomico di Trieste 
+
+**Alice Lucchetti**
+INAF - Osservatorio Astronomico di Padova  https://orcid.org/0000-0001-7413-3058 
+
+**Dario Modenini**
+Alma Mater Studiorum, Università di Bologna  https://orcid.org/0000-0002-1517-3938 
+
+**Maurizio Pajola**
+INAF - Astronomical Observatory of Padova  https://orcid.org/0000-0002-3144-1277 
+
+**Pasquale Palumbo**
+INAF-Istituto di Astrofisica e Planetologia Spaziali 
+
+**Simone Pirrotta**
+ASI  https://orcid.org/0000-0003-0377-8937 
+
+**Giovanni Poggiali**
+INAF Arcetri Astrophysical Observatory  https://orcid.org/0000-0002-3239-1697 
+
+**Alessandro Rossi**
+
+<--- Page Split --->
+
+IFAC-CNR https://orcid.org/0000-0001-9311-2869  
+
+Paolo Tortora Università di Bologna https://orcid.org/0000- 0001- 9259- 7673  
+
+Filippo Tusberti INAF- OAPd https://orcid.org/0000- 0002- 9290- 1679  
+
+Marco Zannoni Università di Bologna https://orcid.org/0000- 0002- 4151- 9656  
+
+Giovanni Zanotti Politecnico di Milano https://orcid.org/0000- 0002- 3157- 7588  
+
+Fabio Ferrari Department of Aerospace Science and Technology, Politecnico di Milano https://orcid.org/0000- 0001- 7537- 4996  
+
+David Glenar Center for Space Science and Technology, University of Maryland  
+
+M.I. Herreros Centro de Astrobiología (CAB), CSIC- INTA, Carretera de Ajalvir km4, 28850 Torrejón de Ardoz, Spain https://orcid.org/0000- 0001- 5284- 8060  
+
+Seth Jacobson Michigan State University https://orcid.org/0000- 0002- 4952- 9007  
+
+Ozgur Karatekin Royal Observatory of Belgium  
+
+Monica Lazzarin University of Padova  
+
+Ramin Lolachi University of Maryland, Baltimore County https://orcid.org/0000- 0001- 5764- 7639  
+
+Michael Lucas University of Notre Dame  
+
+Rahil Makadia University of Illinois at Urbana- Champaign https://orcid.org/0000- 0001- 9265- 2230  
+
+Francesco Marzari Universita di Padova  
+
+Colby Merrill Cornell University https://orcid.org/0000- 0002- 5566- 0618  
+
+Alessandra Migliorini Istituto Nazionale di AstroFisica - Istituto di Astrofisica e Planetologia Spaziali (INAF- IAPS) https://orcid.org/0000- 0001- 7386- 9215  
+
+Ryota Nakano Georgia Institute of Technology  
+
+Jens Ormö
+
+<--- Page Split --->
+
+Centro de Astrobiología (CSIC- INTA)  
+
+Paul Sánchez  University of Colorado Boulder https://orcid.org/0000- 0003- 3610- 5480  
+
+Cem Senel  Royal Observatory of Belgium https://orcid.org/0000- 0002- 7677- 9597  
+
+Stefania Soldini  Department of Mechanical, Materials and Aerospace Engineering, University of Liverpool https://orcid.org/0000- 0003- 3121- 3845  
+
+Timothy Stubbs  NASA Goddard Space Flight Center  
+
+Physical Sciences - Article  
+
+Keywords:  
+
+Posted Date: January 16th, 2024  
+
+DOI: https://doi.org/10.21203/rs.3.rs- 3598104/v1  
+
+License: © © This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License  
+
+Additional Declarations: There is NO Competing Interest.  
+
+Version of Record: A version of this preprint was published at Nature Communications on February 14th, 2025. See the published version at https://doi.org/10.1038/s41467- 025- 56010-w.
+
+<--- Page Split --->
+
+## Author list  
+
+Masatoshi Hirabayashi,1,2 Sabina D. Raducan,3 Jessica M. Sunshine,4 Tony L. Farnham,4 J. D. Prasanna Deshapriya,5 Jian- Yang Li,6 Gonzalo Tancredi,7 Steven R. Chesley,8 R. Terik Daly,9 Carolyn M. Ernst,9 Igor Gai,10 Pedro H. Hasselmann,5 Shantanu P. Naidu,8 Hari Nair,9 Eric E. Palmer,6 C. Dany Waller,9 Angelo Zinzi,11,12 Harrison F. Agrusa,13,3 Brent W. Barbee,14 Megan Bruck Syal,15 Gareth S. Collins,16 Thomas M. Davison,16 Mallory E. DeCoster,9 Martin Jutzi,3 Kathryn M. Kumamoto,15 Nicholas A. Moskovitz,17 Joshua R. Lyzhof,14 Stephen R. Schwartz,6,18 Paul A. Abell,19 Olivier S. Barnouin,9 Nancy L. Chabot,9 Andrew F. Cheng,9 Elisabetta Dotto,5 Eugene G. Fahnestock,8 Patrick Michel,13,20 Derek C. Richardson,3 Andrew S. Rivkin,9 Angela M. Stickle,9 Cristina A. Thomas,21 Joel Beccarelli,22 John R. Brucato,23 Massimo Dall'Ora,24
+
+<--- Page Split --->
+
+Vincenzo Della Corte,24 Elena Mazzotta Epifani,5 Simone leva,5 Gabriele Impresario,11 Stavro Ivanovski,25 Alice Lucchetti,22 Dario Modenini,26 Maurizio Pajola,22 Pasquale Palumbo,27 Simone Pirrotta,11 Giovanni Poggiali,23 Alessandro Rossi,28 Paolo Tortora,26 Filippo Tusberti,22 Marco Zannoni,26 Giovanni Zanotti,29 Fabio Ferrari,29 David A. Glenar,30,14 Isabel Herreros,31 Seth A. Jacobson,32 Özgür Karatekin,33 Monica Lazzarin,34 Ramin Lolachi,30,14 Michael P. Lucas,35 Rahil Makadia,36 Francesco Marzari,34 Colby C. Merrill,37 Alessandra Migliorini,27 Ryota Nakano,1,2 Jens Ormö,31 Paul Sánchez,38 Cem Berk Senel,33,39 Stefania Soldini,40 Timothy J. Stubbs,14
+
+<--- Page Split --->
+
+10Università di Bologna, Bologna, Italy 11Agenzia Spaziale Italiana (ASI), Roma, Italy 12Space Science Data Center, ASI, Roma, Italy 13Université Côte d'Azur, Observatoire de la Côte d'Azur, CNRS, Laboratoire Lagrange, Nice, France 14NASA/Goddard Space Flight Center, Greenbelt, MD, USA 15Lawrence Livermore National Laboratory, Livermore, CA, USA 16Imperial College London, London, UK 17Lowell Observatory, Flagstaff, AZ, USA 18Universidad de Alicante, Alicante, Spain 19NASA Johnson Space Center, Houston, TX, USA 20The University of Tokyo, Tokyo, Japan 21Northern Arizona University, Flagstaff, AZ, USA 22INAF-Osservatorio Astronomico di Padova, Padova, Italy 23INAF-Osservatorio Astronomico di Arcetri, Firenze, Italy 24INAF-Osservatorio Astronomico di Capodimonte, Napoli, Italy 25INAF-Osservatorio Astronomico di Trieste, Trieste, Italy 26Alma Mater Studiorum - Università di Bologna, Forlì, Italy 27INAF-Istituto di Astrofisica e Planetologia Spaziali, Roma, Italy 28IFAC-Istituto di fisica applicata Nello Carrara, Sesto Fiorentino, Italy 29Politecnico di Milano, Milano, Italy 30University of Maryland, Baltimore, MD, USA 31Centro de Astrobiologia (CAB), CSIC-INTA, Madrid, Spain 32Michigan State University, MI, USA 33Royal Observatory of Belgium, Brussels, Belgium 34Università di Padova, Padova, Italy 35University of Notre Dame, Notre Dame, IN, USA 36University of Illinois at Urbana-Champaign, Urbana IL, USA 37Cornell University, Ithaca, NY, USA 38University of Colorado Boulder, Boulder, CO, USA 39Vrije Universiteit Brussel, Brussels, Belgium 40University of Liverpool, Liverpool, UK  
+
+To whom correspondence should be addressed; E- mail: thirabayashi@gatech.edu.
+
+<--- Page Split --->
+
+# Kinetic deflection change due to target global curvature as revealed by NASA/DART  
+
+Author list attached separately  
+
+## ABSTRACT  
+
+Kinetic deflection is a planetary defense technique that delivers spacecraft momentum to a small body to deviate its course from Earth. The deflection efficiency depends strongly on the impactor and target. Among them, the contribution of global curvature was poorly understood. The ejecta plume created by NASA's DART impact on its target asteroid, Dimorphos, exhibited an elliptical shape almost aligned along its north- south direction. Here, we identify that this elliptical ejecta plume resulted from the target's curvature, reducing the momentum transfer to \(44 \pm 10\%\) along the orbit track compared to an equivalent impact on a flat target. We also find lower kinetic deflection of impacts on smaller Near- Earth objects (NEOs) due to higher curvature. A solution to mitigate low deflection efficiency is to apply multiple low- energy impactors rather than a single high- energy impactor. Rapid reconnaissance to acquire a target's properties before deflection enables determining the proper locations and timing of impacts.  
+
+## Main texts  
+
+Planetary defense is an international effort to mitigate threats of small body collisions with Earth \(^{1,2}\) . Among its key planetary defense technologies is kinetic deflection, in which a spacecraft collides with a hazardous body to change its trajectory and eliminate or reduce the risk of its impact on Earth \(^{3}\) . Kinetic deflection is a practical approach when targets are less than \(\sim 500 \mathrm{~m}\) in radius if the encounter with Earth is several decades in the future \(^{1 - 4}\) . In contrast, NEOs less than \(50 \mathrm{~m}\) in radius are the most probable threat and high- priority targets for rapid reconnaissance flyby missions \(^{1 - 4}\) . The momentum transfer enhancement factor, known as \(\beta\) , is a well- used parameter, in its simplest form, the total momentum imparted to the target by the spacecraft and ejecta normalized by its momentum before impact \(^{5 - 7}\) . Recent impact physics studies suggest the dependence of \(\beta\) on the impactor's properties and orientation and the target's composition and strength \(^{8 - 15}\) . However, how a target's global curvature controls kinetic deflection remains poorly constrained.  
+
+NASA's Double Asteroid Redirection Test (DART) mission was the first full- scale planetary defense demonstration mission that deliberately crashed a spacecraft into Dimorphos, the smaller satellite of the binary system (65803) Didymos \(^{16}\) . The measured \(\beta\) ranged between 2.2 and 4.9 (depending on the bulk density, which remains unknown but will be constrained by ESA's Hera mission \(^{17}\) ); for a bulk density of \(2.4 \mathrm{~g / cc}\) , \(\beta\) was determined to be \(3.61_{- 0.25}^{+0.1918}\) . A recent study using images from the Hubble Space Telescope and LICIACube determined that the ejecta cone geometry was elliptic \(^{19}\) . The parameters representing the ejecta cone geometry include the wide- cone opening angle, \(\theta_{1}\) , the narrow- cone opening angle, \(\theta_{2}\) , the azimuthal angle from Dimorphos's north at the impact site defining the wide- cone orientation, \(\phi\) , and the cone axis direction described using Right Ascension, \(RA\) , and Declination, \(DEC\) (Figure 1). The J2000 International Celestial Reference System (later known as J2000) is the baseline coordinate frame defining the cone axis direction, \(RA\) and \(DEC\) . Their solutions with \(1\sigma\) uncertainties were \(\theta_{1} = 133 \pm 9^{\circ}\) , \(\theta_{2} = 95 \pm 6^{\circ}\) , \(\phi = 26 \pm 16^{\circ}\) , \(RA = 141 \pm 4^{\circ}\) , and \(DEC = +20 \pm 8^{\circ}\) , and the ejecta cone's tip (apex) as \((- 4 \pm 6, - 3 \pm 9, 9 \pm 10) \mathrm{~m}\) in the Dimorphos- fixed frame, later known as IAU_DIMORPHOS (Figure 1). These results are consistent with independent work within uncertainties \(^{20}\) .
+
+<--- Page Split --->
+![](images/Figure_1.jpg)
+
+<center>Figure 1. Ejecta cone and impact cratering flow fields. The arrows in light blue show \((x^{\prime},y^{\prime},z^{\prime})\) in J2000, while those in green \((x,y,z)\) are IAU_DIMORPHOS. The arrows in red give the local frame at the impact site. \(z^{\prime \prime}\) is the DART impact direction, \(x^{\prime \prime}\) is orthogonal to Dimorphos's north and \(z^{\prime \prime}\) , and \(y^{\prime \prime}\) is orthogonal to these axes. A and B. Cone geometry and Dimorphos. The cone's perimeter defines its edge. C. Slice in light red representing a plane used for the Maxwell Z-model. The red curve over Dimorphos represents the intersection between the body and the slicing plane. D. Illustrations of streamlines defined as \(SL\) . An example streamtube is a region between \(SL1\) and \(SL2\) . </center>
+
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+
+We use the geometric parameters \(^{19}\) to compute the net geometric factor, \(P_{fl}\) , the ratio of the ejecta momentum on a curved surface target to that on a flat surface (Methods). We apply the Maxwell Z- model to quantify the kinematics of subsurface flow fields and ejecta's ballistic trajectories (Methods). This empirical model applies two kinematic parameters, \(\alpha\) and \(Z\) , representing ejecta's speed and geometry, respectively. We introduce a scalar factor, \(\gamma\) , to use the measured \(\beta\) as a constraint and determine \(P_{fl}\) (Methods). Comparison tests confirm that our approach gives geometric factors consistent with those determined by the iSALE shock- physics code \(^{21 - 24}\) (Methods). Monte Carlo simulations input the cone geometry measurements \((\theta_{1}, \theta_{2}, RA, DEC, \phi)\) to give the azimuthal variations in \(\alpha\) , \(Z\) , and geometric factor (Figure 2). The derived mean value of \(Z = 2.9 \pm 0.4\) is consistent with those observed for a flat surface \(^{25}\) and the ideal case, i.e., \(Z = 3^{26}\) . Similarly, with the \(Z\) value, the mean value of \(\alpha = 3.1 \times 10^{- 4} \mathrm{~hm}^{(Z + 1)} / \mathrm{s}\) offers a transient crater radius of \(\sim 86 \mathrm{~m}\) , which is within the predicted value \(^{27}\) .  
+
+The geometric factor variation along \(\phi\) , \(P_{fl\phi}\) , becomes lower but more variable along the wide cone direction (Figure 2D). The east- west direction \((\phi \sim \pm 90^{\circ})\) tends to have higher \(P_{fl\phi}\) with lower uncertainties. This direction offers a flatter surface, providing positive momentum transfer and, thus, positive \(P_{fl\phi}\) . On the other hand, because of high curvature approximately along the north- south direction \((\phi \sim 0^{\circ}, \pm 180^{\circ})\) , ejected materials tend to depart toward Dimorphos's anti- along track direction. The Dimorphos- south direction \((\phi \sim \pm 180^{\circ})\) tends to have negative \(P_{fl\phi}\) , indicating ejecta's contribution to negative momentum transfer. The ejecta cone's slight twist causes the shift of lower \(P_{fl\phi}\) towards positive \(\phi\) by \(\sim 45^{\circ}\) . The net geometric factor, \(P_{fl}\) , is \(44 \pm 10\%\) for Dimorphos. If the target surface is flat, the derived geometric factor leads to \(\beta = 6.9 \pm 3.5(1\sigma)\) within its predicted range \(^{28}\) , improving almost by a factor of \(\sim 2\) .  
+
+The derived low geometric factor results from Dimorphos's higher curvature in its north- south direction. Based on the asteroid's pre- impact extents, the ratio of the semi- minor axis to the semi- major axis is \(0.64^{16}\) . However, regardless of Dimorphos's high curvature, the typical values of \(Z\) for a flat surface target \(^{26}\) can reproduce the elliptical cone geometry along all azimuthal directions. Because the higher curvature in its north- south direction causes a shorter excavation range, the flow fields beneath the surface are short- lived. Excavated materials cannot change their flow directions before launch well enough to achieve a higher ejection angle from the surface. Such trends are so extreme in some directions that ejecta momenta possess anti- along track components, giving negative momentum transfer (Figure 2D). These mechanisms noticeably reduce the net momentum transfer and result from the impact location in the southern hemisphere, inferring the sensitivity of the kinetic deflection efficiency to global curvature. If the DART impact- driven crater were small relative to Dimorphos's size, local morphological features would be more influential than global curvature. Local topography may generate the observed clumps and boulders ejected from Dimorphos; however, they did not contribute to the along- track momentum transfer component \(^{29}\) .  
+
+We further quantify how \(P_{fl}\) changes due to the impact locations for 103 NEOs less than \(50 \mathrm{~m}\) in radius observed by the MANOS (Mission Accessible Near- Earth Objects Survey) project \(^{30}\) . Given limited constraints, we assume each sample to be a prolate body with identical semi- intermediate and semi- minor axes (Methods). For each body, we consider two impact locations: one along the semi- major axis and the other along the semi- minor axis. Because the impacts at both locations are vertical to the local surface, the impact point along the semi- major axis has higher curvature. Figure 3 shows the distributions of the samples' \(P_{fl\phi}\) . This parameter positively correlates with the target radius and strength (Figure 3A). Given a constant impact energy identical to the DART impact, higher strength and larger size make the crater radius small relative to the body \(^{31}\) , reducing the curvature effect and thus making \(P_{flT}\) higher. The transition zone from zero geometric factors \((= 0\%)\) to high geometric factors \((> \sim 70\%)\) is narrow. This zone also overlaps the predicted catastrophic disruption threshold, which defines an impact condition
+
+<--- Page Split --->
+![](images/Figure_2.jpg)
+
+<center>Figure 2. Variations in Maxwell Z-model parameters and projected cone geometry onto Dimorphos's surface with azimuthal angle from Dimorphos's north. A. Variations in Z. B. Variations in \(\alpha\) . C. Variations in excavation range, which plots \(r_{E}^{*}\) (Figure 1). D. Variations in geometric factor along each piece in an azimuthal direction. Uncertainties are provided in \(1\sigma\) . </center>
+
+<--- Page Split --->
+![](images/Figure_3.jpg)
+
+<center>Figure 3. Geometric factor distributions of 103 small NEOs measured by the MANOS project<sup>30</sup>. A. Geometric factor of an impact along each target's semi-minor axis. B. Relative geometric factor of an impact along the semi-major axis to one along the semi-minor axis. Specifically, the relative geometric factor defines the geometric factor along the semi-major axis minus that along the semi-minor axis. All panels give the geometric factor distributions in percentile as a function of diameter and minimum strength. All negative outcomes in Panel A are truncated and noted as zero geometric factors. The curves in different colors show interpolations between the catastrophic disruption thresholds for a pumice-like target and a cohesionless target (red) and a basalt-like target and a cohesionless target (blue). For the cohesionless target, we assume a minimal strength of 0.01 Pa. The dashed, solid, and dotted lines give bulk densities of \(1000\mathrm{kg / m}^3\) , \(2000\mathrm{kg / m}^3\) , and \(4000\mathrm{kg / m}^3\) . If target asteroids stay on the right side of those thresholds, they do not experience catastrophic disruption. </center>  
+
+when the final target mass is less than half the original (Methods). Figure 3C shows the distribution of the relative geometric factor, defined as the difference between an impact along the semi- major axis and an impact along the semi- minor axis. The results show lower relative geometric factors along the semi- major axis than the semi- minor axis for all samples.  
+
+Our finding suggests that scenarios employing a single impactor having higher kinetic energy are not ideal (Figure 4). The increase in the encounter speed is reported to make such single impacts with high kinetic energy more feasible<sup>32</sup>. Another concept may be to disrupt a target body as part of kinetic deflection<sup>33</sup>. However, the efficiency of momentum transfer changes due to global curvature. A flatter surface target offers higher momentum transfer for a single impact with a given kinetic energy due to higher changes in the subsurface flow fields. Alternatively, a lower kinetic energy impactor results in a smaller crater, less affected by global curvature, increasing the momentum transfer efficiency. With these trends to enhance momentum transfer, employing multiple, smaller impactors is a better solution than having a single, large impactor. In the multiple- impactor scenario, each impactor has a smaller kinetic energy than one in the single- impactor scenario. Still, the net kinetic energy can be comparable when all impactors collide with the target. Practically, the multiple- impactor scenario can send impactors at different times and aim at flatter surface points on the target, maximizing the net momentum transfer (Figure 4). However, the crater size should not be too small because local boulders and topography can become more influential on the ejecta plume formation, as seen by earlier experimental tests<sup>34</sup>, changing the trends of momentum transfer. This condition applies to Deep Impact and Hayabusa2, which observed
+
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+
+complex ejecta formation \(^{35,36}\) .  
+
+Constraining all essential physical properties of a target object before kinetic impact is valuable. While no details have been reported for global curvature \(^{4}\) in the past, our study proposes it as a key contributor that can easily change the efficiency by a factor of a few. The practical approach is to visit the object in situ and conduct key measurements as much as possible before deciding the timing of kinetic deflection. A rapid response to this demand after identifying a potential threat is not yet a mature technology \(^{4}\) . Compared to mass measurement, which requires additional operational constraints, imaging the target even during a fast flyby can provide sufficient information to infer the curvature and surface conditions, significantly improving the accuracy of momentum transfer. Demonstrating capabilities to acquire such properties by a rapid reconnaissance mission is strategic to achieving sophisticated advances in kinetic deflection technologies.  
+
+## Methods  
+
+## Formulation of Maxwell Z-model  
+
+The most basic version of the Maxwell Z- model consists of three kinematic equations that use three parameters to represent the geometry and velocity over each streamtube \(^{37}\) :  
+
+\[\begin{array}{rcl}{r} & = & {r_{0}(1 - \cos \Delta)^{\frac{1}{2 - 2}}}\\ {} & {} & {}\\ {v_{r}} & = & {\frac{\alpha}{rZ}}\\ {} & {} & {}\\ {v_{\Delta}} & = & {u_{r}(Z - 2)\frac{\sin\Delta}{1 + \cos\Delta}} \end{array} \quad (3)\]  
+
+where \(r\) is a mass element's radial location along a streamline, while \(v_{r}\) and \(v_{\Delta}\) are its radial and tangential speeds, respectively. These quantities vary with \(\Delta\) , a counterclockwise angle from the impact incident direction (Figure 1). For a vertical impact on a flat surface, the downward direction is \(\Delta = 0^{\circ}\) . \(r_{0}\) , \(\alpha\) , and \(Z\) represent a streamline's kinematics.  
+
+In the analysis determining the geometric factors of the MAMOS samples, we also apply a conversion formula between \(\alpha\) and the transient crater radius, \(R^{38}\) :  
+
+\[\alpha = \left(\frac{gR^{(2Z + 1)}}{4Z(Z - 2)}\right)^{\frac{1}{2}} \quad (4)\]  
+
+Because our target surface is supposed to have curvature, \(R\) , which is usually defined as a quantity for an impact on a flat surface \(^{31}\) , can only serve as a hypothetical parameter rather than a physically meaningful quantity. Thus, this quantity should be larger than the excavation range, \(r_{E}^{*}\) , generally when the target surface has curvature.  
+
+## Computation of transient crater radius  
+
+The \(\pi\) - scaling relationship offers correlations between the impactor and transient crater conditions based on empirically determined scaling factors \(^{31}\) . This relationship provides the transient crater volume, \(V\) :  
+
+\[V = K_{1}\left(\frac{m_{i}}{\rho_{t}}\right)\left\{\left(\frac{gr_{i}}{v_{t}^{2}}\right)\left(\frac{\rho_{t}}{\rho_{i}}\right)^{-\frac{1}{3}} + \left(\frac{Y}{\rho_{t}v_{t}^{2}}\right)^{\frac{2 + \mu}{2}}\right\}^{-\frac{3\mu}{2 + \mu}}. \quad (5)\]  
+
+where \(K_{1}\) , \(\mu\) , and \(Y\) are empirically determined parameters. \(m_{i}\) , \(r_{i}\) , and \(v_{i}\) are the impactor's mass, radius, and speed, respectively. The used values for the parameters are provided in Supplementary Table S.1. The
+
+<--- Page Split --->
+![](images/Figure_4.jpg)
+
+<center>Figure 4. Schematics for kinetic impact-driven momentum transfer depending on different scenarios. Impactors with two kinetic energies add the same net kinetic energy to a target by performing multiple impacts. Net momentum transfer changes due to orientation and kinetic energy per impactor. The ID of the attached LICIACube image is liciacube_luke_10_1664234219_00112_01.fits. </center>
+
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+
+strength parameter, \(Y\) , is set to be equivalent to the minimum cohesive strength (see below). \(\rho_{t}\) and \(\rho_{i}\) are the bulk density of the target and that of the impactor, respectively. \(g\) is the gravitational acceleration. The following equation then provides the transient crater radius using the transient crater volume:  
+
+\[R = \left(\frac{3V}{\pi}\right)^{\frac{1}{3}} \quad (6)\]  
+
+During the computation of the geometric factors for the MANOS samples, the algorithm inputs \(R\) to determine \(\alpha\) using Equation (4).  
+
+## Computation of minimum cohesive strength  
+
+Equation (5) needs \(Y\) as an input to determine the transient crater volume, which computes the transient crater radius in Equation (6). This parameter is the least constrained quantity in this study. However, the spin state gives the strength levels for objects to remain structurally intact. While this concept only offers a lower bound of strength, it is valuable to characterize how high the strength is in each MANOS sample. One method is to determine the cohesive strength, or shear strength, at zero pressure. When a self- gravitating body spins at a given spin period, body elements experience gravitational and centrifugal loading, which induces a stress field. When the spin is fast enough that the centrifugal loading strongly pulls the elements outward, the body may need cohesive strength to keep its structure intact. The minimum cohesive strength defines the lowest level of such strength in a given element.  
+
+While earlier approaches use Finite Element Modeling to determine the levels of the minimum cohesive strengths in irregularly shaped bodies \(^{39}\) , we apply an analytical work \(^{40,41}\) to simplify computation given limited constraints on the samples' shapes. Given a constant bulk density, this analytical model considers a uniformly rotating triaxial ellipsoid to compute the stress field. The computed stress field is based on linear elasticity, making the equilibrium equations simple to become analytically solvable linear equations. During this operation, the equations no longer depend on Young's modulus. We then convert the derived stress field to the minimum cohesive strength, \(Y\) , by using the Drucker- Prager yield criterion:  
+
+\[\begin{array}{rcl}{Y}&{=}&{\frac{1}{\beta}(\alpha I_{1}+\sqrt{J_{2}})}\\{}&{}&{}\\{\alpha}&{=}&{\frac{2\sin\psi}{\sqrt{3}(3-\sin\psi)}}\\{}&{}&{}\\{\beta}&{=}&{\frac{6\cos\psi}{\sqrt{3}(3-\sin\psi)}}\end{array} \quad (7)\]  
+
+where \(I_{1}\) and \(J_{2}\) are pressure and shear stress invariants, respectively, and \(\psi\) is the angle of friction. This study fixes \(\psi\) at \(35^{\circ}\) . This provides the spatial distribution of the minimum cohesive strength over the entire body. Earlier work suggested that \(Y\) becomes maximum at the center when the spin period is short \(^{41}\) . Because many MANOS samples are fast rotators, we select \(Y\) at their body centers. The \(\pi\) - scaling relationship then uses the computed \(Y\) to determine the transient crater radius, \(R\) .  
+
+## Definition of geometric factor  
+
+The geometric factor, \(P\) , defines the ratio of the along- track momentum carried by ejecta developed by an impact on a curved surface to that by a vertical impact on a geometrical reference:  
+
+\[P = \frac{L_{T}}{L_{T r e f}} = \frac{\beta - 1}{\beta_{r e f} - 1} \quad (10)\]
+
+<--- Page Split --->
+
+where \(L_{T}\) and \(L_{T r e f}\) are the along- track ejecta momenta that form on the curved and reference surfaces, respectively. We also express these scalar quantities using vector notations, \(L_{T} = \vec{L}\cdot \vec{n}_{T}\) , where \(\vec{L}\) is the ejecta momenta on the curved surface and \(\vec{n}_{T}\) is the along- track unit vector, and similarly, \(L_{T r e f} = \vec{L}_{r e f}\cdot \vec{n}_{T}\) , where \(\vec{L}_{r e f}\) is the ejecta momentum on the reference surface. \(P\) can be convertible with \(\beta\) for these targets, where \(\beta_{r e f}\) is \(\beta\) for a reference surface. The reference surface can be arbitrary, but the simplest one may be a flat surface, which generally offers the highest ejecta momentum among any convex surface.  
+
+We consider two reference surfaces in this work. The main study applies a flat- surface target as the reference surface and denotes this geometric factor as \(P_{f l}\) , while the validation analysis comparing our Maxwell Z- model approach with the iSALE- 2D shock- physics code uses a spherical target and defines it as \(P_{s p}\) . The major reason for using these two references is that while it is valuable to apply well- established and calibrated simulation results from iSALE in our validation analysis, using a flat surface, which generally gives the highest efficiency, can offer simple diagnostics of the momentum transfer efficiency. For example, reading its unity value, \(P_{f l}\) can give a direct insight into how close (far) the momentum transfer is to (from) the most ideal case. However, \(P_{s p}\) does not give such insightful views easily because it can still be larger than unity even when the ejecta momentum does not reach the ideal flat surface case.  
+
+## Light curve samples from MANOS  
+
+Samples are available through the MANOS light curve campaigns, which offer samples' spin periods, sizes, and shapes. The project sampled 308 NEOs over 4.5 years<sup>30</sup>. Many samples are smaller targets less than 50 m in radius, unlike those cataloged in the Asteroid Lightcurve Database, which archives larger objects in general<sup>42</sup>. We select 103 out of the samples objects, which have full and partial light curve data over their spin periods<sup>30</sup>. For the shape, we assume that the sample is a biaxial ellipsoid, where its semi- intermediate and semi- minor axis are equal. When the semi- major axis is \(a\) , and the semi- minor (intermediate) axis is \(b\) , this ratio becomes \(b / a\) . Given an available relative amplitude, \(\Delta m\) , we can obtain \(b / a\) by using the following equation:  
+
+\[\Delta m = -2.5\log \left(\frac{b}{a}\right) \quad (11)\]  
+
+## Geometric factor of DART impact on Dimorphos  
+
+We create smaller pieces in Dimorphos's body by slicing the asteroid's body parallel to the DART incident direction to make thin pieces over all azimuthal directions. We call each piece an azimuthal piece. Each azimuthal piece defines a volume at a given azimuthal angle, extending to the normal direction to the DART incident direction, and thus looks like a wedge. While the number of azimuthal pieces is arbitrary, our numerical tests suggest that 100 pieces give acceptable computational accuracy without adding significant computational burdens.  
+
+We then apply the Maxwell Z- model to determine \(\alpha\) , \(Z\) , and a new scaling parameter controlling the net momentum, denoted as \(\gamma\) (see below). Our developed iterative scheme searches for the best set of \(\alpha\) and \(Z\) for each azimuthal piece based on the measured ejecta cone. Given the surface element location in a streamtube, \(r^{*}\) , and the range of excavation, \(r_{E}^{*}\) (Figure 1), we define 10,000 streamtubes in one azimuthal piece and select those with \(r^{*}< r_{E}^{*}\) to compute surface elements' trajectories in all these streamtubes. The spatial distribution of ejected surface elements constructs a simulated cone geometry in each azimuthal direction. We fit the derived distribution with the measured cone geometry at \(0.5\mathrm{- }1.0\mathrm{km}\) from the ejecta cone apex. This process gives a unique set of \(\alpha\) and \(Z\) for each azimuthal piece and applies the same step to all azimuthal pieces.  
+
+Once determining \(\alpha\) and \(Z\) for all azimuthal pieces, we obtain the ejecta momentum over the entire body. When the thickness of each streamtube, characterized by a small differential of \(r_{0}\) , is very small, the
+
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+
+ideal momentum is a multiplication of the mass of the streamtube and the surface velocity, \(d m \vec{v}_{\Delta^{*}}\) , where \(d m\) is the streamtube's mass exceeding the escape velocity and \(\vec{v}_{\Delta^{*}}\) is the ejection velocity. Summing up the momenta of all streamtubes over each azimuthal piece and eventually over all azimuthal pieces gives the net ideal ejecta momentum \(\vec{L}_{p}\) :  
+
+\[\vec{L}_{p} = \sum_{i = 1}^{m}\sum_{j = 1}^{n}d m_{i,j}(\alpha_{i},Z_{i})\vec{v}_{\Delta^{*}i,j}(\alpha_{i},Z_{i}) \quad (12)\]  
+
+where \(i\) and \(j\) are the indices representing an azimuthal piece \((1 \leq i \leq m)\) and a streamtube in one azimuthal piece \((1 \leq j \leq n)\) . However, given the Maxwell Z- model formulation, all materials within a streamtube depart from the surface at the same speed at any time. Therefore, the momentum computation using Equation (12) is unrealistic because this does not account for proper energy loss within each streamtube. For model simplicity, without adding new time- variant parameters, we keep \(\alpha\) and \(Z\) constant but introduce a new scaling parameter, \(\gamma\) , to obtain the ejecta momentum:  
+
+\[\vec{L} = r_{0}^{T}\vec{L}_{p} \quad (13)\]  
+
+\(\gamma\) takes the same value over the entire azimuthal pieces.  
+
+Given the determined geometric parameters, cone apex location, and measured \(\beta\) , the algorithm uses the determined set of \(\alpha\) and \(Z\) for all azimuthal pieces. It performs the above processes iteratively to determine \(\gamma\) such that Equation (14) satisfies under an error threshold for \(\gamma\) of \(0.01\%\) . This process computes the simulated \(\beta\) using its formula \(^{6,18}\) :  
+
+\[\beta = 1 + \frac{\vec{L}_{p}\cdot\vec{n}_{T}}{(\vec{E}\cdot\vec{L}_{sc})\cdot(\vec{E}\cdot\vec{n}_{T})} \quad (14)\]  
+
+where \(\vec{E}\) is the unit vector of the net ejecta momentum, and \(\vec{L}_{sc}\) is the momentum carried by spacecraft. Supplementary Table S.2 gives the values of the Dimorphos along- track direction \((\vec{n}_{T})\) and the DART incident direction in the IAU_DIMORPHOS coordinate frame, both obtained by the SPICE kernel version d430. Running 1,000 Monte Carlo simulations with Gaussian- distributed inputs offers the statistical behaviors of these outputs (Table 1). The key inputs include \(\theta_{1}\) , \(\theta_{2}\) , \(RA\) , \(DEC\) , cone apex location vector, \(\beta\) , and Dimorphos's bulk density. We use the following formula to describe \(\beta\) , depending on the asteroid's bulk density \(^{18}\) :  
+
+\[\beta = (3.61\pm 0.2)\frac{\rho}{\rho_{ref}} -0.03\pm 0.02(1\sigma) \quad (15)\]  
+
+where \(\rho_{ref}\) is the reference bulk density fixed at \(2,400 \mathrm{kg m}^{- 3}\) , and \(\rho\) is the considered bulk density, which is \(2,400 \pm 900(1\sigma) \mathrm{kg m}^{- 3}\) .  
+
+Each Monte Carlo simulation case determines the ejecta momentum on a reference surface, which is assumed to be flat. The algorithm applies the same inputs and derived parameters from the curved surface case, including the azimuthal variations in \(\alpha\) and \(Z\) (Figure 2), to the flat surface target. The normal to the reference surface is parallel to the DART incident direction. Similar to the analysis of Dimorphos's curved surface, we divide each azimuthal piece into narrower streamtubes, determine the ejecta momentum of each streamtube, and compute the net ejecta momentum over the entire excavation. The difference between the reference and curved surface cases is that considering a reference target, the reference surface case applies the same parameters as the curved surface case and does not perform interactive schemes to determine these parameters. Once computing the ejecta momentum on the reference target, we apply Equation (10) to compute the geometric factor, \(P_{fl}\) , relative to the ejecta momentum on a flat target.
+
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+
+
+Table 1. Properties determined by cone measurements<sup>19</sup> and the Maxwell Z-model approach. The errors in Value represent \(1\sigma\) uncertainties. The coordinate frame is J2000, the Dimorphos fixed frame (IAU_DIMORPHOS), or the local coordinate frame (Figure 1B). For the units, \(\mathrm{hm}^{(Z + 1)} / \mathrm{s}\) , hm stands for hectometers \(= 100 \mathrm{m}\) , following the earlier notational definition<sup>25</sup>.   
+
+<table><tr><td>Quantity</td><td>Notation</td><td>Value</td><td>Units</td><td>Frame</td></tr><tr><td colspan="5">Cone geometry</td></tr><tr><td>Cone wide angle</td><td>θ1</td><td>133 ± 9</td><td>deg</td><td>[-]</td></tr><tr><td>Cone narrow angle</td><td>θ2</td><td>95 ± 6</td><td>deg</td><td>[-]</td></tr><tr><td>Axis rotation</td><td>φ</td><td>26 ± 16</td><td>deg</td><td>Local</td></tr><tr><td>Axis right ascension</td><td>RA</td><td>141 ± 4</td><td>deg</td><td>J2000</td></tr><tr><td>Axis declination</td><td>DEC</td><td>20 ± 8</td><td>deg</td><td>J2000</td></tr><tr><td>Apex location, x axis</td><td>x</td><td>-4 ± 6</td><td>m</td><td>IAU_DIMORPHOS</td></tr><tr><td>Apex location, y axis</td><td>y</td><td>-3 ± 9</td><td>m</td><td>IAU_DIMORPHOS</td></tr><tr><td>Apex location, z axis</td><td>z</td><td>9 ± 10</td><td>m</td><td>IAU_DIMORPHOS</td></tr><tr><td colspan="5">Maxwell Z-model</td></tr><tr><td>Streamtube, shape</td><td>Z</td><td>2.9 ± 0.4</td><td>[-]</td><td>[-]</td></tr><tr><td>Streamtube, speed</td><td>α</td><td>(3.1 ± 2.2) × 10-4</td><td>hm(Z+1)/s</td><td>[-]</td></tr><tr><td>Streamtube, momentum</td><td>γ</td><td>0.73 ± 0.12</td><td>[-]</td><td>[-]</td></tr><tr><td>Geometric factor</td><td>Pfl</td><td>44 ± 10</td><td>%</td><td>[-]</td></tr></table>  
+
+## Validation of geometric factor computation by Maxwell Z-model  
+
+The comparisons between the Maxwell Z- model and iSALE- 2D simulations<sup>21- 24</sup> reveal that both models give consistent geometric factors relative to a spherical target (Figure 5). In this test, nine iSALE- 2D simulations with different biaxial ellipsoids offer variations in \(\beta\) , assuming that each target's along- track direction corresponds to an impactor's anti- incident direction. The target dimension is set to be \(2a \times 2b \times 2c\) , where \(b = c\) . The simulations parameterized \(b / a\) , which ranged between 0.4 and 2.0 with an increment of 0.2. The equivalent radius is 75 m for all cases. To mimic the DART impact condition, each case assumes a low- density impactor modeled as a sphere with a radius of 1.2 m and a mass of 580 kg. The impact speed is 6 km/s, and the impact site is along the \(a\) axis. We determine \(\beta\) for each case to obtain \(P_{sp}\) .  
+
+We perform iSALE- 2D simulations based on the parameter settings from earlier work<sup>10, 12</sup>. The impactor's material behavior follows the Tillotson equation of state (EOS) and the Johnson- Cook strength model for aluminum<sup>43</sup>. The target's behavior follows the Tillotson EOS for basalt<sup>44</sup> with a modified grain density of \(3,500 \mathrm{kg} / \mathrm{m}^3\) , which corresponds to the average grain density of L/LL chondrites<sup>45</sup>. The current version of iSALE- 2D sets a simple pressure- dependent strength model to define the target's shear strength<sup>22</sup>, with a cohesive strength of 1 Pa and a coefficient of internal friction of 0.55. The target's porosity is \(45\%\) at the initial condition, and its behavior follows the \(\epsilon - \alpha\) compaction model<sup>23</sup>. All parameters are available in Supplementary Table S.1. Given impact scaling relationships<sup>46</sup>, our iSALE results may recreate impact behaviors given in the range of \(Z = 2 - 3\) , where \(Z\) is the Maxwell Z- model kinematic parameter.  
+
+The Maxwell Z- model approach explores the statistical trends of \(P_{sp}\) by considering Gaussian- based inputs to the model based on our earlier analysis for Dimorphos ( \(Z = 2.932 \pm 0.406\) and \(\gamma = 0.731 \pm 0.120\) )
+
+<--- Page Split --->
+![](images/Figure_5.jpg)
+
+<center>Figure 5. Result comparison between Maxwell Z-model and iSALE-2D simulations. The \(x\) axis is the aspect ratio of the biaxial ellipsoid target with dimensions of \(2a \times 2b \times 2c\) , where \(b = c\) , and the \(y\) axis is the geometric factor relative to a spherical target, \(P_{sp}\) , in percentiles. The aspect ratio is defined as \(b / a\) . The black line resulted from Maxwell Z-model simulations, while the red line was from iSALE-2D simulations. The Maxwell Z-model's error bar gives \(1\sigma\) uncertainties. </center>  
+
+and those from the literature of the \(\pi\) - scaling relationships \((K_{1} = 0.22 \pm 0.02\) and \(\mu = 0.47 \pm 0.07\) ). These \(\pi\) - scaling parameters assume impacts on dry sands and rocks<sup>47</sup>. The impactor's bulk density, another input parameter in the model, is fixed at constant at \(1,925 \mathrm{kg} / \mathrm{m}^{3}\) for all cases to make this test consistent with iSALE- 2D runs. The strength parameter, \(Y\) , is set to be 1 Pa to mimic vertical impacts on cohesionless targets. Our analysis performs 1,200 runs with Gaussian- distributed inputs for each \(b / a\) case. Some unrealistic solutions exist, giving extremely high or low \(P_{sp}\) . Such solutions come from parameter conditions at the tails of their distributions or simply ill- defined numerical values for the parameter conditions. The post- processing steps remove any solutions being higher than \(200\%\) or lower than - 200%, removing \(15 - 25\%\) of all solutions, having no significant impact on the statistical trends of our results.  
+
+## Geometric factors for MANOS samples  
+
+We compute their geometric factors by applying 103 small NEO samples measured by the MANOS project<sup>30</sup>. Simulations for each sample perform two geometric factor computations. The first computation considers an impact along the semi- minor axis, while the second one simulates that along the semi- major axis. All simulations assume vertical impacts with the same impact scale as the DART impact, leading to axisymmetric ejecta momenta. The assumption is that the along- track direction corresponds to an impactor's anti- incident direction. With these simulation settings, impacts along the semi- major axis experience a higher curvature than those along the semi- minor (intermediate) axis.  
+
+The main simulation scheme is the same for the geometric factor computation for the DART impact
+
+<--- Page Split --->
+
+on Dimorphos, which determines \(P_{fl}\) . However, there are two differences. First, rather than determining the necessary parameters iteratively, this scheme directly uses the abovementioned parameters, except for \(\alpha\) . Second, \(\alpha\) comes from the conversion between that parameter and the transient crater radius (Equation 4). The reason is that \(\alpha\) depends on the transient crater radius, \(R\) , and gravity, making the derived \(\alpha\) from the DART impact case inconsistent with the MANOS samples. We use the \(\pi\) - scaling relationships \(^{31}\) to compute \(R\) but need the strength parameter, \(Y\) . In this study, we assume \(Y\) to be equivalent to the minimum cohesive strength. Key inputs in the \(\pi\) - scaling relationship are \(K_{1}\) and \(\mu\) , defined in Supplementary Information Table S.2. Then, substituting the derived \(R\) into Equation (4) yields \(\alpha\) for each sample.  
+
+Monte Carlo simulations offer the statistical behavior of each sample's geometric factor. The two impact scenarios for each sample use the same inputs except for the curvature for the geometric factor computation. To account for the uncertainties of the target bulk densities, we set it to be a uniformly distributed random number between 1,000 and \(4,000\mathrm{kg} / \mathrm{m}^{3}\) . This bulk density variation redefines gravity and strength parameters, resulting in the \(\alpha\) variations. For each sample, we perform 1,200 simulations for one impact scenario, i.e., 2,400 simulations for both scenarios. One issue is that when the transient crater is too large, the computation of the ejecta momentum accumulates numerical errors. This is because \(\Delta\) and \(r_{0}\) become extremely small and large, reducing numerical accuracy. To avoid this issue, the algorithm only considers \(\Delta_{E}^{*} > 20^{\circ}\) , allowing all streamtubes to cover up to \(\sim 83\%\) of the entire volume. The \(\Delta_{E}^{*} > 20^{\circ}\) constraint likely underestimates the geometric factor. However, our experience suggests that such a case makes the geometric factor unrealistic and is rejected by the allowed geometric factor range anyway. Thus, this limit does not influence our results. Furthermore, for one impact scenario of each sample, our sorting processes yield \(\sim 85\%\) of simulations that satisfy a geometric factor ranging between \(- 200\%\) and \(200\%\) .  
+
+## Catastrophic disruption threshold \((Q_{D}^{*})\)  
+
+The catastrophic disruption threshold, \(Q_{D}^{*}\) , defines the specific impact energy per mass required to disperse half of the target material mass, which is given as:  
+
+\[Q_{D}^{*} = \frac{U^{2}}{2}\frac{m_{sc}}{M} \quad (16)\]  
+
+where \(m_{sc}\) is the spacecraft mass, \(M\) is the target mass, and \(U\) is the spacecraft relative impact speed. In the present study, \(m_{sc}\) and \(U\) are identical to DART's, and \(m_{ss} \ll M\) .  
+
+\(Q_{D}^{*}\) is a function of the impactor speed, target radius, and strength \(^{48,49}\) . Our study assumes a constant kinetic energy, providing a condition when the target loses its half mass, given strength and radius. The issue is that no adequate disruption threshold formula covers the applicable parameter range considered in this study. At small scales, \(Q_{D}^{*}\) depends on (size- dependent) target strength, but an explicit relation between \(Q_{D}^{*}\) and strength is not available in existing numerical and experimental data for the conditions investigated here. Accepting this issue, our approach uses two samples with different strengths at different target radii at the threshold and interpolates them to draw the correlations. For each sample, we introduce three bulk density cases, \(1000\mathrm{kg} / \mathrm{m}^{3}\) , \(2000\mathrm{kg} / \mathrm{m}^{3}\) , and \(4000\mathrm{kg} / \mathrm{m}^{3}\) , to show the variations in such correlations.  
+
+The first sample considers targets with higher strength \(^{50}\) . \(Q_{D}^{*}\) for a high- strength material defines the following equation \(^{50}\) :  
+
+\[Q_{D}^{*} = 100^{a_{s}}\times Q_{0}R_{Q_{D}^{*}}^{a_{s}} + 100^{b_{s}}\times B\rho R_{Q_{D}^{*}}^{b_{s}} \quad (17)\]  
+
+where \(R_{Q_{D}^{*}}\) is the disrupting target radius, \(\rho\) is the bulk density, and \(Q_{0}\) , \(a_{s}\) , \(b\) , and \(B\) are the empirical parameters. Following earlier Smooth- Particle Hydrodynamics (Bern SPH) simulations \(^{50}\) , our study applies two high- strength materials. One is a basalt- like target, and the other is a pumice- like target. The parameters used here are based on impact simulations with an impact speed of \(5\mathrm{km / s}\) and a target radius
+
+<--- Page Split --->
+
+of \(1.5 \mathrm{cm}^{50}\) , given in Supplementary Table S.3. We apply Equation (17) to determine \(R_{Q_{D}^{*}}\) at kinetic energy imparted by the DART- like impactor by assuming that the parameters derived for the \(5 - \mathrm{km / s}\) impact speed are still valid.  
+
+We consider the strength parameter, \(Y\) , at a given \(R_{Q_{D}^{*}}\) . The earlier targets \(^{50}\) were \(1.5 \mathrm{cm}\) radius, provided with their strengths at this size, \(Y(1.5 \mathrm{cm})\) . We re- scale \(Y(1.5 \mathrm{cm})\) to \(Y\) by applying the static failure threshold for a specimen failing at the smallest strain, \(\epsilon_{min}\) :  
+
+\[\epsilon_{m i n} = (k V_{Q_{D}^{*}})^{-\frac{1}{m}} \quad (18)\]  
+
+where \(k\) and \(m\) are the Weibull parameters, given in Supplementary Table S.3, and \(V_{Q_{D}^{*}}\) is the disrupting target volume. \(Y\) at a given \(R_{Q_{D}^{*}}\) is written as:  
+
+\[Y\sim \epsilon_{m i n}E_{s} \quad (19)\]  
+
+where \(E_{s} = 5.3 \times 10^{10} \mathrm{~Pa}\) is Young's modulus. Combining these equations with the assumption that the Weinbull parameters and \(E_{s}\) are size- independent yields the relationship between \(Y\) and \(Y(1.5 \mathrm{cm})\) :  
+
+\[Y = \left(\frac{V_{Q_{D}^{*}}}{1.41 \times 10^{-5}}\right)^{-\frac{1}{m}} Y(1.5 \mathrm{cm}) \quad (20)\]  
+
+The second sample considers cohesionless targets following a recent Bern SPH study \(^{28}\) . \(Q_{D}^{*}\) for this case gives the equation \(^{48}\) :  
+
+\[Q_{D}^{*} = a_{g} R_{Q_{D}^{*}}^{3 \mu_{g}} U^{2 - 3 \mu_{g}} \quad (21)\]  
+
+where \(a_{g}\) and \(\mu_{g}\) are empirical parameters, and \(U\) is the impact speed (Supplementary Table S.3). These quantities are based on SPH simulations using an impact speed range of \(3 - 9 \mathrm{~km / s}\) and an impact mass of \(500 \mathrm{~kg}^{28}\) . We set the strength parameter for this scaling relationship as \(10^{- 2} \mathrm{~Pa}\) .  
+
+We interpolate these two samples to give a correlation between \(Y\) and \(R_{Q_{D}^{*}}\) . We assume that the interpolation function follows a power law:  
+
+\[Y = \xi R_{Q_{D}^{*}}^{n} \quad (22)\]  
+
+where \(\xi\) and \(\eta\) come from the constraint that this scaling function must cross the data samples above. The approach considers two scaling functions: the combination of a pumice- like target and a cohesionless target and that of a basalt target and a cohesionless target. Finally, these discussions are based on the level of the tensile strength \(^{28,50}\) ; we assume that it is comparable to the strength parameter discussed above.  
+
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+
+## Acknowledgements  
+
+This work was supported by the DART mission, NASA Contract No. 80MSFC20D0004. This work was supported by the Italian Space Agency (ASI) within the LICIACube project (ASI- INAF agreement n. 2019- 31- HH.0 and its extension 2019- 31- HH.1- 2022). This work is partially supported by NASA through grant HSTGO- 16674 from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5- 26555. Portions of this work were performed by Lawrence Livermore National Laboratory under DOE contract DE- AC52- 07NA27344. LLNL- JRNL- 853920. S.D.R. and M.J. acknowledge support from the Swiss National Science Foundation (project number 200021 207359). Work of E.G.F., S.P.N., and S.R.C. was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration (80NM0018D0004). R.M. acknowledges funding from a NASA Space Technology Graduate Research Opportunities (NSTGRO) award, NASA contract No. 80NSSC22K1173. P.M. acknowledges funding support from the French Space Agency CNES and The University of Tokyo. G.T. acknowledges financial support from project FCE- 1- 2019- 1- 156451 of the Agencia Nacional de Investigación e Innovación ANII and Grupos I+D 2022 CSIC- Udela (Uruguay). The work by J.O. was
+
+<--- Page Split --->
+
+supported by grant PID2021- 125883NB- C22 by the Spanish Ministry of Science and Innovation/State Agency of Research MCIN/AEI/ 10.13039/501100011033 and by "ERDF A way of making Europe." The work by J.O. and I.H. was supported by the Spanish Research Council (CSIC) support for international cooperation: I- LINK project ILINK22061. S.R.S. acknowledges support from the DART Participating Scientist Program, grant no. 80NSSC22K0318. This research was supported in part through research cyberinfrastructure resources and services provided by the Partnership for an Advanced Computing Environment (PACE) at the Georgia Institute of Technology. The authors also acknowledge Mark Cintala for detailed reviews and proofreading of this manuscript.  
+
+## Author contributions statement  
+
+M.H. led this project, developed techniques, conducted analysis and data assessment, and created the full story. S.D.R conducted iSALE simulations and gave interpretations of the DART impacts on Dimorphos. J.M.S. and T.L.F. offered overall guidance on this project and gave interpretations of the ejecta plume evolution. J.D.P.D. shared insights into ejecta plume geometry based on LICIACube data. G.T. offered interpretations of ejecta plume geometry. S.R.C., R.T.D., C.M.E., I.G., S.P.N., H.N., E.E.P, C.D.W., and A.Z. developed the mission- driven data necessary for this work. H.F.A., B.W.B., M.B.S., G.S.C., T.M.D., M.E.D., M.J., K.M.K., N.A.M., J.R.L., and S.R.S. reviewed the techniques used in this work to assess their validity. P.A.A., O.S.B., N.L.C., A.F.C., E.D., E.G.F., P.M., D.C.R., A.S.R., A.M.S., and C.A.T. are the leadership members of DART, LICIACube, and Hera, performing project management and execution and giving advice and comments on this work from mission level. R.T.D., B.W.B., M.B.S., J.R.L., and N.L.C. also gave advice on how to connect this work with planetary defense. J.B., J.R.B., M.D.'O., V.D.C., E.M.E., S.I., G.I., S.I., A.L., D.M., M.P., P.P., S.P., G.P., A.R., P.T., F.T., M.Z., and G.Z. contributed to LICIACube data analysis and advised on how to interpret the data. F.F., D.A.G., I.H., S.A.J., Ö.K., M.L., R.L., M.P.L., R.M., F.M., C.C.M., A.M., R.N., J.O., P.S., C.B.S., S.S., and T.J.S. reviewed the present study. All contributed to the manuscript development.  
+
+## Competing interests  
+
+Authors do not have both financial and non- financial competing interests.  
+
+## Materials & Correspondence  
+
+Geometry factor data and related numerical packages for analysis of both Dimorphos and MAMOS samples will be publicly available before the publication of this work. Further correspondence and material requests should be addressed to M.H., the corresponding author.
+
+<--- Page Split --->
+
+## Supplementary Files  
+
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+- MASIHirabayashi.pdf
+
+<--- Page Split --->

preprint/preprint__c8ea0fd9793775451b1580cefcf4cd08c8dfd9b2baff1b29377d0ff48c5d5b10/preprint__c8ea0fd9793775451b1580cefcf4cd08c8dfd9b2baff1b29377d0ff48c5d5b10_det.mmd

@@ -0,0 +1,749 @@
+<|ref|>title<|/ref|><|det|>[[44, 106, 835, 175]]<|/det|>
+# Kinetic deflection change due to target global curvature as revealed by NASA/DART  
+
+<|ref|>text<|/ref|><|det|>[[44, 195, 308, 240]]<|/det|>
+Masatoshi Hirabayashi  thirabayashi@gatech.edu  
+
+<|ref|>text<|/ref|><|det|>[[50, 268, 690, 288]]<|/det|>
+Georgia Institute of Technology https://orcid.org/0000- 0002- 1821- 5689  
+
+<|ref|>text<|/ref|><|det|>[[44, 293, 576, 335]]<|/det|>
+Sabina Raducan  University of Bern https://orcid.org/0000- 0002- 7478- 0148  
+
+<|ref|>text<|/ref|><|det|>[[44, 340, 253, 381]]<|/det|>
+Jessica Sunshine  University of Maryland  
+
+<|ref|>text<|/ref|><|det|>[[44, 387, 725, 428]]<|/det|>
+Tony Farnham  University of Maryland College Park https://orcid.org/0000- 0002- 4767- 9861  
+
+<|ref|>text<|/ref|><|det|>[[44, 433, 231, 472]]<|/det|>
+Prasanna Deshapriya  INAF  
+
+<|ref|>text<|/ref|><|det|>[[44, 479, 650, 520]]<|/det|>
+Jian- Yang Li  Planetary Science Institute https://orcid.org/0000- 0003- 3841- 9977  
+
+<|ref|>text<|/ref|><|det|>[[44, 525, 572, 566]]<|/det|>
+Gonzalo Tancredi  Facultad Ciencias https://orcid.org/0000- 0002- 4943- 8623  
+
+<|ref|>text<|/ref|><|det|>[[44, 571, 180, 590]]<|/det|>
+Steven Chesley  
+
+<|ref|>text<|/ref|><|det|>[[44, 592, 936, 612]]<|/det|>
+Jet Propulsion Laboratory, California Institute of Technology https://orcid.org/0000- 0003- 3240- 6497  
+
+<|ref|>text<|/ref|><|det|>[[44, 617, 150, 636]]<|/det|>
+Ronald Daly  
+
+<|ref|>text<|/ref|><|det|>[[44, 639, 880, 659]]<|/det|>
+Johns Hopkins University Applied Physics Laboratory https://orcid.org/0000- 0002- 1320- 2985  
+
+<|ref|>text<|/ref|><|det|>[[44, 664, 162, 682]]<|/det|>
+Carolyn Ernst  
+
+<|ref|>text<|/ref|><|det|>[[44, 685, 880, 705]]<|/det|>
+Johns Hopkins University Applied Physics Laboratory https://orcid.org/0000- 0002- 9434- 7886  
+
+<|ref|>text<|/ref|><|det|>[[44, 710, 240, 750]]<|/det|>
+Igor Gai  University of Bologna  
+
+<|ref|>text<|/ref|><|det|>[[44, 755, 410, 796]]<|/det|>
+Pedro Hasselmann  INAF- Osservatorio Astronomico di Roma  
+
+<|ref|>text<|/ref|><|det|>[[44, 802, 185, 820]]<|/det|>
+Shantanu Naidu  
+
+<|ref|>text<|/ref|><|det|>[[44, 823, 936, 844]]<|/det|>
+Jet Propulsion Laboratory, California Institute of Technology https://orcid.org/0000- 0003- 4439- 7014  
+
+<|ref|>text<|/ref|><|det|>[[44, 849, 123, 867]]<|/det|>
+Hari Nair  
+
+<|ref|>text<|/ref|><|det|>[[50, 870, 521, 890]]<|/det|>
+Johns Hopkins University Applied Physics Laboratory  
+
+<|ref|>text<|/ref|><|det|>[[44, 895, 140, 913]]<|/det|>
+Eric Palmer  
+
+<|ref|>text<|/ref|><|det|>[[50, 917, 446, 936]]<|/det|>
+PSI https://orcid.org/0000- 0001- 6755- 8736  
+
+<|ref|>text<|/ref|><|det|>[[44, 942, 123, 960]]<|/det|>
+C. Waller
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[50, 45, 521, 66]]<|/det|>
+Johns Hopkins University Applied Physics Laboratory  
+
+<|ref|>text<|/ref|><|det|>[[44, 71, 510, 112]]<|/det|>
+Angelo Zinzi ASI- SSDC https://orcid.org/0000- 0001- 5263- 5348  
+
+<|ref|>text<|/ref|><|det|>[[44, 118, 771, 160]]<|/det|>
+Harrison Agrusa Universite Cote d'Azur, Observatoire de la Cote d'Azur, CNRS, Laboratoire Lagrange  
+
+<|ref|>text<|/ref|><|det|>[[44, 164, 525, 205]]<|/det|>
+Brent Barbee NASA/GSFC https://orcid.org/0000- 0003- 3739- 3242  
+
+<|ref|>text<|/ref|><|det|>[[44, 210, 587, 252]]<|/det|>
+M. Bruck Syal Lawrence Livermore National Laboratory, Livermore, CA, USA  
+
+<|ref|>text<|/ref|><|det|>[[44, 256, 630, 298]]<|/det|>
+Gareth Collins Imperial College London https://orcid.org/0000- 0002- 6087- 6149  
+
+<|ref|>text<|/ref|><|det|>[[44, 302, 630, 344]]<|/det|>
+Thomas Davison Imperial College London https://orcid.org/0000- 0001- 8790- 873X  
+
+<|ref|>text<|/ref|><|det|>[[44, 348, 880, 391]]<|/det|>
+Mallory DeCoster Johns Hopkins University Applied Physics Laboratory https://orcid.org/0000- 0002- 1139- 9235  
+
+<|ref|>text<|/ref|><|det|>[[44, 395, 216, 436]]<|/det|>
+Martin Jutzi University of Bern  
+
+<|ref|>text<|/ref|><|det|>[[44, 441, 770, 483]]<|/det|>
+Kathryn Kumamoto Lawrence Livermore National Laboratory https://orcid.org/0000- 0002- 0400- 6333  
+
+<|ref|>text<|/ref|><|det|>[[44, 487, 225, 528]]<|/det|>
+Nicholas Moskovitz Lowell Observatory  
+
+<|ref|>text<|/ref|><|det|>[[44, 533, 521, 575]]<|/det|>
+Joshua Lyzhoft NASA GSFC https://orcid.org/0000- 0001- 6420- 8423  
+
+<|ref|>text<|/ref|><|det|>[[44, 580, 290, 621]]<|/det|>
+Stephen Schwartz Planetary Science Institute  
+
+<|ref|>text<|/ref|><|det|>[[44, 626, 368, 667]]<|/det|>
+Paul Abell NASA/Goddard Space Flight Center  
+
+<|ref|>text<|/ref|><|det|>[[44, 672, 880, 714]]<|/det|>
+Olivier Barnouin Johns Hopkins University Applied Physics Laboratory https://orcid.org/0000- 0002- 3578- 7750  
+
+<|ref|>text<|/ref|><|det|>[[44, 718, 880, 760]]<|/det|>
+Nancy Chabot Johns Hopkins University Applied Physics Laboratory https://orcid.org/0000- 0001- 8628- 3176  
+
+<|ref|>text<|/ref|><|det|>[[44, 764, 880, 807]]<|/det|>
+Andy Cheng Johns Hopkins University Applied Physics Laboratory https://orcid.org/0000- 0001- 5375- 4250  
+
+<|ref|>text<|/ref|><|det|>[[44, 811, 504, 852]]<|/det|>
+Elisabetta Dotto INAF- OAR https://orcid.org/0000- 0002- 9335- 1656  
+
+<|ref|>text<|/ref|><|det|>[[44, 857, 580, 899]]<|/det|>
+Eugene Fahnestock Jet Propulsion Laboratory, California Institute of Technology  
+
+<|ref|>text<|/ref|><|det|>[[44, 903, 170, 922]]<|/det|>
+Patrick Michel
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[50, 45, 777, 88]]<|/det|>
+Université Côte d'Azur, Observatoire de la Côte d'Azur, CNRS, Laboratoire Lagrange https://orcid.org/0000-0002-0884-1993 
+
+<|ref|>text<|/ref|><|det|>[[44, 95, 884, 137]]<|/det|>
+**Derek Richardson**
+Department of Astronomy, University of Maryland  https://orcid.org/0000-0002-0054-6850 
+
+<|ref|>text<|/ref|><|det|>[[44, 142, 880, 185]]<|/det|>
+**Andrew Rivkin**
+Johns Hopkins University Applied Physics Laboratory  https://orcid.org/0000-0002-9939-9976 
+
+<|ref|>text<|/ref|><|det|>[[44, 189, 523, 230]]<|/det|>
+**Angela Stickle**
+Johns Hopkins University Applied Physics Laboratory 
+
+<|ref|>text<|/ref|><|det|>[[44, 235, 656, 277]]<|/det|>
+**Cristina Thomas**
+Northern Arizona University  https://orcid.org/0000-0003-3091-5757 
+
+<|ref|>text<|/ref|><|det|>[[44, 281, 430, 323]]<|/det|>
+**Joel Beccarelli**
+INAF-Osservatorio Astronomico di Padova 
+
+<|ref|>text<|/ref|><|det|>[[44, 328, 460, 369]]<|/det|>
+**John Brucato**
+INAF  https://orcid.org/0000-0002-4738-5521 
+
+<|ref|>text<|/ref|><|det|>[[44, 374, 196, 415]]<|/det|>
+**Massimo Dallora**
+INAF 
+
+<|ref|>text<|/ref|><|det|>[[44, 421, 230, 462]]<|/det|>
+**Vincenzo Della Corte**
+INAF 
+
+<|ref|>text<|/ref|><|det|>[[44, 468, 412, 509]]<|/det|>
+**Elena Mazzotta Epifani**
+INAF-Osservatorio Astronomico di Roma 
+
+<|ref|>text<|/ref|><|det|>[[44, 515, 772, 556]]<|/det|>
+**Simone Ieva**
+INAF-Osservatorio Astronomico di Roma  https://orcid.org/0000-0001-8694-9038 
+
+<|ref|>text<|/ref|><|det|>[[44, 561, 447, 602]]<|/det|>
+**Gabriele Impresario**
+ASI  https://orcid.org/0000-0001-8984-4231 
+
+<|ref|>text<|/ref|><|det|>[[44, 608, 432, 648]]<|/det|>
+**Stavro Ivanovski**
+INAF - Osservatorio Astronomico di Trieste 
+
+<|ref|>text<|/ref|><|det|>[[44, 654, 796, 695]]<|/det|>
+**Alice Lucchetti**
+INAF - Osservatorio Astronomico di Padova  https://orcid.org/0000-0001-7413-3058 
+
+<|ref|>text<|/ref|><|det|>[[44, 700, 806, 741]]<|/det|>
+**Dario Modenini**
+Alma Mater Studiorum, Università di Bologna  https://orcid.org/0000-0002-1517-3938 
+
+<|ref|>text<|/ref|><|det|>[[44, 746, 796, 787]]<|/det|>
+**Maurizio Pajola**
+INAF - Astronomical Observatory of Padova  https://orcid.org/0000-0002-3144-1277 
+
+<|ref|>text<|/ref|><|det|>[[44, 792, 490, 833]]<|/det|>
+**Pasquale Palumbo**
+INAF-Istituto di Astrofisica e Planetologia Spaziali 
+
+<|ref|>text<|/ref|><|det|>[[44, 838, 448, 879]]<|/det|>
+**Simone Pirrotta**
+ASI  https://orcid.org/0000-0003-0377-8937 
+
+<|ref|>text<|/ref|><|det|>[[44, 885, 758, 926]]<|/det|>
+**Giovanni Poggiali**
+INAF Arcetri Astrophysical Observatory  https://orcid.org/0000-0002-3239-1697 
+
+<|ref|>text<|/ref|><|det|>[[44, 931, 201, 949]]<|/det|>
+**Alessandro Rossi**
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[52, 45, 500, 64]]<|/det|>
+IFAC-CNR https://orcid.org/0000-0001-9311-2869  
+
+<|ref|>text<|/ref|><|det|>[[44, 70, 600, 110]]<|/det|>
+Paolo Tortora Università di Bologna https://orcid.org/0000- 0001- 9259- 7673  
+
+<|ref|>text<|/ref|><|det|>[[44, 116, 516, 157]]<|/det|>
+Filippo Tusberti INAF- OAPd https://orcid.org/0000- 0002- 9290- 1679  
+
+<|ref|>text<|/ref|><|det|>[[44, 163, 600, 204]]<|/det|>
+Marco Zannoni Università di Bologna https://orcid.org/0000- 0002- 4151- 9656  
+
+<|ref|>text<|/ref|><|det|>[[44, 209, 600, 250]]<|/det|>
+Giovanni Zanotti Politecnico di Milano https://orcid.org/0000- 0002- 3157- 7588  
+
+<|ref|>text<|/ref|><|det|>[[44, 255, 954, 319]]<|/det|>
+Fabio Ferrari Department of Aerospace Science and Technology, Politecnico di Milano https://orcid.org/0000- 0001- 7537- 4996  
+
+<|ref|>text<|/ref|><|det|>[[44, 325, 622, 366]]<|/det|>
+David Glenar Center for Space Science and Technology, University of Maryland  
+
+<|ref|>text<|/ref|><|det|>[[44, 371, 919, 435]]<|/det|>
+M.I. Herreros Centro de Astrobiología (CAB), CSIC- INTA, Carretera de Ajalvir km4, 28850 Torrejón de Ardoz, Spain https://orcid.org/0000- 0001- 5284- 8060  
+
+<|ref|>text<|/ref|><|det|>[[44, 440, 637, 481]]<|/det|>
+Seth Jacobson Michigan State University https://orcid.org/0000- 0002- 4952- 9007  
+
+<|ref|>text<|/ref|><|det|>[[44, 486, 315, 527]]<|/det|>
+Ozgur Karatekin Royal Observatory of Belgium  
+
+<|ref|>text<|/ref|><|det|>[[44, 533, 237, 574]]<|/det|>
+Monica Lazzarin University of Padova  
+
+<|ref|>text<|/ref|><|det|>[[44, 579, 771, 620]]<|/det|>
+Ramin Lolachi University of Maryland, Baltimore County https://orcid.org/0000- 0001- 5764- 7639  
+
+<|ref|>text<|/ref|><|det|>[[44, 625, 275, 666]]<|/det|>
+Michael Lucas University of Notre Dame  
+
+<|ref|>text<|/ref|><|det|>[[44, 671, 781, 713]]<|/det|>
+Rahil Makadia University of Illinois at Urbana- Champaign https://orcid.org/0000- 0001- 9265- 2230  
+
+<|ref|>text<|/ref|><|det|>[[44, 718, 237, 758]]<|/det|>
+Francesco Marzari Universita di Padova  
+
+<|ref|>text<|/ref|><|det|>[[44, 764, 570, 805]]<|/det|>
+Colby Merrill Cornell University https://orcid.org/0000- 0002- 5566- 0618  
+
+<|ref|>text<|/ref|><|det|>[[44, 810, 841, 875]]<|/det|>
+Alessandra Migliorini Istituto Nazionale di AstroFisica - Istituto di Astrofisica e Planetologia Spaziali (INAF- IAPS) https://orcid.org/0000- 0001- 7386- 9215  
+
+<|ref|>text<|/ref|><|det|>[[44, 880, 330, 921]]<|/det|>
+Ryota Nakano Georgia Institute of Technology  
+
+<|ref|>text<|/ref|><|det|>[[44, 926, 142, 944]]<|/det|>
+Jens Ormö
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[55, 45, 373, 64]]<|/det|>
+Centro de Astrobiología (CSIC- INTA)  
+
+<|ref|>text<|/ref|><|det|>[[44, 70, 681, 111]]<|/det|>
+Paul Sánchez  University of Colorado Boulder https://orcid.org/0000- 0003- 3610- 5480  
+
+<|ref|>text<|/ref|><|det|>[[44, 116, 675, 159]]<|/det|>
+Cem Senel  Royal Observatory of Belgium https://orcid.org/0000- 0002- 7677- 9597  
+
+<|ref|>text<|/ref|><|det|>[[44, 163, 825, 227]]<|/det|>
+Stefania Soldini  Department of Mechanical, Materials and Aerospace Engineering, University of Liverpool https://orcid.org/0000- 0003- 3121- 3845  
+
+<|ref|>text<|/ref|><|det|>[[44, 232, 365, 274]]<|/det|>
+Timothy Stubbs  NASA Goddard Space Flight Center  
+
+<|ref|>text<|/ref|><|det|>[[44, 313, 275, 333]]<|/det|>
+Physical Sciences - Article  
+
+<|ref|>text<|/ref|><|det|>[[44, 351, 137, 370]]<|/det|>
+Keywords:  
+
+<|ref|>text<|/ref|><|det|>[[44, 389, 330, 409]]<|/det|>
+Posted Date: January 16th, 2024  
+
+<|ref|>text<|/ref|><|det|>[[44, 427, 474, 448]]<|/det|>
+DOI: https://doi.org/10.21203/rs.3.rs- 3598104/v1  
+
+<|ref|>text<|/ref|><|det|>[[42, 465, 914, 508]]<|/det|>
+License: © © This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License  
+
+<|ref|>text<|/ref|><|det|>[[42, 525, 535, 546]]<|/det|>
+Additional Declarations: There is NO Competing Interest.  
+
+<|ref|>text<|/ref|><|det|>[[42, 580, 950, 624]]<|/det|>
+Version of Record: A version of this preprint was published at Nature Communications on February 14th, 2025. See the published version at https://doi.org/10.1038/s41467- 025- 56010-w.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[115, 91, 196, 106]]<|/det|>
+## Author list  
+
+<|ref|>text<|/ref|><|det|>[[112, 123, 300, 895]]<|/det|>
+Masatoshi Hirabayashi,1,2 Sabina D. Raducan,3 Jessica M. Sunshine,4 Tony L. Farnham,4 J. D. Prasanna Deshapriya,5 Jian- Yang Li,6 Gonzalo Tancredi,7 Steven R. Chesley,8 R. Terik Daly,9 Carolyn M. Ernst,9 Igor Gai,10 Pedro H. Hasselmann,5 Shantanu P. Naidu,8 Hari Nair,9 Eric E. Palmer,6 C. Dany Waller,9 Angelo Zinzi,11,12 Harrison F. Agrusa,13,3 Brent W. Barbee,14 Megan Bruck Syal,15 Gareth S. Collins,16 Thomas M. Davison,16 Mallory E. DeCoster,9 Martin Jutzi,3 Kathryn M. Kumamoto,15 Nicholas A. Moskovitz,17 Joshua R. Lyzhof,14 Stephen R. Schwartz,6,18 Paul A. Abell,19 Olivier S. Barnouin,9 Nancy L. Chabot,9 Andrew F. Cheng,9 Elisabetta Dotto,5 Eugene G. Fahnestock,8 Patrick Michel,13,20 Derek C. Richardson,3 Andrew S. Rivkin,9 Angela M. Stickle,9 Cristina A. Thomas,21 Joel Beccarelli,22 John R. Brucato,23 Massimo Dall'Ora,24
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[112, 88, 290, 712]]<|/det|>
+Vincenzo Della Corte,24 Elena Mazzotta Epifani,5 Simone leva,5 Gabriele Impresario,11 Stavro Ivanovski,25 Alice Lucchetti,22 Dario Modenini,26 Maurizio Pajola,22 Pasquale Palumbo,27 Simone Pirrotta,11 Giovanni Poggiali,23 Alessandro Rossi,28 Paolo Tortora,26 Filippo Tusberti,22 Marco Zannoni,26 Giovanni Zanotti,29 Fabio Ferrari,29 David A. Glenar,30,14 Isabel Herreros,31 Seth A. Jacobson,32 Özgür Karatekin,33 Monica Lazzarin,34 Ramin Lolachi,30,14 Michael P. Lucas,35 Rahil Makadia,36 Francesco Marzari,34 Colby C. Merrill,37 Alessandra Migliorini,27 Ryota Nakano,1,2 Jens Ormö,31 Paul Sánchez,38 Cem Berk Senel,33,39 Stefania Soldini,40 Timothy J. Stubbs,14
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[112, 90, 838, 660]]<|/det|>
+10Università di Bologna, Bologna, Italy 11Agenzia Spaziale Italiana (ASI), Roma, Italy 12Space Science Data Center, ASI, Roma, Italy 13Université Côte d'Azur, Observatoire de la Côte d'Azur, CNRS, Laboratoire Lagrange, Nice, France 14NASA/Goddard Space Flight Center, Greenbelt, MD, USA 15Lawrence Livermore National Laboratory, Livermore, CA, USA 16Imperial College London, London, UK 17Lowell Observatory, Flagstaff, AZ, USA 18Universidad de Alicante, Alicante, Spain 19NASA Johnson Space Center, Houston, TX, USA 20The University of Tokyo, Tokyo, Japan 21Northern Arizona University, Flagstaff, AZ, USA 22INAF-Osservatorio Astronomico di Padova, Padova, Italy 23INAF-Osservatorio Astronomico di Arcetri, Firenze, Italy 24INAF-Osservatorio Astronomico di Capodimonte, Napoli, Italy 25INAF-Osservatorio Astronomico di Trieste, Trieste, Italy 26Alma Mater Studiorum - Università di Bologna, Forlì, Italy 27INAF-Istituto di Astrofisica e Planetologia Spaziali, Roma, Italy 28IFAC-Istituto di fisica applicata Nello Carrara, Sesto Fiorentino, Italy 29Politecnico di Milano, Milano, Italy 30University of Maryland, Baltimore, MD, USA 31Centro de Astrobiologia (CAB), CSIC-INTA, Madrid, Spain 32Michigan State University, MI, USA 33Royal Observatory of Belgium, Brussels, Belgium 34Università di Padova, Padova, Italy 35University of Notre Dame, Notre Dame, IN, USA 36University of Illinois at Urbana-Champaign, Urbana IL, USA 37Cornell University, Ithaca, NY, USA 38University of Colorado Boulder, Boulder, CO, USA 39Vrije Universiteit Brussel, Brussels, Belgium 40University of Liverpool, Liverpool, UK  
+
+<|ref|>text<|/ref|><|det|>[[115, 673, 717, 691]]<|/det|>
+To whom correspondence should be addressed; E- mail: thirabayashi@gatech.edu.
+
+<--- Page Split --->
+<|ref|>title<|/ref|><|det|>[[90, 74, 797, 135]]<|/det|>
+# Kinetic deflection change due to target global curvature as revealed by NASA/DART  
+
+<|ref|>text<|/ref|><|det|>[[90, 145, 376, 164]]<|/det|>
+Author list attached separately  
+
+<|ref|>sub_title<|/ref|><|det|>[[90, 186, 219, 208]]<|/det|>
+## ABSTRACT  
+
+<|ref|>text<|/ref|><|det|>[[94, 225, 905, 397]]<|/det|>
+Kinetic deflection is a planetary defense technique that delivers spacecraft momentum to a small body to deviate its course from Earth. The deflection efficiency depends strongly on the impactor and target. Among them, the contribution of global curvature was poorly understood. The ejecta plume created by NASA's DART impact on its target asteroid, Dimorphos, exhibited an elliptical shape almost aligned along its north- south direction. Here, we identify that this elliptical ejecta plume resulted from the target's curvature, reducing the momentum transfer to \(44 \pm 10\%\) along the orbit track compared to an equivalent impact on a flat target. We also find lower kinetic deflection of impacts on smaller Near- Earth objects (NEOs) due to higher curvature. A solution to mitigate low deflection efficiency is to apply multiple low- energy impactors rather than a single high- energy impactor. Rapid reconnaissance to acquire a target's properties before deflection enables determining the proper locations and timing of impacts.  
+
+<|ref|>sub_title<|/ref|><|det|>[[90, 430, 207, 452]]<|/det|>
+## Main texts  
+
+<|ref|>text<|/ref|><|det|>[[88, 460, 910, 664]]<|/det|>
+Planetary defense is an international effort to mitigate threats of small body collisions with Earth \(^{1,2}\) . Among its key planetary defense technologies is kinetic deflection, in which a spacecraft collides with a hazardous body to change its trajectory and eliminate or reduce the risk of its impact on Earth \(^{3}\) . Kinetic deflection is a practical approach when targets are less than \(\sim 500 \mathrm{~m}\) in radius if the encounter with Earth is several decades in the future \(^{1 - 4}\) . In contrast, NEOs less than \(50 \mathrm{~m}\) in radius are the most probable threat and high- priority targets for rapid reconnaissance flyby missions \(^{1 - 4}\) . The momentum transfer enhancement factor, known as \(\beta\) , is a well- used parameter, in its simplest form, the total momentum imparted to the target by the spacecraft and ejecta normalized by its momentum before impact \(^{5 - 7}\) . Recent impact physics studies suggest the dependence of \(\beta\) on the impactor's properties and orientation and the target's composition and strength \(^{8 - 15}\) . However, how a target's global curvature controls kinetic deflection remains poorly constrained.  
+
+<|ref|>text<|/ref|><|det|>[[88, 664, 910, 921]]<|/det|>
+NASA's Double Asteroid Redirection Test (DART) mission was the first full- scale planetary defense demonstration mission that deliberately crashed a spacecraft into Dimorphos, the smaller satellite of the binary system (65803) Didymos \(^{16}\) . The measured \(\beta\) ranged between 2.2 and 4.9 (depending on the bulk density, which remains unknown but will be constrained by ESA's Hera mission \(^{17}\) ); for a bulk density of \(2.4 \mathrm{~g / cc}\) , \(\beta\) was determined to be \(3.61_{- 0.25}^{+0.1918}\) . A recent study using images from the Hubble Space Telescope and LICIACube determined that the ejecta cone geometry was elliptic \(^{19}\) . The parameters representing the ejecta cone geometry include the wide- cone opening angle, \(\theta_{1}\) , the narrow- cone opening angle, \(\theta_{2}\) , the azimuthal angle from Dimorphos's north at the impact site defining the wide- cone orientation, \(\phi\) , and the cone axis direction described using Right Ascension, \(RA\) , and Declination, \(DEC\) (Figure 1). The J2000 International Celestial Reference System (later known as J2000) is the baseline coordinate frame defining the cone axis direction, \(RA\) and \(DEC\) . Their solutions with \(1\sigma\) uncertainties were \(\theta_{1} = 133 \pm 9^{\circ}\) , \(\theta_{2} = 95 \pm 6^{\circ}\) , \(\phi = 26 \pm 16^{\circ}\) , \(RA = 141 \pm 4^{\circ}\) , and \(DEC = +20 \pm 8^{\circ}\) , and the ejecta cone's tip (apex) as \((- 4 \pm 6, - 3 \pm 9, 9 \pm 10) \mathrm{~m}\) in the Dimorphos- fixed frame, later known as IAU_DIMORPHOS (Figure 1). These results are consistent with independent work within uncertainties \(^{20}\) .
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[85, 102, 912, 750]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[88, 758, 911, 888]]<|/det|>
+<center>Figure 1. Ejecta cone and impact cratering flow fields. The arrows in light blue show \((x^{\prime},y^{\prime},z^{\prime})\) in J2000, while those in green \((x,y,z)\) are IAU_DIMORPHOS. The arrows in red give the local frame at the impact site. \(z^{\prime \prime}\) is the DART impact direction, \(x^{\prime \prime}\) is orthogonal to Dimorphos's north and \(z^{\prime \prime}\) , and \(y^{\prime \prime}\) is orthogonal to these axes. A and B. Cone geometry and Dimorphos. The cone's perimeter defines its edge. C. Slice in light red representing a plane used for the Maxwell Z-model. The red curve over Dimorphos represents the intersection between the body and the slicing plane. D. Illustrations of streamlines defined as \(SL\) . An example streamtube is a region between \(SL1\) and \(SL2\) . </center>
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[89, 78, 910, 281]]<|/det|>
+We use the geometric parameters \(^{19}\) to compute the net geometric factor, \(P_{fl}\) , the ratio of the ejecta momentum on a curved surface target to that on a flat surface (Methods). We apply the Maxwell Z- model to quantify the kinematics of subsurface flow fields and ejecta's ballistic trajectories (Methods). This empirical model applies two kinematic parameters, \(\alpha\) and \(Z\) , representing ejecta's speed and geometry, respectively. We introduce a scalar factor, \(\gamma\) , to use the measured \(\beta\) as a constraint and determine \(P_{fl}\) (Methods). Comparison tests confirm that our approach gives geometric factors consistent with those determined by the iSALE shock- physics code \(^{21 - 24}\) (Methods). Monte Carlo simulations input the cone geometry measurements \((\theta_{1}, \theta_{2}, RA, DEC, \phi)\) to give the azimuthal variations in \(\alpha\) , \(Z\) , and geometric factor (Figure 2). The derived mean value of \(Z = 2.9 \pm 0.4\) is consistent with those observed for a flat surface \(^{25}\) and the ideal case, i.e., \(Z = 3^{26}\) . Similarly, with the \(Z\) value, the mean value of \(\alpha = 3.1 \times 10^{- 4} \mathrm{~hm}^{(Z + 1)} / \mathrm{s}\) offers a transient crater radius of \(\sim 86 \mathrm{~m}\) , which is within the predicted value \(^{27}\) .  
+
+<|ref|>text<|/ref|><|det|>[[89, 282, 910, 464]]<|/det|>
+The geometric factor variation along \(\phi\) , \(P_{fl\phi}\) , becomes lower but more variable along the wide cone direction (Figure 2D). The east- west direction \((\phi \sim \pm 90^{\circ})\) tends to have higher \(P_{fl\phi}\) with lower uncertainties. This direction offers a flatter surface, providing positive momentum transfer and, thus, positive \(P_{fl\phi}\) . On the other hand, because of high curvature approximately along the north- south direction \((\phi \sim 0^{\circ}, \pm 180^{\circ})\) , ejected materials tend to depart toward Dimorphos's anti- along track direction. The Dimorphos- south direction \((\phi \sim \pm 180^{\circ})\) tends to have negative \(P_{fl\phi}\) , indicating ejecta's contribution to negative momentum transfer. The ejecta cone's slight twist causes the shift of lower \(P_{fl\phi}\) towards positive \(\phi\) by \(\sim 45^{\circ}\) . The net geometric factor, \(P_{fl}\) , is \(44 \pm 10\%\) for Dimorphos. If the target surface is flat, the derived geometric factor leads to \(\beta = 6.9 \pm 3.5(1\sigma)\) within its predicted range \(^{28}\) , improving almost by a factor of \(\sim 2\) .  
+
+<|ref|>text<|/ref|><|det|>[[89, 465, 910, 720]]<|/det|>
+The derived low geometric factor results from Dimorphos's higher curvature in its north- south direction. Based on the asteroid's pre- impact extents, the ratio of the semi- minor axis to the semi- major axis is \(0.64^{16}\) . However, regardless of Dimorphos's high curvature, the typical values of \(Z\) for a flat surface target \(^{26}\) can reproduce the elliptical cone geometry along all azimuthal directions. Because the higher curvature in its north- south direction causes a shorter excavation range, the flow fields beneath the surface are short- lived. Excavated materials cannot change their flow directions before launch well enough to achieve a higher ejection angle from the surface. Such trends are so extreme in some directions that ejecta momenta possess anti- along track components, giving negative momentum transfer (Figure 2D). These mechanisms noticeably reduce the net momentum transfer and result from the impact location in the southern hemisphere, inferring the sensitivity of the kinetic deflection efficiency to global curvature. If the DART impact- driven crater were small relative to Dimorphos's size, local morphological features would be more influential than global curvature. Local topography may generate the observed clumps and boulders ejected from Dimorphos; however, they did not contribute to the along- track momentum transfer component \(^{29}\) .  
+
+<|ref|>text<|/ref|><|det|>[[89, 721, 910, 921]]<|/det|>
+We further quantify how \(P_{fl}\) changes due to the impact locations for 103 NEOs less than \(50 \mathrm{~m}\) in radius observed by the MANOS (Mission Accessible Near- Earth Objects Survey) project \(^{30}\) . Given limited constraints, we assume each sample to be a prolate body with identical semi- intermediate and semi- minor axes (Methods). For each body, we consider two impact locations: one along the semi- major axis and the other along the semi- minor axis. Because the impacts at both locations are vertical to the local surface, the impact point along the semi- major axis has higher curvature. Figure 3 shows the distributions of the samples' \(P_{fl\phi}\) . This parameter positively correlates with the target radius and strength (Figure 3A). Given a constant impact energy identical to the DART impact, higher strength and larger size make the crater radius small relative to the body \(^{31}\) , reducing the curvature effect and thus making \(P_{flT}\) higher. The transition zone from zero geometric factors \((= 0\%)\) to high geometric factors \((> \sim 70\%)\) is narrow. This zone also overlaps the predicted catastrophic disruption threshold, which defines an impact condition
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[90, 210, 884, 701]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[88, 710, 895, 785]]<|/det|>
+<center>Figure 2. Variations in Maxwell Z-model parameters and projected cone geometry onto Dimorphos's surface with azimuthal angle from Dimorphos's north. A. Variations in Z. B. Variations in \(\alpha\) . C. Variations in excavation range, which plots \(r_{E}^{*}\) (Figure 1). D. Variations in geometric factor along each piece in an azimuthal direction. Uncertainties are provided in \(1\sigma\) . </center>
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[103, 82, 890, 323]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[88, 332, 904, 534]]<|/det|>
+<center>Figure 3. Geometric factor distributions of 103 small NEOs measured by the MANOS project<sup>30</sup>. A. Geometric factor of an impact along each target's semi-minor axis. B. Relative geometric factor of an impact along the semi-major axis to one along the semi-minor axis. Specifically, the relative geometric factor defines the geometric factor along the semi-major axis minus that along the semi-minor axis. All panels give the geometric factor distributions in percentile as a function of diameter and minimum strength. All negative outcomes in Panel A are truncated and noted as zero geometric factors. The curves in different colors show interpolations between the catastrophic disruption thresholds for a pumice-like target and a cohesionless target (red) and a basalt-like target and a cohesionless target (blue). For the cohesionless target, we assume a minimal strength of 0.01 Pa. The dashed, solid, and dotted lines give bulk densities of \(1000\mathrm{kg / m}^3\) , \(2000\mathrm{kg / m}^3\) , and \(4000\mathrm{kg / m}^3\) . If target asteroids stay on the right side of those thresholds, they do not experience catastrophic disruption. </center>  
+
+<|ref|>text<|/ref|><|det|>[[89, 569, 908, 642]]<|/det|>
+when the final target mass is less than half the original (Methods). Figure 3C shows the distribution of the relative geometric factor, defined as the difference between an impact along the semi- major axis and an impact along the semi- minor axis. The results show lower relative geometric factors along the semi- major axis than the semi- minor axis for all samples.  
+
+<|ref|>text<|/ref|><|det|>[[88, 648, 910, 922]]<|/det|>
+Our finding suggests that scenarios employing a single impactor having higher kinetic energy are not ideal (Figure 4). The increase in the encounter speed is reported to make such single impacts with high kinetic energy more feasible<sup>32</sup>. Another concept may be to disrupt a target body as part of kinetic deflection<sup>33</sup>. However, the efficiency of momentum transfer changes due to global curvature. A flatter surface target offers higher momentum transfer for a single impact with a given kinetic energy due to higher changes in the subsurface flow fields. Alternatively, a lower kinetic energy impactor results in a smaller crater, less affected by global curvature, increasing the momentum transfer efficiency. With these trends to enhance momentum transfer, employing multiple, smaller impactors is a better solution than having a single, large impactor. In the multiple- impactor scenario, each impactor has a smaller kinetic energy than one in the single- impactor scenario. Still, the net kinetic energy can be comparable when all impactors collide with the target. Practically, the multiple- impactor scenario can send impactors at different times and aim at flatter surface points on the target, maximizing the net momentum transfer (Figure 4). However, the crater size should not be too small because local boulders and topography can become more influential on the ejecta plume formation, as seen by earlier experimental tests<sup>34</sup>, changing the trends of momentum transfer. This condition applies to Deep Impact and Hayabusa2, which observed
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[90, 78, 330, 97]]<|/det|>
+complex ejecta formation \(^{35,36}\) .  
+
+<|ref|>text<|/ref|><|det|>[[88, 97, 911, 281]]<|/det|>
+Constraining all essential physical properties of a target object before kinetic impact is valuable. While no details have been reported for global curvature \(^{4}\) in the past, our study proposes it as a key contributor that can easily change the efficiency by a factor of a few. The practical approach is to visit the object in situ and conduct key measurements as much as possible before deciding the timing of kinetic deflection. A rapid response to this demand after identifying a potential threat is not yet a mature technology \(^{4}\) . Compared to mass measurement, which requires additional operational constraints, imaging the target even during a fast flyby can provide sufficient information to infer the curvature and surface conditions, significantly improving the accuracy of momentum transfer. Demonstrating capabilities to acquire such properties by a rapid reconnaissance mission is strategic to achieving sophisticated advances in kinetic deflection technologies.  
+
+<|ref|>sub_title<|/ref|><|det|>[[89, 300, 189, 321]]<|/det|>
+## Methods  
+
+<|ref|>sub_title<|/ref|><|det|>[[89, 329, 391, 348]]<|/det|>
+## Formulation of Maxwell Z-model  
+
+<|ref|>text<|/ref|><|det|>[[88, 349, 907, 387]]<|/det|>
+The most basic version of the Maxwell Z- model consists of three kinematic equations that use three parameters to represent the geometry and velocity over each streamtube \(^{37}\) :  
+
+<|ref|>equation<|/ref|><|det|>[[137, 393, 907, 490]]<|/det|>
+\[\begin{array}{rcl}{r} & = & {r_{0}(1 - \cos \Delta)^{\frac{1}{2 - 2}}}\\ {} & {} & {}\\ {v_{r}} & = & {\frac{\alpha}{rZ}}\\ {} & {} & {}\\ {v_{\Delta}} & = & {u_{r}(Z - 2)\frac{\sin\Delta}{1 + \cos\Delta}} \end{array} \quad (3)\]  
+
+<|ref|>text<|/ref|><|det|>[[88, 492, 909, 566]]<|/det|>
+where \(r\) is a mass element's radial location along a streamline, while \(v_{r}\) and \(v_{\Delta}\) are its radial and tangential speeds, respectively. These quantities vary with \(\Delta\) , a counterclockwise angle from the impact incident direction (Figure 1). For a vertical impact on a flat surface, the downward direction is \(\Delta = 0^{\circ}\) . \(r_{0}\) , \(\alpha\) , and \(Z\) represent a streamline's kinematics.  
+
+<|ref|>text<|/ref|><|det|>[[88, 566, 907, 604]]<|/det|>
+In the analysis determining the geometric factors of the MAMOS samples, we also apply a conversion formula between \(\alpha\) and the transient crater radius, \(R^{38}\) :  
+
+<|ref|>equation<|/ref|><|det|>[[135, 608, 907, 662]]<|/det|>
+\[\alpha = \left(\frac{gR^{(2Z + 1)}}{4Z(Z - 2)}\right)^{\frac{1}{2}} \quad (4)\]  
+
+<|ref|>text<|/ref|><|det|>[[88, 669, 909, 743]]<|/det|>
+Because our target surface is supposed to have curvature, \(R\) , which is usually defined as a quantity for an impact on a flat surface \(^{31}\) , can only serve as a hypothetical parameter rather than a physically meaningful quantity. Thus, this quantity should be larger than the excavation range, \(r_{E}^{*}\) , generally when the target surface has curvature.  
+
+<|ref|>sub_title<|/ref|><|det|>[[88, 757, 450, 776]]<|/det|>
+## Computation of transient crater radius  
+
+<|ref|>text<|/ref|><|det|>[[88, 777, 909, 814]]<|/det|>
+The \(\pi\) - scaling relationship offers correlations between the impactor and transient crater conditions based on empirically determined scaling factors \(^{31}\) . This relationship provides the transient crater volume, \(V\) :  
+
+<|ref|>equation<|/ref|><|det|>[[135, 819, 907, 878]]<|/det|>
+\[V = K_{1}\left(\frac{m_{i}}{\rho_{t}}\right)\left\{\left(\frac{gr_{i}}{v_{t}^{2}}\right)\left(\frac{\rho_{t}}{\rho_{i}}\right)^{-\frac{1}{3}} + \left(\frac{Y}{\rho_{t}v_{t}^{2}}\right)^{\frac{2 + \mu}{2}}\right\}^{-\frac{3\mu}{2 + \mu}}. \quad (5)\]  
+
+<|ref|>text<|/ref|><|det|>[[88, 885, 909, 922]]<|/det|>
+where \(K_{1}\) , \(\mu\) , and \(Y\) are empirically determined parameters. \(m_{i}\) , \(r_{i}\) , and \(v_{i}\) are the impactor's mass, radius, and speed, respectively. The used values for the parameters are provided in Supplementary Table S.1. The
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[90, 92, 905, 816]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[88, 823, 904, 896]]<|/det|>
+<center>Figure 4. Schematics for kinetic impact-driven momentum transfer depending on different scenarios. Impactors with two kinetic energies add the same net kinetic energy to a target by performing multiple impacts. Net momentum transfer changes due to orientation and kinetic energy per impactor. The ID of the attached LICIACube image is liciacube_luke_10_1664234219_00112_01.fits. </center>
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[88, 78, 908, 135]]<|/det|>
+strength parameter, \(Y\) , is set to be equivalent to the minimum cohesive strength (see below). \(\rho_{t}\) and \(\rho_{i}\) are the bulk density of the target and that of the impactor, respectively. \(g\) is the gravitational acceleration. The following equation then provides the transient crater radius using the transient crater volume:  
+
+<|ref|>equation<|/ref|><|det|>[[135, 145, 907, 194]]<|/det|>
+\[R = \left(\frac{3V}{\pi}\right)^{\frac{1}{3}} \quad (6)\]  
+
+<|ref|>text<|/ref|><|det|>[[88, 202, 907, 240]]<|/det|>
+During the computation of the geometric factors for the MANOS samples, the algorithm inputs \(R\) to determine \(\alpha\) using Equation (4).  
+
+<|ref|>sub_title<|/ref|><|det|>[[88, 256, 501, 275]]<|/det|>
+## Computation of minimum cohesive strength  
+
+<|ref|>text<|/ref|><|det|>[[88, 275, 910, 440]]<|/det|>
+Equation (5) needs \(Y\) as an input to determine the transient crater volume, which computes the transient crater radius in Equation (6). This parameter is the least constrained quantity in this study. However, the spin state gives the strength levels for objects to remain structurally intact. While this concept only offers a lower bound of strength, it is valuable to characterize how high the strength is in each MANOS sample. One method is to determine the cohesive strength, or shear strength, at zero pressure. When a self- gravitating body spins at a given spin period, body elements experience gravitational and centrifugal loading, which induces a stress field. When the spin is fast enough that the centrifugal loading strongly pulls the elements outward, the body may need cohesive strength to keep its structure intact. The minimum cohesive strength defines the lowest level of such strength in a given element.  
+
+<|ref|>text<|/ref|><|det|>[[88, 439, 910, 567]]<|/det|>
+While earlier approaches use Finite Element Modeling to determine the levels of the minimum cohesive strengths in irregularly shaped bodies \(^{39}\) , we apply an analytical work \(^{40,41}\) to simplify computation given limited constraints on the samples' shapes. Given a constant bulk density, this analytical model considers a uniformly rotating triaxial ellipsoid to compute the stress field. The computed stress field is based on linear elasticity, making the equilibrium equations simple to become analytically solvable linear equations. During this operation, the equations no longer depend on Young's modulus. We then convert the derived stress field to the minimum cohesive strength, \(Y\) , by using the Drucker- Prager yield criterion:  
+
+<|ref|>equation<|/ref|><|det|>[[134, 575, 907, 703]]<|/det|>
+\[\begin{array}{rcl}{Y}&{=}&{\frac{1}{\beta}(\alpha I_{1}+\sqrt{J_{2}})}\\{}&{}&{}\\{\alpha}&{=}&{\frac{2\sin\psi}{\sqrt{3}(3-\sin\psi)}}\\{}&{}&{}\\{\beta}&{=}&{\frac{6\cos\psi}{\sqrt{3}(3-\sin\psi)}}\end{array} \quad (7)\]  
+
+<|ref|>text<|/ref|><|det|>[[88, 710, 909, 802]]<|/det|>
+where \(I_{1}\) and \(J_{2}\) are pressure and shear stress invariants, respectively, and \(\psi\) is the angle of friction. This study fixes \(\psi\) at \(35^{\circ}\) . This provides the spatial distribution of the minimum cohesive strength over the entire body. Earlier work suggested that \(Y\) becomes maximum at the center when the spin period is short \(^{41}\) . Because many MANOS samples are fast rotators, we select \(Y\) at their body centers. The \(\pi\) - scaling relationship then uses the computed \(Y\) to determine the transient crater radius, \(R\) .  
+
+<|ref|>sub_title<|/ref|><|det|>[[90, 819, 365, 837]]<|/det|>
+## Definition of geometric factor  
+
+<|ref|>text<|/ref|><|det|>[[88, 838, 907, 874]]<|/det|>
+The geometric factor, \(P\) , defines the ratio of the along- track momentum carried by ejecta developed by an impact on a curved surface to that by a vertical impact on a geometrical reference:  
+
+<|ref|>equation<|/ref|><|det|>[[135, 884, 907, 927]]<|/det|>
+\[P = \frac{L_{T}}{L_{T r e f}} = \frac{\beta - 1}{\beta_{r e f} - 1} \quad (10)\]
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[88, 78, 910, 194]]<|/det|>
+where \(L_{T}\) and \(L_{T r e f}\) are the along- track ejecta momenta that form on the curved and reference surfaces, respectively. We also express these scalar quantities using vector notations, \(L_{T} = \vec{L}\cdot \vec{n}_{T}\) , where \(\vec{L}\) is the ejecta momenta on the curved surface and \(\vec{n}_{T}\) is the along- track unit vector, and similarly, \(L_{T r e f} = \vec{L}_{r e f}\cdot \vec{n}_{T}\) , where \(\vec{L}_{r e f}\) is the ejecta momentum on the reference surface. \(P\) can be convertible with \(\beta\) for these targets, where \(\beta_{r e f}\) is \(\beta\) for a reference surface. The reference surface can be arbitrary, but the simplest one may be a flat surface, which generally offers the highest ejecta momentum among any convex surface.  
+
+<|ref|>text<|/ref|><|det|>[[88, 193, 910, 358]]<|/det|>
+We consider two reference surfaces in this work. The main study applies a flat- surface target as the reference surface and denotes this geometric factor as \(P_{f l}\) , while the validation analysis comparing our Maxwell Z- model approach with the iSALE- 2D shock- physics code uses a spherical target and defines it as \(P_{s p}\) . The major reason for using these two references is that while it is valuable to apply well- established and calibrated simulation results from iSALE in our validation analysis, using a flat surface, which generally gives the highest efficiency, can offer simple diagnostics of the momentum transfer efficiency. For example, reading its unity value, \(P_{f l}\) can give a direct insight into how close (far) the momentum transfer is to (from) the most ideal case. However, \(P_{s p}\) does not give such insightful views easily because it can still be larger than unity even when the ejecta momentum does not reach the ideal flat surface case.  
+
+<|ref|>sub_title<|/ref|><|det|>[[90, 371, 409, 391]]<|/det|>
+## Light curve samples from MANOS  
+
+<|ref|>text<|/ref|><|det|>[[88, 391, 910, 537]]<|/det|>
+Samples are available through the MANOS light curve campaigns, which offer samples' spin periods, sizes, and shapes. The project sampled 308 NEOs over 4.5 years<sup>30</sup>. Many samples are smaller targets less than 50 m in radius, unlike those cataloged in the Asteroid Lightcurve Database, which archives larger objects in general<sup>42</sup>. We select 103 out of the samples objects, which have full and partial light curve data over their spin periods<sup>30</sup>. For the shape, we assume that the sample is a biaxial ellipsoid, where its semi- intermediate and semi- minor axis are equal. When the semi- major axis is \(a\) , and the semi- minor (intermediate) axis is \(b\) , this ratio becomes \(b / a\) . Given an available relative amplitude, \(\Delta m\) , we can obtain \(b / a\) by using the following equation:  
+
+<|ref|>equation<|/ref|><|det|>[[137, 539, 907, 580]]<|/det|>
+\[\Delta m = -2.5\log \left(\frac{b}{a}\right) \quad (11)\]  
+
+<|ref|>sub_title<|/ref|><|det|>[[89, 592, 538, 612]]<|/det|>
+## Geometric factor of DART impact on Dimorphos  
+
+<|ref|>text<|/ref|><|det|>[[88, 612, 909, 721]]<|/det|>
+We create smaller pieces in Dimorphos's body by slicing the asteroid's body parallel to the DART incident direction to make thin pieces over all azimuthal directions. We call each piece an azimuthal piece. Each azimuthal piece defines a volume at a given azimuthal angle, extending to the normal direction to the DART incident direction, and thus looks like a wedge. While the number of azimuthal pieces is arbitrary, our numerical tests suggest that 100 pieces give acceptable computational accuracy without adding significant computational burdens.  
+
+<|ref|>text<|/ref|><|det|>[[88, 721, 909, 886]]<|/det|>
+We then apply the Maxwell Z- model to determine \(\alpha\) , \(Z\) , and a new scaling parameter controlling the net momentum, denoted as \(\gamma\) (see below). Our developed iterative scheme searches for the best set of \(\alpha\) and \(Z\) for each azimuthal piece based on the measured ejecta cone. Given the surface element location in a streamtube, \(r^{*}\) , and the range of excavation, \(r_{E}^{*}\) (Figure 1), we define 10,000 streamtubes in one azimuthal piece and select those with \(r^{*}< r_{E}^{*}\) to compute surface elements' trajectories in all these streamtubes. The spatial distribution of ejected surface elements constructs a simulated cone geometry in each azimuthal direction. We fit the derived distribution with the measured cone geometry at \(0.5\mathrm{- }1.0\mathrm{km}\) from the ejecta cone apex. This process gives a unique set of \(\alpha\) and \(Z\) for each azimuthal piece and applies the same step to all azimuthal pieces.  
+
+<|ref|>text<|/ref|><|det|>[[88, 886, 907, 923]]<|/det|>
+Once determining \(\alpha\) and \(Z\) for all azimuthal pieces, we obtain the ejecta momentum over the entire body. When the thickness of each streamtube, characterized by a small differential of \(r_{0}\) , is very small, the
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[88, 78, 908, 153]]<|/det|>
+ideal momentum is a multiplication of the mass of the streamtube and the surface velocity, \(d m \vec{v}_{\Delta^{*}}\) , where \(d m\) is the streamtube's mass exceeding the escape velocity and \(\vec{v}_{\Delta^{*}}\) is the ejection velocity. Summing up the momenta of all streamtubes over each azimuthal piece and eventually over all azimuthal pieces gives the net ideal ejecta momentum \(\vec{L}_{p}\) :  
+
+<|ref|>equation<|/ref|><|det|>[[135, 160, 907, 208]]<|/det|>
+\[\vec{L}_{p} = \sum_{i = 1}^{m}\sum_{j = 1}^{n}d m_{i,j}(\alpha_{i},Z_{i})\vec{v}_{\Delta^{*}i,j}(\alpha_{i},Z_{i}) \quad (12)\]  
+
+<|ref|>text<|/ref|><|det|>[[88, 216, 908, 326]]<|/det|>
+where \(i\) and \(j\) are the indices representing an azimuthal piece \((1 \leq i \leq m)\) and a streamtube in one azimuthal piece \((1 \leq j \leq n)\) . However, given the Maxwell Z- model formulation, all materials within a streamtube depart from the surface at the same speed at any time. Therefore, the momentum computation using Equation (12) is unrealistic because this does not account for proper energy loss within each streamtube. For model simplicity, without adding new time- variant parameters, we keep \(\alpha\) and \(Z\) constant but introduce a new scaling parameter, \(\gamma\) , to obtain the ejecta momentum:  
+
+<|ref|>equation<|/ref|><|det|>[[135, 333, 907, 357]]<|/det|>
+\[\vec{L} = r_{0}^{T}\vec{L}_{p} \quad (13)\]  
+
+<|ref|>text<|/ref|><|det|>[[89, 365, 525, 384]]<|/det|>
+\(\gamma\) takes the same value over the entire azimuthal pieces.  
+
+<|ref|>text<|/ref|><|det|>[[88, 384, 908, 457]]<|/det|>
+Given the determined geometric parameters, cone apex location, and measured \(\beta\) , the algorithm uses the determined set of \(\alpha\) and \(Z\) for all azimuthal pieces. It performs the above processes iteratively to determine \(\gamma\) such that Equation (14) satisfies under an error threshold for \(\gamma\) of \(0.01\%\) . This process computes the simulated \(\beta\) using its formula \(^{6,18}\) :  
+
+<|ref|>equation<|/ref|><|det|>[[135, 464, 907, 511]]<|/det|>
+\[\beta = 1 + \frac{\vec{L}_{p}\cdot\vec{n}_{T}}{(\vec{E}\cdot\vec{L}_{sc})\cdot(\vec{E}\cdot\vec{n}_{T})} \quad (14)\]  
+
+<|ref|>text<|/ref|><|det|>[[88, 517, 909, 648]]<|/det|>
+where \(\vec{E}\) is the unit vector of the net ejecta momentum, and \(\vec{L}_{sc}\) is the momentum carried by spacecraft. Supplementary Table S.2 gives the values of the Dimorphos along- track direction \((\vec{n}_{T})\) and the DART incident direction in the IAU_DIMORPHOS coordinate frame, both obtained by the SPICE kernel version d430. Running 1,000 Monte Carlo simulations with Gaussian- distributed inputs offers the statistical behaviors of these outputs (Table 1). The key inputs include \(\theta_{1}\) , \(\theta_{2}\) , \(RA\) , \(DEC\) , cone apex location vector, \(\beta\) , and Dimorphos's bulk density. We use the following formula to describe \(\beta\) , depending on the asteroid's bulk density \(^{18}\) :  
+
+<|ref|>equation<|/ref|><|det|>[[135, 654, 907, 693]]<|/det|>
+\[\beta = (3.61\pm 0.2)\frac{\rho}{\rho_{ref}} -0.03\pm 0.02(1\sigma) \quad (15)\]  
+
+<|ref|>text<|/ref|><|det|>[[88, 701, 907, 740]]<|/det|>
+where \(\rho_{ref}\) is the reference bulk density fixed at \(2,400 \mathrm{kg m}^{- 3}\) , and \(\rho\) is the considered bulk density, which is \(2,400 \pm 900(1\sigma) \mathrm{kg m}^{- 3}\) .  
+
+<|ref|>text<|/ref|><|det|>[[88, 739, 909, 923]]<|/det|>
+Each Monte Carlo simulation case determines the ejecta momentum on a reference surface, which is assumed to be flat. The algorithm applies the same inputs and derived parameters from the curved surface case, including the azimuthal variations in \(\alpha\) and \(Z\) (Figure 2), to the flat surface target. The normal to the reference surface is parallel to the DART incident direction. Similar to the analysis of Dimorphos's curved surface, we divide each azimuthal piece into narrower streamtubes, determine the ejecta momentum of each streamtube, and compute the net ejecta momentum over the entire excavation. The difference between the reference and curved surface cases is that considering a reference target, the reference surface case applies the same parameters as the curved surface case and does not perform interactive schemes to determine these parameters. Once computing the ejecta momentum on the reference target, we apply Equation (10) to compute the geometric factor, \(P_{fl}\) , relative to the ejecta momentum on a flat target.
+
+<--- Page Split --->
+<|ref|>table<|/ref|><|det|>[[120, 160, 877, 465]]<|/det|>
+<|ref|>table_caption<|/ref|><|det|>[[88, 77, 909, 151]]<|/det|>
+Table 1. Properties determined by cone measurements<sup>19</sup> and the Maxwell Z-model approach. The errors in Value represent \(1\sigma\) uncertainties. The coordinate frame is J2000, the Dimorphos fixed frame (IAU_DIMORPHOS), or the local coordinate frame (Figure 1B). For the units, \(\mathrm{hm}^{(Z + 1)} / \mathrm{s}\) , hm stands for hectometers \(= 100 \mathrm{m}\) , following the earlier notational definition<sup>25</sup>.   
+
+<table><tr><td>Quantity</td><td>Notation</td><td>Value</td><td>Units</td><td>Frame</td></tr><tr><td colspan="5">Cone geometry</td></tr><tr><td>Cone wide angle</td><td>θ1</td><td>133 ± 9</td><td>deg</td><td>[-]</td></tr><tr><td>Cone narrow angle</td><td>θ2</td><td>95 ± 6</td><td>deg</td><td>[-]</td></tr><tr><td>Axis rotation</td><td>φ</td><td>26 ± 16</td><td>deg</td><td>Local</td></tr><tr><td>Axis right ascension</td><td>RA</td><td>141 ± 4</td><td>deg</td><td>J2000</td></tr><tr><td>Axis declination</td><td>DEC</td><td>20 ± 8</td><td>deg</td><td>J2000</td></tr><tr><td>Apex location, x axis</td><td>x</td><td>-4 ± 6</td><td>m</td><td>IAU_DIMORPHOS</td></tr><tr><td>Apex location, y axis</td><td>y</td><td>-3 ± 9</td><td>m</td><td>IAU_DIMORPHOS</td></tr><tr><td>Apex location, z axis</td><td>z</td><td>9 ± 10</td><td>m</td><td>IAU_DIMORPHOS</td></tr><tr><td colspan="5">Maxwell Z-model</td></tr><tr><td>Streamtube, shape</td><td>Z</td><td>2.9 ± 0.4</td><td>[-]</td><td>[-]</td></tr><tr><td>Streamtube, speed</td><td>α</td><td>(3.1 ± 2.2) × 10-4</td><td>hm(Z+1)/s</td><td>[-]</td></tr><tr><td>Streamtube, momentum</td><td>γ</td><td>0.73 ± 0.12</td><td>[-]</td><td>[-]</td></tr><tr><td>Geometric factor</td><td>Pfl</td><td>44 ± 10</td><td>%</td><td>[-]</td></tr></table>  
+
+<|ref|>sub_title<|/ref|><|det|>[[90, 510, 680, 530]]<|/det|>
+## Validation of geometric factor computation by Maxwell Z-model  
+
+<|ref|>text<|/ref|><|det|>[[88, 532, 910, 699]]<|/det|>
+The comparisons between the Maxwell Z- model and iSALE- 2D simulations<sup>21- 24</sup> reveal that both models give consistent geometric factors relative to a spherical target (Figure 5). In this test, nine iSALE- 2D simulations with different biaxial ellipsoids offer variations in \(\beta\) , assuming that each target's along- track direction corresponds to an impactor's anti- incident direction. The target dimension is set to be \(2a \times 2b \times 2c\) , where \(b = c\) . The simulations parameterized \(b / a\) , which ranged between 0.4 and 2.0 with an increment of 0.2. The equivalent radius is 75 m for all cases. To mimic the DART impact condition, each case assumes a low- density impactor modeled as a sphere with a radius of 1.2 m and a mass of 580 kg. The impact speed is 6 km/s, and the impact site is along the \(a\) axis. We determine \(\beta\) for each case to obtain \(P_{sp}\) .  
+
+<|ref|>text<|/ref|><|det|>[[88, 700, 910, 883]]<|/det|>
+We perform iSALE- 2D simulations based on the parameter settings from earlier work<sup>10, 12</sup>. The impactor's material behavior follows the Tillotson equation of state (EOS) and the Johnson- Cook strength model for aluminum<sup>43</sup>. The target's behavior follows the Tillotson EOS for basalt<sup>44</sup> with a modified grain density of \(3,500 \mathrm{kg} / \mathrm{m}^3\) , which corresponds to the average grain density of L/LL chondrites<sup>45</sup>. The current version of iSALE- 2D sets a simple pressure- dependent strength model to define the target's shear strength<sup>22</sup>, with a cohesive strength of 1 Pa and a coefficient of internal friction of 0.55. The target's porosity is \(45\%\) at the initial condition, and its behavior follows the \(\epsilon - \alpha\) compaction model<sup>23</sup>. All parameters are available in Supplementary Table S.1. Given impact scaling relationships<sup>46</sup>, our iSALE results may recreate impact behaviors given in the range of \(Z = 2 - 3\) , where \(Z\) is the Maxwell Z- model kinematic parameter.  
+
+<|ref|>text<|/ref|><|det|>[[90, 886, 907, 922]]<|/det|>
+The Maxwell Z- model approach explores the statistical trends of \(P_{sp}\) by considering Gaussian- based inputs to the model based on our earlier analysis for Dimorphos ( \(Z = 2.932 \pm 0.406\) and \(\gamma = 0.731 \pm 0.120\) )
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[214, 99, 754, 432]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[88, 444, 909, 537]]<|/det|>
+<center>Figure 5. Result comparison between Maxwell Z-model and iSALE-2D simulations. The \(x\) axis is the aspect ratio of the biaxial ellipsoid target with dimensions of \(2a \times 2b \times 2c\) , where \(b = c\) , and the \(y\) axis is the geometric factor relative to a spherical target, \(P_{sp}\) , in percentiles. The aspect ratio is defined as \(b / a\) . The black line resulted from Maxwell Z-model simulations, while the red line was from iSALE-2D simulations. The Maxwell Z-model's error bar gives \(1\sigma\) uncertainties. </center>  
+
+<|ref|>text<|/ref|><|det|>[[88, 565, 910, 730]]<|/det|>
+and those from the literature of the \(\pi\) - scaling relationships \((K_{1} = 0.22 \pm 0.02\) and \(\mu = 0.47 \pm 0.07\) ). These \(\pi\) - scaling parameters assume impacts on dry sands and rocks<sup>47</sup>. The impactor's bulk density, another input parameter in the model, is fixed at constant at \(1,925 \mathrm{kg} / \mathrm{m}^{3}\) for all cases to make this test consistent with iSALE- 2D runs. The strength parameter, \(Y\) , is set to be 1 Pa to mimic vertical impacts on cohesionless targets. Our analysis performs 1,200 runs with Gaussian- distributed inputs for each \(b / a\) case. Some unrealistic solutions exist, giving extremely high or low \(P_{sp}\) . Such solutions come from parameter conditions at the tails of their distributions or simply ill- defined numerical values for the parameter conditions. The post- processing steps remove any solutions being higher than \(200\%\) or lower than - 200%, removing \(15 - 25\%\) of all solutions, having no significant impact on the statistical trends of our results.  
+
+<|ref|>sub_title<|/ref|><|det|>[[89, 753, 452, 772]]<|/det|>
+## Geometric factors for MANOS samples  
+
+<|ref|>text<|/ref|><|det|>[[89, 774, 909, 902]]<|/det|>
+We compute their geometric factors by applying 103 small NEO samples measured by the MANOS project<sup>30</sup>. Simulations for each sample perform two geometric factor computations. The first computation considers an impact along the semi- minor axis, while the second one simulates that along the semi- major axis. All simulations assume vertical impacts with the same impact scale as the DART impact, leading to axisymmetric ejecta momenta. The assumption is that the along- track direction corresponds to an impactor's anti- incident direction. With these simulation settings, impacts along the semi- major axis experience a higher curvature than those along the semi- minor (intermediate) axis.  
+
+<|ref|>text<|/ref|><|det|>[[111, 904, 907, 922]]<|/det|>
+The main simulation scheme is the same for the geometric factor computation for the DART impact
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[88, 78, 909, 227]]<|/det|>
+on Dimorphos, which determines \(P_{fl}\) . However, there are two differences. First, rather than determining the necessary parameters iteratively, this scheme directly uses the abovementioned parameters, except for \(\alpha\) . Second, \(\alpha\) comes from the conversion between that parameter and the transient crater radius (Equation 4). The reason is that \(\alpha\) depends on the transient crater radius, \(R\) , and gravity, making the derived \(\alpha\) from the DART impact case inconsistent with the MANOS samples. We use the \(\pi\) - scaling relationships \(^{31}\) to compute \(R\) but need the strength parameter, \(Y\) . In this study, we assume \(Y\) to be equivalent to the minimum cohesive strength. Key inputs in the \(\pi\) - scaling relationship are \(K_{1}\) and \(\mu\) , defined in Supplementary Information Table S.2. Then, substituting the derived \(R\) into Equation (4) yields \(\alpha\) for each sample.  
+
+<|ref|>text<|/ref|><|det|>[[88, 226, 910, 464]]<|/det|>
+Monte Carlo simulations offer the statistical behavior of each sample's geometric factor. The two impact scenarios for each sample use the same inputs except for the curvature for the geometric factor computation. To account for the uncertainties of the target bulk densities, we set it to be a uniformly distributed random number between 1,000 and \(4,000\mathrm{kg} / \mathrm{m}^{3}\) . This bulk density variation redefines gravity and strength parameters, resulting in the \(\alpha\) variations. For each sample, we perform 1,200 simulations for one impact scenario, i.e., 2,400 simulations for both scenarios. One issue is that when the transient crater is too large, the computation of the ejecta momentum accumulates numerical errors. This is because \(\Delta\) and \(r_{0}\) become extremely small and large, reducing numerical accuracy. To avoid this issue, the algorithm only considers \(\Delta_{E}^{*} > 20^{\circ}\) , allowing all streamtubes to cover up to \(\sim 83\%\) of the entire volume. The \(\Delta_{E}^{*} > 20^{\circ}\) constraint likely underestimates the geometric factor. However, our experience suggests that such a case makes the geometric factor unrealistic and is rejected by the allowed geometric factor range anyway. Thus, this limit does not influence our results. Furthermore, for one impact scenario of each sample, our sorting processes yield \(\sim 85\%\) of simulations that satisfy a geometric factor ranging between \(- 200\%\) and \(200\%\) .  
+
+<|ref|>sub_title<|/ref|><|det|>[[90, 477, 454, 498]]<|/det|>
+## Catastrophic disruption threshold \((Q_{D}^{*})\)  
+
+<|ref|>text<|/ref|><|det|>[[90, 497, 907, 534]]<|/det|>
+The catastrophic disruption threshold, \(Q_{D}^{*}\) , defines the specific impact energy per mass required to disperse half of the target material mass, which is given as:  
+
+<|ref|>equation<|/ref|><|det|>[[135, 540, 907, 581]]<|/det|>
+\[Q_{D}^{*} = \frac{U^{2}}{2}\frac{m_{sc}}{M} \quad (16)\]  
+
+<|ref|>text<|/ref|><|det|>[[90, 586, 907, 623]]<|/det|>
+where \(m_{sc}\) is the spacecraft mass, \(M\) is the target mass, and \(U\) is the spacecraft relative impact speed. In the present study, \(m_{sc}\) and \(U\) are identical to DART's, and \(m_{ss} \ll M\) .  
+
+<|ref|>text<|/ref|><|det|>[[89, 622, 909, 770]]<|/det|>
+\(Q_{D}^{*}\) is a function of the impactor speed, target radius, and strength \(^{48,49}\) . Our study assumes a constant kinetic energy, providing a condition when the target loses its half mass, given strength and radius. The issue is that no adequate disruption threshold formula covers the applicable parameter range considered in this study. At small scales, \(Q_{D}^{*}\) depends on (size- dependent) target strength, but an explicit relation between \(Q_{D}^{*}\) and strength is not available in existing numerical and experimental data for the conditions investigated here. Accepting this issue, our approach uses two samples with different strengths at different target radii at the threshold and interpolates them to draw the correlations. For each sample, we introduce three bulk density cases, \(1000\mathrm{kg} / \mathrm{m}^{3}\) , \(2000\mathrm{kg} / \mathrm{m}^{3}\) , and \(4000\mathrm{kg} / \mathrm{m}^{3}\) , to show the variations in such correlations.  
+
+<|ref|>text<|/ref|><|det|>[[90, 768, 907, 805]]<|/det|>
+The first sample considers targets with higher strength \(^{50}\) . \(Q_{D}^{*}\) for a high- strength material defines the following equation \(^{50}\) :  
+
+<|ref|>equation<|/ref|><|det|>[[135, 811, 907, 840]]<|/det|>
+\[Q_{D}^{*} = 100^{a_{s}}\times Q_{0}R_{Q_{D}^{*}}^{a_{s}} + 100^{b_{s}}\times B\rho R_{Q_{D}^{*}}^{b_{s}} \quad (17)\]  
+
+<|ref|>text<|/ref|><|det|>[[89, 846, 909, 921]]<|/det|>
+where \(R_{Q_{D}^{*}}\) is the disrupting target radius, \(\rho\) is the bulk density, and \(Q_{0}\) , \(a_{s}\) , \(b\) , and \(B\) are the empirical parameters. Following earlier Smooth- Particle Hydrodynamics (Bern SPH) simulations \(^{50}\) , our study applies two high- strength materials. One is a basalt- like target, and the other is a pumice- like target. The parameters used here are based on impact simulations with an impact speed of \(5\mathrm{km / s}\) and a target radius
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[88, 78, 908, 134]]<|/det|>
+of \(1.5 \mathrm{cm}^{50}\) , given in Supplementary Table S.3. We apply Equation (17) to determine \(R_{Q_{D}^{*}}\) at kinetic energy imparted by the DART- like impactor by assuming that the parameters derived for the \(5 - \mathrm{km / s}\) impact speed are still valid.  
+
+<|ref|>text<|/ref|><|det|>[[88, 133, 908, 191]]<|/det|>
+We consider the strength parameter, \(Y\) , at a given \(R_{Q_{D}^{*}}\) . The earlier targets \(^{50}\) were \(1.5 \mathrm{cm}\) radius, provided with their strengths at this size, \(Y(1.5 \mathrm{cm})\) . We re- scale \(Y(1.5 \mathrm{cm})\) to \(Y\) by applying the static failure threshold for a specimen failing at the smallest strain, \(\epsilon_{min}\) :  
+
+<|ref|>equation<|/ref|><|det|>[[137, 196, 907, 223]]<|/det|>
+\[\epsilon_{m i n} = (k V_{Q_{D}^{*}})^{-\frac{1}{m}} \quad (18)\]  
+
+<|ref|>text<|/ref|><|det|>[[88, 230, 908, 269]]<|/det|>
+where \(k\) and \(m\) are the Weibull parameters, given in Supplementary Table S.3, and \(V_{Q_{D}^{*}}\) is the disrupting target volume. \(Y\) at a given \(R_{Q_{D}^{*}}\) is written as:  
+
+<|ref|>equation<|/ref|><|det|>[[137, 276, 907, 297]]<|/det|>
+\[Y\sim \epsilon_{m i n}E_{s} \quad (19)\]  
+
+<|ref|>text<|/ref|><|det|>[[88, 304, 908, 343]]<|/det|>
+where \(E_{s} = 5.3 \times 10^{10} \mathrm{~Pa}\) is Young's modulus. Combining these equations with the assumption that the Weinbull parameters and \(E_{s}\) are size- independent yields the relationship between \(Y\) and \(Y(1.5 \mathrm{cm})\) :  
+
+<|ref|>equation<|/ref|><|det|>[[135, 348, 907, 395]]<|/det|>
+\[Y = \left(\frac{V_{Q_{D}^{*}}}{1.41 \times 10^{-5}}\right)^{-\frac{1}{m}} Y(1.5 \mathrm{cm}) \quad (20)\]  
+
+<|ref|>text<|/ref|><|det|>[[88, 402, 908, 441]]<|/det|>
+The second sample considers cohesionless targets following a recent Bern SPH study \(^{28}\) . \(Q_{D}^{*}\) for this case gives the equation \(^{48}\) :  
+
+<|ref|>equation<|/ref|><|det|>[[135, 447, 907, 479]]<|/det|>
+\[Q_{D}^{*} = a_{g} R_{Q_{D}^{*}}^{3 \mu_{g}} U^{2 - 3 \mu_{g}} \quad (21)\]  
+
+<|ref|>text<|/ref|><|det|>[[88, 486, 908, 541]]<|/det|>
+where \(a_{g}\) and \(\mu_{g}\) are empirical parameters, and \(U\) is the impact speed (Supplementary Table S.3). These quantities are based on SPH simulations using an impact speed range of \(3 - 9 \mathrm{~km / s}\) and an impact mass of \(500 \mathrm{~kg}^{28}\) . We set the strength parameter for this scaling relationship as \(10^{- 2} \mathrm{~Pa}\) .  
+
+<|ref|>text<|/ref|><|det|>[[88, 541, 907, 578]]<|/det|>
+We interpolate these two samples to give a correlation between \(Y\) and \(R_{Q_{D}^{*}}\) . We assume that the interpolation function follows a power law:  
+
+<|ref|>equation<|/ref|><|det|>[[135, 584, 907, 613]]<|/det|>
+\[Y = \xi R_{Q_{D}^{*}}^{n} \quad (22)\]  
+
+<|ref|>text<|/ref|><|det|>[[88, 619, 908, 694]]<|/det|>
+where \(\xi\) and \(\eta\) come from the constraint that this scaling function must cross the data samples above. The approach considers two scaling functions: the combination of a pumice- like target and a cohesionless target and that of a basalt target and a cohesionless target. Finally, these discussions are based on the level of the tensile strength \(^{28,50}\) ; we assume that it is comparable to the strength parameter discussed above.  
+
+<|ref|>sub_title<|/ref|><|det|>[[89, 713, 218, 733]]<|/det|>
+## References  
+
+<|ref|>text<|/ref|><|det|>[[97, 740, 908, 777]]<|/det|>
+1. Interagency Working Group for Detecting and Mitigating the Impact of Earth-bound Near-Earth Objects. National Near-Earth Object Preparedness Strategy and Action Plan (2018).  
+
+<|ref|>text<|/ref|><|det|>[[97, 781, 908, 819]]<|/det|>
+2. Planetary Defense Interagency Working Group. National Near-Earth Object Preparedness Strategy and Action Plan (2023).  
+
+<|ref|>text<|/ref|><|det|>[[97, 824, 908, 862]]<|/det|>
+3. National Research Council. Defending Planet Earth: Near-Earth-Object Surveys and Hazard Mitigation Strategies (The National Academies Press, Washington, DC, 2010).  
+
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+4. National Academies of Sciences, Engineering, and Medicine. Origins, Worlds, and Life: A Decadal Strategy for Planetary Science and Astrobiology 2023-2032 (The National Academies Press, Washington, DC, 2022).
+
+<--- Page Split --->
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+
+<--- Page Split --->
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+22. Collins, G. S., Melosh, H. J. & Ivanov, B. A. Modeling damage and deformation in impact simulations. Meteorit. & Planet. Sci. 39, 217-231, DOI: https://doi.org/10.1111/j.1945-5100.2004.tb00337.x (2004).  
+
+<|ref|>text<|/ref|><|det|>[[88, 140, 910, 195]]<|/det|>
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+
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+40. Nakano, R. & Hirabayashi, M. Mass-shedding Activities of Asteroid (3200) Phaethon Enhanced by Its Rotation. The Astrophys. J. Lett. 892, L22, DOI: https://doi.org/10.3847/2041-8213/ab7d36 (2020).41. Hirabayashi, M. et al. Spin-driven evolution of asteroids' top-shapes at fast and slow spins seen from (101955) bennu and (162173) ryugu. Icarus 352, 113946, DOI: https://doi.org/10.1016/j.icarus.2020.113946 (2020).42. Warner, B., Harris, A. & Pravec, P. Asteroid Lightcurve Database (LCDB) Bundle V3.0 (2019). PDS4 LIDVID: urn:nasa:phs:ast-lightcurve-database::3.0.43. Johnson, G. R. & Cook, W. H. A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures. Proc. 7th Int. Symp. on Ballist. The Hague 541-547 (1983).44. Benz, W. & Asphaug, E. Catastrophic Disruptions Revisited. Icarus 142, 5-20, DOI: https://doi.org/10.1006/icar.1999.6204 (1999).45. Consolmagno, G. J., Britt, D. T. & Macke, R. J. The significance of meteorite density and porosity. Geochemistry 68, 1-29 (2008).46. Housen, K. R. & Holsapple, K. A. Ejecta from impact craters. Icarus 211, 856-875, DOI: https://doi.org/10.1016/j.icarus.2010.09.017 (2011).47. Richardson, J. E., Melosh, H. J., Lisse, C. M. & Carcich, B. A ballistics analysis of the Deep Impact ejecta plume: Determining Comet Tempel 1's gravity, mass, and density. Icarus 191, 176-209, DOI: https://doi.org/10.1016/j.icarus.2007.08.033 (2007).48. Housen, K. R. & Holsapple, K. A. On the fragmentation of asteroids and planetary satellites. Icarus 84, 226-253, DOI: 10.1016/0019-1035(90)90168-9 (1990).49. Housen, K. R. & Holsapple, K. A. Scale effects in strength-dominated collisions of rocky asteroids. Icarus 142, 21-33, DOI: https://doi.org/10.1006/icar.1999.6206 (1999).50. Jutzi, M., Michel, P., Benz, W. & Richardson, D. C. Fragment properties at the catastrophic disruption threshold: The effect of the parent body's internal structure. Icarus 207, 54-65, DOI: 10.1016/j.icarus.2009.11.016 (2010).  
+
+<|ref|>sub_title<|/ref|><|det|>[[91, 639, 312, 661]]<|/det|>
+## Acknowledgements  
+
+<|ref|>text<|/ref|><|det|>[[88, 666, 911, 922]]<|/det|>
+This work was supported by the DART mission, NASA Contract No. 80MSFC20D0004. This work was supported by the Italian Space Agency (ASI) within the LICIACube project (ASI- INAF agreement n. 2019- 31- HH.0 and its extension 2019- 31- HH.1- 2022). This work is partially supported by NASA through grant HSTGO- 16674 from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5- 26555. Portions of this work were performed by Lawrence Livermore National Laboratory under DOE contract DE- AC52- 07NA27344. LLNL- JRNL- 853920. S.D.R. and M.J. acknowledge support from the Swiss National Science Foundation (project number 200021 207359). Work of E.G.F., S.P.N., and S.R.C. was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration (80NM0018D0004). R.M. acknowledges funding from a NASA Space Technology Graduate Research Opportunities (NSTGRO) award, NASA contract No. 80NSSC22K1173. P.M. acknowledges funding support from the French Space Agency CNES and The University of Tokyo. G.T. acknowledges financial support from project FCE- 1- 2019- 1- 156451 of the Agencia Nacional de Investigación e Innovación ANII and Grupos I+D 2022 CSIC- Udela (Uruguay). The work by J.O. was
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[89, 78, 909, 226]]<|/det|>
+supported by grant PID2021- 125883NB- C22 by the Spanish Ministry of Science and Innovation/State Agency of Research MCIN/AEI/ 10.13039/501100011033 and by "ERDF A way of making Europe." The work by J.O. and I.H. was supported by the Spanish Research Council (CSIC) support for international cooperation: I- LINK project ILINK22061. S.R.S. acknowledges support from the DART Participating Scientist Program, grant no. 80NSSC22K0318. This research was supported in part through research cyberinfrastructure resources and services provided by the Partnership for an Advanced Computing Environment (PACE) at the Georgia Institute of Technology. The authors also acknowledge Mark Cintala for detailed reviews and proofreading of this manuscript.  
+
+<|ref|>sub_title<|/ref|><|det|>[[90, 248, 442, 269]]<|/det|>
+## Author contributions statement  
+
+<|ref|>text<|/ref|><|det|>[[88, 275, 910, 549]]<|/det|>
+M.H. led this project, developed techniques, conducted analysis and data assessment, and created the full story. S.D.R conducted iSALE simulations and gave interpretations of the DART impacts on Dimorphos. J.M.S. and T.L.F. offered overall guidance on this project and gave interpretations of the ejecta plume evolution. J.D.P.D. shared insights into ejecta plume geometry based on LICIACube data. G.T. offered interpretations of ejecta plume geometry. S.R.C., R.T.D., C.M.E., I.G., S.P.N., H.N., E.E.P, C.D.W., and A.Z. developed the mission- driven data necessary for this work. H.F.A., B.W.B., M.B.S., G.S.C., T.M.D., M.E.D., M.J., K.M.K., N.A.M., J.R.L., and S.R.S. reviewed the techniques used in this work to assess their validity. P.A.A., O.S.B., N.L.C., A.F.C., E.D., E.G.F., P.M., D.C.R., A.S.R., A.M.S., and C.A.T. are the leadership members of DART, LICIACube, and Hera, performing project management and execution and giving advice and comments on this work from mission level. R.T.D., B.W.B., M.B.S., J.R.L., and N.L.C. also gave advice on how to connect this work with planetary defense. J.B., J.R.B., M.D.'O., V.D.C., E.M.E., S.I., G.I., S.I., A.L., D.M., M.P., P.P., S.P., G.P., A.R., P.T., F.T., M.Z., and G.Z. contributed to LICIACube data analysis and advised on how to interpret the data. F.F., D.A.G., I.H., S.A.J., Ö.K., M.L., R.L., M.P.L., R.M., F.M., C.C.M., A.M., R.N., J.O., P.S., C.B.S., S.S., and T.J.S. reviewed the present study. All contributed to the manuscript development.  
+
+<|ref|>sub_title<|/ref|><|det|>[[90, 570, 319, 591]]<|/det|>
+## Competing interests  
+
+<|ref|>text<|/ref|><|det|>[[90, 597, 663, 615]]<|/det|>
+Authors do not have both financial and non- financial competing interests.  
+
+<|ref|>sub_title<|/ref|><|det|>[[90, 637, 410, 659]]<|/det|>
+## Materials & Correspondence  
+
+<|ref|>text<|/ref|><|det|>[[90, 666, 907, 720]]<|/det|>
+Geometry factor data and related numerical packages for analysis of both Dimorphos and MAMOS samples will be publicly available before the publication of this work. Further correspondence and material requests should be addressed to M.H., the corresponding author.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[43, 42, 312, 70]]<|/det|>
+## Supplementary Files  
+
+<|ref|>text<|/ref|><|det|>[[43, 92, 768, 112]]<|/det|>
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+<|ref|>text<|/ref|><|det|>[[60, 130, 270, 149]]<|/det|>
+- MASIHirabayashi.pdf
+
+<--- Page Split --->

preprint/preprint__c8fb7a8d8c40d5e2a42f5be83ae10eb3cb8b522d1dcebac8cb9e7a35f230204d/images_list.json

@@ -0,0 +1,62 @@
+[
+  {
+    "type": "image",
+    "img_path": "images/Figure_1.jpg",
+    "caption": "Figure 1: Trends in global increase of (a) VR/AR devices and (b) connected car fleet. a, estimated the number of consumer human machine interface devices dedicated to virtual reality (VR) and augmented reality (AR) in major areas including United States, Europe, China and Japan. The estimation suggests a booming of the AR/VR applications with an average annual growth rate (AAGR) of about \\(28\\%\\) from 2021 to 2025, followed by a continuously strong AAGR of about \\(14\\%\\) from 2025 to 2030. The VR/AR devices support time-critical applications such as remote surgery, immersive education, teleconference, online gaming and industrial designs [73] b, Estimations summarised collected by PricewaterhouseCoopers (PwC) and Strategy& [74], showing an increase of the connected cars in operation to 403 million by 2025, featuring an average annual growth rate (AAGR) of \\(14\\%\\) from 2021 to 2025, followed by an AAGR of \\(10\\%\\) , reaching 645 million by 2030. These estimates account for the largest geographical countries for connected cars of the United States, Europe, China and Japan.",
+    "footnote": [],
+    "bbox": [
+      [
+        176,
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+        292
+      ]
+    ],
+    "page_idx": 13
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_2.jpg",
+    "caption": "Figure 2: Concept of clock and optical frequency synchronised frequency division multiplexing (FDM) upstream for time-critical applications. a, a wide-bandwidth closely-spaced frequency comb generated at the edge cloud, referenced to a source clock within an edge data centre; b, filtered frequency comb sent from an edge cloud or optical line terminal (OLT) to users; c, upstream FDM signals, each user wavelength locked to a selected tone in the distributed frequency comb, forming a wide bandwidth optical signal which is detected by a single coherent receiver; d, different wavelength division multiplexing band (e.g. 100-200GHz bandwidth) covers different passive split fibre networks. The blue, green and red colour indicate different WDM bands; e, exemplary time-critical applications including cooperative traffic system and virtual reality (VR).",
+    "footnote": [],
+    "bbox": [
+      [
+        163,
+        508,
+        835,
+        755
+      ]
+    ],
+    "page_idx": 13
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_3.jpg",
+    "caption": "Figure 3: The clock and carrier frequency distribution. a, A continuous wave (CW) laser seeds two stages of comb generator, yielding 1.25-THz bandwidth 2.5-GHz-spacing comb signals with 10-dB flatness. The comb signals are sent to the end-users for clock and carrier frequency synchronisation; b, spectrum of the 25-GHz-spacing comb signals output from the 1st stage, c, spectrum of the generated comb signal output from the 2nd stage; d, demultiplexed comb signals using a 200-GHz WDM each containing 64 2.5-GHz tones with about 10 dB spectral flatness; e, RF spectrum of the detected 2.5-GHz clock signal using channel 4 as example (ITU ch35, 193.4-193.6 THz); f, jitter of the 50-MHz reference clock for end-user transceivers at different received optical power. The increased jitter value from -5 to 0 dBm is due to the saturation of electronic amplifier, the decreased jitter value from -5 to -16 dBm is due to the reduced power; g, measured phase noise of the distributed reference clock signals to different WDM channels, showing a maximum root-mean-square (rms) jitter of <4 ps, integrated over 1 kHz - 10 MHz..",
+    "footnote": [],
+    "bbox": [
+      [
+        185,
+        260,
+        820,
+        576
+      ]
+    ],
+    "page_idx": 14
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_4.jpg",
+    "caption": "Figure 4: Proof-of-concept experiment for the clock and frequency referenced frequency division multiplexing (FDM) upstream data aggregation for time-critical applications. a, the system diagram of our proof-of-concept experiments with three live end-users combined with dummy signals to form 160 GHz optical bandwidth signals. The optically distributed clock is sent to all live end-user transceivers as the clock reference, based on which three sets of field programmable gate arrays (FPGAs) and 4.9 Gas/s digital to analog converters (DACs) generates SCM-QAM signals and drive the corresponding intensity modulators (IMs) to generate upstream signals. The user lasers generate continuous wave (CW) signals with about 150 kHz linewidth and are frequency-locked to neighbouring comb tones using a frequency lock loop (FLL) containing a frequency detector and a proportional integral (PI) controller, with about 10 kHz loop bandwidth. Thermal-electro controller (TEC) provides feedback for long-term stability and coarse frequency tuning. Two couplers and a 10-dB attenuator are used to emulate 1:64 remote node splitting, resulting in a total link loss of about 28 dB (inc. 22 km SSMF loss, WDM loss, and the remote node splitting loss); b, optical spectrum (20 MHz resolution) of combined upstream signals, with all live transceivers locked to 2.5-GHz-spacing tones; c, optical spectrum (20 MHz resolution) of the upstream signals received: red (user1), orange (user1) and blue (user1). Green indicates the modulated dummy channels; d, measured power sensitivity (power per user signal into EDFA3) for different modulation formats at the soft-decision forward error correction code (SD-FEC) threshold of 2e-2 (15.3% overhead [SD-FEC paper]): cross markers (4QAM), open markers (8QAM), close markers (16QAM); e, measured constellation diagrams of user1; f, measured frequency deviation over 24 hours using user 1 locked at 193.407 THz.",
+    "footnote": [],
+    "bbox": [
+      [
+        177,
+        170,
+        820,
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+      ]
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+    "page_idx": 15
+  }
+]

preprint/preprint__c8fb7a8d8c40d5e2a42f5be83ae10eb3cb8b522d1dcebac8cb9e7a35f230204d/preprint__c8fb7a8d8c40d5e2a42f5be83ae10eb3cb8b522d1dcebac8cb9e7a35f230204d.mmd

@@ -0,0 +1,318 @@
+
+# Communications with Guaranteed Low Latency and Bandwidth using Frequency Referenced Multiplexing  
+
+Zichuan Zhou  University College London  
+
+Jinlong Wei  Huawei Technologies Duesseldorf GmbH  
+
+Yuan Luo  the Chinese University of Hong Kong (Shenzhen) https://orcid.org/0000- 0001- 5129- 0130  
+
+Kari Clark  University College London https://orcid.org/0000- 0003- 1988- 3205  
+
+Eric Sillekens  University College London  
+
+Callum Deakin  University College London  
+
+Ronit Sohanpal  University College London  
+
+Radan Slavik  University of Southampton  
+
+Zhixin Liu ( zhixin.liu@ucl.ac.uk)  University College London https://orcid.org/0000- 0002- 9681- 7933  
+
+Keywords:  
+
+Posted Date: April 26th, 2022  
+
+DOI: https://doi.org/10.21203/rs.3.rs- 1558939/v1  
+
+License: © This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License
+
+<--- Page Split --->
+
+# Communications with Guaranteed Low Latency and Bandwidth using Frequency Referenced Multiplexing  
+
+Zichuan Zhou \(^{1}\) , Jinlong Wei \(^{2}\) , Yuan Luo \(^{3}\) , Kari A. Clark \(^{1}\) , Eric Sillekens \(^{1}\) , Callum Deakin \(^{1}\) , Ronit Sohanal \(^{1}\) , Radan Slavik \(^{4}\) , and Zhixin Liu \(^{1}\)  
+
+\(^{1}\) Optical Networks Group, University College London, London, UK \(^{2}\) Huawei Technologies Duesseldorf GmbH, European Research Centre, Munich, Germany \(^{3}\) The Chinese University of Hong Kong (Shenzhen), Shenzhen, China \(^{4}\) Optoelectronic Research Centre, University of Southampton, Southampton, UK \(^{1}\) zhixin.liu@ucl.ac.uk \(^{2}\) jinlongwei2@huawei.com \(^{3}\) luoyuan@cuhk.edu.cn  
+
+## Abstract  
+
+The rise of timing- critical applications such as virtual reality and connected car fleets, combined with the rapid growth of the number of user devices, creates new challenges for the latency and reliability of user- cloud data communications. Currently user- cloud communications rely on time- scheduled data frames through tree- topology fibre networks, incapable of assuring guaranteed connections with low or stable latency, which is necessary for, e.g. remote surgeries and safe operations of self- driven cars. Besides, their scalability to a larger user count is limited. Here we show that clock and optical frequency synchronisation, enabled by burgeoning frequency comb and signal processing techniques, can provide each user with dedicated optical bandwidth to enable scalable user- cloud communications that guarantees simultaneously high per- use data rate and low latency. Our approach provides accurate clock and optical frequency synchronisation over deployed optical fibre links, which will be beneficial for many applications including accurate navigation, quantum communications, and astronomy.  
+
+## 1 Introduction  
+
+Two decades of vigorous growth of cloud services have made them an indispensable part of our everyday lives. It is expected that emerging applications such as virtual reality (VR), augmented reality (AR) and intelligent autonomous vehicles will continue to drive the exponential growth of global data traffic into the next decade [1]. These trends have been captured by several analyses indicating that the optical broadband traffic will outpace or even decuple in a decade [2, 3] and therefore the user bandwidth must scale accordingly to keep up with the demand [4]. These predictions have motivated the active development of electronic and opto- electronic components to 100 GHz bandwidths and beyond [5, 6, 7, 8, 9, 10, 11, 12]. These estimates contribute to the conventional wisdom [13, 14] that as demand for broadband traffic rises rapidly, so too must the end- user bandwidth. Nevertheless, though these extrapolations based on traffic growth are true for long- haul and point- to- point systems, this conventional wisdom will not apply to future user- cloud access networks due to the strong countervailing trends of the growth in the number of user devices (e.g. virtual reality headsets, traffic sensors) and their demand for guaranteed connections as well as low and stable latency to edge data centres [15, 16, 17, 18].  
+
+Here, we integrate recently- published data for VR/AR and intelligent vehicles (see figure 1), showing a radical growth in their numbers within the next decade. This data, together with the stringent requirement of low and stable latency [19], which will need to be guaranteed to, e.g. ensure traffic safety, rather than provide at the 'best effort' bases as today, when an average or mean latency is often used as a metric [18, 20]. All these aspects represent the following new technical requirements of future user- cloud communication infrastructures:
+
+<--- Page Split --->
+
+- They should provide low and stable latency connection in conjunction with the ability to scale across a large number of users, each with a few Gbit/s-level data rate [21, 22, 23] (data summarised in details in Table 1).  
+
+- They should provide a highly accurate synchronised clock to enable sub-nanosecond time synchronisation. For example, VR and self-driving car fleets require low-cost and highly scalable time synchronisation infrastructure to enable sub-meter scale positioning of devices [24]. Although sub-nanosecond time synchronisation is achievable using GPS, it is costly and relies on line-of-sight to the sky, which is difficult or impossible underground, within buildings or in urban canyons [25], and may be inhibited by atmospheric ash during volcanic eruptions or wartime [26]. Therefore, sub-nanosecond time synchronisation through the already deployed optical fibre access networks is highly desired.  
+
+- They should enable reconfigurability for various on-demand services with flexible modulation formats or bandwidths to support widely varying applications [23, 27]. For example, co-operative concerts through the internet only require a moderate data rate but have a stringent requirement of low and stable latency. Low order formats such as quadrature phase shift keying (QPSK) should be used to provide low bit error rate (BER) and forward error correction (FEC) free signalling to minimize latency and power consumption [16]. Remote education and remote work, however, require a high data rate to transmit high resolution video with a relaxed tolerance to latency. Thus, high order formats such as 16 quadrature amplitude modulation (QAM) could be used [28].  
+
+- They should also be compatible with legacy infrastructures such as existing mobile fronthaul and passive optical networks for low-cost deployment [29].  
+
+Current user- cloud data transmission relies on time division multiplexing (TDM) approaches through passive optical networks (for households and buildings) [30, 31] or radio access networks (to base stations and radio units) [32] to provide user- cloud data communications, with both employing tree- topology passive- split fibre links for cost- efficient deployment. Although the cloud- to- user data transmission, known as downstream, can be easily achieved using broadcasting and media access control (MAC) layer protocols [33], the user- to- cloud (upstream) transmission presents a major challenge due to the random and bursty nature of data generated from the users. To avoid contention when multiple users send data simultaneously, time scheduling and buffering of data frames with a large gap in between is required for user registration and dynamic bandwidth allocation (minimum 250 us due to protocols involving several two- way handshakes [34]), leading to an unavoidably large and unpredictable latency [17]. This not only negatively impacts user experience, but also presents potential high risks for user safety in applications such as remote surgery and autonomous vehicles, leading to a recent debate for legislation to provide guaranteed connection for autonomous car fleets [20].  
+
+An alternative to the currently- used TDM approach is wavelength division multiplexing (WDM) [35, 36], which offers dedicated bandwidth to each user and therefore promises guaranteed, low and stable latency user- to- cloud communications. The drawbacks that have prevented this technology from being implemented more widely is the high cost, as it requires WDM components for every remote node and user. Combined WDM- TDM approaches [37] support more users with a lower cost than a WDM- only solution, but the use of TDM still leads to contention and queuing that precludes low and stable latency [38]. Recently, electronic sub- carrier multiplexing (SCM) techniques using coherent transceivers have emerged to overcome these challenges and provide software- defined, bandwidth- flexible cloud- user connections [29, 39]. However, this requires expensive broadband ( \(>50\mathrm{GHz}\) [29]) digital optical coherent transceivers with power- hungry application- specific integrated circuits (ASICs) for every user. This high power consumption and cost runs counter to the need for low cost and low power digital infrastructure [40].  
+
+Finally, current access networks cannot provide scalable and low- cost time synchronisation with subnanosecond accuracy. The low- cost time synchronisation protocols, such as the precision time protocol (PTP), only achieve microsecond accuracies due to clock frequency deviation between device clocks [41]. A possible solution would be to implement rubidium atomic clocks, but equipping each user with such high- cost and high- power- consumption device would be impractical. A more viable solution is therefore user device clock synchronization at ns- level. However, current approaches such as Synchronous Ethernet [42] have up to 20ns time error and are not highly scalable [43]. A highly- scalable and low cost technique to clock synchronise end- user devices with sub- nanosecond accuracy is currently lacking.  
+
+Here, we overcome all the aforementioned challenges using a closely- spaced frequency division multiplexing (FDM) method to provide dedicated bandwidth for every user, enabling contention- free, clock- synchronised user- cloud upstream communication. Although this represents an WDM- only approach, it
+
+<--- Page Split --->
+
+does not require expensive WDM components at the remote node and user side, addressing the main drawback of WDM, i.e. the cost. We achieved this by disseminating a frequency comb to all users, which permits clock synchronisation and optical carrier frequency synchronisation using low- speed frequency locking, facilitating upstream FDM transmission over existing colourless passive power splitting fibre networks. It does not require any modification of deployed fibre infrastructure (i.e. our FDM approach uses conventional deployed TDM networks) and is made practical by the maturation of technologies including frequency comb generation [44, 45], low- cost narrow linewidth lasers [46, 47], laser frequency control [48, 49] and digital optical coherent receiver techniques [50].  
+
+This approach grants all users dedicated optical bandwidth for upstream data transmission without the need for time scheduling or data buffering, ensuring highly- reliable constant user- connections with low and stable latency. Our optical clock dissemination approach permits synchronised clocks for all users, providing low- jitter, highly- scalable clock synchronisation essential for sub- nanosecond timing synchronisation using PTP or SynchE [41, 42]. Further, the user transceivers only require low speed electronic and opto- electronic components (1.25 GHz in our demonstration) to transmit signals at baseband. This significantly saves the cost and power consumption of the transceivers compared to the current TDM approach, which requires each user to operate a full rate. For example, in 50 Gb/s TDM system [34, 51], each user requires a 25 GBd transceiver whilst the average per- user data rate is less than 800 Mb/s (assuming 64 users).  
+
+In this article, we demonstrate frequency comb generation with more than five hundred 2.5- GHz- spaced tones with less than 10 dB power variation, providing clock synchronisation to user transceivers with a \(< 4\) ps root- mean- square (rms) timing jitter (integrated over 1 kHz to 10 MHz) and a \(< 10\) - kHz linewidth optical carrier. Using a low- cost frequency stabilisation method, we demonstrate FDM of 64 user signals with different modulation formats, promising up to 320 users with all five demonstrated WDM bands. Up to 4.3 Gb/s per- user data rate and a total capacity of 240 Gb/s is achieved in a single 200- GHz WDM band, providing sufficient per- user data rate for time- critical applications. The radical new approach presented here promises a viable route to a scalable, future- proof, low- power and low- latency user- cloud access technology for future time- critical applications.  
+
+## 2 Results  
+
+### 2.1 Clock and frequency referenced system architecture  
+
+At the core of our system is an optical frequency comb placed at the edge cloud, which is distributed to users/customers to provide them with both a clock and optical carrier frequency reference (figure 2a). The optical frequency comb is seeded by a narrow linewidth laser to produce a low noise optical frequency reference and the tone spacing is locked to a reference clock to enable clock distribution. The large number of optical frequency comb tones enables FDM for a large number of users (e.g. up to 320 users in this demonstration). The comb tones within the same WDM channel (e.g. 100- 200 GHz bandwidth stated in the ITU- T standard) are routed to users in the same region (figure 2e), who are connected to the same passively split remote node. Each user uses a low- speed photodiode to detect the 2.5- GHz beat note that provides signal for their clock, which is detailed in the following section. Further, the users lock their transmitters to the assigned comb tones (one comb tone per user) and transmit their upstream signals within the designated optical bandwidth. This permits each user to have a dedicated optical bandwidth and synchronised clock for upstream transmission. Figure 2b shows the downstream comb after WDM demultiplexing and routing of each WDM channel to a group of users and figure 2c represents the aggregated upstream FDM signals from users using the same WDM channel.  
+
+The aggregated signals are detected and demodulated by a single broadband (160 GHz) optical coherent receiver at the edge data centre. Since the users signals are transmitted and detected within the designated optical bandwidth, the modulation formats and signal bandwidth can be flexibly adjusted to suit different traffic types without affecting other users. In our demonstration, we use low speed (4.9 GSa/s) and high- resolution (10 bit effective number of bits) digital- to- analog converters (DACs) to generate sub- carrier modulation (SCM) signals of different modulation formats. The electroabsorption modulators (EAMs) used have more than 5 GHz opto- electronic bandwidth, permitting adjustable bandwidth to suit different users' demand. Two example user cases are shown in figure 2e.
+
+<--- Page Split --->
+
+### 2.2 Comb generator and clock phase noise  
+
+Our optical frequency comb generator and the experimental setup for clock and carrier distribution are shown in figure 3a. The optical frequency comb generator comprises a 10- kHz linewidth seed laser followed by two comb generation stages. The first stage consists of an intensity modulator (IM) and two phase modulators (PM) connected in tandem, all driven with in- phase 25- GHz RF signals to yield a 1.25- THz bandwidth frequency comb with 5 dB spectral flatness (see figure 3b). The second comb generator stage uses two cascaded IM and PMs, both driven with 2.5 GHz RF signals to convert each of the 25- GHz spaced comb tones into a 2.5- GHz- spacing frequency comb with a spectral flatness of 6 dB. By locking the 25 GHz electronic phase lock loop 1 ( \(PLL_{1}\) ) with the 2.5 GHz \(PLL_{2}\) to the same 10- MHz clock source, the 2.5- GHz comb signals generated from each 25- GHz- spacing tones are frequency and phase locked, yielding a 1.25 THz bandwidth, 2.5- GHz- spacing comb signals with a spectral flatness better than 10 dB (figure 3c). The comb tones are subsequently amplified to 18 dBm using an erbium- doped fibre amplifier (EDFA) before being WDM de- multiplexed into five 200- GHz WDM grid wavelength channels, each outputting 5 dBm optical power and containing approximately 70 tones (figure 3d). The WDM demultiplexed comb tones are launched into 22 km of standard single mode fiber (SSMF), which emulates the feeder fibre in the optical access links.  
+
+The distributed clock is recovered by each user by detecting the comb beat using a 3 GHz bandwidth photodiode followed by 40 dB RF amplification. The detected 2.5 GHz clock signal shows a clean spectrum (figure 3e) and is subsequently divided to 50 MHz (inset in figure 3e) to serve as the reference clock for the user transceivers. We characterised the power budget for the distributed clock by attenuating the de- multiplexed comb signals using a variable optical attenuator (VOA) and calculating the rms timing jitter by integrating the measured phase noise from 1 kHz to 10 MHz. Using channel 4 (shown in orange in figure 3d, 193.4- 193.6 THz) as an example, the rms jitter remained below 4ps with the optical power between - 3 dBm and - 18 dBm. The abrupt increase of jitter when power drops to - 17 dBm was due to the failure of the frequency locking of the divider. The increased jitter with high optical power is due to the saturation of the RF amplifiers. These results indicate more than 23 dB power budget available for clock dissemination, permitting a remote node split ratio of more than 64. Subsequently, we measured the phase noise and the integrated jitter of the distributed clock for all WDM channels at a received optical power of - 13 dBm. As shown in figure 3g, all WDM channels show sub- 2- ps timing jitter, promising similar system performance over the whole wavelength region.  
+
+### 2.3 FDM data aggregation  
+
+To demonstrate the clock- synchronised FDM transmission, we carried out a series of experiments using a proof- of- concept system shown in figure 4a. Our system contains three live user transceivers whose lasers are frequency- locked to three neighbouring comb tones, resulting in three 2.5- GHz- spaced FDM signals after being combined by a coupler at the remote node (see figure 4b for spectrum). The user transceivers are synchronised to the optically distributed clock, eliminating any need for clock recovery at the receiver side. We use the same type of single- wavelength lasers (about 150 kHz linewidth [46]) for all transceivers. The continuous wave (CW) signals from the lasers are split by a 50:50 coupler for frequency locking and upstream data transmission. To demonstrate the simultaneous detection of all FDM signals within the same wavelength channel, we generate dummy signals by modulating tapped comb signals after 80- km decorrelation fibre and notch- filtering, shown in green in figure 4c. The aggregated upstream signals transmit back to the edge cloud side and are detected by a pre- amplified coherent receiver with 160- GHz optical bandwidth, centred at 193.407 THz (1550.08 nm). The coherent receiver uses the seed laser wavelength filtered from the 1st stage output as the local oscillator (LO). This not only provides the coherent receiver with a narrow linewidth LO, but also promises a deterministic frequency offset for user upstream signals, eliminating the carrier frequency offset (CFO) estimation in the receiver digital signal processing (DSP). We subsequently measure the bit- error- ratio (BER) performance of the upstream SCM quadrature amplitude modulation (QAM) signals. Different orders of QAM signals (4/8/16 QAM) with a root- raise- cosine pulse shape (roll- of- factor of 0.01) are generated using the user transceivers' digital- to- analog converters (DACs).  
+
+To demonstrate ability of each user to lock to any comb tone within the WDM channel necessary for flexible FDM channel allocation, we tune the live users across 160- GHz frequency region (see methods for details), with them always lock to neighbouring comb tones and are combined with dummy signals to populate the 160 GHz bandwidth. Figure 4d shows the measured receiver sensitivities using live user 1 as an example. At the soft- decision forward error code (SD- FEC) bit error rate (BER) threshold of 2e- 2 (15.3% overhead [52]), the required lowest power values are approximately - 47, - 40 and - 35 dBm,
+
+<--- Page Split --->
+
+respectively, for 4/8/16 QAM formats.  
+
+Since the user transceivers output about - 4 dBm, these results indicate a power budget of 43, 36 and 31 dB for an upstream per- use data rate of 2.14, 3.22 and 4.3 Gbit/s using 4/8/16 QAM signals, respectively. The relatively low output power was due to the high coupling loss of the used electroabsorption modulator (EAM) in this experiment (about 10 dB). A potential 4- 6 dB improvement of power budget can be expected by using low- loss modulators such as the integrated EAM [53] or Mach- Zender modulator (MZM) [6, 7].  
+
+Considering a fully populated wavelength channel, the estimated aggregated data rates are about 133, 190 and 240 Gb/s, using 4/8/16 QAM formats, respectively. The reduced power sensitivities at the edge of the optical bandwidth are primarily due to the frequency roll- off of the balanced photodiodes in the coherent receiver. Further, we study the frequency stability of the upstream user lasers. The minimum required power per tone for the frequency lock loop (FLL) is - 44 dBm. At - 35 dBm power, the maximum frequency deviation is less than 1.5 MHz over 24 hours (figure 4f). The stable frequency indicates that the system only requires a small guard band between neighbouring channels for high spectral efficiency.  
+
+## 3 Discussion  
+
+We analysed the data from recently emerging sources and showed that the challenges for future digital infrastructure is how to provide guaranteed connection with low and stable latency for time- critical applications. Our technological novelties to address these challenges include: 1) generation of a 2.5- GHz- space frequency comb using a two- stage configuration which yields a low noise, flat frequency comb with more than 500 tones to act as clock and optical frequency references; 2) dissemination of the frequency comb to users through passive fibre networks, by which we achieved clock and optical frequency synchronization for all users, allowing for dedicated bandwidth for each user using low- cost and low power consumption electronics; 3) demonstration of a proof- of- concept FDM system servicing up to 64 users with an aggregate bandwidth of 160 GHz, showing up to 4.3 Gb/s per user data rate (240Gb/s per WDM channel) with a high receiver sensitivity of - 35 dBm.  
+
+Although our demonstration uses 200- GHz wavelength demultiplexers for each WDM channel, smaller WDM channel bandwidth (e.g. 100- 160 GHz) could be used to fully utilize the available optical spectrum without any gap between neighboring WDM channels. This would straightforwardly increase the number of users to 500 by using multiple coherent receivers to detect signals from all the WDM channels. The number of users could be further increased to more than 1000 by using more wavelength channels within the low loss telecom C band, e.g. 1540- 1562nm. Wide- bandwidth flat spectra combs have been demonstrated in this wavelength region using cascaded opto- electro modulators [44], optical parametric mixing [45] or a combination of both techniques [54]. Although the demonstrated frequency combs have \(>25\) GHz tone spacing, they can be easily engineered to smaller spacing using a second stage as we have demonstrated. Importantly, erbium- doped fibre amplifiers (EDFAs) with high and flat gain over 1535- 1565 nm wavelength region are readily available to ensure sufficient power budget for the clock and optical frequency synchronisation.  
+
+In addition to providing guaranteed bandwidth, our approach also significantly reduces the RF bandwidth of user transceivers by a factor of N (where N is the number of users connect to the same remote node) compared to the conventional TDM approach. This allows for a significant reduction in power consumption and packaging costs as well as enhanced jitter tolerance and fundamentally higher receiver sensitivities due to the reduced band rate. The reduced user transceiver bandwidth also permits using high resolution DAC that cannot be achieved in high band rate signaling [55], enabling high- performance constellations or probabilistic- shaping DSP to improve dynamic range and receiver sensitivity [56]. Besides offering flexible modulation formats, the bandwidth of each user can be further split to multiple sub- bands using digital subcarrier modulation methods for optical- wireless users [57]. The enhanced performance and flexibility offered in this new system architecture opens up new opportunities in software defined networks that enable a simpler and more efficient network resource allocation [58].  
+
+As opposed to OPLL used in analog coherent communications and metrology where high bandwidth OPLLs are required to lock the optical phase [49, 59], our approach only requires stabilizing the user transceivers' frequency within a few MHz of the designated comb tone. Thus, it requires only slow and low- cost feedback control. In this proof- of- concept work, the users' CW lasers are tuned to lock to different tones using thermoelectric coolers (TECs). In practice, the user transceivers should automatically lock to the assigned FDM channels. This could be realised using network protocols or physical layer mechanisms.  
+
+Conventional wisdom in optical access networks is that tunable lasers and laser control are too costly to implement. Whilst this is true for cost- sensitive optical access systems, the new approach we show
+
+<--- Page Split --->
+
+here offers new features to ensure guaranteed bandwidth, low and stable latency, and enhanced power budget (due to low baud rate). The significant progress in laser material and control electronics in the past decade opens up new possibilities to stabilise laser frequency in temperature varying environments [60, 61]. By using the same type of laser for all users, the cost could be brought down significantly with mass production. The frequency comb, user transceivers and coherent receivers can be integrated on readily available InP photonic integration circuit (PIC) platforms [62] and the emerging heterogeneous integration platforms such as III- VI on silicon [63, 64] and thin- film \(LiNbO_{3}\) [65, 66], promising low- cost and low power consumption devices and subsystems.  
+
+The impact of the work presented here can be far beyond cloud- user telecommunications. For example, the narrow linewidth laser and the reference clock that seed the comb generator can be synchronised to light sources and clocks in other data centres [59], enabling global carrier frequency and clock synchronization over telecommunication networks for applications such as metrology, passive radar, radio astronomy as well as navigation [67]. The large coverage through telecommunication networks would provide an alternative to the satellite based clock dissemination systems (e.g. GPS) for emergency responses and recovery. Furthermore, clock and frequency synchronised transmission are desired in many applications including quantum links, telescope and micrometer/millimeter wave generation [68].  
+
+## 4 Methods  
+
+### 4.1 Comb generation and control  
+
+We use a RIO ORION laser emitting 13 dBm at 1550.08 nm as the seed source. The CW light is amplified to 33 dBm before being modulated by two PMs and an IM driven with 25- GHz RF signals generated from a low noise RF synthesizer (Rohde & Schwarz SMA100B). The RF signals that drive the PMs are amplified to 33 dBm, yielding a 25- GHz- spacing comb signal with 1.25 THz bandwidth (50 tones). The output of the 1st stage comb generator is split to two branches. The upper branch is filtered and amplified as the LO of the coherent receiver, while the lower branch seeds the 2nd stage comb generator that consists of a PM and an IM. The PM in the 2nd stage is driven with a 2.5 GHz RF signal with 30 dBm power. Both the 25 GHz and the 2.5 GHz RF signals are phase locked to the same 10 MHz reference clock. The generated 2.5- GHz- spacing comb signals has - 10 dBm optical power and is subsequently amplified to 18dBm using an EDFA.  
+
+### 4.2 End-user transceivers  
+
+We implemented three live user transceivers using the same model of single- wavelength low- cost lasers outputting 8 dBm CW signal with about 150 kHz linewidth [46]. The CW light was split by a 50:50 coupler and mixed with the downstream frequency comb to generate a beat note corresponding to the frequency difference between the CW and the selected reference tone for feedback current control, using a proportional integral (PI) controller. The frequency discriminator is based on analog electronic phase lock loop with 6 MHz locking range. A polarisation controller was used to align the lasers' output to the selected comb tone. This, however, can be eliminated by converting the linear polarisation of the CW to circular polarisation using a quarter wave plate or integrated polarisation converters [69]  
+
+The electroabsorption modulators (EAMs) have 10 dB insertion loss and an extinction ratio of more than 10 dB. They are driven with 1.072 GBaud subcarrier (SCM) QAM signals, generated using 4.9 GSa/s digital- to- analog converters (DACs). The digital SCM- QAM signals were generated offline using a pseudorandom binary sequence (PRBS) of \(2^{15}\) length, mapped to QAM symbols, shaped by a root- raise- cosine filter with a 0.01 roll- off factor, and upconverted to a carrier frequency of 0.635 GHz to generate real- value SCM- QAM signals. This allows for a 0.1 GHz gap between DC and the SCM signals in the generated large- carrier double- side band signal (LC- DSB). The frequency and phase noise can be directly estimated from the carrier [70, 71] in the receiver DSP, precluding complex carrier frequency offset (CFO) and carrier phase estimation (CPE) algorithms.  
+
+The dummy channels were generated by modulating tapped reference comb signals after transmit through 80 km SSMF for decorrelation. The decorrelated comb passes through a tunable notch filter (30 GHz bandwidth) before combining with the live signals to form the 160 GHz bandwidth upstream signals. The dummy channels are modulated by an MZM driven with 1.072 GBaud intensity- modulated SCM- 4QAM signals with a carrier- to- signal- power ratio of about 14 dB, which is similar to that of the live signals. The frequency stability is measured by calculating the spectra of the beat note waveforms.
+
+<--- Page Split --->
+
+### 4.3 Coherent receiver and digital signal processing  
+
+4.3 Coherent receiver and digital signal processingThe upstream signals are pre- amplified using an EDFA (5 dB noise figure), filtered and detected by a 70 GHz bandwidth dual- polarization coherent receiver. The waveforms were subsequently captured by a 100- GHz- bandwidth 256- GSa/s real- time oscilloscope before performing offline DSP, in which the three user channels were demodulated. The coherent receiver is referenced to the same 10- MHz clock source. Thus, no clock recovery is needed in the DSP. In addition, no dispersion compensation was required due to the low band rate per user. Since the frequency offset between the user channel and the LO is known, the received live user signals are down converted to base band without needing CFO estimation. The down converted user signals are match filtered and equalized by a pre- trained Volterra filter [72]. BER results for the live user signals are measured using 400000 bits. The sensitivities for SD- FEC threshold are estimated from the BER curves using linear interpolation (supplementary figure S1). The DSP function blocks are detailed in supplementary section IV.  
+
+### 4.4 BER and sensitivity characterization  
+
+4.4 BER and sensitivity characterizationThe sensitivities in shown in figure 4d are calculated from the BER measurement for the live user 1. The BER values are measured by varying the optical power into EDFA₃ using a variable optical attenuator (VOA), as shown in figure 3a. The power per user channel was measured using an optical spectrum analyser (OSA) of 0.01nm resolution. The each BER value is calculated using a PRBS of \(2^{15}\) length. The detailed BER results for all live users can be found in the Supplementary section I. The aggregated capacity is calculated by multiplying end user data rate with number of channels achieving sub SD- FEC BER. With 4/8/16QAM, 62, 59 and 56 channels can achieve sub SD- FEC BER. The performance of wavelength channels located at optical bandwidth edge is limited by high frequency roll- off of coherent receiver. With wide- bandwidth coherent receivers, the aggregated data rate could be further improved to 275 Gb/s using SCM- 16QAM for all 64 users.  
+
+## 5 Online content  
+
+5 Online contentAny methods, additional references, Nature Research reporting summaries, source data, extended data, supplementary information, acknowledgements, peer review information; details of author contributions and competing interests; and statements of data and code availability are available at UCL RPS.  
+
+## 6 Data availability  
+
+6 Data availabilityThe data that support the plots within this paper and other findings of this study are available from the corresponding author on reasonable request.  
+
+## 7 Author Contributions  
+
+7 Author ContributionsZ.L., Y.L., Z.Z. and K.C prepared the manuscript. Z.L. and J.W. conceived the FDM user multiplexing system architecture. Z.L. and Y.L. conceived the clock and frequency dissemination approach. K.C., R.S and Z.L. developed and implemented the FLL. C.D, R.S., Z.Z. and Z.L. developed the frequency comb source. Z.Z. and C.D. contributed to the phase noise and jitter characterisation. Z.Z. developed the clock synchronisation subsystems and characterise their performance. Z.Z. and Z.L. performed the experiments, including BER and power sensitivity testing, stabilisation of the user lasers, signal generation, coherent detection and associated performance characterisation. E.S. contributed to the coherent signal detection. Z.L., J.W. and Y.L. developed the core digital signal processing. All authors contributed to analysing the experimental results. Z.L. supervised and led the scientific collaboration.  
+
+## Acknowledgements  
+
+AcknowledgementsThe authors acknowledge financial support from EPSRC grants EP/R041792/1, EP/V051377/1, and programme grant TRANSNET EP/R035342/1. The broadband oscilloscope is funded by EPSRC equipment grant EP/V007734/1. The authors also acknowledge the National Natural Science Foundation of China 62102343.
+
+<--- Page Split --->
+
+## 8 Competing Interests Statement  
+
+The authors declare no competing interests.  
+
+## References  
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+
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+
+<--- Page Split --->
+
+
+<table><tr><td colspan="2">Virtual Reality (VR)</td><td rowspan="2">Connected Car Fleet</td></tr><tr><td>Full View</td><td>Field of View</td></tr><tr><td>Data Rate<br>&gt;1.6 Gbps</td><td>Data Rate<br>&gt;870 Mbps</td><td>Data Rate<br>&gt;1 Gbps</td></tr><tr><td>Latency<br>&lt;2 ms</td><td>Latency<br>&lt;2 ms</td><td>Latency<br>&lt;3 ms</td></tr></table>  
+
+Table 1: Future data rate and latency requirement of AR/VR devices and connected car fleet. Here, the estimates for VR targets the highest user experience with 24K resolution and a frame rate of 120 [17]. Note that different VR devices and user experience standard are estimated to co- exist in future deployment. Thus, the user transceivers must be flexible to support different data rate and formats. The estimates for the connected car fleet is obtained by considering 'AI drivers' user cases, where the car fleets exchange information including raw sensor data, vehicles' intention and coordination, enabling cooperative perception for AI drivers [22, 21]. In contrast to conventional applications that predominantly requires high bit rate for data transmission (e.g. video streaming), the above time- critical applications require bounded low latency in conjunction with the ability to scale across a large number of consumer devices.
+
+<--- Page Split --->
+![](images/Figure_1.jpg)
+
+<center>Figure 1: Trends in global increase of (a) VR/AR devices and (b) connected car fleet. a, estimated the number of consumer human machine interface devices dedicated to virtual reality (VR) and augmented reality (AR) in major areas including United States, Europe, China and Japan. The estimation suggests a booming of the AR/VR applications with an average annual growth rate (AAGR) of about \(28\%\) from 2021 to 2025, followed by a continuously strong AAGR of about \(14\%\) from 2025 to 2030. The VR/AR devices support time-critical applications such as remote surgery, immersive education, teleconference, online gaming and industrial designs [73] b, Estimations summarised collected by PricewaterhouseCoopers (PwC) and Strategy& [74], showing an increase of the connected cars in operation to 403 million by 2025, featuring an average annual growth rate (AAGR) of \(14\%\) from 2021 to 2025, followed by an AAGR of \(10\%\) , reaching 645 million by 2030. These estimates account for the largest geographical countries for connected cars of the United States, Europe, China and Japan. </center>  
+
+![](images/Figure_2.jpg)
+
+<center>Figure 2: Concept of clock and optical frequency synchronised frequency division multiplexing (FDM) upstream for time-critical applications. a, a wide-bandwidth closely-spaced frequency comb generated at the edge cloud, referenced to a source clock within an edge data centre; b, filtered frequency comb sent from an edge cloud or optical line terminal (OLT) to users; c, upstream FDM signals, each user wavelength locked to a selected tone in the distributed frequency comb, forming a wide bandwidth optical signal which is detected by a single coherent receiver; d, different wavelength division multiplexing band (e.g. 100-200GHz bandwidth) covers different passive split fibre networks. The blue, green and red colour indicate different WDM bands; e, exemplary time-critical applications including cooperative traffic system and virtual reality (VR). </center>
+
+<--- Page Split --->
+![](images/Figure_3.jpg)
+
+<center>Figure 3: The clock and carrier frequency distribution. a, A continuous wave (CW) laser seeds two stages of comb generator, yielding 1.25-THz bandwidth 2.5-GHz-spacing comb signals with 10-dB flatness. The comb signals are sent to the end-users for clock and carrier frequency synchronisation; b, spectrum of the 25-GHz-spacing comb signals output from the 1st stage, c, spectrum of the generated comb signal output from the 2nd stage; d, demultiplexed comb signals using a 200-GHz WDM each containing 64 2.5-GHz tones with about 10 dB spectral flatness; e, RF spectrum of the detected 2.5-GHz clock signal using channel 4 as example (ITU ch35, 193.4-193.6 THz); f, jitter of the 50-MHz reference clock for end-user transceivers at different received optical power. The increased jitter value from -5 to 0 dBm is due to the saturation of electronic amplifier, the decreased jitter value from -5 to -16 dBm is due to the reduced power; g, measured phase noise of the distributed reference clock signals to different WDM channels, showing a maximum root-mean-square (rms) jitter of <4 ps, integrated over 1 kHz - 10 MHz.. </center>
+
+<--- Page Split --->
+![](images/Figure_4.jpg)
+
+<center>Figure 4: Proof-of-concept experiment for the clock and frequency referenced frequency division multiplexing (FDM) upstream data aggregation for time-critical applications. a, the system diagram of our proof-of-concept experiments with three live end-users combined with dummy signals to form 160 GHz optical bandwidth signals. The optically distributed clock is sent to all live end-user transceivers as the clock reference, based on which three sets of field programmable gate arrays (FPGAs) and 4.9 Gas/s digital to analog converters (DACs) generates SCM-QAM signals and drive the corresponding intensity modulators (IMs) to generate upstream signals. The user lasers generate continuous wave (CW) signals with about 150 kHz linewidth and are frequency-locked to neighbouring comb tones using a frequency lock loop (FLL) containing a frequency detector and a proportional integral (PI) controller, with about 10 kHz loop bandwidth. Thermal-electro controller (TEC) provides feedback for long-term stability and coarse frequency tuning. Two couplers and a 10-dB attenuator are used to emulate 1:64 remote node splitting, resulting in a total link loss of about 28 dB (inc. 22 km SSMF loss, WDM loss, and the remote node splitting loss); b, optical spectrum (20 MHz resolution) of combined upstream signals, with all live transceivers locked to 2.5-GHz-spacing tones; c, optical spectrum (20 MHz resolution) of the upstream signals received: red (user1), orange (user1) and blue (user1). Green indicates the modulated dummy channels; d, measured power sensitivity (power per user signal into EDFA3) for different modulation formats at the soft-decision forward error correction code (SD-FEC) threshold of 2e-2 (15.3% overhead [SD-FEC paper]): cross markers (4QAM), open markers (8QAM), close markers (16QAM); e, measured constellation diagrams of user1; f, measured frequency deviation over 24 hours using user 1 locked at 193.407 THz. </center>
+
+<--- Page Split --->
+
+## Supplementary Files  
+
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+- NEsupplementary.pdf
+
+<--- Page Split --->

preprint/preprint__c8fb7a8d8c40d5e2a42f5be83ae10eb3cb8b522d1dcebac8cb9e7a35f230204d/preprint__c8fb7a8d8c40d5e2a42f5be83ae10eb3cb8b522d1dcebac8cb9e7a35f230204d_det.mmd

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+<|ref|>title<|/ref|><|det|>[[44, 107, 944, 210]]<|/det|>
+# Communications with Guaranteed Low Latency and Bandwidth using Frequency Referenced Multiplexing  
+
+<|ref|>text<|/ref|><|det|>[[44, 230, 285, 272]]<|/det|>
+Zichuan Zhou  University College London  
+
+<|ref|>text<|/ref|><|det|>[[44, 277, 415, 317]]<|/det|>
+Jinlong Wei  Huawei Technologies Duesseldorf GmbH  
+
+<|ref|>text<|/ref|><|det|>[[44, 323, 839, 365]]<|/det|>
+Yuan Luo  the Chinese University of Hong Kong (Shenzhen) https://orcid.org/0000- 0001- 5129- 0130  
+
+<|ref|>text<|/ref|><|det|>[[44, 370, 641, 410]]<|/det|>
+Kari Clark  University College London https://orcid.org/0000- 0003- 1988- 3205  
+
+<|ref|>text<|/ref|><|det|>[[44, 415, 283, 456]]<|/det|>
+Eric Sillekens  University College London  
+
+<|ref|>text<|/ref|><|det|>[[44, 462, 283, 503]]<|/det|>
+Callum Deakin  University College London  
+
+<|ref|>text<|/ref|><|det|>[[44, 508, 283, 549]]<|/det|>
+Ronit Sohanpal  University College London  
+
+<|ref|>text<|/ref|><|det|>[[44, 555, 291, 595]]<|/det|>
+Radan Slavik  University of Southampton  
+
+<|ref|>text<|/ref|><|det|>[[44, 600, 641, 642]]<|/det|>
+Zhixin Liu ( zhixin.liu@ucl.ac.uk)  University College London https://orcid.org/0000- 0002- 9681- 7933  
+
+<|ref|>text<|/ref|><|det|>[[44, 711, 135, 729]]<|/det|>
+Keywords:  
+
+<|ref|>text<|/ref|><|det|>[[44, 760, 299, 778]]<|/det|>
+Posted Date: April 26th, 2022  
+
+<|ref|>text<|/ref|><|det|>[[44, 798, 474, 816]]<|/det|>
+DOI: https://doi.org/10.21203/rs.3.rs- 1558939/v1  
+
+<|ref|>text<|/ref|><|det|>[[44, 835, 910, 877]]<|/det|>
+License: © This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License
+
+<--- Page Split --->
+<|ref|>title<|/ref|><|det|>[[135, 135, 863, 188]]<|/det|>
+# Communications with Guaranteed Low Latency and Bandwidth using Frequency Referenced Multiplexing  
+
+<|ref|>text<|/ref|><|det|>[[168, 202, 828, 240]]<|/det|>
+Zichuan Zhou \(^{1}\) , Jinlong Wei \(^{2}\) , Yuan Luo \(^{3}\) , Kari A. Clark \(^{1}\) , Eric Sillekens \(^{1}\) , Callum Deakin \(^{1}\) , Ronit Sohanal \(^{1}\) , Radan Slavik \(^{4}\) , and Zhixin Liu \(^{1}\)  
+
+<|ref|>text<|/ref|><|det|>[[125, 252, 870, 377]]<|/det|>
+\(^{1}\) Optical Networks Group, University College London, London, UK \(^{2}\) Huawei Technologies Duesseldorf GmbH, European Research Centre, Munich, Germany \(^{3}\) The Chinese University of Hong Kong (Shenzhen), Shenzhen, China \(^{4}\) Optoelectronic Research Centre, University of Southampton, Southampton, UK \(^{1}\) zhixin.liu@ucl.ac.uk \(^{2}\) jinlongwei2@huawei.com \(^{3}\) luoyuan@cuhk.edu.cn  
+
+<|ref|>sub_title<|/ref|><|det|>[[465, 419, 531, 433]]<|/det|>
+## Abstract  
+
+<|ref|>text<|/ref|><|det|>[[156, 438, 842, 590]]<|/det|>
+The rise of timing- critical applications such as virtual reality and connected car fleets, combined with the rapid growth of the number of user devices, creates new challenges for the latency and reliability of user- cloud data communications. Currently user- cloud communications rely on time- scheduled data frames through tree- topology fibre networks, incapable of assuring guaranteed connections with low or stable latency, which is necessary for, e.g. remote surgeries and safe operations of self- driven cars. Besides, their scalability to a larger user count is limited. Here we show that clock and optical frequency synchronisation, enabled by burgeoning frequency comb and signal processing techniques, can provide each user with dedicated optical bandwidth to enable scalable user- cloud communications that guarantees simultaneously high per- use data rate and low latency. Our approach provides accurate clock and optical frequency synchronisation over deployed optical fibre links, which will be beneficial for many applications including accurate navigation, quantum communications, and astronomy.  
+
+<|ref|>sub_title<|/ref|><|det|>[[157, 611, 342, 631]]<|/det|>
+## 1 Introduction  
+
+<|ref|>text<|/ref|><|det|>[[156, 641, 842, 822]]<|/det|>
+Two decades of vigorous growth of cloud services have made them an indispensable part of our everyday lives. It is expected that emerging applications such as virtual reality (VR), augmented reality (AR) and intelligent autonomous vehicles will continue to drive the exponential growth of global data traffic into the next decade [1]. These trends have been captured by several analyses indicating that the optical broadband traffic will outpace or even decuple in a decade [2, 3] and therefore the user bandwidth must scale accordingly to keep up with the demand [4]. These predictions have motivated the active development of electronic and opto- electronic components to 100 GHz bandwidths and beyond [5, 6, 7, 8, 9, 10, 11, 12]. These estimates contribute to the conventional wisdom [13, 14] that as demand for broadband traffic rises rapidly, so too must the end- user bandwidth. Nevertheless, though these extrapolations based on traffic growth are true for long- haul and point- to- point systems, this conventional wisdom will not apply to future user- cloud access networks due to the strong countervailing trends of the growth in the number of user devices (e.g. virtual reality headsets, traffic sensors) and their demand for guaranteed connections as well as low and stable latency to edge data centres [15, 16, 17, 18].  
+
+<|ref|>text<|/ref|><|det|>[[156, 822, 842, 905]]<|/det|>
+Here, we integrate recently- published data for VR/AR and intelligent vehicles (see figure 1), showing a radical growth in their numbers within the next decade. This data, together with the stringent requirement of low and stable latency [19], which will need to be guaranteed to, e.g. ensure traffic safety, rather than provide at the 'best effort' bases as today, when an average or mean latency is often used as a metric [18, 20]. All these aspects represent the following new technical requirements of future user- cloud communication infrastructures:
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[175, 91, 842, 134]]<|/det|>
+- They should provide low and stable latency connection in conjunction with the ability to scale across a large number of users, each with a few Gbit/s-level data rate [21, 22, 23] (data summarised in details in Table 1).  
+
+<|ref|>text<|/ref|><|det|>[[175, 136, 842, 248]]<|/det|>
+- They should provide a highly accurate synchronised clock to enable sub-nanosecond time synchronisation. For example, VR and self-driving car fleets require low-cost and highly scalable time synchronisation infrastructure to enable sub-meter scale positioning of devices [24]. Although sub-nanosecond time synchronisation is achievable using GPS, it is costly and relies on line-of-sight to the sky, which is difficult or impossible underground, within buildings or in urban canyons [25], and may be inhibited by atmospheric ash during volcanic eruptions or wartime [26]. Therefore, sub-nanosecond time synchronisation through the already deployed optical fibre access networks is highly desired.  
+
+<|ref|>text<|/ref|><|det|>[[175, 250, 842, 364]]<|/det|>
+- They should enable reconfigurability for various on-demand services with flexible modulation formats or bandwidths to support widely varying applications [23, 27]. For example, co-operative concerts through the internet only require a moderate data rate but have a stringent requirement of low and stable latency. Low order formats such as quadrature phase shift keying (QPSK) should be used to provide low bit error rate (BER) and forward error correction (FEC) free signalling to minimize latency and power consumption [16]. Remote education and remote work, however, require a high data rate to transmit high resolution video with a relaxed tolerance to latency. Thus, high order formats such as 16 quadrature amplitude modulation (QAM) could be used [28].  
+
+<|ref|>text<|/ref|><|det|>[[175, 365, 841, 394]]<|/det|>
+- They should also be compatible with legacy infrastructures such as existing mobile fronthaul and passive optical networks for low-cost deployment [29].  
+
+<|ref|>text<|/ref|><|det|>[[155, 412, 842, 592]]<|/det|>
+Current user- cloud data transmission relies on time division multiplexing (TDM) approaches through passive optical networks (for households and buildings) [30, 31] or radio access networks (to base stations and radio units) [32] to provide user- cloud data communications, with both employing tree- topology passive- split fibre links for cost- efficient deployment. Although the cloud- to- user data transmission, known as downstream, can be easily achieved using broadcasting and media access control (MAC) layer protocols [33], the user- to- cloud (upstream) transmission presents a major challenge due to the random and bursty nature of data generated from the users. To avoid contention when multiple users send data simultaneously, time scheduling and buffering of data frames with a large gap in between is required for user registration and dynamic bandwidth allocation (minimum 250 us due to protocols involving several two- way handshakes [34]), leading to an unavoidably large and unpredictable latency [17]. This not only negatively impacts user experience, but also presents potential high risks for user safety in applications such as remote surgery and autonomous vehicles, leading to a recent debate for legislation to provide guaranteed connection for autonomous car fleets [20].  
+
+<|ref|>text<|/ref|><|det|>[[155, 592, 842, 758]]<|/det|>
+An alternative to the currently- used TDM approach is wavelength division multiplexing (WDM) [35, 36], which offers dedicated bandwidth to each user and therefore promises guaranteed, low and stable latency user- to- cloud communications. The drawbacks that have prevented this technology from being implemented more widely is the high cost, as it requires WDM components for every remote node and user. Combined WDM- TDM approaches [37] support more users with a lower cost than a WDM- only solution, but the use of TDM still leads to contention and queuing that precludes low and stable latency [38]. Recently, electronic sub- carrier multiplexing (SCM) techniques using coherent transceivers have emerged to overcome these challenges and provide software- defined, bandwidth- flexible cloud- user connections [29, 39]. However, this requires expensive broadband ( \(>50\mathrm{GHz}\) [29]) digital optical coherent transceivers with power- hungry application- specific integrated circuits (ASICs) for every user. This high power consumption and cost runs counter to the need for low cost and low power digital infrastructure [40].  
+
+<|ref|>text<|/ref|><|det|>[[155, 758, 842, 868]]<|/det|>
+Finally, current access networks cannot provide scalable and low- cost time synchronisation with subnanosecond accuracy. The low- cost time synchronisation protocols, such as the precision time protocol (PTP), only achieve microsecond accuracies due to clock frequency deviation between device clocks [41]. A possible solution would be to implement rubidium atomic clocks, but equipping each user with such high- cost and high- power- consumption device would be impractical. A more viable solution is therefore user device clock synchronization at ns- level. However, current approaches such as Synchronous Ethernet [42] have up to 20ns time error and are not highly scalable [43]. A highly- scalable and low cost technique to clock synchronise end- user devices with sub- nanosecond accuracy is currently lacking.  
+
+<|ref|>text<|/ref|><|det|>[[155, 869, 841, 911]]<|/det|>
+Here, we overcome all the aforementioned challenges using a closely- spaced frequency division multiplexing (FDM) method to provide dedicated bandwidth for every user, enabling contention- free, clock- synchronised user- cloud upstream communication. Although this represents an WDM- only approach, it
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[155, 91, 842, 202]]<|/det|>
+does not require expensive WDM components at the remote node and user side, addressing the main drawback of WDM, i.e. the cost. We achieved this by disseminating a frequency comb to all users, which permits clock synchronisation and optical carrier frequency synchronisation using low- speed frequency locking, facilitating upstream FDM transmission over existing colourless passive power splitting fibre networks. It does not require any modification of deployed fibre infrastructure (i.e. our FDM approach uses conventional deployed TDM networks) and is made practical by the maturation of technologies including frequency comb generation [44, 45], low- cost narrow linewidth lasers [46, 47], laser frequency control [48, 49] and digital optical coherent receiver techniques [50].  
+
+<|ref|>text<|/ref|><|det|>[[155, 202, 842, 341]]<|/det|>
+This approach grants all users dedicated optical bandwidth for upstream data transmission without the need for time scheduling or data buffering, ensuring highly- reliable constant user- connections with low and stable latency. Our optical clock dissemination approach permits synchronised clocks for all users, providing low- jitter, highly- scalable clock synchronisation essential for sub- nanosecond timing synchronisation using PTP or SynchE [41, 42]. Further, the user transceivers only require low speed electronic and opto- electronic components (1.25 GHz in our demonstration) to transmit signals at baseband. This significantly saves the cost and power consumption of the transceivers compared to the current TDM approach, which requires each user to operate a full rate. For example, in 50 Gb/s TDM system [34, 51], each user requires a 25 GBd transceiver whilst the average per- user data rate is less than 800 Mb/s (assuming 64 users).  
+
+<|ref|>text<|/ref|><|det|>[[155, 341, 842, 467]]<|/det|>
+In this article, we demonstrate frequency comb generation with more than five hundred 2.5- GHz- spaced tones with less than 10 dB power variation, providing clock synchronisation to user transceivers with a \(< 4\) ps root- mean- square (rms) timing jitter (integrated over 1 kHz to 10 MHz) and a \(< 10\) - kHz linewidth optical carrier. Using a low- cost frequency stabilisation method, we demonstrate FDM of 64 user signals with different modulation formats, promising up to 320 users with all five demonstrated WDM bands. Up to 4.3 Gb/s per- user data rate and a total capacity of 240 Gb/s is achieved in a single 200- GHz WDM band, providing sufficient per- user data rate for time- critical applications. The radical new approach presented here promises a viable route to a scalable, future- proof, low- power and low- latency user- cloud access technology for future time- critical applications.  
+
+<|ref|>sub_title<|/ref|><|det|>[[155, 486, 281, 505]]<|/det|>
+## 2 Results  
+
+<|ref|>sub_title<|/ref|><|det|>[[155, 516, 707, 534]]<|/det|>
+### 2.1 Clock and frequency referenced system architecture  
+
+<|ref|>text<|/ref|><|det|>[[155, 540, 842, 736]]<|/det|>
+At the core of our system is an optical frequency comb placed at the edge cloud, which is distributed to users/customers to provide them with both a clock and optical carrier frequency reference (figure 2a). The optical frequency comb is seeded by a narrow linewidth laser to produce a low noise optical frequency reference and the tone spacing is locked to a reference clock to enable clock distribution. The large number of optical frequency comb tones enables FDM for a large number of users (e.g. up to 320 users in this demonstration). The comb tones within the same WDM channel (e.g. 100- 200 GHz bandwidth stated in the ITU- T standard) are routed to users in the same region (figure 2e), who are connected to the same passively split remote node. Each user uses a low- speed photodiode to detect the 2.5- GHz beat note that provides signal for their clock, which is detailed in the following section. Further, the users lock their transmitters to the assigned comb tones (one comb tone per user) and transmit their upstream signals within the designated optical bandwidth. This permits each user to have a dedicated optical bandwidth and synchronised clock for upstream transmission. Figure 2b shows the downstream comb after WDM demultiplexing and routing of each WDM channel to a group of users and figure 2c represents the aggregated upstream FDM signals from users using the same WDM channel.  
+
+<|ref|>text<|/ref|><|det|>[[155, 736, 842, 845]]<|/det|>
+The aggregated signals are detected and demodulated by a single broadband (160 GHz) optical coherent receiver at the edge data centre. Since the users signals are transmitted and detected within the designated optical bandwidth, the modulation formats and signal bandwidth can be flexibly adjusted to suit different traffic types without affecting other users. In our demonstration, we use low speed (4.9 GSa/s) and high- resolution (10 bit effective number of bits) digital- to- analog converters (DACs) to generate sub- carrier modulation (SCM) signals of different modulation formats. The electroabsorption modulators (EAMs) used have more than 5 GHz opto- electronic bandwidth, permitting adjustable bandwidth to suit different users' demand. Two example user cases are shown in figure 2e.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[155, 88, 577, 106]]<|/det|>
+### 2.2 Comb generator and clock phase noise  
+
+<|ref|>text<|/ref|><|det|>[[155, 111, 842, 320]]<|/det|>
+Our optical frequency comb generator and the experimental setup for clock and carrier distribution are shown in figure 3a. The optical frequency comb generator comprises a 10- kHz linewidth seed laser followed by two comb generation stages. The first stage consists of an intensity modulator (IM) and two phase modulators (PM) connected in tandem, all driven with in- phase 25- GHz RF signals to yield a 1.25- THz bandwidth frequency comb with 5 dB spectral flatness (see figure 3b). The second comb generator stage uses two cascaded IM and PMs, both driven with 2.5 GHz RF signals to convert each of the 25- GHz spaced comb tones into a 2.5- GHz- spacing frequency comb with a spectral flatness of 6 dB. By locking the 25 GHz electronic phase lock loop 1 ( \(PLL_{1}\) ) with the 2.5 GHz \(PLL_{2}\) to the same 10- MHz clock source, the 2.5- GHz comb signals generated from each 25- GHz- spacing tones are frequency and phase locked, yielding a 1.25 THz bandwidth, 2.5- GHz- spacing comb signals with a spectral flatness better than 10 dB (figure 3c). The comb tones are subsequently amplified to 18 dBm using an erbium- doped fibre amplifier (EDFA) before being WDM de- multiplexed into five 200- GHz WDM grid wavelength channels, each outputting 5 dBm optical power and containing approximately 70 tones (figure 3d). The WDM demultiplexed comb tones are launched into 22 km of standard single mode fiber (SSMF), which emulates the feeder fibre in the optical access links.  
+
+<|ref|>text<|/ref|><|det|>[[155, 320, 842, 513]]<|/det|>
+The distributed clock is recovered by each user by detecting the comb beat using a 3 GHz bandwidth photodiode followed by 40 dB RF amplification. The detected 2.5 GHz clock signal shows a clean spectrum (figure 3e) and is subsequently divided to 50 MHz (inset in figure 3e) to serve as the reference clock for the user transceivers. We characterised the power budget for the distributed clock by attenuating the de- multiplexed comb signals using a variable optical attenuator (VOA) and calculating the rms timing jitter by integrating the measured phase noise from 1 kHz to 10 MHz. Using channel 4 (shown in orange in figure 3d, 193.4- 193.6 THz) as an example, the rms jitter remained below 4ps with the optical power between - 3 dBm and - 18 dBm. The abrupt increase of jitter when power drops to - 17 dBm was due to the failure of the frequency locking of the divider. The increased jitter with high optical power is due to the saturation of the RF amplifiers. These results indicate more than 23 dB power budget available for clock dissemination, permitting a remote node split ratio of more than 64. Subsequently, we measured the phase noise and the integrated jitter of the distributed clock for all WDM channels at a received optical power of - 13 dBm. As shown in figure 3g, all WDM channels show sub- 2- ps timing jitter, promising similar system performance over the whole wavelength region.  
+
+<|ref|>sub_title<|/ref|><|det|>[[156, 530, 427, 547]]<|/det|>
+### 2.3 FDM data aggregation  
+
+<|ref|>text<|/ref|><|det|>[[155, 553, 842, 817]]<|/det|>
+To demonstrate the clock- synchronised FDM transmission, we carried out a series of experiments using a proof- of- concept system shown in figure 4a. Our system contains three live user transceivers whose lasers are frequency- locked to three neighbouring comb tones, resulting in three 2.5- GHz- spaced FDM signals after being combined by a coupler at the remote node (see figure 4b for spectrum). The user transceivers are synchronised to the optically distributed clock, eliminating any need for clock recovery at the receiver side. We use the same type of single- wavelength lasers (about 150 kHz linewidth [46]) for all transceivers. The continuous wave (CW) signals from the lasers are split by a 50:50 coupler for frequency locking and upstream data transmission. To demonstrate the simultaneous detection of all FDM signals within the same wavelength channel, we generate dummy signals by modulating tapped comb signals after 80- km decorrelation fibre and notch- filtering, shown in green in figure 4c. The aggregated upstream signals transmit back to the edge cloud side and are detected by a pre- amplified coherent receiver with 160- GHz optical bandwidth, centred at 193.407 THz (1550.08 nm). The coherent receiver uses the seed laser wavelength filtered from the 1st stage output as the local oscillator (LO). This not only provides the coherent receiver with a narrow linewidth LO, but also promises a deterministic frequency offset for user upstream signals, eliminating the carrier frequency offset (CFO) estimation in the receiver digital signal processing (DSP). We subsequently measure the bit- error- ratio (BER) performance of the upstream SCM quadrature amplitude modulation (QAM) signals. Different orders of QAM signals (4/8/16 QAM) with a root- raise- cosine pulse shape (roll- of- factor of 0.01) are generated using the user transceivers' digital- to- analog converters (DACs).  
+
+<|ref|>text<|/ref|><|det|>[[155, 817, 842, 901]]<|/det|>
+To demonstrate ability of each user to lock to any comb tone within the WDM channel necessary for flexible FDM channel allocation, we tune the live users across 160- GHz frequency region (see methods for details), with them always lock to neighbouring comb tones and are combined with dummy signals to populate the 160 GHz bandwidth. Figure 4d shows the measured receiver sensitivities using live user 1 as an example. At the soft- decision forward error code (SD- FEC) bit error rate (BER) threshold of 2e- 2 (15.3% overhead [52]), the required lowest power values are approximately - 47, - 40 and - 35 dBm,
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[156, 92, 411, 105]]<|/det|>
+respectively, for 4/8/16 QAM formats.  
+
+<|ref|>text<|/ref|><|det|>[[156, 105, 841, 189]]<|/det|>
+Since the user transceivers output about - 4 dBm, these results indicate a power budget of 43, 36 and 31 dB for an upstream per- use data rate of 2.14, 3.22 and 4.3 Gbit/s using 4/8/16 QAM signals, respectively. The relatively low output power was due to the high coupling loss of the used electroabsorption modulator (EAM) in this experiment (about 10 dB). A potential 4- 6 dB improvement of power budget can be expected by using low- loss modulators such as the integrated EAM [53] or Mach- Zender modulator (MZM) [6, 7].  
+
+<|ref|>text<|/ref|><|det|>[[156, 188, 841, 286]]<|/det|>
+Considering a fully populated wavelength channel, the estimated aggregated data rates are about 133, 190 and 240 Gb/s, using 4/8/16 QAM formats, respectively. The reduced power sensitivities at the edge of the optical bandwidth are primarily due to the frequency roll- off of the balanced photodiodes in the coherent receiver. Further, we study the frequency stability of the upstream user lasers. The minimum required power per tone for the frequency lock loop (FLL) is - 44 dBm. At - 35 dBm power, the maximum frequency deviation is less than 1.5 MHz over 24 hours (figure 4f). The stable frequency indicates that the system only requires a small guard band between neighbouring channels for high spectral efficiency.  
+
+<|ref|>sub_title<|/ref|><|det|>[[156, 306, 317, 325]]<|/det|>
+## 3 Discussion  
+
+<|ref|>text<|/ref|><|det|>[[156, 335, 841, 475]]<|/det|>
+We analysed the data from recently emerging sources and showed that the challenges for future digital infrastructure is how to provide guaranteed connection with low and stable latency for time- critical applications. Our technological novelties to address these challenges include: 1) generation of a 2.5- GHz- space frequency comb using a two- stage configuration which yields a low noise, flat frequency comb with more than 500 tones to act as clock and optical frequency references; 2) dissemination of the frequency comb to users through passive fibre networks, by which we achieved clock and optical frequency synchronization for all users, allowing for dedicated bandwidth for each user using low- cost and low power consumption electronics; 3) demonstration of a proof- of- concept FDM system servicing up to 64 users with an aggregate bandwidth of 160 GHz, showing up to 4.3 Gb/s per user data rate (240Gb/s per WDM channel) with a high receiver sensitivity of - 35 dBm.  
+
+<|ref|>text<|/ref|><|det|>[[156, 474, 841, 640]]<|/det|>
+Although our demonstration uses 200- GHz wavelength demultiplexers for each WDM channel, smaller WDM channel bandwidth (e.g. 100- 160 GHz) could be used to fully utilize the available optical spectrum without any gap between neighboring WDM channels. This would straightforwardly increase the number of users to 500 by using multiple coherent receivers to detect signals from all the WDM channels. The number of users could be further increased to more than 1000 by using more wavelength channels within the low loss telecom C band, e.g. 1540- 1562nm. Wide- bandwidth flat spectra combs have been demonstrated in this wavelength region using cascaded opto- electro modulators [44], optical parametric mixing [45] or a combination of both techniques [54]. Although the demonstrated frequency combs have \(>25\) GHz tone spacing, they can be easily engineered to smaller spacing using a second stage as we have demonstrated. Importantly, erbium- doped fibre amplifiers (EDFAs) with high and flat gain over 1535- 1565 nm wavelength region are readily available to ensure sufficient power budget for the clock and optical frequency synchronisation.  
+
+<|ref|>text<|/ref|><|det|>[[156, 640, 841, 792]]<|/det|>
+In addition to providing guaranteed bandwidth, our approach also significantly reduces the RF bandwidth of user transceivers by a factor of N (where N is the number of users connect to the same remote node) compared to the conventional TDM approach. This allows for a significant reduction in power consumption and packaging costs as well as enhanced jitter tolerance and fundamentally higher receiver sensitivities due to the reduced band rate. The reduced user transceiver bandwidth also permits using high resolution DAC that cannot be achieved in high band rate signaling [55], enabling high- performance constellations or probabilistic- shaping DSP to improve dynamic range and receiver sensitivity [56]. Besides offering flexible modulation formats, the bandwidth of each user can be further split to multiple sub- bands using digital subcarrier modulation methods for optical- wireless users [57]. The enhanced performance and flexibility offered in this new system architecture opens up new opportunities in software defined networks that enable a simpler and more efficient network resource allocation [58].  
+
+<|ref|>text<|/ref|><|det|>[[156, 792, 841, 875]]<|/det|>
+As opposed to OPLL used in analog coherent communications and metrology where high bandwidth OPLLs are required to lock the optical phase [49, 59], our approach only requires stabilizing the user transceivers' frequency within a few MHz of the designated comb tone. Thus, it requires only slow and low- cost feedback control. In this proof- of- concept work, the users' CW lasers are tuned to lock to different tones using thermoelectric coolers (TECs). In practice, the user transceivers should automatically lock to the assigned FDM channels. This could be realised using network protocols or physical layer mechanisms.  
+
+<|ref|>text<|/ref|><|det|>[[155, 874, 841, 902]]<|/det|>
+Conventional wisdom in optical access networks is that tunable lasers and laser control are too costly to implement. Whilst this is true for cost- sensitive optical access systems, the new approach we show
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[155, 91, 842, 202]]<|/det|>
+here offers new features to ensure guaranteed bandwidth, low and stable latency, and enhanced power budget (due to low baud rate). The significant progress in laser material and control electronics in the past decade opens up new possibilities to stabilise laser frequency in temperature varying environments [60, 61]. By using the same type of laser for all users, the cost could be brought down significantly with mass production. The frequency comb, user transceivers and coherent receivers can be integrated on readily available InP photonic integration circuit (PIC) platforms [62] and the emerging heterogeneous integration platforms such as III- VI on silicon [63, 64] and thin- film \(LiNbO_{3}\) [65, 66], promising low- cost and low power consumption devices and subsystems.  
+
+<|ref|>text<|/ref|><|det|>[[155, 202, 842, 314]]<|/det|>
+The impact of the work presented here can be far beyond cloud- user telecommunications. For example, the narrow linewidth laser and the reference clock that seed the comb generator can be synchronised to light sources and clocks in other data centres [59], enabling global carrier frequency and clock synchronization over telecommunication networks for applications such as metrology, passive radar, radio astronomy as well as navigation [67]. The large coverage through telecommunication networks would provide an alternative to the satellite based clock dissemination systems (e.g. GPS) for emergency responses and recovery. Furthermore, clock and frequency synchronised transmission are desired in many applications including quantum links, telescope and micrometer/millimeter wave generation [68].  
+
+<|ref|>sub_title<|/ref|><|det|>[[156, 333, 298, 353]]<|/det|>
+## 4 Methods  
+
+<|ref|>sub_title<|/ref|><|det|>[[156, 364, 489, 382]]<|/det|>
+### 4.1 Comb generation and control  
+
+<|ref|>text<|/ref|><|det|>[[155, 387, 842, 528]]<|/det|>
+We use a RIO ORION laser emitting 13 dBm at 1550.08 nm as the seed source. The CW light is amplified to 33 dBm before being modulated by two PMs and an IM driven with 25- GHz RF signals generated from a low noise RF synthesizer (Rohde & Schwarz SMA100B). The RF signals that drive the PMs are amplified to 33 dBm, yielding a 25- GHz- spacing comb signal with 1.25 THz bandwidth (50 tones). The output of the 1st stage comb generator is split to two branches. The upper branch is filtered and amplified as the LO of the coherent receiver, while the lower branch seeds the 2nd stage comb generator that consists of a PM and an IM. The PM in the 2nd stage is driven with a 2.5 GHz RF signal with 30 dBm power. Both the 25 GHz and the 2.5 GHz RF signals are phase locked to the same 10 MHz reference clock. The generated 2.5- GHz- spacing comb signals has - 10 dBm optical power and is subsequently amplified to 18dBm using an EDFA.  
+
+<|ref|>sub_title<|/ref|><|det|>[[156, 544, 415, 560]]<|/det|>
+### 4.2 End-user transceivers  
+
+<|ref|>text<|/ref|><|det|>[[155, 566, 842, 678]]<|/det|>
+We implemented three live user transceivers using the same model of single- wavelength low- cost lasers outputting 8 dBm CW signal with about 150 kHz linewidth [46]. The CW light was split by a 50:50 coupler and mixed with the downstream frequency comb to generate a beat note corresponding to the frequency difference between the CW and the selected reference tone for feedback current control, using a proportional integral (PI) controller. The frequency discriminator is based on analog electronic phase lock loop with 6 MHz locking range. A polarisation controller was used to align the lasers' output to the selected comb tone. This, however, can be eliminated by converting the linear polarisation of the CW to circular polarisation using a quarter wave plate or integrated polarisation converters [69]  
+
+<|ref|>text<|/ref|><|det|>[[155, 678, 842, 802]]<|/det|>
+The electroabsorption modulators (EAMs) have 10 dB insertion loss and an extinction ratio of more than 10 dB. They are driven with 1.072 GBaud subcarrier (SCM) QAM signals, generated using 4.9 GSa/s digital- to- analog converters (DACs). The digital SCM- QAM signals were generated offline using a pseudorandom binary sequence (PRBS) of \(2^{15}\) length, mapped to QAM symbols, shaped by a root- raise- cosine filter with a 0.01 roll- off factor, and upconverted to a carrier frequency of 0.635 GHz to generate real- value SCM- QAM signals. This allows for a 0.1 GHz gap between DC and the SCM signals in the generated large- carrier double- side band signal (LC- DSB). The frequency and phase noise can be directly estimated from the carrier [70, 71] in the receiver DSP, precluding complex carrier frequency offset (CFO) and carrier phase estimation (CPE) algorithms.  
+
+<|ref|>text<|/ref|><|det|>[[155, 802, 842, 886]]<|/det|>
+The dummy channels were generated by modulating tapped reference comb signals after transmit through 80 km SSMF for decorrelation. The decorrelated comb passes through a tunable notch filter (30 GHz bandwidth) before combining with the live signals to form the 160 GHz bandwidth upstream signals. The dummy channels are modulated by an MZM driven with 1.072 GBaud intensity- modulated SCM- 4QAM signals with a carrier- to- signal- power ratio of about 14 dB, which is similar to that of the live signals. The frequency stability is measured by calculating the spectra of the beat note waveforms.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[156, 88, 658, 107]]<|/det|>
+### 4.3 Coherent receiver and digital signal processing  
+
+<|ref|>text<|/ref|><|det|>[[155, 111, 842, 265]]<|/det|>
+4.3 Coherent receiver and digital signal processingThe upstream signals are pre- amplified using an EDFA (5 dB noise figure), filtered and detected by a 70 GHz bandwidth dual- polarization coherent receiver. The waveforms were subsequently captured by a 100- GHz- bandwidth 256- GSa/s real- time oscilloscope before performing offline DSP, in which the three user channels were demodulated. The coherent receiver is referenced to the same 10- MHz clock source. Thus, no clock recovery is needed in the DSP. In addition, no dispersion compensation was required due to the low band rate per user. Since the frequency offset between the user channel and the LO is known, the received live user signals are down converted to base band without needing CFO estimation. The down converted user signals are match filtered and equalized by a pre- trained Volterra filter [72]. BER results for the live user signals are measured using 400000 bits. The sensitivities for SD- FEC threshold are estimated from the BER curves using linear interpolation (supplementary figure S1). The DSP function blocks are detailed in supplementary section IV.  
+
+<|ref|>sub_title<|/ref|><|det|>[[156, 281, 562, 299]]<|/det|>
+### 4.4 BER and sensitivity characterization  
+
+<|ref|>text<|/ref|><|det|>[[155, 304, 842, 444]]<|/det|>
+4.4 BER and sensitivity characterizationThe sensitivities in shown in figure 4d are calculated from the BER measurement for the live user 1. The BER values are measured by varying the optical power into EDFA₃ using a variable optical attenuator (VOA), as shown in figure 3a. The power per user channel was measured using an optical spectrum analyser (OSA) of 0.01nm resolution. The each BER value is calculated using a PRBS of \(2^{15}\) length. The detailed BER results for all live users can be found in the Supplementary section I. The aggregated capacity is calculated by multiplying end user data rate with number of channels achieving sub SD- FEC BER. With 4/8/16QAM, 62, 59 and 56 channels can achieve sub SD- FEC BER. The performance of wavelength channels located at optical bandwidth edge is limited by high frequency roll- off of coherent receiver. With wide- bandwidth coherent receivers, the aggregated data rate could be further improved to 275 Gb/s using SCM- 16QAM for all 64 users.  
+
+<|ref|>sub_title<|/ref|><|det|>[[156, 464, 366, 484]]<|/det|>
+## 5 Online content  
+
+<|ref|>text<|/ref|><|det|>[[156, 494, 842, 536]]<|/det|>
+5 Online contentAny methods, additional references, Nature Research reporting summaries, source data, extended data, supplementary information, acknowledgements, peer review information; details of author contributions and competing interests; and statements of data and code availability are available at UCL RPS.  
+
+<|ref|>sub_title<|/ref|><|det|>[[156, 556, 386, 576]]<|/det|>
+## 6 Data availability  
+
+<|ref|>text<|/ref|><|det|>[[155, 586, 841, 614]]<|/det|>
+6 Data availabilityThe data that support the plots within this paper and other findings of this study are available from the corresponding author on reasonable request.  
+
+<|ref|>sub_title<|/ref|><|det|>[[156, 635, 449, 655]]<|/det|>
+## 7 Author Contributions  
+
+<|ref|>text<|/ref|><|det|>[[155, 664, 842, 790]]<|/det|>
+7 Author ContributionsZ.L., Y.L., Z.Z. and K.C prepared the manuscript. Z.L. and J.W. conceived the FDM user multiplexing system architecture. Z.L. and Y.L. conceived the clock and frequency dissemination approach. K.C., R.S and Z.L. developed and implemented the FLL. C.D, R.S., Z.Z. and Z.L. developed the frequency comb source. Z.Z. and C.D. contributed to the phase noise and jitter characterisation. Z.Z. developed the clock synchronisation subsystems and characterise their performance. Z.Z. and Z.L. performed the experiments, including BER and power sensitivity testing, stabilisation of the user lasers, signal generation, coherent detection and associated performance characterisation. E.S. contributed to the coherent signal detection. Z.L., J.W. and Y.L. developed the core digital signal processing. All authors contributed to analysing the experimental results. Z.L. supervised and led the scientific collaboration.  
+
+<|ref|>sub_title<|/ref|><|det|>[[157, 810, 376, 830]]<|/det|>
+## Acknowledgements  
+
+<|ref|>text<|/ref|><|det|>[[156, 840, 842, 896]]<|/det|>
+AcknowledgementsThe authors acknowledge financial support from EPSRC grants EP/R041792/1, EP/V051377/1, and programme grant TRANSNET EP/R035342/1. The broadband oscilloscope is funded by EPSRC equipment grant EP/V007734/1. The authors also acknowledge the National Natural Science Foundation of China 62102343.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[155, 85, 559, 107]]<|/det|>
+## 8 Competing Interests Statement  
+
+<|ref|>text<|/ref|><|det|>[[156, 116, 447, 131]]<|/det|>
+The authors declare no competing interests.  
+
+<|ref|>sub_title<|/ref|><|det|>[[156, 150, 281, 170]]<|/det|>
+## References  
+
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+
+<--- Page Split --->
+<|ref|>table<|/ref|><|det|>[[205, 88, 790, 230]]<|/det|>
+
+<table><tr><td colspan="2">Virtual Reality (VR)</td><td rowspan="2">Connected Car Fleet</td></tr><tr><td>Full View</td><td>Field of View</td></tr><tr><td>Data Rate<br>&gt;1.6 Gbps</td><td>Data Rate<br>&gt;870 Mbps</td><td>Data Rate<br>&gt;1 Gbps</td></tr><tr><td>Latency<br>&lt;2 ms</td><td>Latency<br>&lt;2 ms</td><td>Latency<br>&lt;3 ms</td></tr></table>  
+
+<|ref|>text<|/ref|><|det|>[[153, 238, 845, 391]]<|/det|>
+Table 1: Future data rate and latency requirement of AR/VR devices and connected car fleet. Here, the estimates for VR targets the highest user experience with 24K resolution and a frame rate of 120 [17]. Note that different VR devices and user experience standard are estimated to co- exist in future deployment. Thus, the user transceivers must be flexible to support different data rate and formats. The estimates for the connected car fleet is obtained by considering 'AI drivers' user cases, where the car fleets exchange information including raw sensor data, vehicles' intention and coordination, enabling cooperative perception for AI drivers [22, 21]. In contrast to conventional applications that predominantly requires high bit rate for data transmission (e.g. video streaming), the above time- critical applications require bounded low latency in conjunction with the ability to scale across a large number of consumer devices.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[176, 100, 838, 292]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[152, 305, 845, 460]]<|/det|>
+<center>Figure 1: Trends in global increase of (a) VR/AR devices and (b) connected car fleet. a, estimated the number of consumer human machine interface devices dedicated to virtual reality (VR) and augmented reality (AR) in major areas including United States, Europe, China and Japan. The estimation suggests a booming of the AR/VR applications with an average annual growth rate (AAGR) of about \(28\%\) from 2021 to 2025, followed by a continuously strong AAGR of about \(14\%\) from 2025 to 2030. The VR/AR devices support time-critical applications such as remote surgery, immersive education, teleconference, online gaming and industrial designs [73] b, Estimations summarised collected by PricewaterhouseCoopers (PwC) and Strategy& [74], showing an increase of the connected cars in operation to 403 million by 2025, featuring an average annual growth rate (AAGR) of \(14\%\) from 2021 to 2025, followed by an AAGR of \(10\%\) , reaching 645 million by 2030. These estimates account for the largest geographical countries for connected cars of the United States, Europe, China and Japan. </center>  
+
+<|ref|>image<|/ref|><|det|>[[163, 508, 835, 755]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[152, 774, 845, 901]]<|/det|>
+<center>Figure 2: Concept of clock and optical frequency synchronised frequency division multiplexing (FDM) upstream for time-critical applications. a, a wide-bandwidth closely-spaced frequency comb generated at the edge cloud, referenced to a source clock within an edge data centre; b, filtered frequency comb sent from an edge cloud or optical line terminal (OLT) to users; c, upstream FDM signals, each user wavelength locked to a selected tone in the distributed frequency comb, forming a wide bandwidth optical signal which is detected by a single coherent receiver; d, different wavelength division multiplexing band (e.g. 100-200GHz bandwidth) covers different passive split fibre networks. The blue, green and red colour indicate different WDM bands; e, exemplary time-critical applications including cooperative traffic system and virtual reality (VR). </center>
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[185, 260, 820, 576]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[152, 617, 845, 770]]<|/det|>
+<center>Figure 3: The clock and carrier frequency distribution. a, A continuous wave (CW) laser seeds two stages of comb generator, yielding 1.25-THz bandwidth 2.5-GHz-spacing comb signals with 10-dB flatness. The comb signals are sent to the end-users for clock and carrier frequency synchronisation; b, spectrum of the 25-GHz-spacing comb signals output from the 1st stage, c, spectrum of the generated comb signal output from the 2nd stage; d, demultiplexed comb signals using a 200-GHz WDM each containing 64 2.5-GHz tones with about 10 dB spectral flatness; e, RF spectrum of the detected 2.5-GHz clock signal using channel 4 as example (ITU ch35, 193.4-193.6 THz); f, jitter of the 50-MHz reference clock for end-user transceivers at different received optical power. The increased jitter value from -5 to 0 dBm is due to the saturation of electronic amplifier, the decreased jitter value from -5 to -16 dBm is due to the reduced power; g, measured phase noise of the distributed reference clock signals to different WDM channels, showing a maximum root-mean-square (rms) jitter of <4 ps, integrated over 1 kHz - 10 MHz.. </center>
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[177, 170, 820, 540]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[152, 555, 845, 833]]<|/det|>
+<center>Figure 4: Proof-of-concept experiment for the clock and frequency referenced frequency division multiplexing (FDM) upstream data aggregation for time-critical applications. a, the system diagram of our proof-of-concept experiments with three live end-users combined with dummy signals to form 160 GHz optical bandwidth signals. The optically distributed clock is sent to all live end-user transceivers as the clock reference, based on which three sets of field programmable gate arrays (FPGAs) and 4.9 Gas/s digital to analog converters (DACs) generates SCM-QAM signals and drive the corresponding intensity modulators (IMs) to generate upstream signals. The user lasers generate continuous wave (CW) signals with about 150 kHz linewidth and are frequency-locked to neighbouring comb tones using a frequency lock loop (FLL) containing a frequency detector and a proportional integral (PI) controller, with about 10 kHz loop bandwidth. Thermal-electro controller (TEC) provides feedback for long-term stability and coarse frequency tuning. Two couplers and a 10-dB attenuator are used to emulate 1:64 remote node splitting, resulting in a total link loss of about 28 dB (inc. 22 km SSMF loss, WDM loss, and the remote node splitting loss); b, optical spectrum (20 MHz resolution) of combined upstream signals, with all live transceivers locked to 2.5-GHz-spacing tones; c, optical spectrum (20 MHz resolution) of the upstream signals received: red (user1), orange (user1) and blue (user1). Green indicates the modulated dummy channels; d, measured power sensitivity (power per user signal into EDFA3) for different modulation formats at the soft-decision forward error correction code (SD-FEC) threshold of 2e-2 (15.3% overhead [SD-FEC paper]): cross markers (4QAM), open markers (8QAM), close markers (16QAM); e, measured constellation diagrams of user1; f, measured frequency deviation over 24 hours using user 1 locked at 193.407 THz. </center>
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[44, 42, 311, 70]]<|/det|>
+## Supplementary Files  
+
+<|ref|>text<|/ref|><|det|>[[44, 93, 765, 113]]<|/det|>
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+<|ref|>text<|/ref|><|det|>[[61, 130, 272, 150]]<|/det|>
+- NEsupplementary.pdf
+
+<--- Page Split --->

preprint/preprint__c8fb81b15cc6e5507468ca0a96ab9e39e6be1e3d5cd413cdf2ddb6f5b3dd8b5c/images_list.json

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+    "caption": "Fig. 1 Experimental overview. a, Schematic diagram of the active levitated optomechanical system, including an active optical cavity (red) and a dual-beam optical tweezer (green). WDM, wavelength division multiplexer; \\(\\mathrm{C_1}\\) , \\(\\mathrm{C_2}\\) , collimators; \\(\\mathrm{L_1} \\sim \\mathrm{L_4}\\) , lenses; PBS, polarizing beam splitter; HBD, heterodyne balanced detection. b, Measured power spectra of phonons in an active cavity (coloured curve) and a passive cavity (grey curve). Inset: Photograph of the levitated microsphere detected with a Scanning Electron Microscope (SEM).",
+    "footnote": [],
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+    "caption": "Fig. 2 Experimental results of nonlinear phonon lasers with higher-order sidebands. a, Phonon population with fundamental frequency \\(\\Omega_{0}\\) as a function of intracavity mean power \\(P\\) . The measured threshold power is in good agreement with the theoretical prediction. The insets show (i) the phonon probability distributions, and (ii, iii) the phonon power spectra below and above the oscillation threshold. b, Measured oscillation dynamics (upper panel) and linewidths (lower panel) of the fundamental mode by tracing the \\(2\\mu \\mathrm{m} \\mathrm{SiO}_{2}\\) micro-sphere. c, Threshold behaviour of the nonlinear phonon laser with double frequency \\(2\\Omega_{0}\\) (white solid curve). The white dashed curves represent \\(\\pm 1\\) s.d. of each measurement, consisting of \\(5 \\times 10^{5}\\) samples. The normalized phonon probability distribution is displayed in colour. d, Measured second-order phonon autocorrelation function at zero time delay \\(g^{(2)}(0)\\) versus \\(P\\) for \\(\\Omega_{0}\\) . Inset: Measured \\(g^{(2)}(0)\\) with \\(2\\Omega_{0}\\) above the threshold. The solid curves are theoretical results. Error bars represent \\(\\pm 1\\) s.d. of each measurement, consisting of \\(5 \\times 10^{5}\\) samples.",
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+    "caption": "Fig. 3 Optical gain induced nonlinear phonon lasing with double and triple frequencies. a, Normalized optical force distributions for active (red solid curve) and passive (grey dashed curve) setups. The active case shows a strongly nonlinear distribution for the position \\(x\\) between -1 \\(\\mu \\mathrm{m}\\) and 1 \\(\\mu \\mathrm{m}\\) , while the distribution is linear in the passive case. Insets: Schematic diagrams of the active (upper panel) and passive (lower panel) cases. b, Power spectra around \\(2\\Omega_{0}\\) in the active (blue curve) and passive (grey curve) cases. Inset: 30 times magnified spectrum for better view. c, Phonon population with the triple frequency \\(3\\Omega_{0}\\) versus the intracavity mean power \\(P\\) . Phonon laser with \\(3\\Omega_{0}\\) (green dots) and thermal",
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preprint/preprint__c8fb81b15cc6e5507468ca0a96ab9e39e6be1e3d5cd413cdf2ddb6f5b3dd8b5c/preprint__c8fb81b15cc6e5507468ca0a96ab9e39e6be1e3d5cd413cdf2ddb6f5b3dd8b5c.mmd

@@ -0,0 +1,211 @@
+
+# Nonlinear phonon laser with dissipation-governed levitated optomechanics  
+
+Tengfang Kuang National University of Defense Technology  
+
+R. Huang Hunan Normal University  
+
+Wei Xiong National University of Defense Technology  
+
+Yunlan Zuo Hunan Normal University  
+
+Xiang Han National University of Defense Technology  
+
+Franco Nori RIKEN https://orcid.org/0000- 0003- 3682- 7432  
+
+Cheng- Wei Qiu National University of Singapore https://orcid.org/0000- 0002- 6605- 500X  
+
+Hui Luo National University of Defense Technology  
+
+H. Jing Hunan Normal University  
+
+Guangzong Xiao (xiaoguangzong@nudt.edu.cn) National University of Defense Technology https://orcid.org/0000- 0002- 6753- 9858  
+
+Article  
+
+Keywords:  
+
+Posted Date: January 25th, 2022  
+
+DOI: https://doi.org/10.21203/rs.3.rs- 1252606/v1  
+
+License: © This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License
+
+<--- Page Split --->
+
+# Nonlinear phonon laser with dissipation-governed levitated optomechanics  
+
+Tengfang Kuang \(^{1,5}\) , Ran Huang \(^{2,5}\) , Wei Xiong \(^{1}\) , Yunlan Zuo \(^{2}\) , Xiang Han \(^{1}\) , Franco Nori \(^{3}\) , Chengwei Qiu \(^{4,*}\) , Hui Luo \(^{1,*}\) , Hui Jing \(^{2,*}\) , Guangzong, Xiao \(^{1,*}\) \(^{1}\) College of Advanced Interdisciplinary Studies, NUDT, Changsha Hunan, 410073, China \(^{2}\) Department of Physics and Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University, Changsha 410081, China \(^{3}\) Theoretical Quantum Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako- shi, Saitama 351- 0198, Japan \(^{4}\) Department of Electrical and Computer Engineering, National University of Singapore, 4 Engineering Drive 3, Singapore, 117576, Singapore \(^{5}\) These authors contribute equally to this work \(^{*}\) email: chengwei.qiu@nus.edu.sg; luohui.luo@163. com; jinghui73@foxmail.com; xiaoguangzong@nudt.edu.cn.  
+
+Phonon lasers, exploiting coherent amplifications of phonons, have been a cornerstone for exploring quantum phononics, imaging nanomaterial structures, and realizing force sensors or phonon frequency combs. Single- mode phonon lasers, governed by dispersive optomechanical coupling, have been recently demonstrated via levitating a nanoparticle using an optical tweezer. Such levitated optomechanical (LOM) devices, with fundamental minimum of noises in high vacuum, can flexibly control large- mass objects with no internal discrete energy levels. However, it is still elusive to realize nonlinear multi- frequency phonon lasing with levitated microscale objects, dominated instead by dissipative LOM coupling due to much stronger optical scattering loss. Here, we report such a nonlinear phonon laser by employing a \(\mathrm{Yb^{3 + }}\) - doped active LOM system. We observe a 3- order of magnitude enhancement for the fundamental- mode phonon lasing, compared with that in its passive counterparts. Above the lasing threshold, higher- order mechanical sidebands emerge spontaneously. Coherent correlations are also identified for the phonon modes. Our gain- assisted dissipative LOM platform no longer relies on any complicated external feedback control.
+
+<--- Page Split --->
+
+Our work drives LOM into a new regime where it becomes promising to study mechanical properties or quantum entanglement of typical micro- size objects, such as atmospheric particulates and living cells, and build levitated force sensors with these objects for biomedical or astronomical applications.  
+
+Conventional optomechanical systems rely on fixed frames to support mechanical elements, leading to unavoidable energy dissipation and thermal loading at the nanoscale'. Levitated optomechanics (LOM), i.e., controlling motions of levitated objects with optical forces?, have provided unique advantages?, such as fundamental minimum of damping and noise, the possibility for levitating large and complex objects, as well as high degree of control over both conservative dynamics and coupling to the environment. These advantages are of significance for both fundamental studies of non- equilibrium physics or thermodynamics and applications in metrology4- 11. In recent years, remarkable achievements have been witnessed in LOM12- 14, such as the realizations of motional ground- state cooling15,16, room- temperature strong coupling17, or ultrahigh- precision torque sensing18, to name only a few. In a very recent work19, a phonon laser or coherent amplification of phonons, the quanta of vibrations, was demonstrated for a levitated nanosphere, based on dispersive LOM coupling, in which the optical resonance frequency is modulated by mechanical motion. This work offers exciting opportunities of exploring the boundary of classical and quantum worlds with levitated macroscopic objects16,20,21, as well as making hybrid quantum sensors with levitated spins22,23. Nevertheless, sophisticated external feedback controls based on electronic loops19 are needed to compensate the purely passive optical field, in order to reach the phonon lasing regime. Only single- mode output was observed for phonons above the lasing threshold, without any evidence of nonlinear high- order sidebands.  
+
+Except for LOM systems, phonon lasers have also been built by using e.g., semiconductor superlattices24, nanomagnets25, single ions26, and nanomechanical27 or electromechanical28 devices. These coherent sound sources, with shorter wavelength of operation than that of a photon laser of the same frequency, are indispensable in steering phonon chips30, improving the resolution of motional sensors31, and making nonreciprocal or non- Hermitian devices32- 34. However, as far as we know, the ability of achieving nonlinear phonon lasers with multiple frequencies, has not been reported. This ability can provide the first step for many important applications such as
+
+<--- Page Split --->
+
+mechanical frequency conversion, acoustic frequency combs<sup>35</sup>, multi-wave mixing or squeezing of phonons<sup>36- 39</sup> and multi-frequency motional sensors.  
+
+In this Letter, we develop a strategy to achieve nonlinear phonon lasers for a levitated object at microscales by utilizing an active LOM system. We show that in such a system, dissipative optomechanical coupling<sup>40- 43</sup> can be significantly enhanced by introducing an optical gain, thus leading to tunable and efficient multi- frequency phonon lasers. Our system is immune from external feedback control<sup>19</sup> for achieving such phonon lasers, due to the critical role of gain. In fact, for passive systems, only thermal phonons exist for a levitated sphere with the radius \(\sim 2 \mu \mathrm{m}\) and the mass \(1 \times 10^{- 4} \mathrm{kg}\) (see Table. 1). To steer this system from a chaotic regime into a phonon lasing regime, we introduce an optical gain to increase the photon lifetime and enhance the photon- phonon coupling, thus achieving three- order- enhancement in the power spectrum of the fundamental- mode phonons, with also 30- fold narrowing in its linewidth. More importantly, above the lasing threshold, we observe higher- order sidebands with double and triple mechanical frequencies, featuring the gain- enhanced nonlinearity in this system.  
+
+Table 1|Optomechanical systems for phonon lasing   
+
+<table><tr><td>Features</td><td>WGM cavities<sup>33,44</sup></td><td>F-P cavities<sup>37</sup></td><td>Passive LOM<sup>19</sup></td><td>Active LOM</td></tr><tr><td>Optical gain</td><td>×</td><td>×</td><td>×</td><td>✓</td></tr><tr><td>Optomechanical coupling</td><td>Dispersive</td><td>Dispersive</td><td>Dispersive</td><td>Dissipative</td></tr><tr><td>External feedback</td><td>×</td><td>×</td><td>✓</td><td>×</td></tr><tr><td>Size of the oscillator</td><td>~ 50 μm</td><td>~ 1 mm</td><td>~ 0.1 μm</td><td>~ 2 μm</td></tr><tr><td>Mass of the oscillator</td><td>~ 10-9 kg</td><td>~ 10-9 kg</td><td>~ 10-18 kg</td><td>~ 10-14 kg</td></tr><tr><td>Mechanical frequency</td><td>10 ~ 100 MHz</td><td>~ 100 kHz</td><td>~ 100 kHz</td><td>~ 10 kHz</td></tr><tr><td>Nonlinear sidebands</td><td>×</td><td>×</td><td>×</td><td>✓</td></tr></table>
+
+Notation: WGM, whispering-gallery-mode; F-P, Fabry-Perot; LOM, Levitated optomechanics; \(\checkmark\) for Yes; \(\times\) for No.  
+
+New characteristics of our work include the following 3 major points. First, oscillators of the phonon lasers are significantly distinct: the size or the mass of our micro- sphere is 3 or 4 orders larger than the nano- sphere<sup>19</sup>, and our LOM systems can thus capture typical micro- size objects and measure their mechanical properties, which is unattainable by nanoscale levitated devices. Second, the physical mechanisms are fundamentally different: our system is governed by the dissipative LOM coupling, due to much stronger optical scattering losses by much larger objects, in contrast to the dispersive LOM coupling in previous works dealing with nanoscale
+
+<--- Page Split --->
+
+objects; Third, the nature of phonon lasers are clearly different: we not only demonstrate a fundamental- mode phonon laser, but also observe for the first time coherent higher- order phonon sidebands, including their lasing threshold feature and second- order correlations. In a broader view, our gain- assisted dissipative LOM platform opens the possibility to achieve highly- sensitive LOM control of various micro- size objects, which is of utmost importance for both fundamental studies of macroscopic quantum physics and practical metrology.  
+
+![](images/Figure_1.jpg)
+
+<center>Fig. 1 Experimental overview. a, Schematic diagram of the active levitated optomechanical system, including an active optical cavity (red) and a dual-beam optical tweezer (green). WDM, wavelength division multiplexer; \(\mathrm{C_1}\) , \(\mathrm{C_2}\) , collimators; \(\mathrm{L_1} \sim \mathrm{L_4}\) , lenses; PBS, polarizing beam splitter; HBD, heterodyne balanced detection. b, Measured power spectra of phonons in an active cavity (coloured curve) and a passive cavity (grey curve). Inset: Photograph of the levitated microsphere detected with a Scanning Electron Microscope (SEM). </center>  
+
+\(1\mu \mathrm{s}\) , which benefits enhanced coherent vibrational amplifications of the sphere. In addition, due to the presence of the optical cavity, our system is free of any need of using complicated feedback control devices \(^{19}\) (see Supplementary Section 1 for details). As shown in Fig. 1b, essentially different features can be observed in the power spectrums of phonons between our active LOM system and the purely passive system. We see that in the absence of any gain, only thermal phonons can exist; in sharp contrast, three- order- of- magnitude enhancement is achieved in the presence of an
+
+<--- Page Split --->
+
+Moreover, by tuning the pump power, high-order sidebands with mechanical multiple frequencies \(2\Omega_{0}\) , \(3\Omega_{0}\) , ... can also be observed in the spectrum (see also Supplementary Section 1). This enables us to realize a nonlinear multiple-frequency phonon laser in such an active LOM system.  
+
+![](images/Figure_2.jpg)
+
+<center>Fig. 2 Experimental results of nonlinear phonon lasers with higher-order sidebands. a, Phonon population with fundamental frequency \(\Omega_{0}\) as a function of intracavity mean power \(P\) . The measured threshold power is in good agreement with the theoretical prediction. The insets show (i) the phonon probability distributions, and (ii, iii) the phonon power spectra below and above the oscillation threshold. b, Measured oscillation dynamics (upper panel) and linewidths (lower panel) of the fundamental mode by tracing the \(2\mu \mathrm{m} \mathrm{SiO}_{2}\) micro-sphere. c, Threshold behaviour of the nonlinear phonon laser with double frequency \(2\Omega_{0}\) (white solid curve). The white dashed curves represent \(\pm 1\) s.d. of each measurement, consisting of \(5 \times 10^{5}\) samples. The normalized phonon probability distribution is displayed in colour. d, Measured second-order phonon autocorrelation function at zero time delay \(g^{(2)}(0)\) versus \(P\) for \(\Omega_{0}\) . Inset: Measured \(g^{(2)}(0)\) with \(2\Omega_{0}\) above the threshold. The solid curves are theoretical results. Error bars represent \(\pm 1\) s.d. of each measurement, consisting of \(5 \times 10^{5}\) samples. </center>  
+
+\(\langle N \rangle = M \Omega_{0} \langle x^{2} \rangle / \hbar\) , where \(M\) is the mass of the levitated sphere, \(\Omega_{0}\) is the oscillation frequency of the mode, \(x\) is the centre of
+
+<--- Page Split --->
+
+\(h\) is the reduced Planck's constant. Explicit signatures of a lasing threshold can be observed for the fundamental mode with the frequency \(\Omega_0\) , as shown in Fig. 2a, by increasing the intracavity mean power \(P\) . The threshold value is \(P_{\mathrm{th}} = 0.37 \mathrm{mW}\) , which agrees well with theoretical calculations (Supplementary Section 2). The insets of Fig. 2a showcase a linewidth narrowing, accompanying the transition from thermal to coherent oscillations. Below the threshold, the oscillator experiences thermal dynamics with mean phonon number \(5.89 \times 10^8\) , and the phonon probability distribution is well described by the Boltzmann distribution. By surpassing the lasing threshold, the phonon number is greatly enhanced to \(1.02 \times 10^{10}\) at \(P = 1.2 \mathrm{mW}\) , also in conjunction with significant narrowing of linewidth. This is closely related to the fact that the system is switched from spontaneous to stimulated emissions above lasing threshold, resulting in the Gaussian distribution of the generated coherent phonons.  
+
+Figure 2b further presents the experimental results of the dynamical behaviours of the sphere. We find that significant vibrational amplifications of the micro- sphere emerge above the lasing threshold. 30- fold improvement in linewidth narrowing is achieved here, compared to purely lossy systems. Clearly, in the passive system, the interaction between the intracavity light and the levitated microsphere is rather weak, due to the large optical loss, that the linewidth remains at about \(2.5 \mathrm{kHz}\) . However, when introducing the gain, the linewidth can be significantly modulated by the intracavity power \(P\) , and approaches as low as \(0.08 \mathrm{kHz}\) (above the threshold).  
+
+Intriguingly, apart from the giant enhancement of fundamental- mode phonon lasing, we also observe spontaneously emerging mechanical higher- order sidebands. Therefore, we reveal the phonon population of the double- frequency mode by filtering out thermal phonons and fundamental- mode phonons. We find similar lasing features for the double- frequency mechanical mode as seen in Fig. 2c, differing from the single- mode phonon laser achieved in the previous works<sup>19,26,28,33,44</sup>. It is also distinguished from the multi- mode phonon laser demonstrated with a flat membrane trapped in a Fabre- Perot cavity<sup>37</sup>, in which mode competitions make it only possible to stimulate one single phonon mode into the lasing regime.  
+
+\[g^{(2)}(0) = (\langle N^2 \rangle - \langle N \rangle) / \langle N \rangle^2\]  
+
+, where \(\langle N^2 \rangle\) is the second moment of this distribution (Fig. 2d). For the lowest- order
+
+<--- Page Split --->
+
+\(\Omega_{0}\) , we find \(g^{(2)}(0) = 2\) below the threshold \(P_{\mathrm{th}}\) , demonstrating the thermal statistics. As \(P\) well exceeds \(P_{\mathrm{th}}\) , \(g^{(2)}(0)\) is decreased to 1, which indicates that the phonon dynamics changes from thermal state to coherent state, i.e., the oscillation of the levitated micro-sphere is stimulated into the lasing regime. Moreover, we find \(g^{(2)}(0)\) approaches 1 for the nonlinear phonon laser with \(2\Omega_{0}\) when operating in the lasing regime, as shown in the onset of Fig. 2d.  
+
+![](images/Figure_3.jpg)
+
+<center>Fig. 3 Optical gain induced nonlinear phonon lasing with double and triple frequencies. a, Normalized optical force distributions for active (red solid curve) and passive (grey dashed curve) setups. The active case shows a strongly nonlinear distribution for the position \(x\) between -1 \(\mu \mathrm{m}\) and 1 \(\mu \mathrm{m}\) , while the distribution is linear in the passive case. Insets: Schematic diagrams of the active (upper panel) and passive (lower panel) cases. b, Power spectra around \(2\Omega_{0}\) in the active (blue curve) and passive (grey curve) cases. Inset: 30 times magnified spectrum for better view. c, Phonon population with the triple frequency \(3\Omega_{0}\) versus the intracavity mean power \(P\) . Phonon laser with \(3\Omega_{0}\) (green dots) and thermal </center>
+
+<--- Page Split --->
+
+phonons (grey curve) are observed in the active and passive cases, respectively. Inset: Power spectra around \(3\Omega_0\) in the passive and active cases.  
+
+This nonlinear phonon laser results from the anharmonic optical potential produced by the optical- gain- enhanced nonlinearity. Without optical gain, the intracavity light is scattered by the levitated sphere of larger size than that in Ref. \(^{19}\) , leading to a small cavity quality factor and a weak interaction between the cavity field and mechanical oscillator. Therefore, one can find the intracavity optical power \(P\) is independent of the \(x\) - position of the oscillator (Supplementary Section 3), while the optical force \(F_{\mathrm{opt}}\) , relying on both of \(P\) and \(x\) , responds linearly to the position \(x\) (Fig. 3a). However, for the active case, the intracavity optical power can be modulated by the mechanical position due to the strong interaction between the light and oscillator. Thus, we can find a strongly nonlinear optical force for the active case, as shown in Fig. 3a. As a result, the double- frequency component emerges in the phonon power spectrum (Fig. 3b). We find a two- order- of- magnitude enhanced amplitude in our active system compared to the conventional passive system with the same intracavity mean power \(P = 1.2 \mathrm{mW}\) . Similar lasing features are also observed for the phonon mode with the triple- frequency \(3\Omega_0\) as shown in Fig. 3c, which again cannot be achieved in the absence of optical gain.  
+
+In summary, we have experimentally reported nonlinear phonon lasers in active LOM. By introducing optical gain, we have realized a phonon laser on the fundamental mode with three- order- of- magnitude enhancement in the power spectrum, and thirty- fold improvement in linewidth narrowing, without the need of any complicated external feedback control techniques. We also present unequivocal evidence of lasing threshold behaviour, and the phase transition from thermal to coherent phonons by measuring the phonon autocorrelations. More interestingly, for the first time, we observe nonlinear phonon lasers with multiple frequencies, resulting from the optical- gain- enhanced nonlinearity. As far as we know, this is the first observation of such nonlinear mechanical sidebands in LOM systems, which does not rely on the specific material or the shape of the oscillator \(^{45}\) . We measured also quantum correlations \(g^{(2)}(0)\) of sideband phonon lasing for the first time. These results push forward phonon lasers into the nonlinear regime and make many exciting applications more accessible, such as optomechanical combs \(^{35}\) , high- precision metrology, and non- classical state engineering. Our work opens up new perspectives for achieving levitated phonon devices with active LOM, and enables a wide range of applications such as quantum
+
+<--- Page Split --->
+
+phononics, multi- frequency mechanical sensors, and high- precision acoustic frequency combs.  
+
+## Methods  
+
+Cavity alignment. We mount the pumping laser to one collimator (Thorlabs, ZC618FC- B), and a power meter to another. The alignment is evaluated by the coupling coefficient from one collimator to another. Through adjusting the lenses and mirrors, the loss of the free- space optical path can be regulated to its lowest value (usually lower than 0.31 dB).  
+
+Micro- sphere trapping. The micro- sphere (diameter, \(2\mu \mathrm{m}\) ) was loaded to the trapping region by using an ultrasonic nebulizer, composed of an ultrasonic sheet metal with a great number of \(5\mu \mathrm{m}\) holes distributed. It was trapped at atmospheric pressure. In most cases, a micro- sphere can be trapped within \(30\mathrm{s}\) . Then, we reduced the pressure to the desired experimental level.  
+
+## Data availability  
+
+The data that support this article are available from the corresponding author upon reasonable request.  
+
+## References  
+
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+
+## Acknowledgements  
+
+This work is supported by the National Natural Science Foundation of China (Grants Nos. 61975237, 11904405, 11935006 and 11774086), the Science and Technology Innovation Program of Hunan Province (Grant No. 2020RC4047), Independent Scientific Research Project of National University of Defense Technology (Grant No. ZZKY-YX-07-02), and Scientific Research Project of National University of Defense Technology (Grant No. ZK20-14). F.N. is supported in part by NTT Research, JST [via Q- LEAP, Moonshot R&D, and CREST], JSPS [via KAKENHI], ARO, AOARD, and FQXi. We gratefully acknowledge the valuable assistance from Bin Luo at the BUPT, Yafeng Jiao, Xunwei Xu at HNU, and Zijie Liu, Weiqin Zeng, and Xinlin Chen at NUDT.  
+
+## Author contributions  
+
+G.X. and H.J. conceived the idea. T.K. and G.X. designed the experiments. T.K., W.X. and X.H. performed the experiments and analyzed the experimental data with the help of G.X. R.H. and T.K. performed the theoretical analysis and numerical simulations, guided by H.J. R.H., T.K. and Y.Z. wrote the manuscript with contributions from G.X., H.J., F.N. and C.W.Q. G.X., H.J. and H.L. support the project.
+
+<--- Page Split --->
+
+Competing interestsThe authors declare no competing interests.Additional informationSupplementary information is available for this paper at http/
+
+<--- Page Split --->
+
+## Supplementary Files  
+
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+NonlinearphononlaserAppendix.docx FigS1.1.png FigS1.2.png FigS1.3.png FigS1.4.png FigS3.1.png
+
+<--- Page Split --->

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+<|ref|>title<|/ref|><|det|>[[44, 106, 914, 175]]<|/det|>
+# Nonlinear phonon laser with dissipation-governed levitated optomechanics  
+
+<|ref|>text<|/ref|><|det|>[[44, 196, 428, 238]]<|/det|>
+Tengfang Kuang National University of Defense Technology  
+
+<|ref|>text<|/ref|><|det|>[[44, 243, 275, 284]]<|/det|>
+R. Huang Hunan Normal University  
+
+<|ref|>text<|/ref|><|det|>[[44, 290, 428, 331]]<|/det|>
+Wei Xiong National University of Defense Technology  
+
+<|ref|>text<|/ref|><|det|>[[44, 336, 275, 377]]<|/det|>
+Yunlan Zuo Hunan Normal University  
+
+<|ref|>text<|/ref|><|det|>[[44, 383, 428, 424]]<|/det|>
+Xiang Han National University of Defense Technology  
+
+<|ref|>text<|/ref|><|det|>[[44, 429, 470, 470]]<|/det|>
+Franco Nori RIKEN https://orcid.org/0000- 0003- 3682- 7432  
+
+<|ref|>text<|/ref|><|det|>[[44, 475, 697, 516]]<|/det|>
+Cheng- Wei Qiu National University of Singapore https://orcid.org/0000- 0002- 6605- 500X  
+
+<|ref|>text<|/ref|><|det|>[[44, 521, 428, 562]]<|/det|>
+Hui Luo National University of Defense Technology  
+
+<|ref|>text<|/ref|><|det|>[[44, 567, 275, 608]]<|/det|>
+H. Jing Hunan Normal University  
+
+<|ref|>text<|/ref|><|det|>[[44, 613, 785, 655]]<|/det|>
+Guangzong Xiao (xiaoguangzong@nudt.edu.cn) National University of Defense Technology https://orcid.org/0000- 0002- 6753- 9858  
+
+<|ref|>text<|/ref|><|det|>[[44, 694, 102, 712]]<|/det|>
+Article  
+
+<|ref|>text<|/ref|><|det|>[[44, 732, 137, 751]]<|/det|>
+Keywords:  
+
+<|ref|>text<|/ref|><|det|>[[44, 770, 330, 790]]<|/det|>
+Posted Date: January 25th, 2022  
+
+<|ref|>text<|/ref|><|det|>[[44, 808, 475, 828]]<|/det|>
+DOI: https://doi.org/10.21203/rs.3.rs- 1252606/v1  
+
+<|ref|>text<|/ref|><|det|>[[44, 846, 910, 890]]<|/det|>
+License: © This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License
+
+<--- Page Split --->
+<|ref|>title<|/ref|><|det|>[[168, 84, 828, 129]]<|/det|>
+# Nonlinear phonon laser with dissipation-governed levitated optomechanics  
+
+<|ref|>text<|/ref|><|det|>[[102, 152, 840, 460]]<|/det|>
+Tengfang Kuang \(^{1,5}\) , Ran Huang \(^{2,5}\) , Wei Xiong \(^{1}\) , Yunlan Zuo \(^{2}\) , Xiang Han \(^{1}\) , Franco Nori \(^{3}\) , Chengwei Qiu \(^{4,*}\) , Hui Luo \(^{1,*}\) , Hui Jing \(^{2,*}\) , Guangzong, Xiao \(^{1,*}\) \(^{1}\) College of Advanced Interdisciplinary Studies, NUDT, Changsha Hunan, 410073, China \(^{2}\) Department of Physics and Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University, Changsha 410081, China \(^{3}\) Theoretical Quantum Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako- shi, Saitama 351- 0198, Japan \(^{4}\) Department of Electrical and Computer Engineering, National University of Singapore, 4 Engineering Drive 3, Singapore, 117576, Singapore \(^{5}\) These authors contribute equally to this work \(^{*}\) email: chengwei.qiu@nus.edu.sg; luohui.luo@163. com; jinghui73@foxmail.com; xiaoguangzong@nudt.edu.cn.  
+
+<|ref|>text<|/ref|><|det|>[[97, 490, 852, 927]]<|/det|>
+Phonon lasers, exploiting coherent amplifications of phonons, have been a cornerstone for exploring quantum phononics, imaging nanomaterial structures, and realizing force sensors or phonon frequency combs. Single- mode phonon lasers, governed by dispersive optomechanical coupling, have been recently demonstrated via levitating a nanoparticle using an optical tweezer. Such levitated optomechanical (LOM) devices, with fundamental minimum of noises in high vacuum, can flexibly control large- mass objects with no internal discrete energy levels. However, it is still elusive to realize nonlinear multi- frequency phonon lasing with levitated microscale objects, dominated instead by dissipative LOM coupling due to much stronger optical scattering loss. Here, we report such a nonlinear phonon laser by employing a \(\mathrm{Yb^{3 + }}\) - doped active LOM system. We observe a 3- order of magnitude enhancement for the fundamental- mode phonon lasing, compared with that in its passive counterparts. Above the lasing threshold, higher- order mechanical sidebands emerge spontaneously. Coherent correlations are also identified for the phonon modes. Our gain- assisted dissipative LOM platform no longer relies on any complicated external feedback control.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[146, 81, 852, 199]]<|/det|>
+Our work drives LOM into a new regime where it becomes promising to study mechanical properties or quantum entanglement of typical micro- size objects, such as atmospheric particulates and living cells, and build levitated force sensors with these objects for biomedical or astronomical applications.  
+
+<|ref|>text<|/ref|><|det|>[[144, 216, 852, 704]]<|/det|>
+Conventional optomechanical systems rely on fixed frames to support mechanical elements, leading to unavoidable energy dissipation and thermal loading at the nanoscale'. Levitated optomechanics (LOM), i.e., controlling motions of levitated objects with optical forces?, have provided unique advantages?, such as fundamental minimum of damping and noise, the possibility for levitating large and complex objects, as well as high degree of control over both conservative dynamics and coupling to the environment. These advantages are of significance for both fundamental studies of non- equilibrium physics or thermodynamics and applications in metrology4- 11. In recent years, remarkable achievements have been witnessed in LOM12- 14, such as the realizations of motional ground- state cooling15,16, room- temperature strong coupling17, or ultrahigh- precision torque sensing18, to name only a few. In a very recent work19, a phonon laser or coherent amplification of phonons, the quanta of vibrations, was demonstrated for a levitated nanosphere, based on dispersive LOM coupling, in which the optical resonance frequency is modulated by mechanical motion. This work offers exciting opportunities of exploring the boundary of classical and quantum worlds with levitated macroscopic objects16,20,21, as well as making hybrid quantum sensors with levitated spins22,23. Nevertheless, sophisticated external feedback controls based on electronic loops19 are needed to compensate the purely passive optical field, in order to reach the phonon lasing regime. Only single- mode output was observed for phonons above the lasing threshold, without any evidence of nonlinear high- order sidebands.  
+
+<|ref|>text<|/ref|><|det|>[[145, 710, 852, 901]]<|/det|>
+Except for LOM systems, phonon lasers have also been built by using e.g., semiconductor superlattices24, nanomagnets25, single ions26, and nanomechanical27 or electromechanical28 devices. These coherent sound sources, with shorter wavelength of operation than that of a photon laser of the same frequency, are indispensable in steering phonon chips30, improving the resolution of motional sensors31, and making nonreciprocal or non- Hermitian devices32- 34. However, as far as we know, the ability of achieving nonlinear phonon lasers with multiple frequencies, has not been reported. This ability can provide the first step for many important applications such as
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[147, 82, 850, 126]]<|/det|>
+mechanical frequency conversion, acoustic frequency combs<sup>35</sup>, multi-wave mixing or squeezing of phonons<sup>36- 39</sup> and multi-frequency motional sensors.  
+
+<|ref|>text<|/ref|><|det|>[[147, 132, 852, 479]]<|/det|>
+In this Letter, we develop a strategy to achieve nonlinear phonon lasers for a levitated object at microscales by utilizing an active LOM system. We show that in such a system, dissipative optomechanical coupling<sup>40- 43</sup> can be significantly enhanced by introducing an optical gain, thus leading to tunable and efficient multi- frequency phonon lasers. Our system is immune from external feedback control<sup>19</sup> for achieving such phonon lasers, due to the critical role of gain. In fact, for passive systems, only thermal phonons exist for a levitated sphere with the radius \(\sim 2 \mu \mathrm{m}\) and the mass \(1 \times 10^{- 4} \mathrm{kg}\) (see Table. 1). To steer this system from a chaotic regime into a phonon lasing regime, we introduce an optical gain to increase the photon lifetime and enhance the photon- phonon coupling, thus achieving three- order- enhancement in the power spectrum of the fundamental- mode phonons, with also 30- fold narrowing in its linewidth. More importantly, above the lasing threshold, we observe higher- order sidebands with double and triple mechanical frequencies, featuring the gain- enhanced nonlinearity in this system.  
+
+<|ref|>table<|/ref|><|det|>[[150, 515, 845, 696]]<|/det|>
+<|ref|>table_caption<|/ref|><|det|>[[157, 512, 496, 526]]<|/det|>
+Table 1|Optomechanical systems for phonon lasing   
+
+<table><tr><td>Features</td><td>WGM cavities<sup>33,44</sup></td><td>F-P cavities<sup>37</sup></td><td>Passive LOM<sup>19</sup></td><td>Active LOM</td></tr><tr><td>Optical gain</td><td>×</td><td>×</td><td>×</td><td>✓</td></tr><tr><td>Optomechanical coupling</td><td>Dispersive</td><td>Dispersive</td><td>Dispersive</td><td>Dissipative</td></tr><tr><td>External feedback</td><td>×</td><td>×</td><td>✓</td><td>×</td></tr><tr><td>Size of the oscillator</td><td>~ 50 μm</td><td>~ 1 mm</td><td>~ 0.1 μm</td><td>~ 2 μm</td></tr><tr><td>Mass of the oscillator</td><td>~ 10-9 kg</td><td>~ 10-9 kg</td><td>~ 10-18 kg</td><td>~ 10-14 kg</td></tr><tr><td>Mechanical frequency</td><td>10 ~ 100 MHz</td><td>~ 100 kHz</td><td>~ 100 kHz</td><td>~ 10 kHz</td></tr><tr><td>Nonlinear sidebands</td><td>×</td><td>×</td><td>×</td><td>✓</td></tr></table>
+
+<|ref|>table_footnote<|/ref|><|det|>[[156, 695, 839, 710]]<|/det|>
+Notation: WGM, whispering-gallery-mode; F-P, Fabry-Perot; LOM, Levitated optomechanics; \(\checkmark\) for Yes; \(\times\) for No.  
+
+<|ref|>text<|/ref|><|det|>[[147, 736, 833, 926]]<|/det|>
+New characteristics of our work include the following 3 major points. First, oscillators of the phonon lasers are significantly distinct: the size or the mass of our micro- sphere is 3 or 4 orders larger than the nano- sphere<sup>19</sup>, and our LOM systems can thus capture typical micro- size objects and measure their mechanical properties, which is unattainable by nanoscale levitated devices. Second, the physical mechanisms are fundamentally different: our system is governed by the dissipative LOM coupling, due to much stronger optical scattering losses by much larger objects, in contrast to the dispersive LOM coupling in previous works dealing with nanoscale
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[145, 81, 833, 249]]<|/det|>
+objects; Third, the nature of phonon lasers are clearly different: we not only demonstrate a fundamental- mode phonon laser, but also observe for the first time coherent higher- order phonon sidebands, including their lasing threshold feature and second- order correlations. In a broader view, our gain- assisted dissipative LOM platform opens the possibility to achieve highly- sensitive LOM control of various micro- size objects, which is of utmost importance for both fundamental studies of macroscopic quantum physics and practical metrology.  
+
+<|ref|>image<|/ref|><|det|>[[163, 280, 835, 499]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[145, 524, 851, 633]]<|/det|>
+<center>Fig. 1 Experimental overview. a, Schematic diagram of the active levitated optomechanical system, including an active optical cavity (red) and a dual-beam optical tweezer (green). WDM, wavelength division multiplexer; \(\mathrm{C_1}\) , \(\mathrm{C_2}\) , collimators; \(\mathrm{L_1} \sim \mathrm{L_4}\) , lenses; PBS, polarizing beam splitter; HBD, heterodyne balanced detection. b, Measured power spectra of phonons in an active cavity (coloured curve) and a passive cavity (grey curve). Inset: Photograph of the levitated microsphere detected with a Scanning Electron Microscope (SEM). </center>  
+
+<|ref|>text<|/ref|><|det|>[[145, 758, 852, 927]]<|/det|>
+\(1\mu \mathrm{s}\) , which benefits enhanced coherent vibrational amplifications of the sphere. In addition, due to the presence of the optical cavity, our system is free of any need of using complicated feedback control devices \(^{19}\) (see Supplementary Section 1 for details). As shown in Fig. 1b, essentially different features can be observed in the power spectrums of phonons between our active LOM system and the purely passive system. We see that in the absence of any gain, only thermal phonons can exist; in sharp contrast, three- order- of- magnitude enhancement is achieved in the presence of an
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[147, 112, 850, 211]]<|/det|>
+Moreover, by tuning the pump power, high-order sidebands with mechanical multiple frequencies \(2\Omega_{0}\) , \(3\Omega_{0}\) , ... can also be observed in the spectrum (see also Supplementary Section 1). This enables us to realize a nonlinear multiple-frequency phonon laser in such an active LOM system.  
+
+<|ref|>image<|/ref|><|det|>[[150, 240, 845, 644]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[147, 654, 850, 828]]<|/det|>
+<center>Fig. 2 Experimental results of nonlinear phonon lasers with higher-order sidebands. a, Phonon population with fundamental frequency \(\Omega_{0}\) as a function of intracavity mean power \(P\) . The measured threshold power is in good agreement with the theoretical prediction. The insets show (i) the phonon probability distributions, and (ii, iii) the phonon power spectra below and above the oscillation threshold. b, Measured oscillation dynamics (upper panel) and linewidths (lower panel) of the fundamental mode by tracing the \(2\mu \mathrm{m} \mathrm{SiO}_{2}\) micro-sphere. c, Threshold behaviour of the nonlinear phonon laser with double frequency \(2\Omega_{0}\) (white solid curve). The white dashed curves represent \(\pm 1\) s.d. of each measurement, consisting of \(5 \times 10^{5}\) samples. The normalized phonon probability distribution is displayed in colour. d, Measured second-order phonon autocorrelation function at zero time delay \(g^{(2)}(0)\) versus \(P\) for \(\Omega_{0}\) . Inset: Measured \(g^{(2)}(0)\) with \(2\Omega_{0}\) above the threshold. The solid curves are theoretical results. Error bars represent \(\pm 1\) s.d. of each measurement, consisting of \(5 \times 10^{5}\) samples. </center>  
+
+<|ref|>text<|/ref|><|det|>[[147, 888, 850, 937]]<|/det|>
+\(\langle N \rangle = M \Omega_{0} \langle x^{2} \rangle / \hbar\) , where \(M\) is the mass of the levitated sphere, \(\Omega_{0}\) is the oscillation frequency of the mode, \(x\) is the centre of
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[144, 82, 852, 415]]<|/det|>
+\(h\) is the reduced Planck's constant. Explicit signatures of a lasing threshold can be observed for the fundamental mode with the frequency \(\Omega_0\) , as shown in Fig. 2a, by increasing the intracavity mean power \(P\) . The threshold value is \(P_{\mathrm{th}} = 0.37 \mathrm{mW}\) , which agrees well with theoretical calculations (Supplementary Section 2). The insets of Fig. 2a showcase a linewidth narrowing, accompanying the transition from thermal to coherent oscillations. Below the threshold, the oscillator experiences thermal dynamics with mean phonon number \(5.89 \times 10^8\) , and the phonon probability distribution is well described by the Boltzmann distribution. By surpassing the lasing threshold, the phonon number is greatly enhanced to \(1.02 \times 10^{10}\) at \(P = 1.2 \mathrm{mW}\) , also in conjunction with significant narrowing of linewidth. This is closely related to the fact that the system is switched from spontaneous to stimulated emissions above lasing threshold, resulting in the Gaussian distribution of the generated coherent phonons.  
+
+<|ref|>text<|/ref|><|det|>[[145, 419, 852, 617]]<|/det|>
+Figure 2b further presents the experimental results of the dynamical behaviours of the sphere. We find that significant vibrational amplifications of the micro- sphere emerge above the lasing threshold. 30- fold improvement in linewidth narrowing is achieved here, compared to purely lossy systems. Clearly, in the passive system, the interaction between the intracavity light and the levitated microsphere is rather weak, due to the large optical loss, that the linewidth remains at about \(2.5 \mathrm{kHz}\) . However, when introducing the gain, the linewidth can be significantly modulated by the intracavity power \(P\) , and approaches as low as \(0.08 \mathrm{kHz}\) (above the threshold).  
+
+<|ref|>text<|/ref|><|det|>[[145, 623, 852, 840]]<|/det|>
+Intriguingly, apart from the giant enhancement of fundamental- mode phonon lasing, we also observe spontaneously emerging mechanical higher- order sidebands. Therefore, we reveal the phonon population of the double- frequency mode by filtering out thermal phonons and fundamental- mode phonons. We find similar lasing features for the double- frequency mechanical mode as seen in Fig. 2c, differing from the single- mode phonon laser achieved in the previous works<sup>19,26,28,33,44</sup>. It is also distinguished from the multi- mode phonon laser demonstrated with a flat membrane trapped in a Fabre- Perot cavity<sup>37</sup>, in which mode competitions make it only possible to stimulate one single phonon mode into the lasing regime.  
+
+<|ref|>equation<|/ref|><|det|>[[611, 872, 846, 895]]<|/det|>
+\[g^{(2)}(0) = (\langle N^2 \rangle - \langle N \rangle) / \langle N \rangle^2\]  
+
+<|ref|>text<|/ref|><|det|>[[144, 904, 850, 924]]<|/det|>
+, where \(\langle N^2 \rangle\) is the second moment of this distribution (Fig. 2d). For the lowest- order
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[144, 82, 850, 247]]<|/det|>
+\(\Omega_{0}\) , we find \(g^{(2)}(0) = 2\) below the threshold \(P_{\mathrm{th}}\) , demonstrating the thermal statistics. As \(P\) well exceeds \(P_{\mathrm{th}}\) , \(g^{(2)}(0)\) is decreased to 1, which indicates that the phonon dynamics changes from thermal state to coherent state, i.e., the oscillation of the levitated micro-sphere is stimulated into the lasing regime. Moreover, we find \(g^{(2)}(0)\) approaches 1 for the nonlinear phonon laser with \(2\Omega_{0}\) when operating in the lasing regime, as shown in the onset of Fig. 2d.  
+
+<|ref|>image<|/ref|><|det|>[[312, 258, 670, 830]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[145, 840, 850, 947]]<|/det|>
+<center>Fig. 3 Optical gain induced nonlinear phonon lasing with double and triple frequencies. a, Normalized optical force distributions for active (red solid curve) and passive (grey dashed curve) setups. The active case shows a strongly nonlinear distribution for the position \(x\) between -1 \(\mu \mathrm{m}\) and 1 \(\mu \mathrm{m}\) , while the distribution is linear in the passive case. Insets: Schematic diagrams of the active (upper panel) and passive (lower panel) cases. b, Power spectra around \(2\Omega_{0}\) in the active (blue curve) and passive (grey curve) cases. Inset: 30 times magnified spectrum for better view. c, Phonon population with the triple frequency \(3\Omega_{0}\) versus the intracavity mean power \(P\) . Phonon laser with \(3\Omega_{0}\) (green dots) and thermal </center>
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[145, 82, 848, 111]]<|/det|>
+phonons (grey curve) are observed in the active and passive cases, respectively. Inset: Power spectra around \(3\Omega_0\) in the passive and active cases.  
+
+<|ref|>text<|/ref|><|det|>[[145, 120, 852, 528]]<|/det|>
+This nonlinear phonon laser results from the anharmonic optical potential produced by the optical- gain- enhanced nonlinearity. Without optical gain, the intracavity light is scattered by the levitated sphere of larger size than that in Ref. \(^{19}\) , leading to a small cavity quality factor and a weak interaction between the cavity field and mechanical oscillator. Therefore, one can find the intracavity optical power \(P\) is independent of the \(x\) - position of the oscillator (Supplementary Section 3), while the optical force \(F_{\mathrm{opt}}\) , relying on both of \(P\) and \(x\) , responds linearly to the position \(x\) (Fig. 3a). However, for the active case, the intracavity optical power can be modulated by the mechanical position due to the strong interaction between the light and oscillator. Thus, we can find a strongly nonlinear optical force for the active case, as shown in Fig. 3a. As a result, the double- frequency component emerges in the phonon power spectrum (Fig. 3b). We find a two- order- of- magnitude enhanced amplitude in our active system compared to the conventional passive system with the same intracavity mean power \(P = 1.2 \mathrm{mW}\) . Similar lasing features are also observed for the phonon mode with the triple- frequency \(3\Omega_0\) as shown in Fig. 3c, which again cannot be achieved in the absence of optical gain.  
+
+<|ref|>text<|/ref|><|det|>[[145, 533, 852, 927]]<|/det|>
+In summary, we have experimentally reported nonlinear phonon lasers in active LOM. By introducing optical gain, we have realized a phonon laser on the fundamental mode with three- order- of- magnitude enhancement in the power spectrum, and thirty- fold improvement in linewidth narrowing, without the need of any complicated external feedback control techniques. We also present unequivocal evidence of lasing threshold behaviour, and the phase transition from thermal to coherent phonons by measuring the phonon autocorrelations. More interestingly, for the first time, we observe nonlinear phonon lasers with multiple frequencies, resulting from the optical- gain- enhanced nonlinearity. As far as we know, this is the first observation of such nonlinear mechanical sidebands in LOM systems, which does not rely on the specific material or the shape of the oscillator \(^{45}\) . We measured also quantum correlations \(g^{(2)}(0)\) of sideband phonon lasing for the first time. These results push forward phonon lasers into the nonlinear regime and make many exciting applications more accessible, such as optomechanical combs \(^{35}\) , high- precision metrology, and non- classical state engineering. Our work opens up new perspectives for achieving levitated phonon devices with active LOM, and enables a wide range of applications such as quantum
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[145, 83, 850, 124]]<|/det|>
+phononics, multi- frequency mechanical sensors, and high- precision acoustic frequency combs.  
+
+<|ref|>sub_title<|/ref|><|det|>[[148, 187, 234, 203]]<|/det|>
+## Methods  
+
+<|ref|>text<|/ref|><|det|>[[147, 211, 851, 288]]<|/det|>
+Cavity alignment. We mount the pumping laser to one collimator (Thorlabs, ZC618FC- B), and a power meter to another. The alignment is evaluated by the coupling coefficient from one collimator to another. Through adjusting the lenses and mirrors, the loss of the free- space optical path can be regulated to its lowest value (usually lower than 0.31 dB).  
+
+<|ref|>text<|/ref|><|det|>[[147, 295, 851, 379]]<|/det|>
+Micro- sphere trapping. The micro- sphere (diameter, \(2\mu \mathrm{m}\) ) was loaded to the trapping region by using an ultrasonic nebulizer, composed of an ultrasonic sheet metal with a great number of \(5\mu \mathrm{m}\) holes distributed. It was trapped at atmospheric pressure. In most cases, a micro- sphere can be trapped within \(30\mathrm{s}\) . Then, we reduced the pressure to the desired experimental level.  
+
+<|ref|>sub_title<|/ref|><|det|>[[148, 408, 303, 425]]<|/det|>
+## Data availability  
+
+<|ref|>text<|/ref|><|det|>[[147, 433, 838, 450]]<|/det|>
+The data that support this article are available from the corresponding author upon reasonable request.  
+
+<|ref|>sub_title<|/ref|><|det|>[[148, 488, 260, 504]]<|/det|>
+## References  
+
+<|ref|>text<|/ref|><|det|>[[145, 510, 851, 936]]<|/det|>
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+
+<|ref|>sub_title<|/ref|><|det|>[[147, 594, 340, 611]]<|/det|>
+## Acknowledgements  
+
+<|ref|>text<|/ref|><|det|>[[144, 617, 852, 781]]<|/det|>
+This work is supported by the National Natural Science Foundation of China (Grants Nos. 61975237, 11904405, 11935006 and 11774086), the Science and Technology Innovation Program of Hunan Province (Grant No. 2020RC4047), Independent Scientific Research Project of National University of Defense Technology (Grant No. ZZKY-YX-07-02), and Scientific Research Project of National University of Defense Technology (Grant No. ZK20-14). F.N. is supported in part by NTT Research, JST [via Q- LEAP, Moonshot R&D, and CREST], JSPS [via KAKENHI], ARO, AOARD, and FQXi. We gratefully acknowledge the valuable assistance from Bin Luo at the BUPT, Yafeng Jiao, Xunwei Xu at HNU, and Zijie Liu, Weiqin Zeng, and Xinlin Chen at NUDT.  
+
+<|ref|>sub_title<|/ref|><|det|>[[147, 809, 352, 826]]<|/det|>
+## Author contributions  
+
+<|ref|>text<|/ref|><|det|>[[144, 832, 852, 935]]<|/det|>
+G.X. and H.J. conceived the idea. T.K. and G.X. designed the experiments. T.K., W.X. and X.H. performed the experiments and analyzed the experimental data with the help of G.X. R.H. and T.K. performed the theoretical analysis and numerical simulations, guided by H.J. R.H., T.K. and Y.Z. wrote the manuscript with contributions from G.X., H.J., F.N. and C.W.Q. G.X., H.J. and H.L. support the project.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[88, 85, 579, 225]]<|/det|>
+Competing interestsThe authors declare no competing interests.Additional informationSupplementary information is available for this paper at http/
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[43, 43, 311, 71]]<|/det|>
+## Supplementary Files  
+
+<|ref|>text<|/ref|><|det|>[[43, 93, 765, 113]]<|/det|>
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+<|ref|>text<|/ref|><|det|>[[59, 130, 405, 285]]<|/det|>
+NonlinearphononlaserAppendix.docx FigS1.1.png FigS1.2.png FigS1.3.png FigS1.4.png FigS3.1.png
+
+<--- Page Split --->

preprint/preprint__c90f4017680b98500a5db25a16ef09adb5706709585c5cf4d8925e4fbc71488d/images_list.json

@@ -0,0 +1,227 @@
+[
+  {
+    "type": "image",
+    "img_path": "images/Figure_1.jpg",
+    "caption": "Fig. 1 The age distributions of our star sample. a, \\(\\mathrm{R}_{\\mathrm{guide -zmax}}\\) distributions of sample stars, colour-coded by stellar ages. The vertical dashed lines in the top panel indicate the division into three \\(\\mathrm{R}_{\\mathrm{guide}}\\) bins (inner, local, and outer) at \\(\\mathrm{R}_{\\mathrm{guide}} = 7\\) and \\(9\\mathrm{kpc}\\) . The horizontal dashed line indicates the division of each R mean bin into three \\(\\mathrm{z}_{\\mathrm{max}}\\) bins (high- \\(\\mathrm{z}_{\\mathrm{max}}\\) , intermediate- \\(\\mathrm{z}_{\\mathrm{max}}\\) , low- \\(\\mathrm{z}_{\\mathrm{max}}\\) ) at \\(\\mathrm{z}_{\\mathrm{max}} = 0.3\\) and \\(0.7\\mathrm{kpc}\\) . b, The age distributions (based on the kernel density estimates) of spatially selected subsamples (inner, local, and outer) in high- \\(\\mathrm{z}_{\\mathrm{max}}\\) region. c, The age distributions of spatially selected subsamples (inner, local, and outer) in intermediate- \\(\\mathrm{z}_{\\mathrm{max}}\\) region. d, The age distributions of spatially selected subsamples (inner, local, and outer) in low- \\(\\mathrm{z}_{\\mathrm{max}}\\) region.",
+    "footnote": [],
+    "bbox": [
+      [
+        125,
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+        848,
+        360
+      ]
+    ],
+    "page_idx": 3
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_2.jpg",
+    "caption": "Fig. 2 Stellar age–abundance relation of local disc revealed by our star sample. a, b, c, \\(\\mathrm{Age - [Fe / H]}\\) distributions of the local disc stars at high- \\(\\mathrm{z}_{\\mathrm{max}}\\) , intermediate- \\(\\mathrm{z}_{\\mathrm{max}}\\) , and low- \\(\\mathrm{z}_{\\mathrm{max}}\\) regions, according to the division in Fig.1a. The gray dashed lines represent the simulated M54 + Sgr star formation history (SFH) from literature [1]. d, e, f, \\(\\mathrm{Age - [O / Fe]}\\) distributions of the local disc stars at high- \\(\\mathrm{z}_{\\mathrm{max}}\\) , intermediate- \\(\\mathrm{z}_{\\mathrm{max}}\\) , and low- \\(\\mathrm{z}_{\\mathrm{max}}\\) regions. The black dashed lines indicate the young O-rich stars. a, Probability distribution of stellar age \\(\\mathrm{p}(\\tau |[\\mathrm{Fe / H}])\\) , normalised to the peak value for each \\([\\mathrm{Fe / H}]\\) , for local disc stars at high- \\(\\mathrm{z}_{\\mathrm{max}}\\) region. d, Probability distribution of stellar age \\(\\mathrm{p}(\\tau |[\\mathrm{O / Fe}])\\) , normalised to the peak value for each \\([\\mathrm{Fe / H}]\\) , for local disc stars at high- \\(\\mathrm{z}_{\\mathrm{max}}\\) region. b, c, Similar to a but for local disc stars at intermediate- \\(\\mathrm{z}_{\\mathrm{max}}\\) and low- \\(\\mathrm{z}_{\\mathrm{max}}\\) regions. The black dashed boxes indicate the overdensities in the \\(\\mathrm{p}(\\tau |[\\mathrm{Fe / H}])\\) distribution of local disc. e, f, Similar to d but for local disc stars at intermediate- \\(\\mathrm{z}_{\\mathrm{max}}\\) and low- \\(\\mathrm{z}_{\\mathrm{max}}\\) regions. The blue dashed boxes show the young oxygen-enhanced populations in the local disc.",
+    "footnote": [],
+    "bbox": [
+      [
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+      ]
+    ],
+    "page_idx": 4
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_3.jpg",
+    "caption": "Fig. 3 Radial abundance profile in bins of age. a, Radial [Fe/H] profile in bins of age, each line represent the local nonparametric regression fitting to the distribution of sample stars in this age bins. The shaded regions indicate the 95% confidence interval around the fitting result by performing bootstrap resampling. b, Similar to a but for radial [O/Fe] profile in bins of age.",
+    "footnote": [],
+    "bbox": [
+      [
+        108,
+        87,
+        810,
+        293
+      ]
+    ],
+    "page_idx": 6
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_4.jpg",
+    "caption": "Fig. 4 Age dependence of the radial abundance gradient and the corresponding abundance dispersion around the gradient. a, Age dependence of the radial \\(\\mathrm{[Fe / H]}\\) (black) gradient and radial \\(\\mathrm{[O / Fe]}\\) (blue) gradient, in terms of guiding-centre radii \\(\\mathrm{(R_{guide})}\\) . Each point was obtained by 3-parameter (slope, intercept, and dispersion) Bayesian fits to the \\(\\mathrm{[Fe / H] / [O / Fe]}\\) -Rguide distribution, using only data in the respective age bin, restricted to \\(|Z_{\\mathrm{Gal}}|< 0.3\\) kpc and 5 kpc \\(< \\mathrm{R}_{\\mathrm{Gal}}< 11\\) kpc. The grey-shaded area marks the age interval in which we expect to see signatures from the Gaia Sausage/Enceladus (GSE) merger event, while the red-shaded area marks the age interval for the effect of (Sagittarius dwarf galaxy) passage. b, Age dependence of the \\(\\mathrm{[Fe / H]}\\) (black) and \\(\\mathrm{[O / Fe]}\\) (blue) dispersion around the radial \\(\\mathrm{[Fe / H] / [O / Fe]}\\) gradient (a), in terms of \\(\\mathrm{R_{guide}}\\) .",
+    "footnote": [],
+    "bbox": [
+      [
+        130,
+        85,
+        875,
+        295
+      ]
+    ],
+    "page_idx": 7
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_5.jpg",
+    "caption": "Fig. 5 Stellar age-abundance relation of local disc at low-\\(z_{\\mathrm{max}}\\) region, revealed by our star sample. a, b, Age- [Mg/Fe] and age-\\([\\mathrm{Ca / Fe}]\\) distributions for local disc stars at low-\\(z_{\\mathrm{max}}\\) region, colour-coded by the stellar number density, N. The black dashed lines represent the fitting result by local nonparametric regression. c, d, Probability distribution of stellar age \\(\\mathrm{p}(\\tau [\\mathrm{Mg / Fe}]) / \\mathrm{p}(\\tau [\\mathrm{Ca / Fe}])\\) , normalised to the peak value for \\([\\mathrm{Mg / Fe}] / [\\mathrm{Ca / Fe}]\\) , similar to Fig.2, but for other \\(\\alpha\\) -elements (Mg and Ca). The black dashed lines represent the location at age \\(= 4\\) Gyr.",
+    "footnote": [],
+    "bbox": [
+      [
+        110,
+        85,
+        810,
+        362
+      ]
+    ],
+    "page_idx": 8
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_0.jpg",
+    "caption": "Fig. A1 The MSTO and subgiant star sample with precise ages. a, HR diagram of the stars from the GALAH DR3 data (grey dots) and the selected sample (red dots). The black dashed line indicates the cut made to exclude giant stars. b, Kiel diagram of the stars from the GALAH DR3 data (grey dots), the selected sample (red dots), and the targets used in our work (blue dots). The MSTO and subgiant stars are delimited by black dashed lines ( \\(3.2 < \\log g < 4.1\\) and \\(4800 \\mathrm{K} < T_{\\mathrm{eff}} < 7000 \\mathrm{K}\\) ). c, Number density distribution in the age uncertainties as a function of age. Black dashed lines represent the 5, 15, and 30 per cent fractional uncertainty levels, respectively.",
+    "footnote": [],
+    "bbox": [
+      [
+        124,
+        88,
+        810,
+        272
+      ]
+    ],
+    "page_idx": 11
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_1.jpg",
+    "caption": "Fig. A2 Age-[Fe/H] distributions of the six spatially selected subsamples. a-i, arranged according to the division in Figure 1. a-h, colour-coded by the stellar number density, N. i, red dots represent the stars in outer disc at low-\\(z_{\\mathrm{max}}\\) region. The numbers of stars in each bin are shown in the top-right corner of each panel.",
+    "footnote": [],
+    "bbox": [
+      [
+        122,
+        362,
+        863,
+        767
+      ]
+    ],
+    "page_idx": 11
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_1.jpg",
+    "caption": "Fig. A3 Age- [O/Fe] distributions of the six spatially selected subsamples. a-i, arranged according to the division in Figure 1. a-h, colour-coded by the stellar number density, N. i, red dots represent the stars in outer disc at low-\\(z_{\\mathrm{max}}\\) region. The numbers of stars in each bin are shown in the bottom-right corner of each panel. The black dashed lines represent the fitting result by local nonparametric regression.",
+    "footnote": [],
+    "bbox": [
+      [
+        110,
+        85,
+        848,
+        489
+      ]
+    ],
+    "page_idx": 12
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_1.jpg",
+    "caption": "Fig. A4 Comparison of the radial [Fe/H] gradient and the corresponding [Fe/H] dispersion around the gradient in this work, with the results from LAMOST and APOGEE. a, b, The black lines in each panel represent the result of this work, using the GALAH subgiant and MSTO stars; the blue and green lines represent the results from the LAMOST data (LAMOST DR7 subgiant sample [16]) and literature [23] (based on APOGEE DR17 data [30]), respectively.",
+    "footnote": [],
+    "bbox": [
+      [
+        140,
+        95,
+        860,
+        330
+      ]
+    ],
+    "page_idx": 13
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_2.jpg",
+    "caption": "Fig. A5 Distribution of the our sample stars in the [Fe/H]-[O/Fe] plane at different ages. a-h, The contour lines show a kernel density estimation (KDE) with the distribution of the disc stars. The gray dots represent the disc stars in each age bins. The Sgr stars (red dots) are overplotted (a, h) for comparison. b-h, colour-coded by the stellar number density, N.",
+    "footnote": [],
+    "bbox": [
+      [
+        123,
+        414,
+        866,
+        672
+      ]
+    ],
+    "page_idx": 13
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_3.jpg",
+    "caption": "Fig. A6 Distribution of the young stars in the [Fe/H]-[X/Fe] plane at 1-4 Gyr. a, b, Distribution of the stars in the [Fe/H]-[X/Fe] ([Mg/Fe] and [Ca/Fe]) plane at 3-4 Gyr, and the Sgr stars (red dots) are overplotted for comparison. The red dashed boxes indicate the Mg-poor stars. c, d, Similar to a, b, but for the younger stars with age between 1-3 Gyr. The red dashed boxes show the Ca-rich stars.",
+    "footnote": [],
+    "bbox": [
+      [
+        110,
+        87,
+        833,
+        450
+      ]
+    ],
+    "page_idx": 14
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_4.jpg",
+    "caption": "Fig. A7 Age-velocity dispersion relationship of our sample stars in local disc. a, Age-velocity dispersion relationship (AVR) of the local disc stars with \\(7\\mathrm{kpc}< \\mathrm{R}_{\\mathrm{Gal}}< 9\\mathrm{kpc}\\) . The black line represents the result of this work, using the GALAH subgiant and MSTO stars; the blue and green lines represent the results from the LAMOST data (LAMOST DR7 subgiant sample [16]) and APOGEE data [23] (APOGEE DR17 red giant sample [30]), respectively. Also plotted are the results for open clusters in the solar vicinity in literature [49]. The black dashed line corresponds to a simple power-law fit for ages \\(< 7\\) Gyr in the Galactocentric distance bin 7-9 kpc, while the blue and green dashed lines corresponds to the simple power-law fit for the LAMOST subgiants and APOGEE red giants. The shaded region highlights the age range in which we see a steepening in the AVR, potentially related to the GSE merger event. b, Similar to a but for the local disc stars with \\(7\\mathrm{kpc}< \\mathrm{R}_{\\mathrm{guide}}< 9\\mathrm{kpc}\\) .",
+    "footnote": [],
+    "bbox": [
+      [
+        144,
+        95,
+        856,
+        333
+      ]
+    ],
+    "page_idx": 15
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_5.jpg",
+    "caption": "Fig. A8 Examples of the fits to the [Fe/H] vs. \\(\\mathbf{R}_{\\mathrm{guide}}\\) distributions for age bins of 1.5-2.5 Gyr. The black dots represent the distribution of the sample stars in this age bin. The thick black line shows the result of a naive least-squares linear fit. The thin grey lines show 30 realisations drawn from the linear gradient + intrinsic scatter posterior, while the shaded band corresponds the \\(1\\sigma\\) dispersion around the gradient.",
+    "footnote": [],
+    "bbox": [
+      [
+        122,
+        96,
+        572,
+        372
+      ]
+    ],
+    "page_idx": 16
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_6.jpg",
+    "caption": "Fig. A9 Posterior distributions of the fit parameters \\(\\mathrm{(m = \\partial[Fe / H] / \\partial R}\\) , b (intercept at \\(\\mathrm{R} = 0\\) ), and \\(\\sigma\\) (intrinsic [Fe/H] dispersion).",
+    "footnote": [],
+    "bbox": [
+      [
+        137,
+        92,
+        738,
+        530
+      ]
+    ],
+    "page_idx": 17
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_7.jpg",
+    "caption": "Fig. A10 The oxygen abundance of GALAH stars. a, Kiel diagram of the stars from the GALAH DR3 data, colour-coded by oxygen abundance. b, Kiel diagram of the stars from the GALAH DR3 data, colour-coded by ages from GALAH value-added catalogue [6]. The black dashed boxes indicate the young O-rich stars.",
+    "footnote": [],
+    "bbox": [
+      [
+        110,
+        85,
+        808,
+        323
+      ]
+    ],
+    "page_idx": 18
+  }
+]

preprint/preprint__c90f4017680b98500a5db25a16ef09adb5706709585c5cf4d8925e4fbc71488d/preprint__c90f4017680b98500a5db25a16ef09adb5706709585c5cf4d8925e4fbc71488d.mmd

@@ -0,0 +1,351 @@
+
+# Imprints of Sagittarius accretion event: Young O-rich stars and discontinuous chemical evolution in Milky Way disc  
+
+Shao- Lan Bi bis1@bnu.edu.cn  
+
+Department of Astronomy, Beijing Normal UniversityTiancheng SunDepartment of Astronomy, Beijing Normal University https://orcid.org/0000- 0003- 0795- 4854  
+
+Xunzhou ChenZhejiang Laboratory https://orcid.org/0000- 0003- 3957- 9067  
+
+Yuqin ChenNational Astronomical Observatories  
+
+Chao LiuNational Astronomical Observatories https://orcid.org/0000- 0002- 1802- 6917  
+
+Xianfei ZhangDepartment of Astronomy, Beijing Normal University https://orcid.org/0000- 0002- 3672- 2166  
+
+Tanda LiDepartment of Astronomy, Beijing Normal University  
+
+Yaguang LiUniversity of Hawai'i  
+
+Ya- Qian Wu  
+
+Key Laboratory of Optical Astronomy, National Astronomical Observatories, Chinese Academy of Sciences  
+
+Zhishuai GeBeijing Academy of Science and Technology  
+
+Lifei YeDepartment of Astronomy, Beijing Normal University  
+
+Article  
+
+Keywords:  
+
+Posted Date: November 7th, 2023
+
+<--- Page Split --->
+
+DOI: https://doi.org/10.21203/rs.3.rs- 3415389/v1  
+
+License: © This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License  
+
+Additional Declarations: There is NO Competing Interest.  
+
+Version of Record: A version of this preprint was published at Nature Communications on February 12th, 2025. See the published version at https://doi.org/10.1038/s41467- 025- 56550- 1.
+
+<--- Page Split --->
+
+# Imprints of Sagittarius accretion event: Young O-rich stars and discontinuous chemical evolution in Milky Way disc  
+
+Tiancheng Sun \(^{1,2}\) , Shaolan Bi \(^{1,2*}\) , Xunzhou Chen \(^{3*}\) , Yuqin Chen \(^{4,1,5}\) , Chao Liu \(^{4,1,5}\) , Xianfei Zhang \(^{1,2}\) , Tanda Li \(^{1,2}\) , Yaguang Li \(^{6}\) , Yaqian Wu \(^{4}\) , Zhishuai Ge \(^{7}\) , Lifei Ye \(^{1,2}\)  
+
+\(^{1*}\) Institute for Frontiers in Astronomy and Astrophysics, Beijing Normal University, Beijing, 102206, China. \(^{2}\) Department of Astronomy, Beijing Normal University, Beijing, 100875, China. \(^{3}\) Research Center for Intelligent Computing Platforms, Zhejiang Laboratory, Hangzhou, 311100, China. \(^{4}\) Key Lab of Space Astronomy and Technology, National Astronomical Observatories, Beijing, 100101, China. \(^{5}\) University of Chinese Academy of Sciences, Beijing, 100049, China. \(^{6}\) Institute for Astronomy, University of Hawai'i, 2680 Woodlawn Drive, Honolulu, HI 96822, USA. \(^{7}\) Beijing Planetarium, Beijing Academy of Science and Technology, Beijing, 100044, China.  
+
+\*Corresponding author(s). E- mail(s): bisl@bnu.edu.cn; cxz@zhejianglab.com;  
+
+## Abstract  
+
+The Milky Way has undergone significant transformations in its early history, characterised by violent mergers and the accretion of satellite galaxies. Among these events, the infall of the satellite galaxy Gaia- Enceladus/Sausage is recognised as the last major merger event, fundamentally altering the evolution of the Milky Way and shaping its chemo- dynamical structure. However, recent observational evidence suggests that the Milky Way remains undergone notable events of star formation in the past 4 Gyr, which is thought to be triggered by the perturbations from Sagittarius dwarf galaxy (Sgr). Here we report chemical signatures of the Sgr accretion event in the past 4 Gyr, using the [Fe/H] and [O/Fe] ratios in the thin disc, which is reported for the first time. It reveals that the previously discovered V- shape structure of age- [Fe/H] relation varies across different Galactic locations and has rich substructures. Interestingly, we discover a discontinuous structure at \(z_{\mathrm{max}} < 0.3\) kpc, interrupted by a recent burst of star formation from 4 Gyr to 2 Gyr ago. In this episode, we find a significant rise in oxygen abundance leading to a distinct [O/Fe] gradient, contributing to the formation of young O- rich stars. Combined with the simulated star formation history and chemical abundance of Sgr, we suggest that the Sgr is an important actor in the discontinuous chemical evolution of the Milky Way disc.  
+
+Recent findings, utilising data from the European Space Agency (ESA) Gaia mission [2, 3] and the Galactic Archaeology with HERMES (GALAH)  
+
+[4- 6] survey, have revealed an enhanced star formation rate during the past 2- 4 Gyr [7- 10]. This phenomenon is believed to be associated with the
+
+<--- Page Split --->
+![](images/Figure_1.jpg)
+
+<center>Fig. 1 The age distributions of our star sample. a, \(\mathrm{R}_{\mathrm{guide -zmax}}\) distributions of sample stars, colour-coded by stellar ages. The vertical dashed lines in the top panel indicate the division into three \(\mathrm{R}_{\mathrm{guide}}\) bins (inner, local, and outer) at \(\mathrm{R}_{\mathrm{guide}} = 7\) and \(9\mathrm{kpc}\) . The horizontal dashed line indicates the division of each R mean bin into three \(\mathrm{z}_{\mathrm{max}}\) bins (high- \(\mathrm{z}_{\mathrm{max}}\) , intermediate- \(\mathrm{z}_{\mathrm{max}}\) , low- \(\mathrm{z}_{\mathrm{max}}\) ) at \(\mathrm{z}_{\mathrm{max}} = 0.3\) and \(0.7\mathrm{kpc}\) . b, The age distributions (based on the kernel density estimates) of spatially selected subsamples (inner, local, and outer) in high- \(\mathrm{z}_{\mathrm{max}}\) region. c, The age distributions of spatially selected subsamples (inner, local, and outer) in intermediate- \(\mathrm{z}_{\mathrm{max}}\) region. d, The age distributions of spatially selected subsamples (inner, local, and outer) in low- \(\mathrm{z}_{\mathrm{max}}\) region. </center>  
+
+pericentre passages of the Sagittarius dwarf galaxy (Sgr) [11- 13]. Here we employ an oxygen- enhanced stellar model [10] to reliably determine the ages of main- sequence turnoff and subgiant stars from the Third Data Release of GALAH [6] (GALAH DR3) focusing primarily of unveiling the impact on star formation history by recent accretion events. Our approach utilises a Bayesian methodology [14], incorporating spectroscopic chemical abundances, specifically [Fe/H], [ \(\alpha /\mathrm{Fe}\) ] (where \(\alpha\) refers to Mg, Si, Ca, and Ti), and [O/Fe], alongside \(\mathrm{T}_{\mathrm{eff}}\) and luminosity [15]. The application of the oxygen- enhanced stellar model together with precise luminosity from Gaia and reliable abundance measurements from GALAH enable us to ascertain the age- abundance relations and track the evolution of the abundance gradient in the Galactic disc with unparalleled precision.  
+
+## 1 Age-abundance distribution of the Milky Way disc  
+
+Fig.1 shows the \(\mathrm{R}_{\mathrm{guide}}\) versus \(\mathrm{z}_{\mathrm{max}}\) diagram and the derived age distributions of spatially selected  
+
+1 Age- abundance distribution of the Milky Way discFig.1 shows the \(\mathrm{R}_{\mathrm{guide}}\) versus \(\mathrm{z}_{\mathrm{max}}\) diagram and the derived age distributions of spatially selected subsamples. It is found that there are clear differences in age distributions (Fig.1b,c,d) with \(\mathrm{R}_{\mathrm{guide}}\) (guiding radius) and \(\mathrm{z}_{\mathrm{max}}\) (maximum vertical distance from the disc plane). The mean ages of disc components (inner, local, and outer disc) at low- \(\mathrm{z}_{\mathrm{max}}\) region are younger on average than the intermediate- \(\mathrm{z}_{\mathrm{max}}\) and high- \(\mathrm{z}_{\mathrm{max}}\) regions with most stars younger than 8 Gyr. It is noted that there is a young peak at \(\sim 3\) Gyr in the age distributions of local and outer disc at low- \(\mathrm{z}_{\mathrm{max}}\) region (Fig.1d), which is more prominent for local disc. This bump is also seen in the intermediate- \(\mathrm{z}_{\mathrm{max}}\) region (Fig.1c) but disappears in the high- \(\mathrm{z}_{\mathrm{max}}\) region (Fig.1b). In addition, most of subsamples have an age peak at 5- 6 Gyr, except for the inner disc at high- \(\mathrm{z}_{\mathrm{max}}\) region, which has an age peak at \(\sim 10.5\) Gyr. The young peak of age distributions indicate that there is a recent burst of star formation in the local and outer disc \(\sim 3\) Gyr ago, while the intermediate- aged peak at 5- 6 Gyr is thought to be the star formation triggered by the first pericentric passages of Sgr ( \(\sim 5.5\) Gyr ago) [12].
+
+<--- Page Split --->
+![](images/Figure_2.jpg)
+
+<center>Fig. 2 Stellar age–abundance relation of local disc revealed by our star sample. a, b, c, \(\mathrm{Age - [Fe / H]}\) distributions of the local disc stars at high- \(\mathrm{z}_{\mathrm{max}}\) , intermediate- \(\mathrm{z}_{\mathrm{max}}\) , and low- \(\mathrm{z}_{\mathrm{max}}\) regions, according to the division in Fig.1a. The gray dashed lines represent the simulated M54 + Sgr star formation history (SFH) from literature [1]. d, e, f, \(\mathrm{Age - [O / Fe]}\) distributions of the local disc stars at high- \(\mathrm{z}_{\mathrm{max}}\) , intermediate- \(\mathrm{z}_{\mathrm{max}}\) , and low- \(\mathrm{z}_{\mathrm{max}}\) regions. The black dashed lines indicate the young O-rich stars. a, Probability distribution of stellar age \(\mathrm{p}(\tau |[\mathrm{Fe / H}])\) , normalised to the peak value for each \([\mathrm{Fe / H}]\) , for local disc stars at high- \(\mathrm{z}_{\mathrm{max}}\) region. d, Probability distribution of stellar age \(\mathrm{p}(\tau |[\mathrm{O / Fe}])\) , normalised to the peak value for each \([\mathrm{Fe / H}]\) , for local disc stars at high- \(\mathrm{z}_{\mathrm{max}}\) region. b, c, Similar to a but for local disc stars at intermediate- \(\mathrm{z}_{\mathrm{max}}\) and low- \(\mathrm{z}_{\mathrm{max}}\) regions. The black dashed boxes indicate the overdensities in the \(\mathrm{p}(\tau |[\mathrm{Fe / H}])\) distribution of local disc. e, f, Similar to d but for local disc stars at intermediate- \(\mathrm{z}_{\mathrm{max}}\) and low- \(\mathrm{z}_{\mathrm{max}}\) regions. The blue dashed boxes show the young oxygen-enhanced populations in the local disc. </center>  
+
+The distributions of nine spatially selected subsamples in age- \([\mathrm{Fe / H}]\) and age- \([\mathrm{O / Fe}]\) planes are presented in Fig.A2 and Fig.A3. Fig.A3 shows that there is a increasing trend of \([\mathrm{O / Fe}]\) with decreasing age in young (age \(< 3\) Gyr) and intermediate (4 Gyr \(< \mathrm{age} < 6\) Gyr) populations.  
+
+The oxygen- enhancement of young populations is most prominent in local age- \([\mathrm{O / Fe}]\) relations (Fig.A3e,h), which correspond to the overdensities in local age- \([\mathrm{Fe / H}]\) relations (Fig.A2e,h).
+
+<--- Page Split --->
+
+To better investigate the elemental enrichment history of the local disc, we employ a normalization procedure for the distribution \(p(\tau ,[\mathrm{Fe / H}])\) of local disc stars to obtain \(p(\tau |[\mathrm{Fe / H}])\) , the age distribution at a specified \([\mathrm{Fe / H}]\) . As presented in Fig.2a,b,c, the resulting \(p(\tau |[\mathrm{Fe / H}])\) distribution of local disc exhibit a gradual variation with \(z_{\mathrm{max}}\) , from a so called "V- shape" [10, 16] (at age \(< 8\) Gyr) at high- \(z_{\mathrm{max}}\) and intermediate- \(z_{\mathrm{max}}\) regions to a discontinuous structure at low- \(z_{\mathrm{max}}\) region. This feature implies that the previously discovered V- shape structure [10, 16] depends on the location in the Milky Way disc. For the local disc at high- \(z_{\mathrm{max}}\) region, the distribution of \(p(\tau |[\mathrm{Fe / H}])\) exhibits a V- shape; at intermediate- \(z_{\mathrm{max}}\) region, this V- shape is more pronounced and an overdensity with near- solar metallicity appears at 2- 4 Gyr. In the low- \(z_{\mathrm{max}}\) region, the V- shape structure becomes discontinuous, and this discontinuity corresponds to a decrease (Fig.2c) in iron abundance and an sharp increase (Fig.2f) in oxygen abundance, suggesting that a fresh gas interrupted the secular evolution of the Milky Way disc [17]. To our knowledge, this feature has not been seen before.  
+
+The increasing trend of oxygen abundance from 4 Gyr to 2 Gyr (Fig.2f) is a strong evidence of enhanced star formation in the local disc, as the oxygen is mainly produced by hydrostatic burning in massive stars and subsequently dispersed to the interstellar medium in SNeII (Type II supernovae) explosions [18, 19]. This increasing trend is also visible in Fig.2e and disappears in Fig.2d, contributing to the formation of young O- rich stellar population. On the other hand, it is noted that the age- \([\mathrm{Fe / H}]\) relations observed in Fig.2a,b,c are in consistent with the simulated star formation history (SFH) of the M54+ Sgr system based on Hubble Space Telescope photometry [20], which find an intermediate- aged star formation epochs from 6 Gyr at \([\mathrm{Fe / H}] = - 0.6\) to 4 Gyr at \([\mathrm{Fe / H}] = - 0.4\) , plus a prominent, \(\sim 2.3\) Gyr old Sgr population of near- solar abundance [1]. The metal- poor branch with \([\mathrm{Fe / H}] \lesssim - 0.2\) in Fig.2a,b,c, and the overdensity of near- solar \([\mathrm{Fe / H}]\) in Fig.2b,c, demonstrate a similarity (falls between two simulated SFH) with the SFH of M54+Sgr, and reinforce the idea of Sgr being the main actor behind conspicuous enhancements of star formation in the Milky Way during the past 6 Gyr.  
+
+## 2 Temporal evolution of radial abundance gradient  
+
+The oxygen enrichment and metallicity depletion \(([\mathrm{Fe / H}])\) strongly suggest that Sgr have influenced the evolution of our Galaxy in the past few billion years. Previous studies on the Gaia- Enceladus/Sausage (GSE) have highlighted the significant role of massive mergers in shaping the Galactic disc and altering the radial metallicity gradient in the past 8- 11 Gyr [21- 24]. To study the influence of minor merger events (Sgr accretion) on the radial metallicity gradient during the later stages of Galaxy evolution. We examine the temporal evolution of the radial abundance gradient in the Milky Way disc by utilising precise stellar ages from our stellar models.  
+
+Fig.3 presents the radial profiles of \([\mathrm{Fe / H}]\) and \([\mathrm{O / Fe}]\) for disc stars divided into eight age bins. Notably, the \([\mathrm{Fe / H}]\) profile undergoes a substantial transformation, transitioning from a positive gradient at 12- 14 Gyr to a negative gradient at 6- 8 Gyr, and subsequently maintaining a relatively steady negative gradient until 3 Gyr ago. A significant departure from this stable gradient occurs at 1- 3 Gyr, as the \([\mathrm{Fe / H}]\) profile becomes flatter compared to the 3- 8 Gyr period and resembles the gradient observed at 8- 10 Gyr. This behaviour indicates that the recent star formation burst has a global effect on the evolution of thin disc, flattening the radial metallicity gradient.  
+
+The radial \([\mathrm{Fe / H}]\) profile at 10- 12 Gyr exhibits a break at \(\sim 7.5\) kpc, featuring a positive slope within the break radius and a negative slope beyond it. Similarly, the radial \([\mathrm{Fe / H}]\) profile at 8- 10 Gyr ago shows a break at \(\sim 6.5\) kpc, with a flat slope within the break radius and a negative slope beyond it. These break radii is consistent with the break radius observed in the radial profile of integrated stellar metallicity using red giant branch stars [25]. Moreover, leveraging the high precision in age, we identify that these breaks primarily occur within the 8- 12 Gyr, which was not apparent in the metallicity profiles of mono- age populations in previous studies [25].  
+
+The radial \([\mathrm{O / Fe}]\) profile exhibits a transition from a negative gradient at 12- 14 Gyr to a positive gradient at 6- 8 Gyr, followed by a relatively stable positive gradient until 3 Gyr ago. Similar to the radial \([\mathrm{Fe / H}]\) profile, a significant departure
+
+<--- Page Split --->
+![](images/Figure_3.jpg)
+
+<center>Fig. 3 Radial abundance profile in bins of age. a, Radial [Fe/H] profile in bins of age, each line represent the local nonparametric regression fitting to the distribution of sample stars in this age bins. The shaded regions indicate the 95% confidence interval around the fitting result by performing bootstrap resampling. b, Similar to a but for radial [O/Fe] profile in bins of age. </center>  
+
+from this stable radial [O/Fe] profile occurs at 1- 3 Gyr, with a flatter gradient compared to the 3- 8 Gyr period. Overall, the flattened radial [Fe/H] and radial [O/Fe] profiles imply that an accretion event has diluted the metallicity of the disc and led to an enhancement of oxygen abundance.  
+
+The Bayesian linear fitting [26] are performed to the radial [Fe/H]/[O/Fe] profiles in 1 Gyr age bins (Fig. 4) to present the distinctive characteristics of them. These analyses are restricted to a thinner slice of the Galactic disc ( \(|Z_{\mathrm{Gal}}|< 0.3\mathrm{kpc}\) and \(5\mathrm{kpc}< \mathrm{R}_{\mathrm{Gal}}< 11\mathrm{kpc}\) ), as the young peak of age distribution is mainly observed in the low \(z_{\mathrm{max}}\) disc. Fig.4a shows a rise in [Fe/H] and [O/Fe] gradient between 4 and 2 Gyr ago, which corresponds to the enhanced star formation episode triggered by second passages of the Sgr galaxy [11, 12]. During this episode, an enhanced dispersion about radial [O/Fe] gradient with respect to the trend appears between 6 and 4 Gyr ago, indicating that an accretion event influencing the overall evolution of the thin disc. However, there is no obvious feature of enhanced dispersion about radial [Fe/H] gradient. The difference between the dispersion of [Fe/H] and [O/Fe] suggests that this accretion event was a minor merger event and thus introduced a small dispersion of [Fe/H] (the overdensity in Fig.2e). Furthermore, at the early stage (8- 11 Gyr) of Milky Way, there is a quick steepening in [Fe/H] and [O/Fe] gradient, linked to the effect of the GSE merger event [22, 24], slighter later (by  
+
+\(\sim 0.5\) Gyr, see Fig.A4) than the epoch based on the LAMOST [27, 28] and APOGEE [29, 30] data [22, 23]. These discrepancies could be attributed to different methods of age determination. Compared to the results from \(\alpha \mathrm{EM}\) model (e.g., Yonsei- Yale stellar isochrones used in LAMOST data), the ages of thick disc stars are significantly younger based on the oxygen- enhanced stellar models [10].  
+
+## 3 Evidence for the pericentric passage of Sagittarius  
+
+All results presented in this study strongly suggest the occurrence of a recent star formation burst in the Milky Way disc within the epoch of the recent passages of the Sgr (2- 3 Gyr ago) [1, 11, 31], altering the radial abundance profiles. Previous investigations toward the chemical compositions of Sgr stars have found that the stars with [Fe/H] \(\geq - 0.5\) exhibit notable deficiencies in [Mg/Fe] compared to the Milky Way disc [32- 38]. Fig.5 shows the abundance- age relations (age- [Mg/Fe] and age- [Ca/Fe]) of local low \(z_{\mathrm{max}}\) disc. Intriguingly, there is a notable declining trend of [Mg/Fe] with age from 4 Gyr to \(\sim 2\) Gyr, indicating that the newly formed disc stars are Mg- poor. The magnesium and oxygen are believed to be primarily synthesised during the hydrostatic burning phase of massive stars and subsequently ejected via the SNeII explosions [18, 19]. Despite some works
+
+<--- Page Split --->
+![](images/Figure_4.jpg)
+
+<center>Fig. 4 Age dependence of the radial abundance gradient and the corresponding abundance dispersion around the gradient. a, Age dependence of the radial \(\mathrm{[Fe / H]}\) (black) gradient and radial \(\mathrm{[O / Fe]}\) (blue) gradient, in terms of guiding-centre radii \(\mathrm{(R_{guide})}\) . Each point was obtained by 3-parameter (slope, intercept, and dispersion) Bayesian fits to the \(\mathrm{[Fe / H] / [O / Fe]}\) -Rguide distribution, using only data in the respective age bin, restricted to \(|Z_{\mathrm{Gal}}|< 0.3\) kpc and 5 kpc \(< \mathrm{R}_{\mathrm{Gal}}< 11\) kpc. The grey-shaded area marks the age interval in which we expect to see signatures from the Gaia Sausage/Enceladus (GSE) merger event, while the red-shaded area marks the age interval for the effect of (Sagittarius dwarf galaxy) passage. b, Age dependence of the \(\mathrm{[Fe / H]}\) (black) and \(\mathrm{[O / Fe]}\) (blue) dispersion around the radial \(\mathrm{[Fe / H] / [O / Fe]}\) gradient (a), in terms of \(\mathrm{R_{guide}}\) . </center>  
+
+[39, 40] have shown that Mg might also be partially released into the interstellar medium by SNe Ia (type Ia supernovae), this can not explain the opposite trend of O and Mg versus age from 4 Gyr to 2 Gyr ago. In addition, similar to the trend of oxygen abundance, an increasing trend of \(\mathrm{[Ca / Fe]}\) from 4 Gyr to 2 Gyr is observed. The peculiar behaviours of magnesium and oxygen abundances could be attributed to gas dilution from Sgr, with gas stripping estimated to be 30- 50 percent complete at its disc crossing approximately 2.7 Gyr ago [11].  
+
+Although Sgr is not the only satellite of the Milky Way that might be affecting our Galaxy presently, it exhibits the closest resemblance in chemical signature to the infalling gas responsible for the observed deficiencies in magnesium abundance. A comparative analysis [38] of the chemical compositions of various Milky Way dwarf satellite galaxies, based on APOGEE data [29, 30], has shown that among the ten known Milky Way dwarf satellites, Sgr stands out as the only satellite possessing near- solar metallicity \(\mathrm{[Fe / H]}\) \(\sim - 0.1\) ) and a deficit in \(\mathrm{[Mg / Fe]}\) \(\sim - 0.2\) . In contrast, another satellite within a similar metallicity range, the Large Magellanic Cloud (LMC), does  
+
+not exhibit a distinct depletion in \(\mathrm{[Mg / Fe]}\) , with \(\mathrm{[Mg / Fe]}\) \(\sim - 0.05\) at the metal- rich end [38].  
+
+We utilise data from the APOGEE DR17 [30] to compare the chemical composition of Sgr stars [36] with the young population (1- 4 Gyr) in our sample (see Fig. A5 and Fig. A6). The results clearly demonstrate that between 3- 4 Gyr, the \(\mathrm{[Mg / Fe]}\) ratios of metal- rich Sgr stars are \(\sim - 0.2\) dex at \(\mathrm{[Fe / H] = - 0.2}\) , which is lower than that of disc stars in the Milky Way at the same \(\mathrm{[Fe / H]}\) value. Conversely, the \(\mathrm{[Ca / Fe]}\) ratios of metal- rich Sgr stars are \(\sim 0\) dex, slightly higher (by around 0.1 dex) than those of Ca- poor disc stars in the Milky Way at fixed \(\mathrm{[Fe / H]}\) . A similar pattern is observed for O, which is more pronounced than Ca. In the later epoch of 1- 3 Gyr, there is an increased presence of Mg- poor stars in the Milky Way disc, as also shown in Fig.5c. Meanwhile, these stars exhibit enhancement in O and Ca. The comparison of Sgr stars and Milky Way disc stars in \(\mathrm{[Fe / H] - [X / Fe]}\) planes indicates that the infall gas from Sgr influences subsequent star formation in the Milky Way disc.  
+
+We suggest that the behaviour of \(\alpha\) - elements during the 1- 3 Gyr epoch depends on two factors: 1. the chemical abundance of Sgr relative to
+
+<--- Page Split --->
+![](images/Figure_5.jpg)
+
+<center>Fig. 5 Stellar age-abundance relation of local disc at low-\(z_{\mathrm{max}}\) region, revealed by our star sample. a, b, Age- [Mg/Fe] and age-\([\mathrm{Ca / Fe}]\) distributions for local disc stars at low-\(z_{\mathrm{max}}\) region, colour-coded by the stellar number density, N. The black dashed lines represent the fitting result by local nonparametric regression. c, d, Probability distribution of stellar age \(\mathrm{p}(\tau [\mathrm{Mg / Fe}]) / \mathrm{p}(\tau [\mathrm{Ca / Fe}])\) , normalised to the peak value for \([\mathrm{Mg / Fe}] / [\mathrm{Ca / Fe}]\) , similar to Fig.2, but for other \(\alpha\) -elements (Mg and Ca). The black dashed lines represent the location at age \(= 4\) Gyr. </center>  
+
+the Milky Way disc, specifically whether each \(\alpha\) - element is deficient or enhanced compared to disc stars; 2. the recent star formation in the Galactic disc triggered by Sgr, which produces a substantial amount of \(\alpha\) - elements and leads to their enrichment in newly formed stars. In the two factors, Mg exhibits distinct behaviours. They are significantly deficient in Sgr relative to the disc stars in the Milky Way, explaining the observed decreasing trend in Fig.5c. In contrast, O and Ca show a monotonous increasing trend.  
+
+In this work, we find that the V- shape structure of age- [Fe/H] relation depends on the location in the Galactic disc. This structure becomes discontinuous at \(z_{\mathrm{max}} < 0.3\) kpc, interrupted by a decrease in metallicity ([Fe/H]) and a significant increase in oxygen abundance from 4 Gyr to 2 Gyr ago, which is reported for the first time. The timing and chemical signature of this event is consistent with the simulated chemical evolution of Sgr. In addition, this event gives rise to distinct radial profiles of [Fe/H]/[O/Fe] compared to earlier stage. The dispersion around the radial [O/Fe] gradient exhibits a remarkable increase as age decreases within the same epoch (2- 4 Gyr). These  
+
+findings indicate that Sagittarius dwarf galaxy can trigger star formation burst across the disc, reshaping the chemical evolution of the Milky Way disc, contributing to the formation of young O- rich stars. Moreover, this study imposes important constraints on the chemical evolution models of the Milky Way, highlighting the need for further analysis to unravel the underlying physical mechanisms responsible for the global effects of star formation events induced by interactions with low- mass satellites such as Sgr.  
+
+Acknowledgments. The authors acknowledge Joss Bland- Hawthorn and Sven Buder for helpful discussions. The authors thank Thomas G. Bisbas for improving the presentation of manuscript. This work used the data from the GALAH survey, which is based on observations made at the Anglo Australian Telescope, under programs A/2013B/13, A/2014A/25, A/2015A/19, A/2017A/18, and 2020B/23. This work has made use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC, https://www.cosmos.esa.int/web/
+
+<--- Page Split --->
+
+gaia/dpac/consortium). Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement. This work has made use of data and analysis code from the Anders et al. 2023 (https://github.com/fjaellet/xgboost_chem_ages) [23]. This work is supported by the Joint Research Fund in Astronomy (U2031203) under cooperative agreement between the National Natural Science Foundation of China (NSFC) and Chinese Academy of Sciences (CAS), the NSFC grants (12090040, 12090042, 12373020), and the National Key R&D Program of China No. 2019YFA0405503, 2023YFE0107800. This work is partially supported by the Scholar Program of Beijing Academy of Science and Technology (DZ:BS202002).  
+
+## Declarations  
+
+- Data availability The relevant datasets are available from the corresponding author upon reasonable request.- Code availability No new codes are developed in this paper.  
+
+## Appendix A Method  
+
+## A.1 GALAH data and sample selection  
+
+This work is based on the data from the Third Data Release of the Galactic Archaeology with HERMES survey (GALAH DR3) [6]. GALAH DR3 [6] provides stellar parameters ( \(T_{\mathrm{eff}}\) , \(\log g\) , [Fe/H], \(V_{mic}\) , \(V_{broad}\) , \(V_{rad}\) ) and up to 30 elemental abundances for 588,571 stars, derived from optical spectra at a typical resolution of \(\mathrm{R} \sim 28,000\) . The [Fe/H], [O/Fe], [Mg/Fe], [Si/Fe], [Ca/Fe] ratios from GALAH DR3 was calculated based on a non-LTE method (LTE: local thermodynamic equilibrium) [41]. The data set used in this work is mainly from Sun et al. 2023 [10]. We extended this sample [10] to cover a \(T_{\mathrm{eff}}\) range of 4800- 7000 K, and a \(\log g\) range of 3.2- 4.1. Following the recommendations in GALAH DR3, we apply stringent selection criteria to ensure reliable stellar parameters, including iron, \(\alpha\) - elements, and oxygen abundances (flag- sp = 0, flag- fe- h = 0, flag- alpha- fe = 0, and flag- o- fe = 0), requiring  
+
+an \(\mathrm{SNR} > 30\) , a \(\mathrm{chi2\_sp} < 4\) (Chi2 value of stellar parameter fitting), and a quality flag = 0. Binary systems identified by Traven et al. 2020 [42] and Yu et al. 2023 [15] are excluded. Additionally, we apply a single cut based on the Gaia DR3 parameters by selecting stars with a Gaia re- normalised unit weight error (RUWE) of less than 1.2. Giant stars are excluded by applying the absolute magnitude cut [9]:  
+
+\[\begin{array}{r}M_{K_s} = m_{K_s} - A_{K_s} - 5\log 10[(100\mathrm{mas}) / \varpi ] > \\ 8.5 - T_{\mathrm{eff}} / (700\mathrm{K}) \end{array} \quad (A1)\]  
+
+The extinction values \(A_{K_s}\) and the 2MASS \(m_{K_s}\) magnitudes [43] used here are taken from the GALAH catalogue. In addition, we remove all stars with \(M_{\mathrm{K}}\) brighter than 0.5 mag to avoid contamination from He- burning horizontal branch stars [16]. To focus on disc stars, we select samples with \([\mathrm{Fe / H}] > - 1\) , eccentricity \(< 0.5\) , and \(|Z_{\mathrm{Gal}}| < 1\) kpc, and removed the halo stars mentioned in Sun et al. 2023 [10]. To ensure the accuracy of our results, we remove stars with a relative age uncertainty greater than 30 per cent. Additionally, we exclude 2 stars with significant model systematic bias, whose inferred ages are 2 \(\sigma\) larger than the age of the Universe (13.8 Gyr) [44]. After applying these cuts, our final sample consisted of 45,186 MSTO and subgiant stars, with a median relative age uncertainty of 9.8 per cent across the age range of 1- 13.8 Gyr, as shown in Fig.A1. We obtain the luminosities of sample stars by cross- match them with the catalogue from Yu et al. 2023 [15], which provides the luminosity of 1.5 million stars using astrometric data from GAIA DR3 [45] and improved interstellar extinction measurements.  
+
+We utilised the orbital parameters (eccentricity) and velocities (U, V, W, and \(\mathrm{V}_{\mathrm{Z}}\) ) from the GALAH DR3 value- added catalogue (VAC) [6]. These values are calculated from the astrometry provided by Gaia EDR3 and radial velocities determined from the GALAH spectra [46]. The orbital parameters in this catalogue are calculated using the Python package Galpy [47], with the details of assumed Milky Way potential and solar kinematic parameters presented in Buder et al. 2021 [6]. We calculated the guiding radii \(\mathrm{R}_{\mathrm{guide}}\) with the same input parameters (distance, ra, dec,
+
+<--- Page Split --->
+
+radial velocity, pmra, pmdec), Milky Way potential, and solar kinematic parameters presented in Buder et al. 2021 [6].  
+
+## A.2 Age estimation based on Oxygen-enhanced stellar models  
+
+We use oxygen- enhanced stellar evolution models to estimate ages of sample stars. The oxygen- enhanced stellar models use an individual O enhancement factor, thereby allowing the O abundance to be specified independently (see Sun et al. 2023 [10] for details). The other \(\alpha\) - elements (i.e., Ne, Mg, Si, S, Ca, and Ti) are maintained with the same enhancement factor. Neglecting to account for the independent enhancement of oxygen abundance in age determination would result in significant age biases, which would obscure the age- [O/Fe] relation [48]. Therefore, the oxygen- enhanced models could accurately characterising the age- [O/Fe] relation of sample stars.  
+
+The ages of the MTSO and subgiant sample stars are determined by matching the Gaia Luminosity [15], the GALAH spectroscopic stellar parameters \(T_{\mathrm{eff}}\) , [Fe/H], \([\alpha /\mathrm{Fe}]\) , and [O/Fe], with the Oxygen- enhanced stellar models [10] using a Bayesian approach [14] (Sun et al. 2023 [10], for more details).  
+
+Since our age estimates are independent from kinematics of sample stars. As an test for our age estimation, we show the age- velocity relation (AVR) of sample stars in Fig.A7. Fig.A7a shows the AVR of our sample in local region, with a Galactocentric distance between 7 kpc and 9 kpc. Since the age range of our sample does not cover the youngest stars, we also plot the AVR recently obtained by Tarricq et al. 2021 [49] using a sample of 418 Gaia- confirmed OCs (open clusters) in the solar neighbourhood. We note that the AVR at age \(< 7\) Gyr can be well described with a power law [50- 53], which is different from the power- law fitting of OC sample. Fig.A7b shows the AVR of local disc stars with a guiding radius between 7 kpc and 9 kpc. Compared with the result based on APOGEE DR17 red giants, we find that our result is more consistent with the result from open clusters [49]. Moreover, the AVR of our sample stars at age \(< 7\) Gyr is in good agreement with those of LAMOST subgiants [16], indicating a good age precision of our sample stars.  
+
+## A.3 Bayesian linear fits to the radial abundance profiles  
+
+In Fig.4 and Fig.A4, we presented the results of Bayesian fits to the radial [Fe/H]/[O/Fe] abundance distributions in age bins of 1 Gyr, using the fitting method described in Anders et al. 2017 [26]. We present the detailed results of these fits for age bins of 1.5- 2.5 Gyr in Fig.A8 and Fig.A9.  
+
+## A.4 The oxygen abundance of young stars from GALAH  
+
+To verify that our findings are not caused by artefacts due to selection effects, we plot the Kiel diagram of the stars from the GALAH DR3 in Fig.A10a, color- coded by oxygen abundance. As shown in the Fig.A10, the high temperature MSTO stars with \(6200\mathrm{K}< T_{\mathrm{eff}}< 7000\mathrm{K}\) behave oxygen- enhancement compared with stars at lower temperature end. Most of these oxygen- enhanced stars at high temperature end have ages less than 4 Gyr, which is consistent with our result in Sec.1. Consequently, the oxygen- enhancement in young disc stars in Fig.2 is not due to selection effects, but is directly observed by GALAH survey, and the precise ages of our sample stars allow us to accurately characterize the variation in oxygen abundance of disc stars. In addition, we have examine the oxygen abundance of \(\sim 15000\) common stars from GALAH DR3 and APOGEE DR17, and we did not observe any significant systematic differences in oxygen abundances till 7000 K.  
+
+## References  
+
+[1] Siegel, M. H. et al. The ACS Survey of Galactic Globular Clusters: M54 and Young Populations in the Sagittarius Dwarf Spheroidal Galaxy. Astrophys. J. Lett. 667, L57- L60 (2007). [2] Gaia Collaboration et al. Gaia Data Release 2. Summary of the contents and survey properties. Astron. Astrophys. 616, A1 (2018). [3] Gaia Collaboration et al. Gaia Data Release 3. Summary of the content and survey properties. Astron. Astrophys. 674, A1 (2023).
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+![](images/Figure_unknown_0.jpg)
+
+<center>Fig. A1 The MSTO and subgiant star sample with precise ages. a, HR diagram of the stars from the GALAH DR3 data (grey dots) and the selected sample (red dots). The black dashed line indicates the cut made to exclude giant stars. b, Kiel diagram of the stars from the GALAH DR3 data (grey dots), the selected sample (red dots), and the targets used in our work (blue dots). The MSTO and subgiant stars are delimited by black dashed lines ( \(3.2 < \log g < 4.1\) and \(4800 \mathrm{K} < T_{\mathrm{eff}} < 7000 \mathrm{K}\) ). c, Number density distribution in the age uncertainties as a function of age. Black dashed lines represent the 5, 15, and 30 per cent fractional uncertainty levels, respectively. </center>  
+
+![](images/Figure_1.jpg)
+
+<center>Fig. A2 Age-[Fe/H] distributions of the six spatially selected subsamples. a-i, arranged according to the division in Figure 1. a-h, colour-coded by the stellar number density, N. i, red dots represent the stars in outer disc at low-\(z_{\mathrm{max}}\) region. The numbers of stars in each bin are shown in the top-right corner of each panel. </center>
+
+<--- Page Split --->
+![](images/Figure_1.jpg)
+
+<center>Fig. A3 Age- [O/Fe] distributions of the six spatially selected subsamples. a-i, arranged according to the division in Figure 1. a-h, colour-coded by the stellar number density, N. i, red dots represent the stars in outer disc at low-\(z_{\mathrm{max}}\) region. The numbers of stars in each bin are shown in the bottom-right corner of each panel. The black dashed lines represent the fitting result by local nonparametric regression. </center>  
+
+[4] De Silva, G. M. et al. The GALAH survey: scientific motivation. Mon. Not. R. Astron. Soc. 449, 2604- 2617 (2015).  
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+
+<--- Page Split --->
+![](images/Figure_unknown_1.jpg)
+
+<center>Fig. A4 Comparison of the radial [Fe/H] gradient and the corresponding [Fe/H] dispersion around the gradient in this work, with the results from LAMOST and APOGEE. a, b, The black lines in each panel represent the result of this work, using the GALAH subgiant and MSTO stars; the blue and green lines represent the results from the LAMOST data (LAMOST DR7 subgiant sample [16]) and literature [23] (based on APOGEE DR17 data [30]), respectively. </center>  
+
+![](images/Figure_unknown_2.jpg)
+
+<center>Fig. A5 Distribution of the our sample stars in the [Fe/H]-[O/Fe] plane at different ages. a-h, The contour lines show a kernel density estimation (KDE) with the distribution of the disc stars. The gray dots represent the disc stars in each age bins. The Sgr stars (red dots) are overplotted (a, h) for comparison. b-h, colour-coded by the stellar number density, N. </center>  
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+<--- Page Split --->
+![](images/Figure_unknown_3.jpg)
+
+<center>Fig. A6 Distribution of the young stars in the [Fe/H]-[X/Fe] plane at 1-4 Gyr. a, b, Distribution of the stars in the [Fe/H]-[X/Fe] ([Mg/Fe] and [Ca/Fe]) plane at 3-4 Gyr, and the Sgr stars (red dots) are overplotted for comparison. The red dashed boxes indicate the Mg-poor stars. c, d, Similar to a, b, but for the younger stars with age between 1-3 Gyr. The red dashed boxes show the Ca-rich stars. </center>  
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+<--- Page Split --->
+![](images/Figure_unknown_4.jpg)
+
+<center>Fig. A7 Age-velocity dispersion relationship of our sample stars in local disc. a, Age-velocity dispersion relationship (AVR) of the local disc stars with \(7\mathrm{kpc}< \mathrm{R}_{\mathrm{Gal}}< 9\mathrm{kpc}\) . The black line represents the result of this work, using the GALAH subgiant and MSTO stars; the blue and green lines represent the results from the LAMOST data (LAMOST DR7 subgiant sample [16]) and APOGEE data [23] (APOGEE DR17 red giant sample [30]), respectively. Also plotted are the results for open clusters in the solar vicinity in literature [49]. The black dashed line corresponds to a simple power-law fit for ages \(< 7\) Gyr in the Galactocentric distance bin 7-9 kpc, while the blue and green dashed lines corresponds to the simple power-law fit for the LAMOST subgiants and APOGEE red giants. The shaded region highlights the age range in which we see a steepening in the AVR, potentially related to the GSE merger event. b, Similar to a but for the local disc stars with \(7\mathrm{kpc}< \mathrm{R}_{\mathrm{guide}}< 9\mathrm{kpc}\) . </center>  
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+
+<--- Page Split --->
+![](images/Figure_unknown_5.jpg)
+
+<center>Fig. A8 Examples of the fits to the [Fe/H] vs. \(\mathbf{R}_{\mathrm{guide}}\) distributions for age bins of 1.5-2.5 Gyr. The black dots represent the distribution of the sample stars in this age bin. The thick black line shows the result of a naive least-squares linear fit. The thin grey lines show 30 realisations drawn from the linear gradient + intrinsic scatter posterior, while the shaded band corresponds the \(1\sigma\) dispersion around the gradient. </center>  
+
+(2012).  
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+
+<--- Page Split --->
+![](images/Figure_unknown_6.jpg)
+
+<center>Fig. A9 Posterior distributions of the fit parameters \(\mathrm{(m = \partial[Fe / H] / \partial R}\) , b (intercept at \(\mathrm{R} = 0\) ), and \(\sigma\) (intrinsic [Fe/H] dispersion). </center>  
+
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+[44] Planck Collaboration et al. Planck 2015 results. XIII. Cosmological parameters.
+
+<--- Page Split --->
+![](images/Figure_unknown_7.jpg)
+
+<center>Fig. A10 The oxygen abundance of GALAH stars. a, Kiel diagram of the stars from the GALAH DR3 data, colour-coded by oxygen abundance. b, Kiel diagram of the stars from the GALAH DR3 data, colour-coded by ages from GALAH value-added catalogue [6]. The black dashed boxes indicate the young O-rich stars. </center>  
+
+Astron. Astrophys. 594, A13 (2016).  
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+
+<--- Page Split --->

preprint/preprint__c90f4017680b98500a5db25a16ef09adb5706709585c5cf4d8925e4fbc71488d/preprint__c90f4017680b98500a5db25a16ef09adb5706709585c5cf4d8925e4fbc71488d_det.mmd

@@ -0,0 +1,478 @@
+<|ref|>title<|/ref|><|det|>[[44, 108, 951, 208]]<|/det|>
+# Imprints of Sagittarius accretion event: Young O-rich stars and discontinuous chemical evolution in Milky Way disc  
+
+<|ref|>text<|/ref|><|det|>[[44, 230, 223, 275]]<|/det|>
+Shao- Lan Bi bis1@bnu.edu.cn  
+
+<|ref|>text<|/ref|><|det|>[[44, 301, 874, 370]]<|/det|>
+Department of Astronomy, Beijing Normal UniversityTiancheng SunDepartment of Astronomy, Beijing Normal University https://orcid.org/0000- 0003- 0795- 4854  
+
+<|ref|>text<|/ref|><|det|>[[44, 374, 592, 417]]<|/det|>
+Xunzhou ChenZhejiang Laboratory https://orcid.org/0000- 0003- 3957- 9067  
+
+<|ref|>text<|/ref|><|det|>[[44, 421, 380, 461]]<|/det|>
+Yuqin ChenNational Astronomical Observatories  
+
+<|ref|>text<|/ref|><|det|>[[44, 467, 740, 509]]<|/det|>
+Chao LiuNational Astronomical Observatories https://orcid.org/0000- 0002- 1802- 6917  
+
+<|ref|>text<|/ref|><|det|>[[44, 513, 872, 555]]<|/det|>
+Xianfei ZhangDepartment of Astronomy, Beijing Normal University https://orcid.org/0000- 0002- 3672- 2166  
+
+<|ref|>text<|/ref|><|det|>[[44, 560, 511, 601]]<|/det|>
+Tanda LiDepartment of Astronomy, Beijing Normal University  
+
+<|ref|>text<|/ref|><|det|>[[44, 606, 235, 646]]<|/det|>
+Yaguang LiUniversity of Hawai'i  
+
+<|ref|>text<|/ref|><|det|>[[44, 652, 188, 671]]<|/det|>
+Ya- Qian Wu  
+
+<|ref|>text<|/ref|><|det|>[[44, 675, 896, 716]]<|/det|>
+Key Laboratory of Optical Astronomy, National Astronomical Observatories, Chinese Academy of Sciences  
+
+<|ref|>text<|/ref|><|det|>[[44, 721, 444, 763]]<|/det|>
+Zhishuai GeBeijing Academy of Science and Technology  
+
+<|ref|>text<|/ref|><|det|>[[44, 768, 511, 809]]<|/det|>
+Lifei YeDepartment of Astronomy, Beijing Normal University  
+
+<|ref|>text<|/ref|><|det|>[[44, 850, 102, 867]]<|/det|>
+Article  
+
+<|ref|>text<|/ref|><|det|>[[44, 888, 137, 905]]<|/det|>
+Keywords:  
+
+<|ref|>text<|/ref|><|det|>[[44, 925, 338, 944]]<|/det|>
+Posted Date: November 7th, 2023
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[42, 45, 475, 64]]<|/det|>
+DOI: https://doi.org/10.21203/rs.3.rs- 3415389/v1  
+
+<|ref|>text<|/ref|><|det|>[[42, 82, 916, 125]]<|/det|>
+License: © This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License  
+
+<|ref|>text<|/ref|><|det|>[[42, 143, 535, 163]]<|/det|>
+Additional Declarations: There is NO Competing Interest.  
+
+<|ref|>text<|/ref|><|det|>[[42, 199, 950, 242]]<|/det|>
+Version of Record: A version of this preprint was published at Nature Communications on February 12th, 2025. See the published version at https://doi.org/10.1038/s41467- 025- 56550- 1.
+
+<--- Page Split --->
+<|ref|>title<|/ref|><|det|>[[152, 144, 834, 194]]<|/det|>
+# Imprints of Sagittarius accretion event: Young O-rich stars and discontinuous chemical evolution in Milky Way disc  
+
+<|ref|>text<|/ref|><|det|>[[130, 215, 855, 252]]<|/det|>
+Tiancheng Sun \(^{1,2}\) , Shaolan Bi \(^{1,2*}\) , Xunzhou Chen \(^{3*}\) , Yuqin Chen \(^{4,1,5}\) , Chao Liu \(^{4,1,5}\) , Xianfei Zhang \(^{1,2}\) , Tanda Li \(^{1,2}\) , Yaguang Li \(^{6}\) , Yaqian Wu \(^{4}\) , Zhishuai Ge \(^{7}\) , Lifei Ye \(^{1,2}\)  
+
+<|ref|>text<|/ref|><|det|>[[135, 259, 844, 432]]<|/det|>
+\(^{1*}\) Institute for Frontiers in Astronomy and Astrophysics, Beijing Normal University, Beijing, 102206, China. \(^{2}\) Department of Astronomy, Beijing Normal University, Beijing, 100875, China. \(^{3}\) Research Center for Intelligent Computing Platforms, Zhejiang Laboratory, Hangzhou, 311100, China. \(^{4}\) Key Lab of Space Astronomy and Technology, National Astronomical Observatories, Beijing, 100101, China. \(^{5}\) University of Chinese Academy of Sciences, Beijing, 100049, China. \(^{6}\) Institute for Astronomy, University of Hawai'i, 2680 Woodlawn Drive, Honolulu, HI 96822, USA. \(^{7}\) Beijing Planetarium, Beijing Academy of Science and Technology, Beijing, 100044, China.  
+
+<|ref|>text<|/ref|><|det|>[[180, 464, 800, 481]]<|/det|>
+\*Corresponding author(s). E- mail(s): bisl@bnu.edu.cn; cxz@zhejianglab.com;  
+
+<|ref|>sub_title<|/ref|><|det|>[[457, 508, 526, 521]]<|/det|>
+## Abstract  
+
+<|ref|>text<|/ref|><|det|>[[149, 524, 835, 720]]<|/det|>
+The Milky Way has undergone significant transformations in its early history, characterised by violent mergers and the accretion of satellite galaxies. Among these events, the infall of the satellite galaxy Gaia- Enceladus/Sausage is recognised as the last major merger event, fundamentally altering the evolution of the Milky Way and shaping its chemo- dynamical structure. However, recent observational evidence suggests that the Milky Way remains undergone notable events of star formation in the past 4 Gyr, which is thought to be triggered by the perturbations from Sagittarius dwarf galaxy (Sgr). Here we report chemical signatures of the Sgr accretion event in the past 4 Gyr, using the [Fe/H] and [O/Fe] ratios in the thin disc, which is reported for the first time. It reveals that the previously discovered V- shape structure of age- [Fe/H] relation varies across different Galactic locations and has rich substructures. Interestingly, we discover a discontinuous structure at \(z_{\mathrm{max}} < 0.3\) kpc, interrupted by a recent burst of star formation from 4 Gyr to 2 Gyr ago. In this episode, we find a significant rise in oxygen abundance leading to a distinct [O/Fe] gradient, contributing to the formation of young O- rich stars. Combined with the simulated star formation history and chemical abundance of Sgr, we suggest that the Sgr is an important actor in the discontinuous chemical evolution of the Milky Way disc.  
+
+<|ref|>text<|/ref|><|det|>[[110, 760, 473, 804]]<|/det|>
+Recent findings, utilising data from the European Space Agency (ESA) Gaia mission [2, 3] and the Galactic Archaeology with HERMES (GALAH)  
+
+<|ref|>text<|/ref|><|det|>[[508, 760, 874, 804]]<|/det|>
+[4- 6] survey, have revealed an enhanced star formation rate during the past 2- 4 Gyr [7- 10]. This phenomenon is believed to be associated with the
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[125, 88, 848, 360]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[122, 368, 887, 448]]<|/det|>
+<center>Fig. 1 The age distributions of our star sample. a, \(\mathrm{R}_{\mathrm{guide -zmax}}\) distributions of sample stars, colour-coded by stellar ages. The vertical dashed lines in the top panel indicate the division into three \(\mathrm{R}_{\mathrm{guide}}\) bins (inner, local, and outer) at \(\mathrm{R}_{\mathrm{guide}} = 7\) and \(9\mathrm{kpc}\) . The horizontal dashed line indicates the division of each R mean bin into three \(\mathrm{z}_{\mathrm{max}}\) bins (high- \(\mathrm{z}_{\mathrm{max}}\) , intermediate- \(\mathrm{z}_{\mathrm{max}}\) , low- \(\mathrm{z}_{\mathrm{max}}\) ) at \(\mathrm{z}_{\mathrm{max}} = 0.3\) and \(0.7\mathrm{kpc}\) . b, The age distributions (based on the kernel density estimates) of spatially selected subsamples (inner, local, and outer) in high- \(\mathrm{z}_{\mathrm{max}}\) region. c, The age distributions of spatially selected subsamples (inner, local, and outer) in intermediate- \(\mathrm{z}_{\mathrm{max}}\) region. d, The age distributions of spatially selected subsamples (inner, local, and outer) in low- \(\mathrm{z}_{\mathrm{max}}\) region. </center>  
+
+<|ref|>text<|/ref|><|det|>[[123, 466, 486, 724]]<|/det|>
+pericentre passages of the Sagittarius dwarf galaxy (Sgr) [11- 13]. Here we employ an oxygen- enhanced stellar model [10] to reliably determine the ages of main- sequence turnoff and subgiant stars from the Third Data Release of GALAH [6] (GALAH DR3) focusing primarily of unveiling the impact on star formation history by recent accretion events. Our approach utilises a Bayesian methodology [14], incorporating spectroscopic chemical abundances, specifically [Fe/H], [ \(\alpha /\mathrm{Fe}\) ] (where \(\alpha\) refers to Mg, Si, Ca, and Ti), and [O/Fe], alongside \(\mathrm{T}_{\mathrm{eff}}\) and luminosity [15]. The application of the oxygen- enhanced stellar model together with precise luminosity from Gaia and reliable abundance measurements from GALAH enable us to ascertain the age- abundance relations and track the evolution of the abundance gradient in the Galactic disc with unparalleled precision.  
+
+<|ref|>sub_title<|/ref|><|det|>[[124, 738, 485, 776]]<|/det|>
+## 1 Age-abundance distribution of the Milky Way disc  
+
+<|ref|>text<|/ref|><|det|>[[123, 785, 486, 813]]<|/det|>
+Fig.1 shows the \(\mathrm{R}_{\mathrm{guide}}\) versus \(\mathrm{z}_{\mathrm{max}}\) diagram and the derived age distributions of spatially selected  
+
+<|ref|>text<|/ref|><|det|>[[523, 466, 886, 797]]<|/det|>
+1 Age- abundance distribution of the Milky Way discFig.1 shows the \(\mathrm{R}_{\mathrm{guide}}\) versus \(\mathrm{z}_{\mathrm{max}}\) diagram and the derived age distributions of spatially selected subsamples. It is found that there are clear differences in age distributions (Fig.1b,c,d) with \(\mathrm{R}_{\mathrm{guide}}\) (guiding radius) and \(\mathrm{z}_{\mathrm{max}}\) (maximum vertical distance from the disc plane). The mean ages of disc components (inner, local, and outer disc) at low- \(\mathrm{z}_{\mathrm{max}}\) region are younger on average than the intermediate- \(\mathrm{z}_{\mathrm{max}}\) and high- \(\mathrm{z}_{\mathrm{max}}\) regions with most stars younger than 8 Gyr. It is noted that there is a young peak at \(\sim 3\) Gyr in the age distributions of local and outer disc at low- \(\mathrm{z}_{\mathrm{max}}\) region (Fig.1d), which is more prominent for local disc. This bump is also seen in the intermediate- \(\mathrm{z}_{\mathrm{max}}\) region (Fig.1c) but disappears in the high- \(\mathrm{z}_{\mathrm{max}}\) region (Fig.1b). In addition, most of subsamples have an age peak at 5- 6 Gyr, except for the inner disc at high- \(\mathrm{z}_{\mathrm{max}}\) region, which has an age peak at \(\sim 10.5\) Gyr. The young peak of age distributions indicate that there is a recent burst of star formation in the local and outer disc \(\sim 3\) Gyr ago, while the intermediate- aged peak at 5- 6 Gyr is thought to be the star formation triggered by the first pericentric passages of Sgr ( \(\sim 5.5\) Gyr ago) [12].
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[110, 87, 805, 578]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[109, 584, 875, 700]]<|/det|>
+<center>Fig. 2 Stellar age–abundance relation of local disc revealed by our star sample. a, b, c, \(\mathrm{Age - [Fe / H]}\) distributions of the local disc stars at high- \(\mathrm{z}_{\mathrm{max}}\) , intermediate- \(\mathrm{z}_{\mathrm{max}}\) , and low- \(\mathrm{z}_{\mathrm{max}}\) regions, according to the division in Fig.1a. The gray dashed lines represent the simulated M54 + Sgr star formation history (SFH) from literature [1]. d, e, f, \(\mathrm{Age - [O / Fe]}\) distributions of the local disc stars at high- \(\mathrm{z}_{\mathrm{max}}\) , intermediate- \(\mathrm{z}_{\mathrm{max}}\) , and low- \(\mathrm{z}_{\mathrm{max}}\) regions. The black dashed lines indicate the young O-rich stars. a, Probability distribution of stellar age \(\mathrm{p}(\tau |[\mathrm{Fe / H}])\) , normalised to the peak value for each \([\mathrm{Fe / H}]\) , for local disc stars at high- \(\mathrm{z}_{\mathrm{max}}\) region. d, Probability distribution of stellar age \(\mathrm{p}(\tau |[\mathrm{O / Fe}])\) , normalised to the peak value for each \([\mathrm{Fe / H}]\) , for local disc stars at high- \(\mathrm{z}_{\mathrm{max}}\) region. b, c, Similar to a but for local disc stars at intermediate- \(\mathrm{z}_{\mathrm{max}}\) and low- \(\mathrm{z}_{\mathrm{max}}\) regions. The black dashed boxes indicate the overdensities in the \(\mathrm{p}(\tau |[\mathrm{Fe / H}])\) distribution of local disc. e, f, Similar to d but for local disc stars at intermediate- \(\mathrm{z}_{\mathrm{max}}\) and low- \(\mathrm{z}_{\mathrm{max}}\) regions. The blue dashed boxes show the young oxygen-enhanced populations in the local disc. </center>  
+
+<|ref|>text<|/ref|><|det|>[[110, 717, 473, 801]]<|/det|>
+The distributions of nine spatially selected subsamples in age- \([\mathrm{Fe / H}]\) and age- \([\mathrm{O / Fe}]\) planes are presented in Fig.A2 and Fig.A3. Fig.A3 shows that there is a increasing trend of \([\mathrm{O / Fe}]\) with decreasing age in young (age \(< 3\) Gyr) and intermediate (4 Gyr \(< \mathrm{age} < 6\) Gyr) populations.  
+
+<|ref|>text<|/ref|><|det|>[[509, 717, 873, 772]]<|/det|>
+The oxygen- enhancement of young populations is most prominent in local age- \([\mathrm{O / Fe}]\) relations (Fig.A3e,h), which correspond to the overdensities in local age- \([\mathrm{Fe / H}]\) relations (Fig.A2e,h).
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[122, 87, 486, 442]]<|/det|>
+To better investigate the elemental enrichment history of the local disc, we employ a normalization procedure for the distribution \(p(\tau ,[\mathrm{Fe / H}])\) of local disc stars to obtain \(p(\tau |[\mathrm{Fe / H}])\) , the age distribution at a specified \([\mathrm{Fe / H}]\) . As presented in Fig.2a,b,c, the resulting \(p(\tau |[\mathrm{Fe / H}])\) distribution of local disc exhibit a gradual variation with \(z_{\mathrm{max}}\) , from a so called "V- shape" [10, 16] (at age \(< 8\) Gyr) at high- \(z_{\mathrm{max}}\) and intermediate- \(z_{\mathrm{max}}\) regions to a discontinuous structure at low- \(z_{\mathrm{max}}\) region. This feature implies that the previously discovered V- shape structure [10, 16] depends on the location in the Milky Way disc. For the local disc at high- \(z_{\mathrm{max}}\) region, the distribution of \(p(\tau |[\mathrm{Fe / H}])\) exhibits a V- shape; at intermediate- \(z_{\mathrm{max}}\) region, this V- shape is more pronounced and an overdensity with near- solar metallicity appears at 2- 4 Gyr. In the low- \(z_{\mathrm{max}}\) region, the V- shape structure becomes discontinuous, and this discontinuity corresponds to a decrease (Fig.2c) in iron abundance and an sharp increase (Fig.2f) in oxygen abundance, suggesting that a fresh gas interrupted the secular evolution of the Milky Way disc [17]. To our knowledge, this feature has not been seen before.  
+
+<|ref|>text<|/ref|><|det|>[[123, 444, 486, 811]]<|/det|>
+The increasing trend of oxygen abundance from 4 Gyr to 2 Gyr (Fig.2f) is a strong evidence of enhanced star formation in the local disc, as the oxygen is mainly produced by hydrostatic burning in massive stars and subsequently dispersed to the interstellar medium in SNeII (Type II supernovae) explosions [18, 19]. This increasing trend is also visible in Fig.2e and disappears in Fig.2d, contributing to the formation of young O- rich stellar population. On the other hand, it is noted that the age- \([\mathrm{Fe / H}]\) relations observed in Fig.2a,b,c are in consistent with the simulated star formation history (SFH) of the M54+ Sgr system based on Hubble Space Telescope photometry [20], which find an intermediate- aged star formation epochs from 6 Gyr at \([\mathrm{Fe / H}] = - 0.6\) to 4 Gyr at \([\mathrm{Fe / H}] = - 0.4\) , plus a prominent, \(\sim 2.3\) Gyr old Sgr population of near- solar abundance [1]. The metal- poor branch with \([\mathrm{Fe / H}] \lesssim - 0.2\) in Fig.2a,b,c, and the overdensity of near- solar \([\mathrm{Fe / H}]\) in Fig.2b,c, demonstrate a similarity (falls between two simulated SFH) with the SFH of M54+Sgr, and reinforce the idea of Sgr being the main actor behind conspicuous enhancements of star formation in the Milky Way during the past 6 Gyr.  
+
+<|ref|>sub_title<|/ref|><|det|>[[523, 82, 860, 120]]<|/det|>
+## 2 Temporal evolution of radial abundance gradient  
+
+<|ref|>text<|/ref|><|det|>[[523, 130, 886, 330]]<|/det|>
+The oxygen enrichment and metallicity depletion \(([\mathrm{Fe / H}])\) strongly suggest that Sgr have influenced the evolution of our Galaxy in the past few billion years. Previous studies on the Gaia- Enceladus/Sausage (GSE) have highlighted the significant role of massive mergers in shaping the Galactic disc and altering the radial metallicity gradient in the past 8- 11 Gyr [21- 24]. To study the influence of minor merger events (Sgr accretion) on the radial metallicity gradient during the later stages of Galaxy evolution. We examine the temporal evolution of the radial abundance gradient in the Milky Way disc by utilising precise stellar ages from our stellar models.  
+
+<|ref|>text<|/ref|><|det|>[[523, 331, 886, 530]]<|/det|>
+Fig.3 presents the radial profiles of \([\mathrm{Fe / H}]\) and \([\mathrm{O / Fe}]\) for disc stars divided into eight age bins. Notably, the \([\mathrm{Fe / H}]\) profile undergoes a substantial transformation, transitioning from a positive gradient at 12- 14 Gyr to a negative gradient at 6- 8 Gyr, and subsequently maintaining a relatively steady negative gradient until 3 Gyr ago. A significant departure from this stable gradient occurs at 1- 3 Gyr, as the \([\mathrm{Fe / H}]\) profile becomes flatter compared to the 3- 8 Gyr period and resembles the gradient observed at 8- 10 Gyr. This behaviour indicates that the recent star formation burst has a global effect on the evolution of thin disc, flattening the radial metallicity gradient.  
+
+<|ref|>text<|/ref|><|det|>[[523, 531, 886, 728]]<|/det|>
+The radial \([\mathrm{Fe / H}]\) profile at 10- 12 Gyr exhibits a break at \(\sim 7.5\) kpc, featuring a positive slope within the break radius and a negative slope beyond it. Similarly, the radial \([\mathrm{Fe / H}]\) profile at 8- 10 Gyr ago shows a break at \(\sim 6.5\) kpc, with a flat slope within the break radius and a negative slope beyond it. These break radii is consistent with the break radius observed in the radial profile of integrated stellar metallicity using red giant branch stars [25]. Moreover, leveraging the high precision in age, we identify that these breaks primarily occur within the 8- 12 Gyr, which was not apparent in the metallicity profiles of mono- age populations in previous studies [25].  
+
+<|ref|>text<|/ref|><|det|>[[523, 729, 886, 800]]<|/det|>
+The radial \([\mathrm{O / Fe}]\) profile exhibits a transition from a negative gradient at 12- 14 Gyr to a positive gradient at 6- 8 Gyr, followed by a relatively stable positive gradient until 3 Gyr ago. Similar to the radial \([\mathrm{Fe / H}]\) profile, a significant departure
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[108, 87, 810, 293]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[108, 303, 875, 350]]<|/det|>
+<center>Fig. 3 Radial abundance profile in bins of age. a, Radial [Fe/H] profile in bins of age, each line represent the local nonparametric regression fitting to the distribution of sample stars in this age bins. The shaded regions indicate the 95% confidence interval around the fitting result by performing bootstrap resampling. b, Similar to a but for radial [O/Fe] profile in bins of age. </center>  
+
+<|ref|>text<|/ref|><|det|>[[110, 366, 473, 451]]<|/det|>
+from this stable radial [O/Fe] profile occurs at 1- 3 Gyr, with a flatter gradient compared to the 3- 8 Gyr period. Overall, the flattened radial [Fe/H] and radial [O/Fe] profiles imply that an accretion event has diluted the metallicity of the disc and led to an enhancement of oxygen abundance.  
+
+<|ref|>text<|/ref|><|det|>[[110, 453, 473, 809]]<|/det|>
+The Bayesian linear fitting [26] are performed to the radial [Fe/H]/[O/Fe] profiles in 1 Gyr age bins (Fig. 4) to present the distinctive characteristics of them. These analyses are restricted to a thinner slice of the Galactic disc ( \(|Z_{\mathrm{Gal}}|< 0.3\mathrm{kpc}\) and \(5\mathrm{kpc}< \mathrm{R}_{\mathrm{Gal}}< 11\mathrm{kpc}\) ), as the young peak of age distribution is mainly observed in the low \(z_{\mathrm{max}}\) disc. Fig.4a shows a rise in [Fe/H] and [O/Fe] gradient between 4 and 2 Gyr ago, which corresponds to the enhanced star formation episode triggered by second passages of the Sgr galaxy [11, 12]. During this episode, an enhanced dispersion about radial [O/Fe] gradient with respect to the trend appears between 6 and 4 Gyr ago, indicating that an accretion event influencing the overall evolution of the thin disc. However, there is no obvious feature of enhanced dispersion about radial [Fe/H] gradient. The difference between the dispersion of [Fe/H] and [O/Fe] suggests that this accretion event was a minor merger event and thus introduced a small dispersion of [Fe/H] (the overdensity in Fig.2e). Furthermore, at the early stage (8- 11 Gyr) of Milky Way, there is a quick steepening in [Fe/H] and [O/Fe] gradient, linked to the effect of the GSE merger event [22, 24], slighter later (by  
+
+<|ref|>text<|/ref|><|det|>[[510, 366, 873, 479]]<|/det|>
+\(\sim 0.5\) Gyr, see Fig.A4) than the epoch based on the LAMOST [27, 28] and APOGEE [29, 30] data [22, 23]. These discrepancies could be attributed to different methods of age determination. Compared to the results from \(\alpha \mathrm{EM}\) model (e.g., Yonsei- Yale stellar isochrones used in LAMOST data), the ages of thick disc stars are significantly younger based on the oxygen- enhanced stellar models [10].  
+
+<|ref|>sub_title<|/ref|><|det|>[[510, 496, 870, 534]]<|/det|>
+## 3 Evidence for the pericentric passage of Sagittarius  
+
+<|ref|>text<|/ref|><|det|>[[510, 543, 873, 800]]<|/det|>
+All results presented in this study strongly suggest the occurrence of a recent star formation burst in the Milky Way disc within the epoch of the recent passages of the Sgr (2- 3 Gyr ago) [1, 11, 31], altering the radial abundance profiles. Previous investigations toward the chemical compositions of Sgr stars have found that the stars with [Fe/H] \(\geq - 0.5\) exhibit notable deficiencies in [Mg/Fe] compared to the Milky Way disc [32- 38]. Fig.5 shows the abundance- age relations (age- [Mg/Fe] and age- [Ca/Fe]) of local low \(z_{\mathrm{max}}\) disc. Intriguingly, there is a notable declining trend of [Mg/Fe] with age from 4 Gyr to \(\sim 2\) Gyr, indicating that the newly formed disc stars are Mg- poor. The magnesium and oxygen are believed to be primarily synthesised during the hydrostatic burning phase of massive stars and subsequently ejected via the SNeII explosions [18, 19]. Despite some works
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[130, 85, 875, 295]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[122, 319, 887, 411]]<|/det|>
+<center>Fig. 4 Age dependence of the radial abundance gradient and the corresponding abundance dispersion around the gradient. a, Age dependence of the radial \(\mathrm{[Fe / H]}\) (black) gradient and radial \(\mathrm{[O / Fe]}\) (blue) gradient, in terms of guiding-centre radii \(\mathrm{(R_{guide})}\) . Each point was obtained by 3-parameter (slope, intercept, and dispersion) Bayesian fits to the \(\mathrm{[Fe / H] / [O / Fe]}\) -Rguide distribution, using only data in the respective age bin, restricted to \(|Z_{\mathrm{Gal}}|< 0.3\) kpc and 5 kpc \(< \mathrm{R}_{\mathrm{Gal}}< 11\) kpc. The grey-shaded area marks the age interval in which we expect to see signatures from the Gaia Sausage/Enceladus (GSE) merger event, while the red-shaded area marks the age interval for the effect of (Sagittarius dwarf galaxy) passage. b, Age dependence of the \(\mathrm{[Fe / H]}\) (black) and \(\mathrm{[O / Fe]}\) (blue) dispersion around the radial \(\mathrm{[Fe / H] / [O / Fe]}\) gradient (a), in terms of \(\mathrm{R_{guide}}\) . </center>  
+
+<|ref|>text<|/ref|><|det|>[[123, 428, 485, 599]]<|/det|>
+[39, 40] have shown that Mg might also be partially released into the interstellar medium by SNe Ia (type Ia supernovae), this can not explain the opposite trend of O and Mg versus age from 4 Gyr to 2 Gyr ago. In addition, similar to the trend of oxygen abundance, an increasing trend of \(\mathrm{[Ca / Fe]}\) from 4 Gyr to 2 Gyr is observed. The peculiar behaviours of magnesium and oxygen abundances could be attributed to gas dilution from Sgr, with gas stripping estimated to be 30- 50 percent complete at its disc crossing approximately 2.7 Gyr ago [11].  
+
+<|ref|>text<|/ref|><|det|>[[123, 600, 485, 797]]<|/det|>
+Although Sgr is not the only satellite of the Milky Way that might be affecting our Galaxy presently, it exhibits the closest resemblance in chemical signature to the infalling gas responsible for the observed deficiencies in magnesium abundance. A comparative analysis [38] of the chemical compositions of various Milky Way dwarf satellite galaxies, based on APOGEE data [29, 30], has shown that among the ten known Milky Way dwarf satellites, Sgr stands out as the only satellite possessing near- solar metallicity \(\mathrm{[Fe / H]}\) \(\sim - 0.1\) ) and a deficit in \(\mathrm{[Mg / Fe]}\) \(\sim - 0.2\) . In contrast, another satellite within a similar metallicity range, the Large Magellanic Cloud (LMC), does  
+
+<|ref|>text<|/ref|><|det|>[[523, 428, 885, 456]]<|/det|>
+not exhibit a distinct depletion in \(\mathrm{[Mg / Fe]}\) , with \(\mathrm{[Mg / Fe]}\) \(\sim - 0.05\) at the metal- rich end [38].  
+
+<|ref|>text<|/ref|><|det|>[[523, 457, 886, 756]]<|/det|>
+We utilise data from the APOGEE DR17 [30] to compare the chemical composition of Sgr stars [36] with the young population (1- 4 Gyr) in our sample (see Fig. A5 and Fig. A6). The results clearly demonstrate that between 3- 4 Gyr, the \(\mathrm{[Mg / Fe]}\) ratios of metal- rich Sgr stars are \(\sim - 0.2\) dex at \(\mathrm{[Fe / H] = - 0.2}\) , which is lower than that of disc stars in the Milky Way at the same \(\mathrm{[Fe / H]}\) value. Conversely, the \(\mathrm{[Ca / Fe]}\) ratios of metal- rich Sgr stars are \(\sim 0\) dex, slightly higher (by around 0.1 dex) than those of Ca- poor disc stars in the Milky Way at fixed \(\mathrm{[Fe / H]}\) . A similar pattern is observed for O, which is more pronounced than Ca. In the later epoch of 1- 3 Gyr, there is an increased presence of Mg- poor stars in the Milky Way disc, as also shown in Fig.5c. Meanwhile, these stars exhibit enhancement in O and Ca. The comparison of Sgr stars and Milky Way disc stars in \(\mathrm{[Fe / H] - [X / Fe]}\) planes indicates that the infall gas from Sgr influences subsequent star formation in the Milky Way disc.  
+
+<|ref|>text<|/ref|><|det|>[[523, 757, 886, 797]]<|/det|>
+We suggest that the behaviour of \(\alpha\) - elements during the 1- 3 Gyr epoch depends on two factors: 1. the chemical abundance of Sgr relative to
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[110, 85, 810, 362]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[109, 370, 875, 428]]<|/det|>
+<center>Fig. 5 Stellar age-abundance relation of local disc at low-\(z_{\mathrm{max}}\) region, revealed by our star sample. a, b, Age- [Mg/Fe] and age-\([\mathrm{Ca / Fe}]\) distributions for local disc stars at low-\(z_{\mathrm{max}}\) region, colour-coded by the stellar number density, N. The black dashed lines represent the fitting result by local nonparametric regression. c, d, Probability distribution of stellar age \(\mathrm{p}(\tau [\mathrm{Mg / Fe}]) / \mathrm{p}(\tau [\mathrm{Ca / Fe}])\) , normalised to the peak value for \([\mathrm{Mg / Fe}] / [\mathrm{Ca / Fe}]\) , similar to Fig.2, but for other \(\alpha\) -elements (Mg and Ca). The black dashed lines represent the location at age \(= 4\) Gyr. </center>  
+
+<|ref|>text<|/ref|><|det|>[[110, 446, 473, 600]]<|/det|>
+the Milky Way disc, specifically whether each \(\alpha\) - element is deficient or enhanced compared to disc stars; 2. the recent star formation in the Galactic disc triggered by Sgr, which produces a substantial amount of \(\alpha\) - elements and leads to their enrichment in newly formed stars. In the two factors, Mg exhibits distinct behaviours. They are significantly deficient in Sgr relative to the disc stars in the Milky Way, explaining the observed decreasing trend in Fig.5c. In contrast, O and Ca show a monotonous increasing trend.  
+
+<|ref|>text<|/ref|><|det|>[[110, 603, 473, 800]]<|/det|>
+In this work, we find that the V- shape structure of age- [Fe/H] relation depends on the location in the Galactic disc. This structure becomes discontinuous at \(z_{\mathrm{max}} < 0.3\) kpc, interrupted by a decrease in metallicity ([Fe/H]) and a significant increase in oxygen abundance from 4 Gyr to 2 Gyr ago, which is reported for the first time. The timing and chemical signature of this event is consistent with the simulated chemical evolution of Sgr. In addition, this event gives rise to distinct radial profiles of [Fe/H]/[O/Fe] compared to earlier stage. The dispersion around the radial [O/Fe] gradient exhibits a remarkable increase as age decreases within the same epoch (2- 4 Gyr). These  
+
+<|ref|>text<|/ref|><|det|>[[510, 446, 874, 600]]<|/det|>
+findings indicate that Sagittarius dwarf galaxy can trigger star formation burst across the disc, reshaping the chemical evolution of the Milky Way disc, contributing to the formation of young O- rich stars. Moreover, this study imposes important constraints on the chemical evolution models of the Milky Way, highlighting the need for further analysis to unravel the underlying physical mechanisms responsible for the global effects of star formation events induced by interactions with low- mass satellites such as Sgr.  
+
+<|ref|>text<|/ref|><|det|>[[510, 609, 874, 808]]<|/det|>
+Acknowledgments. The authors acknowledge Joss Bland- Hawthorn and Sven Buder for helpful discussions. The authors thank Thomas G. Bisbas for improving the presentation of manuscript. This work used the data from the GALAH survey, which is based on observations made at the Anglo Australian Telescope, under programs A/2013B/13, A/2014A/25, A/2015A/19, A/2017A/18, and 2020B/23. This work has made use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC, https://www.cosmos.esa.int/web/
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[122, 87, 486, 328]]<|/det|>
+gaia/dpac/consortium). Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement. This work has made use of data and analysis code from the Anders et al. 2023 (https://github.com/fjaellet/xgboost_chem_ages) [23]. This work is supported by the Joint Research Fund in Astronomy (U2031203) under cooperative agreement between the National Natural Science Foundation of China (NSFC) and Chinese Academy of Sciences (CAS), the NSFC grants (12090040, 12090042, 12373020), and the National Key R&D Program of China No. 2019YFA0405503, 2023YFE0107800. This work is partially supported by the Scholar Program of Beijing Academy of Science and Technology (DZ:BS202002).  
+
+<|ref|>sub_title<|/ref|><|det|>[[123, 344, 271, 362]]<|/det|>
+## Declarations  
+
+<|ref|>text<|/ref|><|det|>[[123, 373, 486, 444]]<|/det|>
+- Data availability The relevant datasets are available from the corresponding author upon reasonable request.- Code availability No new codes are developed in this paper.  
+
+<|ref|>sub_title<|/ref|><|det|>[[125, 459, 390, 479]]<|/det|>
+## Appendix A Method  
+
+<|ref|>sub_title<|/ref|><|det|>[[125, 488, 435, 521]]<|/det|>
+## A.1 GALAH data and sample selection  
+
+<|ref|>text<|/ref|><|det|>[[123, 528, 486, 797]]<|/det|>
+This work is based on the data from the Third Data Release of the Galactic Archaeology with HERMES survey (GALAH DR3) [6]. GALAH DR3 [6] provides stellar parameters ( \(T_{\mathrm{eff}}\) , \(\log g\) , [Fe/H], \(V_{mic}\) , \(V_{broad}\) , \(V_{rad}\) ) and up to 30 elemental abundances for 588,571 stars, derived from optical spectra at a typical resolution of \(\mathrm{R} \sim 28,000\) . The [Fe/H], [O/Fe], [Mg/Fe], [Si/Fe], [Ca/Fe] ratios from GALAH DR3 was calculated based on a non-LTE method (LTE: local thermodynamic equilibrium) [41]. The data set used in this work is mainly from Sun et al. 2023 [10]. We extended this sample [10] to cover a \(T_{\mathrm{eff}}\) range of 4800- 7000 K, and a \(\log g\) range of 3.2- 4.1. Following the recommendations in GALAH DR3, we apply stringent selection criteria to ensure reliable stellar parameters, including iron, \(\alpha\) - elements, and oxygen abundances (flag- sp = 0, flag- fe- h = 0, flag- alpha- fe = 0, and flag- o- fe = 0), requiring  
+
+<|ref|>text<|/ref|><|det|>[[523, 86, 886, 216]]<|/det|>
+an \(\mathrm{SNR} > 30\) , a \(\mathrm{chi2\_sp} < 4\) (Chi2 value of stellar parameter fitting), and a quality flag = 0. Binary systems identified by Traven et al. 2020 [42] and Yu et al. 2023 [15] are excluded. Additionally, we apply a single cut based on the Gaia DR3 parameters by selecting stars with a Gaia re- normalised unit weight error (RUWE) of less than 1.2. Giant stars are excluded by applying the absolute magnitude cut [9]:  
+
+<|ref|>equation<|/ref|><|det|>[[533, 226, 884, 262]]<|/det|>
+\[\begin{array}{r}M_{K_s} = m_{K_s} - A_{K_s} - 5\log 10[(100\mathrm{mas}) / \varpi ] > \\ 8.5 - T_{\mathrm{eff}} / (700\mathrm{K}) \end{array} \quad (A1)\]  
+
+<|ref|>text<|/ref|><|det|>[[523, 290, 886, 616]]<|/det|>
+The extinction values \(A_{K_s}\) and the 2MASS \(m_{K_s}\) magnitudes [43] used here are taken from the GALAH catalogue. In addition, we remove all stars with \(M_{\mathrm{K}}\) brighter than 0.5 mag to avoid contamination from He- burning horizontal branch stars [16]. To focus on disc stars, we select samples with \([\mathrm{Fe / H}] > - 1\) , eccentricity \(< 0.5\) , and \(|Z_{\mathrm{Gal}}| < 1\) kpc, and removed the halo stars mentioned in Sun et al. 2023 [10]. To ensure the accuracy of our results, we remove stars with a relative age uncertainty greater than 30 per cent. Additionally, we exclude 2 stars with significant model systematic bias, whose inferred ages are 2 \(\sigma\) larger than the age of the Universe (13.8 Gyr) [44]. After applying these cuts, our final sample consisted of 45,186 MSTO and subgiant stars, with a median relative age uncertainty of 9.8 per cent across the age range of 1- 13.8 Gyr, as shown in Fig.A1. We obtain the luminosities of sample stars by cross- match them with the catalogue from Yu et al. 2023 [15], which provides the luminosity of 1.5 million stars using astrometric data from GAIA DR3 [45] and improved interstellar extinction measurements.  
+
+<|ref|>text<|/ref|><|det|>[[523, 618, 886, 789]]<|/det|>
+We utilised the orbital parameters (eccentricity) and velocities (U, V, W, and \(\mathrm{V}_{\mathrm{Z}}\) ) from the GALAH DR3 value- added catalogue (VAC) [6]. These values are calculated from the astrometry provided by Gaia EDR3 and radial velocities determined from the GALAH spectra [46]. The orbital parameters in this catalogue are calculated using the Python package Galpy [47], with the details of assumed Milky Way potential and solar kinematic parameters presented in Buder et al. 2021 [6]. We calculated the guiding radii \(\mathrm{R}_{\mathrm{guide}}\) with the same input parameters (distance, ra, dec,
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[110, 87, 473, 130]]<|/det|>
+radial velocity, pmra, pmdec), Milky Way potential, and solar kinematic parameters presented in Buder et al. 2021 [6].  
+
+<|ref|>sub_title<|/ref|><|det|>[[111, 145, 411, 194]]<|/det|>
+## A.2 Age estimation based on Oxygen-enhanced stellar models  
+
+<|ref|>text<|/ref|><|det|>[[110, 201, 473, 400]]<|/det|>
+We use oxygen- enhanced stellar evolution models to estimate ages of sample stars. The oxygen- enhanced stellar models use an individual O enhancement factor, thereby allowing the O abundance to be specified independently (see Sun et al. 2023 [10] for details). The other \(\alpha\) - elements (i.e., Ne, Mg, Si, S, Ca, and Ti) are maintained with the same enhancement factor. Neglecting to account for the independent enhancement of oxygen abundance in age determination would result in significant age biases, which would obscure the age- [O/Fe] relation [48]. Therefore, the oxygen- enhanced models could accurately characterising the age- [O/Fe] relation of sample stars.  
+
+<|ref|>text<|/ref|><|det|>[[110, 400, 473, 499]]<|/det|>
+The ages of the MTSO and subgiant sample stars are determined by matching the Gaia Luminosity [15], the GALAH spectroscopic stellar parameters \(T_{\mathrm{eff}}\) , [Fe/H], \([\alpha /\mathrm{Fe}]\) , and [O/Fe], with the Oxygen- enhanced stellar models [10] using a Bayesian approach [14] (Sun et al. 2023 [10], for more details).  
+
+<|ref|>text<|/ref|><|det|>[[110, 500, 473, 814]]<|/det|>
+Since our age estimates are independent from kinematics of sample stars. As an test for our age estimation, we show the age- velocity relation (AVR) of sample stars in Fig.A7. Fig.A7a shows the AVR of our sample in local region, with a Galactocentric distance between 7 kpc and 9 kpc. Since the age range of our sample does not cover the youngest stars, we also plot the AVR recently obtained by Tarricq et al. 2021 [49] using a sample of 418 Gaia- confirmed OCs (open clusters) in the solar neighbourhood. We note that the AVR at age \(< 7\) Gyr can be well described with a power law [50- 53], which is different from the power- law fitting of OC sample. Fig.A7b shows the AVR of local disc stars with a guiding radius between 7 kpc and 9 kpc. Compared with the result based on APOGEE DR17 red giants, we find that our result is more consistent with the result from open clusters [49]. Moreover, the AVR of our sample stars at age \(< 7\) Gyr is in good agreement with those of LAMOST subgiants [16], indicating a good age precision of our sample stars.  
+
+<|ref|>sub_title<|/ref|><|det|>[[510, 86, 822, 118]]<|/det|>
+## A.3 Bayesian linear fits to the radial abundance profiles  
+
+<|ref|>text<|/ref|><|det|>[[510, 125, 874, 210]]<|/det|>
+In Fig.4 and Fig.A4, we presented the results of Bayesian fits to the radial [Fe/H]/[O/Fe] abundance distributions in age bins of 1 Gyr, using the fitting method described in Anders et al. 2017 [26]. We present the detailed results of these fits for age bins of 1.5- 2.5 Gyr in Fig.A8 and Fig.A9.  
+
+<|ref|>sub_title<|/ref|><|det|>[[510, 225, 825, 258]]<|/det|>
+## A.4 The oxygen abundance of young stars from GALAH  
+
+<|ref|>text<|/ref|><|det|>[[510, 265, 874, 563]]<|/det|>
+To verify that our findings are not caused by artefacts due to selection effects, we plot the Kiel diagram of the stars from the GALAH DR3 in Fig.A10a, color- coded by oxygen abundance. As shown in the Fig.A10, the high temperature MSTO stars with \(6200\mathrm{K}< T_{\mathrm{eff}}< 7000\mathrm{K}\) behave oxygen- enhancement compared with stars at lower temperature end. Most of these oxygen- enhanced stars at high temperature end have ages less than 4 Gyr, which is consistent with our result in Sec.1. Consequently, the oxygen- enhancement in young disc stars in Fig.2 is not due to selection effects, but is directly observed by GALAH survey, and the precise ages of our sample stars allow us to accurately characterize the variation in oxygen abundance of disc stars. In addition, we have examine the oxygen abundance of \(\sim 15000\) common stars from GALAH DR3 and APOGEE DR17, and we did not observe any significant systematic differences in oxygen abundances till 7000 K.  
+
+<|ref|>sub_title<|/ref|><|det|>[[510, 580, 637, 597]]<|/det|>
+## References  
+
+<|ref|>text<|/ref|><|det|>[[518, 608, 874, 788]]<|/det|>
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+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[124, 88, 810, 272]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[122, 275, 888, 344]]<|/det|>
+<center>Fig. A1 The MSTO and subgiant star sample with precise ages. a, HR diagram of the stars from the GALAH DR3 data (grey dots) and the selected sample (red dots). The black dashed line indicates the cut made to exclude giant stars. b, Kiel diagram of the stars from the GALAH DR3 data (grey dots), the selected sample (red dots), and the targets used in our work (blue dots). The MSTO and subgiant stars are delimited by black dashed lines ( \(3.2 < \log g < 4.1\) and \(4800 \mathrm{K} < T_{\mathrm{eff}} < 7000 \mathrm{K}\) ). c, Number density distribution in the age uncertainties as a function of age. Black dashed lines represent the 5, 15, and 30 per cent fractional uncertainty levels, respectively. </center>  
+
+<|ref|>image<|/ref|><|det|>[[122, 362, 863, 767]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[122, 772, 888, 809]]<|/det|>
+<center>Fig. A2 Age-[Fe/H] distributions of the six spatially selected subsamples. a-i, arranged according to the division in Figure 1. a-h, colour-coded by the stellar number density, N. i, red dots represent the stars in outer disc at low-\(z_{\mathrm{max}}\) region. The numbers of stars in each bin are shown in the top-right corner of each panel. </center>
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[110, 85, 848, 489]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[109, 494, 875, 542]]<|/det|>
+<center>Fig. A3 Age- [O/Fe] distributions of the six spatially selected subsamples. a-i, arranged according to the division in Figure 1. a-h, colour-coded by the stellar number density, N. i, red dots represent the stars in outer disc at low-\(z_{\mathrm{max}}\) region. The numbers of stars in each bin are shown in the bottom-right corner of each panel. The black dashed lines represent the fitting result by local nonparametric regression. </center>  
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+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[140, 95, 860, 330]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[122, 346, 888, 394]]<|/det|>
+<center>Fig. A4 Comparison of the radial [Fe/H] gradient and the corresponding [Fe/H] dispersion around the gradient in this work, with the results from LAMOST and APOGEE. a, b, The black lines in each panel represent the result of this work, using the GALAH subgiant and MSTO stars; the blue and green lines represent the results from the LAMOST data (LAMOST DR7 subgiant sample [16]) and literature [23] (based on APOGEE DR17 data [30]), respectively. </center>  
+
+<|ref|>image<|/ref|><|det|>[[123, 414, 866, 672]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[122, 678, 887, 725]]<|/det|>
+<center>Fig. A5 Distribution of the our sample stars in the [Fe/H]-[O/Fe] plane at different ages. a-h, The contour lines show a kernel density estimation (KDE) with the distribution of the disc stars. The gray dots represent the disc stars in each age bins. The Sgr stars (red dots) are overplotted (a, h) for comparison. b-h, colour-coded by the stellar number density, N. </center>  
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+<|ref|>image<|/ref|><|det|>[[110, 87, 833, 450]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[108, 456, 875, 502]]<|/det|>
+<center>Fig. A6 Distribution of the young stars in the [Fe/H]-[X/Fe] plane at 1-4 Gyr. a, b, Distribution of the stars in the [Fe/H]-[X/Fe] ([Mg/Fe] and [Ca/Fe]) plane at 3-4 Gyr, and the Sgr stars (red dots) are overplotted for comparison. The red dashed boxes indicate the Mg-poor stars. c, d, Similar to a, b, but for the younger stars with age between 1-3 Gyr. The red dashed boxes show the Ca-rich stars. </center>  
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+<|ref|>image_caption<|/ref|><|det|>[[122, 346, 888, 450]]<|/det|>
+<center>Fig. A7 Age-velocity dispersion relationship of our sample stars in local disc. a, Age-velocity dispersion relationship (AVR) of the local disc stars with \(7\mathrm{kpc}< \mathrm{R}_{\mathrm{Gal}}< 9\mathrm{kpc}\) . The black line represents the result of this work, using the GALAH subgiant and MSTO stars; the blue and green lines represent the results from the LAMOST data (LAMOST DR7 subgiant sample [16]) and APOGEE data [23] (APOGEE DR17 red giant sample [30]), respectively. Also plotted are the results for open clusters in the solar vicinity in literature [49]. The black dashed line corresponds to a simple power-law fit for ages \(< 7\) Gyr in the Galactocentric distance bin 7-9 kpc, while the blue and green dashed lines corresponds to the simple power-law fit for the LAMOST subgiants and APOGEE red giants. The shaded region highlights the age range in which we see a steepening in the AVR, potentially related to the GSE merger event. b, Similar to a but for the local disc stars with \(7\mathrm{kpc}< \mathrm{R}_{\mathrm{guide}}< 9\mathrm{kpc}\) . </center>  
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+<|ref|>image_caption<|/ref|><|det|>[[109, 388, 875, 437]]<|/det|>
+<center>Fig. A8 Examples of the fits to the [Fe/H] vs. \(\mathbf{R}_{\mathrm{guide}}\) distributions for age bins of 1.5-2.5 Gyr. The black dots represent the distribution of the sample stars in this age bin. The thick black line shows the result of a naive least-squares linear fit. The thin grey lines show 30 realisations drawn from the linear gradient + intrinsic scatter posterior, while the shaded band corresponds the \(1\sigma\) dispersion around the gradient. </center>  
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+<|ref|>image_caption<|/ref|><|det|>[[107, 329, 874, 364]]<|/det|>
+<center>Fig. A10 The oxygen abundance of GALAH stars. a, Kiel diagram of the stars from the GALAH DR3 data, colour-coded by oxygen abundance. b, Kiel diagram of the stars from the GALAH DR3 data, colour-coded by ages from GALAH value-added catalogue [6]. The black dashed boxes indicate the young O-rich stars. </center>  
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+<--- Page Split --->

preprint/preprint__c9162071c35d5eb78e1ca9308636755550c9c87b98e90f2fae67eb34fcccb0c1/images_list.json

@@ -0,0 +1,251 @@
+[
+  {
+    "type": "image",
+    "img_path": "images/Figure_1.jpg",
+    "caption": "Figure 1. Activation of the SOBIR1/BAK1-containing immune complex by transphosphorylation events between SOBIR1 and BAK1. a, Schematic diagram of the kinase domain of NbSOBIR1. The amino acid sequence of the activation segment of NbSOBIR1 is shown below the diagram. Possible phosphorylation sites are denoted in red. b-e, Complementation with NbSOBIR1 T522A fails to restore Avr4/Cf-4-triggered HR (b and c), MAPK activation (d), and ROS burst (e) in N. benthamiana:Cf-4 sobir1 knock-out plants. The development of HR was imaged (b) and quantified (c) at 5 days post infiltration (dpi). Data shown are the average relative intensities of the HR + standard error of the mean (SEM) (one-way ANOVA/Dunnett's multiple comparison test, \\(***p< 0.0001\\) , \\(n\\geq 6\\) ). f, Thr522 is required for the intrinsic kinase activity of NbSOBIR1. After SDS-PAGE of the E. coli lysates, the recombinant GST-NbSOBIR1 cytoplasmic kinase domain and its various mutants were stained with Coomassie brilliant blue (CBB) (bottom panel), whereas their accumulation was detected by western blotting (middle panel), and phosphorylation status was determined by performing a Pro-Q Diamond stain (top panel). g, NbSOBIR1 WT directly phosphorylates kinase-dead NbBAK1 D418N. h, NbBAK1 WT directly phosphorylates kinase-dead NbSOBIR1 D482N. Non-fused GST and His tags served as negative controls. Bands with the expected sizes are indicated with an asterisk. Experiments were repeated at least three times with similar results, and representative results are shown.",
+    "footnote": [],
+    "bbox": [
+      [
+        198,
+        95,
+        789,
+        565
+      ]
+    ],
+    "page_idx": 25
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_2.jpg",
+    "caption": "Figure 2. Tyr469 of the kinase domain of SOBIR1 is crucial for the Avr4/Cf-4-triggered HR and MAPK activation, but not for ROS production and intrinsic kinase activity. a, Schematic diagram of the kinase domain of NbsOBIR1, with the location of the activation segment, the RD motif, and all Tyr (Y) residues indicated. b-d, Complementation with NbsOBIR1 Y469F fails to restore Avr4/Cf-4-triggered HR and MAPK activation in N. benthamiana:Cf-4 sobir1 knock-out plants. The development of HR was imaged (b) and quantified (c) at 5 dpi. Data shown are the average relative intensities of the HR + SEM (one-way ANOVA/Dunnett's multiple comparison test, \\*\\*\\* p < 0.0001, n≥6). e, Transient expression of NbsOBIR1 Y469F restores the Avr4/Cf-4-triggered ROS accumulation in N. benthamiana:Cf-4 sobir1 knock-out plants. All the tested NbsOBIR1 Tyr mutants restored the Avr4/Cf-4-triggered ROS production in this complementation study, similar to NbsOBIR1 WT. Only the results from NbsOBIR1 WT, Y469F, and D482N are shown. f, NbsOBIR1 Y469F exhibits intrinsic kinase activity. Experiments were repeated at least three times with similar results, and representative results are shown.",
+    "footnote": [],
+    "bbox": [
+      [
+        144,
+        90,
+        848,
+        451
+      ]
+    ],
+    "page_idx": 26
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_3.jpg",
+    "caption": "Figure 3. Members of RLCK-VII-6, -7, and -8 differentially contribute to ROS accumulation in N. benthamiana induced by various ExIPs. N. benthamiana:Cf-4 rlck-vii-6, rlck-vii-7, and rlck-",
+    "footnote": [],
+    "bbox": [
+      [
+        125,
+        91,
+        872,
+        555
+      ]
+    ],
+    "page_idx": 27
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_5.jpg",
+    "caption": "Figure 5. Members of N. benthamiana RLCK-VII-6, -7, and -8 are directly transphosphorylated by both SOBIR1 and BAK1 in vitro. Two members were randomly selected from RLCK-VII-6, -7, and -8 and their kinase-dead mutants were co-expressed with either the cytoplasmic kinase domain from NbSOBIR1 WT or its D482N kinase-dead mutant (a-c), or with either the cytoplasmic kinase domain from NbBAK1 WT or its D418N kinase-dead mutant (d-f), in E. coli. After SDS-PAGE of the boiled cell lysate, the phosphorylation status of the recombinant proteins was determined by performing a Pro-Q Diamond stain (top panels), while the total proteins were stained",
+    "footnote": [],
+    "bbox": [],
+    "page_idx": 28
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_0.jpg",
+    "caption": "Figure S2. The analogous residues of NbSOBIR1 Thr522 in both tomato SOBIR1 and SOBIR1-like play a crucial role in mounting Avr4/Cf-4-triggered immune responses. a, Schematic diagram of the kinase domain of SOBIR1, with the activation segment indicated. The amino acid sequences of the activation segments of NbSOBIR1, S/soBIR1 and S/soBIR1-like are aligned and are shown below the diagram. Conserved residues acting as potential phosphorylation",
+    "footnote": [],
+    "bbox": [
+      [
+        190,
+        90,
+        780,
+        800
+      ]
+    ],
+    "page_idx": 30
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_1.jpg",
+    "caption": "Figure S4. The kinase domains of SOBIR1 and BAK1 trans-phosphorylate each other in vitro. a,b, S/SOBIR1 Thr513 and S/SOBIR1-like Thr526 are essential for their intrinsic kinase activity. The N-terminally GST-tagged cytoplasmic kinase domains of (a) S/SOBIR1 WT, kinase-dead mutant D473N, and five Ser/Thr-to Ala mutants, and (b) S/SOBIR1-like WT, kinase-dead mutant D486N, and five Ser/Thr-to-Ala mutants were produced in E. coli, followed by being subjected to western blotting and in vitro phosphorylation assay. The phosphorylation status of the recombinant proteins was determined by using the Pro-Q Diamond stain, which specifically stains the phosphorylated proteins (top panels). The production of SOBIR1 kinase domains was confirmed by western blotting, using SOBIR1 antibodies (middle panels), and the recombinant proteins were stained by Coomassie brilliant blue (bottom panels). c,d, S/SOBIR1 WT and S/SOBIR1-like WT directly phosphorylate the kinase-dead mutant of S/BAK1 D418N. The N-terminally GST-tagged cytoplasmic domains of S/SOBIR1 WT or D473N (c) and S/SOBIR1-like WT or D486N (d) were co-expressed with the N-terminally His-tagged cytoplasmic domain of S/BAK1 D418N in E. coli. After SDS-PAGE of the E. coli lysates, a Pro-Q Diamond stain was employed to detect the phosphorylated recombinant proteins (top panels), while Coomassie brilliant blue was used to visualize all proteins (bottom panels). e,f, S/BAK1 WT directly phosphorylates the kinase-dead mutant of S/SOBIR1 D473N and S/SOBIR1-like D486N. The cytoplasmic domain of S/BAK1 WT or D418N, which was fused to a His tag at its N-terminus, was co-expressed with the cytoplasmic domain of S/SOBIR1 D473N (e) or S/SOBIR1-like D486N (f), which was fused to a GST tag at its N-terminus, in E. coli. The recombinant proteins were then subjected to SDS-PAGE, followed by being stained by Pro-Q Diamond stain (top panels) and Coomassie brilliant blue (bottom panels). Bands with the expected sizes are indicated with an asterisk. Experiments were repeated at least three times with similar results, and representative pictures are shown.",
+    "footnote": [],
+    "bbox": [],
+    "page_idx": 32
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_3.jpg",
+    "caption": "Figure S6. S/SOBIR1 Tyr460 and S/SOBIR1-like Tyr473, which are the analogous residues of NbSOBIR1 Tyr469, are essential for the Avr4/Cf-4-triggered HR in N. benthamiana. a, Schematic diagrams of the kinase domains of NbSOBIR1, S/SOBIR1 and S/SOBIR1-like, with the location of the activation segment, the RD motif, and all Tyr residues indicated. b-e, Mutagenesis screen of all putative Tyr phosphorylation sites in S/SOBIR1 (b and c) and S/SOBIR1-like (d and e), as described in Figure 3, to determine their importance in immune signalling by complementation. Statistical analysis was performed with an ANOVA/Dunnett's multiple comparison test, compared with their corresponding WT. \\(**p < 0.01\\) ; \\(***p < 0.001\\) ; \\(****p < 0.0001\\) . Experiments were repeated at least three times, with similar results and representative pictures are shown.",
+    "footnote": [],
+    "bbox": [
+      [
+        128,
+        120,
+        870,
+        485
+      ]
+    ],
+    "page_idx": 34
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_2.jpg",
+    "caption": "Figure S7. Accumulation levels of NbSOBIR1 Y469F, S/SOBIR1 Y460F and S/SOBIR1-like Y473F, as well as their corresponding WT and kinase-dead (D to N) versions, in planta. NbSOBIR1 Y469F, S/SOBIR1 Y460F and S/SOBIR1-like Y473F, which fail to fully restore the Avr4-triggered HR in N. benthamiana: Cf-4 sobir1 knock-out plants, were transiently expressed in N. benthamiana: Cf-4 sobir1 knock-out plants in combination with Avr4 (both at an OD600 of 0.8), next to their respective WT that was combined with Avr4 as a positive control, and their kinase-dead D to N version that was combined with Avr4 as a negative control. Leaf samples were collected at 2 dpi and total protein extracts were subjected to IP of the GFP-tagged SOBIR1 mutants using GFP-affinity beads, followed by WB with aGFP antibody (upper panels). The amount of total protein that was used for the IP is reflected by the Rubisco band present in the stain-free gel (lower panels). Arrowheads indicate the band representing SOBIR1-eGFP. Note that transient expression of SOBIR1 WT in combination with Avr4 triggers an HR in N. benthamiana: Cf-4 sobir1 plants, which explains the low accumulation levels of SOBIR1 WT.",
+    "footnote": [],
+    "bbox": [
+      [
+        282,
+        110,
+        730,
+        231
+      ]
+    ],
+    "page_idx": 35
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_3.jpg",
+    "caption": "Figure S8. S/SOBIR1 Tyr460 and S/SOBIR1-like Tyr473 are required for Avr4/Cf-4-induced MAPK activation, but not for ROS accumulation and their intrinsic kinase activity. a,b, The different Tyr mutants of S/SOBIR1 and S/SOBIR1-like were transiently expressed in leaves of the N. benthamiana:Cf-4 sobir1 knock-out line, with their corresponding WTs as positive controls and kinase-dead mutants as negative controls. Leaf discs were taken from these plants at 24 hours after agro-infiltration, followed by adding \\(0.1\\mu M\\) Avr4 protein and measuring ROS accumulation over time. ROS production is expressed as RLUs, and the data are represented as mean + SEM. c,d, S/SOBIR1 Y460F and S/SOBIR1-like Y473F, as well as their corresponding WTs and kinase-dead mutants, were transiently co-expressed with Avr4 in leaves of N. benthamiana:Cf-4 sobir1 knock-out plants. Leaf samples were collected at 2 dpi and total protein extracts were subjected to immunoblotting with a p42/p44-erk antibody to determine the activation of downstream MAPKs by phosphorylation. e,f, The N-terminally GST-tagged cytoplasmic kinase domains of S/SOBIR1 Y460F and S/SOBIR1-like Y473F were produced in E. coli, with their corresponding WTs as positive controls and their kinase-dead mutants as negative controls. After SDS-PAGE of the E. coli lysates, the recombinant proteins were stained with Coomassie brilliant blue (lower panels), whereas the phosphorylation status of the kinase domains was determined by performing a Pro-Q Diamond stain (upper panels). Experiments were repeated at least three times and similar results were obtained. Representative pictures are shown.",
+    "footnote": [],
+    "bbox": [
+      [
+        156,
+        120,
+        850,
+        420
+      ]
+    ],
+    "page_idx": 37
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_4.jpg",
+    "caption": "Figure S9. Phylogenetic analysis of BIK1 homologs from Arabidopsis, tomato, and N. benthamiana. a, The amino acid sequences of only the kinase domain were extracted from all RLCK members from Arabidopsis, tomato, and N. benthamiana and aligned to subsequently generate a neighbour-joining phylogenetic tree, using QuickTree (Howe et al., 2002). The sub-clade of putative BIK1 homologs, which comprises 123 sequences, including AtBIK1 (bootstrap support higher than 90%) is shown in red. b, Phylogenetic analysis of the RLCK-VII subfamily members from Arabidopsis, tomato, and N. benthamiana. Amino acid motifs identified in the complete protein sequence using MEME are shown (Bailey et al., 2009). All the members present in this tree were further assigned to six subfamilies, which are depicted in different colours. These subfamilies are referred to as subfamily 4, 5, 6, 7, 8, and 9, according to the RLCK-VII subfamilies in Arabidopsis reported previously by Rao et al. (2018).",
+    "footnote": [],
+    "bbox": [],
+    "page_idx": 38
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_5.jpg",
+    "caption": "Figure S10. Gene expression patterns of the 14 members from N. benthamiana RLCK-VII-6. Heat map of the relative expression (log2) of all 14 RLCK members of subfamily 6, as determined upon transient expression of Avr4, constitutively active NRC1 (Gabriëls et al., 2007), or the coat protein (CP) of potato virus X (Tameling et al., 2010), in leaves of N. benthamiana plants transgenic for both Cf-4 and Rx, with the latter gene mediating recognition of the CP of PVX. The RLCK-encoding genes that were selected to be knocked-out are highlighted in pink. NRC1, NB-LRR PROTEIN REQUIRED FOR HR-ASSOCIATED CELL DEATH 1; CP, coat protein.",
+    "footnote": [],
+    "bbox": [
+      [
+        298,
+        120,
+        728,
+        415
+      ]
+    ],
+    "page_idx": 39
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_6.jpg",
+    "caption": "Figure S11. Various subfamilies from RLCK-VII play an important role in the Avr4/Cf-4/SOBIR1-triggered ROS burst in N. benthamiana:Cf-4. Selected members from each RLCK-VII subfamily, being subfamilies 4, 5, 6, 7, 8 and 9, were targeted for knock-out in N. benthamiana:Cf-4 by multiplex CRISPR/Cas technology. Subsequently, ROS accumulation induced upon Avr4 protein treatment of leaf discs obtained from five individual rlcK-vii-4 knock-out transformants (a), four rlcK-vii-5 knock-out transformants (b), seven rlcK-vii-6 knock-out transformants (c), four rlcK-vii-7 knock-out transformants (d), three rlcK-vii-8 knock-out transformants (e) and five rlcK-vii-9 knock-out transformants (f), was determined. For this, leaf discs were treated with \\(0.1\\mu M\\) Avr4 protein, and the generation of ROS was monitored. Note that all rlcK knock-out transformants were tested in the T1 generation. ROS production is expressed as RLUs, and the data are represented as mean + SEM (n≥6). The ROS profiles of the positive control (N. benthamiana:Cf-4), included in all assays, are indicated in red in all the line charts. Similar results were obtained in three replicates and data from one representative experiment are shown.",
+    "footnote": [],
+    "bbox": [
+      [
+        144,
+        88,
+        860,
+        491
+      ]
+    ],
+    "page_idx": 40
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_7.jpg",
+    "caption": "Figure S12. RLCK-VII-6, -7 and -8 from N. benthamiana also play a positive role in the flg22/FLS2-triggered ROS burst. ROS production, triggered upon treatment with flg22, by discs taken from leaves of rlck-vii-4 (a), rlck-vii-5 (b), rlck-vii-6 (c), rlck-vii-7 (d), rlck-vii-8 (e) and rlck-vii-9 (f) N. benthamiana: Cf-4 knock-out plants from the T1 generation, was measured. For this, leaf discs were taken from the different knock-out plants, as well as from N. benthamiana: Cf-4 (the positive control), followed by treatment with a final concentration of 0.1 μM flg22 peptide and subsequent monitoring of the accumulation of ROS. ROS production is expressed as RLUs, and the data are represented as mean plus the standard error of the mean (SEM) (n≥6). The ROS traces of the positive control are indicated in red in all the line charts. All experiments were repeated at least three times and data from one representative experiment are shown.",
+    "footnote": [],
+    "bbox": [
+      [
+        201,
+        98,
+        800,
+        479
+      ]
+    ],
+    "page_idx": 41
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_8.jpg",
+    "caption": "Figure S13. RLCK-VII-7 is required for the Avr4/Cf-4-triggered HR in N. benthamiana:Cf-4. A solution of \\(5\\mu \\mathrm{M}\\) pure Avr4 protein was infiltrated in leaves of the N. benthamiana:Cf-4 rlcK-vii-4 (a), rlcK-vii-5 (b), rlcK-vii-6 (c), rlcK-vii-7 (d), rlcK-vii-8 (e) and rlcK-vii-9 (f) transformants, and the Avr4/Cf-4-triggered HR was subsequently imaged using the ChemiDoc and quantified using Image Lab, at 2 dpi. All individual quantifications are shown as dots ( \\(n\\geq 6\\) ) and the means as lines. Statistical analysis was performed with an ANOVA/Dunnett's multiple comparison test, compared with N. benthamiana:Cf-4. \\(*p< 0.05\\) ; \\(***p< 0.001\\) ; \\(****p< 0.0001\\) . Experiments were repeated at least three times with similar results, and representative results are shown.",
+    "footnote": [],
+    "bbox": [
+      [
+        172,
+        95,
+        815,
+        430
+      ]
+    ],
+    "page_idx": 42
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_9.jpg",
+    "caption": "Figure S14. Genotypes and morphological phenotypes of the different rlcK-vii knock-out lines. Overview of the types of mutations present in all the RLCK-VII-6 members (a), RLCK-VII-7 members (c), and RLCK-VII-8 members (e) in the independent homozygous N. benthamiana: Cf-4 knock-out lines. Morphological phenotypes of N. benthamiana: Cf-4 and the three independent rlcK-vii-6 (b), two independent rlcK-vii-7 (d), and two independent rlcK-vii-8 (f) knock-out lines. All plants were grown in soil under the same conditions and were photographed when they were four to five weeks old.",
+    "footnote": [],
+    "bbox": [
+      [
+        228,
+        95,
+        755,
+        740
+      ]
+    ],
+    "page_idx": 43
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_10.jpg",
+    "caption": "Figure S15. Members of RLCK-VII-6, -7, and -8 differentially contribute to ROS accumulation in N. benthamiana induced by nlp20/RLP23 and pg13/RLP42 combinations. Leaf discs taken from independent N. benthamiana: Cf-4 rlcK-vii-6 (a and b), rlcK-vii-7 (c and d), and rlcK-vii-8 (e and f) lines, as well as from N. benthamiana: Cf-4, transiently expressing either RLP23 or RLP42, were treated with the corresponding elicitors at a \\(1\\mu \\mathrm{M}\\) concentration and the accumulation of ROS was monitored. ROS production is expressed as RLUs, and the data are represented as mean + SEM \\((n\\geq 6)\\) .",
+    "footnote": [],
+    "bbox": [
+      [
+        155,
+        100,
+        852,
+        560
+      ]
+    ],
+    "page_idx": 44
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_11.jpg",
+    "caption": "Figure S16. The Avr4 protein triggers a swift MAPK activation in N. benthamiana:Cf-4. Water (mock) or \\(5\\mu \\mathrm{M}\\) of pure Avr4 protein was infiltrated in leaves of N. benthamiana:Cf-4. Leaf samples were taken at the indicated time points after Avr4 infiltration, and total protein extracts were subjected to immunoblotting using a p42/p44-erk antibody specifically detecting MAPKs that are activated by phosphorylation (a-pMAPK). Rubisco is shown as a total protein loading control. O/N, overnight. The experiment was repeated two times with similar results and a representative result is shown.",
+    "footnote": [],
+    "bbox": [
+      [
+        213,
+        111,
+        810,
+        227
+      ]
+    ],
+    "page_idx": 45
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_12.jpg",
+    "caption": "Figure S17. The overall structure of the inactive AtSOBIR1 kinase domain and position of the important Tyr residues. The ribbon diagram of the SOBIR1 kinase domain is coloured in light blue. The non-hydrolysable ATP analogue AMP-PNP and \\(\\mathrm{Mg^{2 + }}\\) are presented as an orange stick and a green sphere, respectively. AtSOBIR1 Tyr476, which is analogous to NbSOBIR1 Tyr469, is indicated as a yellow stick.",
+    "footnote": [],
+    "bbox": [
+      [
+        360,
+        141,
+        664,
+        455
+      ]
+    ],
+    "page_idx": 46
+  }
+]

preprint/preprint__c9193543f5cc6175958579c90a2d0403f3c3a53648bc7c941f638012a3553e29/images_list.json

@@ -0,0 +1,242 @@
+[
+  {
+    "type": "image",
+    "img_path": "images/Figure_1.jpg",
+    "caption": "Fig. 1: Process of unsupervised modulation recognition algorithm based on comparative learning.",
+    "footnote": [],
+    "bbox": [
+      [
+        77,
+        85,
+        489,
+        124
+      ]
+    ],
+    "page_idx": 3
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_2.jpg",
+    "caption": "Fig. 2: The three types of AMR methods all start from the baseband signal and subsequently diverge from each other. The subsequent processes of baseband-based AMR, multi-input based AMR, and the proposed MAC-based UAMR are illustrated in the top, middle, and bottom branches, respectively.",
+    "footnote": [],
+    "bbox": [
+      [
+        88,
+        68,
+        905,
+        339
+      ]
+    ],
+    "page_idx": 5
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_3.jpg",
+    "caption": "Fig. 3: The workflow of MAC-based UAMR framework. Firstly, the unsupervised training module performs representation learning on unlabeled signals, bringing positive samples closer and negative samples farther apart in the feature space, respectively. Secondly, DA module selects features from the representation domains. Finally, the AMR tasks are performed by linear evaluation.",
+    "footnote": [],
+    "bbox": [
+      [
+        88,
+        70,
+        909,
+        337
+      ]
+    ],
+    "page_idx": 6
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_4.jpg",
+    "caption": "Fig. 4: The relationship between I-Q components and amplitude-phase characterization in Constellation diagram. e.g., 16QAM.",
+    "footnote": [],
+    "bbox": [
+      [
+        115,
+        68,
+        451,
+        345
+      ]
+    ],
+    "page_idx": 7
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_5.jpg",
+    "caption": "Fig. 5: Different data augmentation methods for modulation signals used for SD representation learning: (a) rotation. (b) flip. (c) Gaussian noise. (d) section mask.",
+    "footnote": [],
+    "bbox": [
+      [
+        79,
+        68,
+        480,
+        228
+      ]
+    ],
+    "page_idx": 8
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_6.jpg",
+    "caption": "Fig. 6: \"I-Q single centralization\" multi-representation domain loss calculation strategy.",
+    "footnote": [],
+    "bbox": [
+      [
+        88,
+        68,
+        475,
+        208
+      ]
+    ],
+    "page_idx": 9
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_7.jpg",
+    "caption": "Fig. 7: DA module for attention inference.",
+    "footnote": [],
+    "bbox": [
+      [
+        507,
+        70,
+        923,
+        181
+      ]
+    ],
+    "page_idx": 9
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_8.jpg",
+    "caption": "Fig. 8: Performance comparison of the proposed method with different domain stack sizes on the RML2016.10A and RML2016.10B datasets. (a) MAC-D1 on RML2016.10A, (b) MAC-MT4 on RML2016.10A, (c) MAC-D1 on RML2016.10B, (d) MAC-MT4 on RML2016.10B.",
+    "footnote": [],
+    "bbox": [
+      [
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+        225,
+        910,
+        365
+      ]
+    ],
+    "page_idx": 11
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_9.jpg",
+    "caption": "Fig. 9: Validation comparative loss curves of unsupervised training on the RML2016.10A dataset(a). Linear evaluation validation loss on ablation of different modules(b). \\(V_{1},V_{2},V_{3},V_{4}\\) Representing the combination of transformation domains \\(\\{A\\phi \\} ,\\{A f\\} ,\\{\\mathcal{F}\\} ,\\{W T\\}\\) separately.",
+    "footnote": [],
+    "bbox": [
+      [
+        506,
+        424,
+        925,
+        562
+      ]
+    ],
+    "page_idx": 11
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_10.jpg",
+    "caption": "Fig. 10: The confusion matrix of the proposed MAC-MT4 at SNR=0dB (1) and 8dB (2) on RML2016.10A (a) and RML2016.10B (b) datasets.",
+    "footnote": [],
+    "bbox": [
+      [
+        86,
+        330,
+        896,
+        485
+      ]
+    ],
+    "page_idx": 13
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_11.jpg",
+    "caption": "Fig. 11: Distribution of intra-class (a) and inter-class (b) similarity density of MAC-MT4 and TAC-MT4.",
+    "footnote": [],
+    "bbox": [
+      [
+        84,
+        540,
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+        673
+      ]
+    ],
+    "page_idx": 13
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_12.jpg",
+    "caption": "Fig. 12: Intuitive demonstrations of the feature-level representation domain selection of MAC-MT4. A sampled signal of SNR=0 dB is taken as an example for each modulation. In each subfigure, the normalized attention vectors \\(\\hat{\\gamma}\\) are shown on the left, and signal waveform with attention distribution of MAC is shown on the right side. (a) 8PSK. (b) AM-DSB. (c) BPSK. (d) CPFSK. (e) GFSK. (f) PAM4. (g) 16QAM. (h) 64QAM. (i) QPSK. (j) WBFM.",
+    "footnote": [],
+    "bbox": [
+      [
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+      ]
+    ],
+    "page_idx": 14
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_13.jpg",
+    "caption": "Fig. 13: Recognition performance comparison of existing unsupervised frameworks and the proposed MAC-MT4.",
+    "footnote": [],
+    "bbox": [
+      [
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+        250,
+        488,
+        502
+      ]
+    ],
+    "page_idx": 15
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_14.jpg",
+    "caption": "Fig. 14: The confusion matrix of the proposed MAC-MT4 generalization experiment at \\(\\mathrm{SNR} = 0\\mathrm{dB}\\) (a), 8dB (b)",
+    "footnote": [],
+    "bbox": [
+      [
+        80,
+        277,
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+      ]
+    ],
+    "page_idx": 16
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_15.jpg",
+    "caption": "Fig. 15: Distribution of similarity ratio \\(\\mathcal{R}\\) density of supervised frameworks and the proposed framework. (a) RML2016.10A trained; RML2016.10A tested. (b) RML2016.10A trained; RML2016.10B tested.",
+    "footnote": [],
+    "bbox": [
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+      ]
+    ],
+    "page_idx": 17
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_16.jpg",
+    "caption": "Fig. 16: Feature visualization results for MAC-MT4 at different SNRs and training epochs of RML2016.10A dataset. (a) epoch=1. (b) epoch=50. (c) epoch=100. (d) epoch=150. (e) epoch=240. I SNR=8dB. II SNR=8dB. III SNR=8dB. IV SNR=12dB.",
+    "footnote": [],
+    "bbox": [
+      [
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+        530
+      ]
+    ],
+    "page_idx": 18
+  }
+]

preprint/preprint__c9193543f5cc6175958579c90a2d0403f3c3a53648bc7c941f638012a3553e29/preprint__c9193543f5cc6175958579c90a2d0403f3c3a53648bc7c941f638012a3553e29.mmd

@@ -0,0 +1,560 @@
+
+# Multi-Representation Domain Attentive Contrastive Learning Based Unsupervised Automatic Modulation Recognition  
+
+Xiaoran Shi  
+
+xrshi@xidian.edu.cn  
+
+North Campus of Xi'an University of Electronic Science and Technology, No. 2 Taibai South Road, Yanta District, Xi'an City, Shaanxi Province https://orcid.org/0000- 0003- 4636- 2966  
+
+Yu Li  
+
+North Campus of Xi'an University of Electronic Science and Technology, No. 2 Taibai South Road, Yanta District, Xi'an City, Shaanxi Province https://orcid.org/0009- 0001- 6951- 083X  
+
+Haoyue Tan  
+
+North Campus of Xi'an University of Electronic Science and Technology, No. 2 Taibai South Road, Yanta District, Xi'an City, Shaanxi Province https://orcid.org/0009- 0000- 4987- 6909  
+
+Xinyao Yang  
+
+North Campus of Xi'an University of Electronic Science and Technology, No. 2 Taibai South Road, Yanta District, Xi'an City, Shaanxi Province  
+
+Feng Zhou  
+
+North Campus of Xi'an University of Electronic Science and Technology, No. 2 Taibai South Road, Yanta District, Xi'an City, Shaanxi Province  
+
+## Article  
+
+Keywords: Unsupervised learning, attention mechanism, multi- domain representation, contrastive learning, automatic modulation recognition  
+
+Posted Date: January 22nd, 2024  
+
+DOI: https://doi.org/10.21203/rs.3.rs- 3696311/v1  
+
+License: © This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License  
+
+Additional Declarations: There is NO Competing Interest.
+
+<--- Page Split --->
+
+Version of Record: A version of this preprint was published at Nature Communications on July 1st, 2025. See the published version at https://doi.org/10.1038/s41467-025-60921-z.
+
+<--- Page Split --->
+
+# Multi-Representation Domain Attentive Contrastive Learning Based Unsupervised Automatic Modulation Recognition  
+
+Yu Li, Member, IEEE, Xiaoran Shi Member, IEEE, Haoyue Tan, Xinyao Yang, and Feng Zhou, Member, IEEE Key Laboratory of Electronic Information Countermeasure and Simulation Technology, Ministry of Education Xidian University, Xi'an, China  
+
+Abstract—Automatic modulation recognition (AMR) is a crucial technology in the domain of electronic reconnaissance. Benefiting from the powerful feature extraction ability of deep neural networks, the AMR algorithms based on supervised deep learning usually achieve pleasant performance. However, in noncooperative scenarios, high- quality and reliable modulation labels are difficult to obtain. Therefore, this paper proposes a novel unsupervised framework for AMR called Multi- representation Attentive domain Contrastive learning (MAC). Carefully utilizing unlabeled signal data with a unsupervised contrastive learning method across multi- representation domains is a more effective way than directly using different representations as inputs. MAC aims to obtain high- quality signal feature information from unlabelled signals. In detail, inter- domain and intra- domain contrastive learning maximize the mutual modulation features between different representation domains and preserve self- information in In- Phase and Quadrature (I- Q) representation, respectively. Furthermore, the Domain Attention (DA) module shifts the selection of representation domains from the signal level to the feature level. The performance of the proposed framework was assessed through publicly available datasets. The conducted experiments clearly showed that MAC remarkably outperforms existing unsupervised algorithms in modulation recognition and exhibits superior generalization ability. Moreover, our framework can be extended to accommodate various representation domains and trained end- to- end, thereby significantly enhancing the efficacy of training deep neural networks for automatic modulation classification without the need for labeled data. These results highlight the substantial reduction in the disparity between unsupervised and supervised representation learning in the domain of AMR.  
+
+Index Terms—Unsupervised learning, attention mechanism, multi- domain representation, contrastive learning, automatic modulation recognition.  
+
+## I. INTRODUCTION  
+
+Acquiring military information in modern warfare relies heavily on communication intelligence collecting [1], which serves as a fundamental prerequisite for electronic warfare and interference operations. Modulation recognition of wireless signals is a widely employed technique for communication reconnaissance [2], [3]. The purpose of automatic modulation recognition (AMR) is to identify the modulation scheme employed in wireless signals and discern their types and characteristics. In non- cooperative scenarios like electronic surveillance and intelligence collecting, AMR functions as a pivotal intermediary signal processing stage between signal detection and demodulation [4].   
+
+In general, traditional approaches to AMR can be broadly classified into two types based on their underlying principles: likelihood- based AMR (LB- AMR) and feature- based AMR (FB- AMR). LB- AMR algorithms treat the modulation recognition problem as a multi- hypothesis testing problem and employ principles derived from maximum likelihood theory [5]. These methods have the potential to achieve optimal recognition accuracy from a Bayesian estimation perspective and often do not require a large number of training samples. However, they are associated with relatively high computational complexity. FB- AMR algorithms, on the other hand, extract discriminative representative features from signal samples and employ suitable classifiers for signal classification. The selection of features and classifiers depends on the specific requirements of the AMR task.  
+
+The powerful feature extraction capability offered by the stacked layers of artificial neurons has sparked a significant expansion of research in the field of wireless signal detection and recognition using deep learning (DL) methods. Data- driven DL- AMR approaches typically employ supervised learning, where well- designed deep neural networks are trained by a large number of labeled samples. These trained networks can effectively extract high- dimensional features from input signals, enabling the differentiation of various modulation types. The aforementioned supervised models have shown impressive results when trained on a substantial number of labeled samples [6]. Nevertheless, the process of annotating a large volume of labeled signal samples necessitates substantial investments in terms of time and financial resources. Moreover, in non- cooperative scenarios, acquiring accurate modulation labels for a considerable number of received wireless signals at the receiver poses inherent difficulties. These challenges significantly impede the training of supervised models.  
+
+The mechanism of unsupervised learning offers a novel approach to tackle the aforementioned problem. Unsupervised learning has demonstrated remarkable success in the realm of natural language processing, exemplified by models such as GPT [7] and BERT [8].  
+
+The key of unsupervised automatic modulation recognition (UAMR) critically depends on the approach to signal rep
+
+<--- Page Split --->
+![](images/Figure_1.jpg)
+
+<center>Fig. 1: Process of unsupervised modulation recognition algorithm based on comparative learning. </center>  
+
+resentation learning. Recent research [9], [10] has provided compelling evidence of the superior performance achieved through the utilization of contrastive loss in unsupervised representation learning. Contrastive learning aims to learn representations by minimizing the distance between positive samples and maximizing the distance between negative samples in the feature space. Remarkably, this representation learning process operates without the need for any label. The signal representation obtained through unsupervised learning can be applied to downstream tasks after fine- tuning in specific scenarios. The workflow of the proposed unsupervised modulation recognition algorithm based on contrastive learning is depicted in Fig. 1.  
+
+In this work, we propose a novel unsupervised framework for AMR called Multi- representation Attentive domain Contrastive learning (MAC). The framework integrates multi- domain signal representation with contrastive learning. Positive and negative samples of unlabeled signals are generated through signal transformations and data augmentation. MAC performs contrastive learning during intra- domain and inter- domain to extract domain- invariant modulation features, and solves the problem of unlabeled signals unable to support AMR for supervised training in non- cooperative scenarios. Additionally, we propose the "I- Q single- centering" optimization strategy, which extends the proposed MAC to the arbitrary number of representation domains. Distinguished with some typical AMR methods that utilize multiple input information, the Domain Attention (DA) module is proposed to differentiate and balance different representation domain features. Above all, the proposed MAC integrates non- expert- assisted representation domain selection and multi- representation domain UAMR into an end- to- end neural network and obtains the best performance of not only high classification accuracy in the field of UAMR but also strong generalization abilities.  
+
+The contributions of this paper can be summarized as follows.  
+
+To address the challenges associated with the need for a large number of accurately labeled modulation signal samples in supervised learning and the lack of labeled samples in non- cooperative scenarios, we have developed an end- to- end framework for unsupervised representation learning of wireless modulation signals called MAC- based UAMR. Observing a modulation signal from different representation domains is akin to viewing an image from different perspectives, where the modulation type remains invariant across all representation domains. MAC maximizes the mutual information between representations of the signal in different domains, constructing dual- domain feature dictionaries for wireless signals. By  
+
+leveraging proxy tasks, MAC achieves signal representation learning in unlabeled scenarios. To the best of our knowledge, our proposed unsupervised representation learning framework is pioneering in the field of modulation recognition.  
+
+Contrast to previous multi- input AMR algorithms, the proposed DA aimed at emphasizing deep features from multiple representation domains based on their contextual relevance. DA disregards irrelevant or redundant features, ensuring that the final classifier focuses accurately on meaningful features. From another perspective, the selection of appropriate transformation domains for different modulation types is finished at the feature level, which is more robust than relying on expert knowledge during the signal preprocessing level. Feature- Level representation domain selection is intuitively demonstrated to enhance the interpretability of the DA module.  
+
+A new optimization strategy is proposed that extends the MAC framework to an arbitrary number of representation domains while maximizing the mutual information between modulation signal domains at lower algorithmic complexity.  
+
+To mitigate the challenges encountered during the reception of wireless signals, including issues such as low signal- to- noise ratio (SNR), missing symbols, frequency offset, and phase offset, we employed four data augmentation techniques to construct positive and negative sample pairs in representation learning of I- Q domain.  
+
+We propose an intra- inter domain dual- cycle contrastive loss calculation method for the MAC- based UAMR framework, which enables exploration of the signal representations in intra- domain and the domain- invariant modulation features in inter- domain simultaneously.  
+
+The rest of this paper is organized as follows. In Section II the related works on AMR and unsupervised contrastive learning are introduced. In Section III the wireless signal model and problem formulation of UAMR are described. In Section IV, the principles and basic framework of the proposed MAC- based UAMR method are presented detailedly, the intra- inter domain dual- cycle contrastive loss function is constructed, and the implementation for DA is provided. In Section V, experiments are demonstrated to verify the effectiveness and generalization ability of MAC on serval datasets. Finally, conclusions are drawn in Section VI.  
+
+## II. RELATED WORK  
+
+### A. DL-AMR  
+
+Deep neural networks have gained significant attention in the field of modulation recognition due to their powerful learning capability and excellent nonlinear mapping properties. Some continuous advancements in research findings and algorithms in AMR have been witnessed in recent years. Scholars have demonstrated that deep neural networks are particularly well- suited for feature extraction and recognition of wireless time series sample data, surpassing the performance of traditional classifiers based on manual features [11].
+
+<--- Page Split --->
+
+CNN- type networks have shown great promise [12], [13]. To be specific, in 2016, O'Shea et al. [14] utilized convolutional neural networks (CNN) for automatic feature extraction from I- Q quadrature signals. They employed a simple four- layer CNN model to recognize three analog modulation types and eight digital modulation types, achieving a recognition rate of over \(70\%\) when the SNR was greater than 2dB. Mendis et al. [15] used the cyclostationary spectrum of modulation signals as inputs to a deep neural network for recognizing five modulation types, achieving an average recognition rate of over \(90\%\) when the SNR was greater than - 2dB. CNN networks are particularly effective at extracting spatial correlation features from signals [16]. In addition, wireless signals also exhibit temporal correlation features [17], which can be effectively learned using recurrent neural networks (RNN) [17], [18]. Pure CNN or RNN models focus solely on either the spatial or temporal dimension of wireless signals. However, an increasing number of researchers have started investigating hybrid models that combine both CNN and RNN architectures for AMR [19], [20]. West et al. [16] proposed a convolutional long short- term deep neural network (CLDNN) that combines temporal and spatial information and achieved an \(84\%\) recognition accuracy for eleven modulation types under the SNR of 4dB.  
+
+Wang et al. [21] employed the mapping of signal sequences to scatter plots in the complex plane and utilized constellation diagram images as inputs to a deep learning network for the classification of six modulation types. Daldal et al. [11] utilized the short- time Fourier transform to generate spectrograms of signals, which were then used as input to a convolutional neural network for the recognition of six digital modulation types. Hanna et al. [22] proposed a dual- path network that combined feature extraction networks with digital signal processing (DSP) signal recovery, enabling the later stage of feature extraction to benefit from the recovered signals and handle variable- length input signals.  
+
+Both manual and deep learning- based feature extraction methods have demonstrated that modulation information in wireless signals is distributed across multiple representation domains. This parallels the way humans gather information and exhibit enhanced confidence in their judgments through the integration of inputs from multiple sensory modalities, including vision, hearing, touch, and taste. Methods that leverage information from multi- representation domains often achieve superior recognition performance.  
+
+### B. Unsupervised contrastive learning  
+
+In recent years, there has been notable progress in unsupervised contrastive learning methods, which derives representations by contrasting positive and negative examples without using sample labels. It quantifies the similarity between positive and negative sample pairs in the representation space using contrastive loss and optimizes the representation extractor accordingly. Hjelm et al. [10] employed local structures within images to learn their representations and discriminate between global and local features belonging to the same image.  
+
+Wu et al. [23] considered each sample as an individual category and captured feature representations that exhibit visual similarity, resulting in the highest top- 1 classification accuracy on the ImageNet 1K dataset. Oord et al. [24] encoded information from preceding time steps filtered out low- level information and noise from the lower layers, and utilized autoregressive models to predict information beyond the current time step, thereby acquiring temporal representations of the samples. Tian et al. [25] employed various views of the same image (depth, brightness, contrast, color, etc.) as transformations to acquire invariant representations across different views.   
+
+However, these unsupervised representation learning methods were originally designed for image or speech recognition tasks. When applied directly to the AMR field, they do not yield satisfactory performance. This is primarily because the construction of positive and negative sample pairs for wireless modulated signals differs from that of images and speech signals. Moreover, the transformations used to generate different representations of the same image, although more intuitive, may not be applicable to wireless signals that inherently embody modulation information.  
+
+To tackle this issue, our work begins by delving into the fundamental nature of symbol combinations in modulated signals. We actively explore diverse perspectives of modulation symbols within the same class and learn signal representations leveraging modulation characteristics, which remain invariant across different domains.  
+
+### C. Attention mechanisms  
+
+Humans do not always recognize the targets or make decisions based on a holistic perspective of the target but rather focus their attention on some key informations. Some previous works have incorporated attention mechanisms into their neural networks. Inspired by SENet [26], Lin et al. [27] designed a channel- wise attention module between convolutional layers and employed a dual classifier with bidirectional gate recurrent units (Bi- GRUs) to capture temporal dependencies, resulting in improving AMC performance. Qi et al. [4] explored a combination of knowledge- based and data- driven approaches. They fused manually extracted features with network- extracted features, incorporated attention mechanisms, and proposed an AMR dataset containing a large number of modulation types, achieving recognition of thirty- six modulation types. Chen et al. [28] utilized attention mechanisms to focus their network on relevant hidden states generated by the layers, aiding in the capture of temporal features. These works have benefited from attention mechanisms, leading to enhanced AMC performance.  
+
+However, the interpretability of the improvements from the attention mechanism is lacking to some extent. Our research migrates attention mechanisms to the representation domain selection task, which relied on prior scenes and human expertise, to the feature level. Additionally, the representation domain selection results are visualized, greatly enhancing the interpretability of the network.  
+
+## III. SIGNAL MODEL AND PROBLEM FORMULATION  
+
+Consider the baseband wireless signal model after down- conversion at the receiver. At any discrete time instant, the
+
+<--- Page Split --->
+![](images/Figure_2.jpg)
+
+<center>Fig. 2: The three types of AMR methods all start from the baseband signal and subsequently diverge from each other. The subsequent processes of baseband-based AMR, multi-input based AMR, and the proposed MAC-based UAMR are illustrated in the top, middle, and bottom branches, respectively. </center>  
+
+relationship between the transmitted signal and the received signal can be represented as  
+
+\[s_{r}(n) = s_{t}^{l}(n)*h(n)e^{j(2\pi n\Delta f + \phi_{0})} + w(n) \quad (1)\]  
+
+where \(s_{r}(n)\) is the received baseband signal, \(s_{t}^{l}(n)\) is the modulated signal generated from one of \(\bar{L}\) modulation schemes \(\{s^{1}(n),s^{2}(n),\dots ,s^{\bar{L}}(n)\}\) \(h(n)\) is the pulse response of the wireless transmission channel, \(^*\) denotes the convolution operation, \(w(n)\) is the noise, \(\Delta f\) and \(\phi_0\) represents the additional carrier frequency offset and phase jitter during the transmission process. \(n = 0,1,\ldots ,N - 1,N\) represents the total length of the signal.  
+
+The in- phase and quadrature components of \(s_{r}(n)\) , also known as I- Q components, are stacked in parallel for the convenience of implementation. The I- Q components can be represented by  
+
+\[\begin{array}{l}I(n) = \mathrm{real}(s_r(n))\\ Q(n) = \mathrm{imag}(s_r(n)) \end{array} \quad (2)\]  
+
+where \(I(n)\) and \(Q(n)\) respectively denote the in- phase and quadrature components of \(s_{r}(n)\) , while the operations \(real(\cdot)\) and \(imag(\cdot)\) indicate the extraction of the real and imaginary parts of the complex signal.  
+
+As shown in Fig. 2, the radio frequency (RF) signal is converted into a baseband digital signal via carrier removal and analog- to- digital converter (ADC) module. Then, baseband signal- based AMC methods could be used directly to classify modulation types. Namely, signal- based AMC methods need to find out which modulation owns the maximum probability to match the corresponding signal samples, and this problem can be formulated as  
+
+\[\hat{I} = \arg \max_{I\in \{1,\ldots ,L\}}P(M_{I}\mid s_{r}(n)) \quad (3)\]  
+
+The AMC method based on multi- input uses different representation domains. Note that the selection of the signal  
+
+representation domain is based on expert knowledge at the signal level. The well- known constellation diagram is important for PSK and QAM signals, while AM, MASK, and other amplitude modulation signals have great differences in instantaneous amplitude characteristics. AMC based on multi- input achieves pleasant performance when the input form and characteristics of the signal can be selected properly. It is assumed that a preprocessing transformation operation on the input signal can be expressed as  
+
+\[V_{k} = \mathcal{T}_{k}\left(s_{r}\left(n\right)\right) \quad (4)\]  
+
+where \(\mathcal{T}_{k}(\cdot)\) denotes the \(k\) - th preprocessing transformation operation for I- Q sequence of baseband signal. Besides, \(V_{k}\) and \(s_{r}(n)\) denote the transformed result and the original signal to be transformed respectively.  
+
+The modulation identification problem based on signals from multi- domain can be formulated as  
+
+\[\hat{I} = \arg \max_{I\in \{1,\ldots ,L\}}P\left(M_{I}\mid \sum_{k = 1}\mathcal{T}_{k}\left(s_{r}\left(n\right)\right)\right) \quad (5)\]  
+
+which is convenient to solve via DL when there is a direct association between samples and labels. However, supervised networks struggle to be trained in scenarios where sample labels are lacking. Even when high- quality annotated samples are used for supervised training, the resulting models exhibit poor generalization performance.  
+
+The adverse channel conditions further exacerbate the problem of directly inputting multiple forms of signals into the network, leading to redundant or even erroneous features. Coupled with inappropriate feature selection, these factors contribute to the degradation of AMR performance. How to alleviate this problem will be discussed in the following.
+
+<--- Page Split --->
+![](images/Figure_3.jpg)
+
+<center>Fig. 3: The workflow of MAC-based UAMR framework. Firstly, the unsupervised training module performs representation learning on unlabeled signals, bringing positive samples closer and negative samples farther apart in the feature space, respectively. Secondly, DA module selects features from the representation domains. Finally, the AMR tasks are performed by linear evaluation. </center>  
+
+## IV. PROPOSED MAC-BASED UAMR FRAMEWORK  
+
+This section introduces the proposed MAC- based UAMR framework, as illustrated in Fig. 3. Firstly, unsupervised learning of MAC can be divided into two parts: inter- domain contrastive learning and intra- domain contrastive learning. In inter- domain contrastive learning part, multi- representation domain signals are taken to construct positive and negative sample pairs, which focuses on the similarities and differences between different representation domains. Then, we establish intra- domain contrastive learning framework within the representation domain by leveraging the augmented samples, which maintains robust features within SD during the process of maximizing inter- domain mutual information. Additionally, we extend MAC to handle any number of representation domains by "I- Q single centralization", DA module is proposed to leverages attention mechanisms to shift the selection of signal preprocessing forms from the signal level to the feature level. Finally, the AMR tasks are performed by linear evaluation.  
+
+### A. Signal multi-representation domain  
+
+Research on UAMR is still limited in the domain of signal processing and recognition. One possible reason is the disparity in representation space between modulation signals and natural language. In natural language processing tasks, discrete signal units like word vectors or character vectors are readily available, enabling unsupervised learning to construct dictionaries and learn contextual relationships. Conversely, modulation signals reside in a continuous, high- dimensional space, with the modulation information of individual symbols embedded within the signal. This characteristic makes it impractical to decompose them into discrete individual vectors with meaningful interpretations.  
+
+From this perspective, the unsupervised learning of wireless signal representations encompasses two key aspects: the construction of a feature dictionary for modulation signals and the design of proxy tasks and corresponding loss functions. Intuitively, the feature dictionary should effectively capture the essential characteristics of modulation styles. Over the years, researchers have extensively explored the utilization of various transform- domain information for wireless signals [29] [30] [18]. By leveraging a dictionary that integrates multi- representation domain features, the subsequent matching of queries and the learning of modulation details can be facilitated [4].   
+
+Consequently, we construct a feature dictionary from multi- representation domains of modulation signals, MAC aims to investigate the invariant modulation information concealed across multi- representation domains. The definitions and input forms of modulation signals in different representation domains will be first provided.  
+
+1) Constellation space representation domain: We employ the instantaneous amplitude and instantaneous phase as the constellation space representation domain denoted as \(\{IQ, A\varphi \}\) . Searching for the correlation between two representations in constellation space. As illustrated in Fig. 4.  
+
+2) Frequency representation domain: Mining invariant modulation features between one-to-one correspondence in time and frequency domains. We consider the frequency spectrum sequence obtained by the fourier transform (FT) on the signal as the frequency representation domain denoted as \(\{IQ, \mathcal{F}\}\) .  
+
+3) Local scale representation domain: The projection between the wavelet transformed signal and the original signal allows for the examination of both global and local spatial characteristics [31], [32]. We consider the wavelet threshold denoised I-Q sequence as the local-scale contrast representation domain, denoted as \(\{IQ, WT\}\) .  
+
+As is known, The employment of multi-representation do
+
+<--- Page Split --->
+![](images/Figure_4.jpg)
+
+<center>Fig. 4: The relationship between I-Q components and amplitude-phase characterization in Constellation diagram. e.g., 16QAM. </center>  
+
+mains in AMR methods is not uncommon [33]. However, the approach of directly considering multiple forms as inputs and relying solely on the network for automatic feature extraction often fails to meet expectations and lack interpretability. If AMR architecture is able to avoid overly emphasizing sample details and extracting redundant features, this AMC architecture will achieve pleasant performance.  
+
+### B. Unsupervise learning of MAC  
+
+We will first explain the principles of MAC with two domains and then extend the framework to scenarios involving any number of representation domains.  
+
+1) Inter-domain contrastive learning: Considering a collection of representation domain datasets, denoted as \(\pmb {V_D} =\) \(\{V_1,V_2\dots V_K\}\) . For each domain, we define \(x_{i}^{j}\) as the \(i\) -th signal sample in the \(t\) -th domain dataset. \(V_{t}\) \(V_{s}\) from \(\pmb {V_D}\) represent the two representation domain datasets for wireless signal.  
+
+\(V_{s}\) represents the I- Q source domain (SD). \(V_{t}\) represents the outcome of a target signal processing transformation, referred to as TD. The dataset comprises sample pairs \(\{x_{s}^{i},x_{t}^{j}\}_{i = 1}^{N}\) with a total of \(N\) pairs, forming a contrastive domain of signal samples between domains \(V_{s}\) and \(V_{t}\)  
+
+Positive sample pairs of inter- domain contrastive learning are those originating from the joint distribution \(\alpha = \{x_{s}^{i},x_{t}^{j}\}\) while negative sample pairs come from the marginal product \(\beta = \{x_{s}^{i},x_{t}^{T}\} i\neq \tau\) . Our objective is to train a discriminator that can differentiate between the SD and TDs by assigning high scores to positive sample pairs and low scores to negative sample pairs. Due to the absence of labeled data, we adopt a proxy task akin to signal individual identification to assist in the training of the encoder. However, such unsupervised training approaches encounter two main challenges [34].  
+
+The trade- off between consistency and invariance of signal features.  
+
+TABLE I ENCODER AND PROJECTION HEAD NETWORK STRUCTURE   
+
+<table><tr><td>module</td><td>Layer</td><td>Channels</td><td>Filer Size</td><td>Dropout</td><td>Nonlinearity</td></tr><tr><td rowspan="3">f (·)</td><td>Conv1</td><td>50</td><td>1×8</td><td>0.5</td><td>ReLU</td></tr><tr><td>Conv2</td><td>50</td><td>2×8</td><td>0.5</td><td>ReLU</td></tr><tr><td>Flatten</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>g (·)</td><td>Dense</td><td>256</td><td>-</td><td>0.5</td><td>ReLU</td></tr></table>  
+
+The number of negative samples in a mini- batch contrastive learning.  
+
+In a previous study [10], a large dictionary was utilized to store all the feature vectors extracted by the encoder. It allows for an increased number of negative samples in single- batch contrastive learning. Performing negative sample similarity calculations for the entire dictionary through traversal is computationally expensive. Inspired by the approach proposed in [25], we construct separate feature dictionaries, denoted as \(Q_{s}\) and \(Q_{t}\) , for the SD and TDs respectively. For each sample pair \(\{x^{i},x^{i}\}_{t}\) in both domains, we employ an encoder \(f_{s / t}\) (·) to extract features \(\left(h_{s}^{i},h_{t}^{i}\right)\) . These extracted signal features are subsequently refined, projected, and stored in the dictionaries using a projection head \(g_{s / t}\) (·), which can be computed as \(q_{s}^{i} = g_{s}\left(f_{s}\left(x_{s}^{i}\right)\right),q_{t}^{i} = g_{t}\left(f_{t}\left(x_{t}^{i}\right)\right)\) .  
+
+The dictionaries constructed for the SD and TD signal features can be represented as \(Q_{s} = \{q_{s}^{1},q_{s}^{2},\dots,q_{s}^{k_{m}}\} ,Q_{t} = \{q_{t}^{1},q_{t}^{2},\dots,q_{t}^{k_{m}}\}\) . For SD sample \(x_{s}^{i}\) , To form a mini- batch contrastive set \(U_{s\sim t} = \{\alpha ,\beta_{1},\beta_{2}\dots \beta_{\zeta}\}\) . We select the positive sample pair \(\alpha = \{x_{s}^{i},x_{t}^{i}\}\) corresponding to \(x_{s}^{i}\) , and randomly sample \(\zeta\) negative sample pairs from the dictionary, ensuring a sufficient number of negative samples while introducing a controlled level of randomness. \(x_{s}^{i}\) should exhibit similarity to its counterparts \(x_{t}^{i}\) in different TDs, while being dissimilar to the remaining samples \(x_{t}^{T} i\neq \tau\) . The proxy task of individual identification is employed to identify the positive sample pair \(x_{t}^{i}\) that corresponds to the sample \(x_{s}^{i}\) from \(\zeta +1\) unlabeled samples in the contrastive dictionary \(U_{s\sim t}\) .  
+
+In contrast to the customized network design for supervised training, our unsupervised framework emphasizes representation learning across different domains, rather than designing networks specific to a particular dataset distribution. Hence, in this paper, all encoders \(f\) are implemented using CNN [14]. The structure of the CNN network, depicted in Table I, comprises two straightforward 2D CNN layers. This selection aims to showcase the effectiveness and generalizability of the proposed framework.  
+
+2) Intra-domain contrastive learning: For a given signal sample \(x\) , we contemplate multiple data augmentation techniques denoted as \(\{\hat{x}_A,\hat{x}_B\dots \hat{x}_m\}\) within SD. Fig. 5 illustrates the impact of various data augmentation techniques on the signal in the constellation diagram. I-Q signal flipping, rotation, additive Gaussian noise, and local area occlusion correspond to scenarios involving random phase shifts, timing synchronization errors, low SNR, and symbol loss, respectively. During intra-domain contrastive learning, \(\hat{x}_A^i\) and \(\hat{x}_B^i\) forms a positive sample pair \(\alpha = \{\hat{x}_A^i,\hat{x}_B^i\}\) . When \(\hat{x}_A^i\) is used as the query sample, the negative sample pair \(\beta = \{\hat{x}_A^i,\hat{x}_B^i\} i\neq \tau\) is defined. In addition, we utilize a trainable encoder \(f_A(\cdot)\) to extract features \(h_A^i\) from the query sample \(\hat{x}_A^i\) and project them into
+
+<--- Page Split --->
+![](images/Figure_5.jpg)
+
+<center>Fig. 5: Different data augmentation methods for modulation signals used for SD representation learning: (a) rotation. (b) flip. (c) Gaussian noise. (d) section mask. </center>  
+
+the query feature vector \(q_{A}^{i}\) . Similarly, we project all key samples into feature vectors \(q_{B}\) , which can be computed as \(q^{i}A = g_{A}\left(f_{A}\left(\hat{x}_{A}^{i}\right)\right)\) and \(q^{i}B = g_{B}\left(f_{B}\left(\hat{x}_{B}^{i}\right)\right)\) .  
+
+Likewise, we construct a feature dictionary denoted as \(Q_{B} = \{q_{B}^{1}, q_{B}^{2}, \ldots , q_{B}^{km}\}\) . During each mini- batch training, \(\zeta\) negative sample pairs are randomly sampled from \(Q_{B}\) to form a batch- wise contrastive set \(U_{AB} = \{\alpha , \beta_{1}, \beta_{2} \ldots \beta_{\zeta}\}\) . Our objective is to bring the query sample \(\hat{x}_{A}^{i}\) closer to its positive sample pair while distancing it from the negative samples in the batch- wise contrastive set, depicted in Fig. 3.  
+
+However, updating the parameters of \(f_{B}(\cdot)\) through backpropagation is unreasonable due to the substantial differences in the distribution of feature vectors caused by different encoders. One straightforward approach is to copy the parameters of encoder \(f_{A}(\cdot)\) to \(f_{B}(\cdot)\) ensuring consistent updates of the feature vectors. We find that as encoder \(f_{A}(\cdot)\) experiences rapid changes, the feature dictionary gradually loses its consistency over time, with feature vectors becoming outdated after a certain period. To address this issue, we draw inspiration from the concept proposed in [34] and utilize a momentum- based updating method to adjust the parameters of encoder \(f_{A}(\cdot)\) , can be expressed as  
+
+\[\theta_{B} = \rho \theta_{B} + (1 - \rho)\theta_{A} \quad (6)\]  
+
+where \(\rho \in [0,1)\) denotes the momentum update coefficient, while \(\theta_{A}\) and \(\theta_{B}\) represent the parameters of encoder \(f_{A}(\cdot)\) and \(f_{B}(\cdot)\) respectively. Only the parameters of encoder \(f_{A}(\cdot)\) undergo iteration through back propagation, while the parameters of \(f_{B}(\cdot)\) are gradually updated by receiving the parameter values from \(f_{A}(\cdot)\) during the training process. Momentum update can ensure the consistency of features in the domain dictionary, which will be discussed in detail in V- C.  
+
+3) Intra-inter domain dual-cycle loss function: For the proxy task of signal individual identification between the SD and TDs, we consider computing the cosine similarity of latent features extracted through dictionary sampling as the discriminative score. The similarity score for a pair of positive sample pairs can be expressed as  
+
+\[S_{\{s,t\}}^{i} = \exp \left(\frac{g_{s}\left(f_{s}\left(x_{s}^{i}\right)\right)g_{t}\left(f_{t}\left(x_{t}^{i}\right)\right)}{\left\|g_{s}\left(f_{s}\left(x_{s}^{i}\right)\right)\right\| \cdot \left\|g_{t}\left(f_{t}\left(x_{t}^{i}\right)\right)\right\| \cdot \mu}\right) \quad (7)\]  
+
+where the hyperparameter \(\mu\) acts as a temperature coefficient that scales the range of similarity scores. A higher value of \(\mu\)  
+
+shifts the emphasis towards negative sample pairs with smaller similarity differences. Our aspiration is to train a discriminator to identify a single positive sample from a batched contrastive set \(U_{s - t} = \{\alpha , \beta_{1}, \beta_{2} \ldots \beta_{\zeta}\}\) which includes \(\zeta\) negative samples. The "SD- TD" contrastive loss function can be defined as  
+
+\[\mathcal{L}_{S \sim t} = -\underset {U_{S \sim t}}{\mathbb{E}}\left[\log \frac{S_{S}^{i}}{\left(S_{S}^{i}\right) + \sum_{j = 1}^{\zeta}S_{S}^{i,j}}\right] \quad (8)\]  
+
+As is known, wireless signal receivers typically provide complex time- domain signals, traditional AMR algorithms have primarily focused on the original I- Q format of the signals. However, when viewed from a high- dimensional feature space, each representation domain of the signal is merely a form of representation. Symmetrically, we not only consider the negative sample similarity \(\sum_{j = 1}^{\zeta}S_{S}^{i,j}\) when traversing the TD \(V_{t}\) using the SD \(V_{s}\) as the query set, but also take into account the negative sample discriminative score \(\sum_{j = 1}^{\zeta}S_{S}^{i,j}\) obtained by swapping the query relationship between SD and TDs.  
+
+\[\mathcal{L}_{inter}^{V_{s},V_{t}} = \mathcal{L}_{S \sim t} + \mathcal{L}_{t \sim s} \quad (9)\]  
+
+where \(\mathcal{L}_{inter}^{V_{s},V_{t}}\) represents the inter- domain contrastive loss between the two representation domains. Similar to the construction of inter- domain contrastive similarity, we define the similarity between a pair of positive samples within the same domain as  
+
+\[S_{\{A,B\}}^{i} = \exp \left(\frac{g_{A}\left(f_{A}\left(\hat{x}_{A}^{i}\right)\right)g_{B}\left(f_{B}\left(\hat{x}_{B}^{i}\right)\right)}{\left\|g_{A}\left(f_{A}\left(\hat{x}_{A}^{i}\right)\right)\right\| \cdot \left\|g_{B}\left(f_{B}\left(\hat{x}_{B}^{i}\right)\right)\right\| \cdot \mu}\right) \quad (10)\]  
+
+The intra- domain contrastive loss can be represented as  
+
+\[\mathcal{L}_{intra} = -\underset {U_{AB}}{\mathbb{E}}\left[\log \frac{S_{A,B}^{i}}{\left(S_{A,B}^{i}\right) + \sum_{j = 1}^{\zeta}S_{A,B}^{i,j}}\right] \quad (11)\]  
+
+Intra- inter domain dual- cycle loss for scenarios involving two representation domains is derived by combining Eq. (9) and Eq. (11).  
+
+\[\mathcal{L}\left(V_{s},V_{t}\right) = \mathcal{L}_{intra} + \mathcal{L}_{inter}^{V_{s},V_{t}} \quad (12)\]  
+
+### C. MAC with more than two representation domains  
+
+1) "I-Q single centralization" strategy: Here, we present more general formulations of Eq. (12) that can handle any number of signal representation domains. From the perspective of the signal representation space, a straightforward approach is to establish strong associations between all domains, known as the "fully centralized". Specifically, for any domain's dataset in the set \(V_{D} = \{V_{1}, V_{2} \ldots V_{K}\}\) , computing the contrastive similarity with the remaining \(K - 1\) datasets. However, this approach incurs a high computational cost. In the case of considering \(K\) transformation domains, the complexity of computing the contrastive loss becomes \(O(K^{2})\).  
+
+We proposed another approach called the "I- Q single- centering" strategy. The correlation between different representation domains of wireless signals decreases with nonlinear signal processing steps. Hence, we select the SD I- Q signal
+
+<--- Page Split --->
+![](images/Figure_6.jpg)
+
+<center>Fig. 6: "I-Q single centralization" multi-representation domain loss calculation strategy. </center>  
+
+as the center domain and focus on optimizing the feature representation of the center domain through contrastive learning in relation to other TDs. This approach effectively reduces the computational complexity to \(O(K)\) . In the case of "I- Q single- centering" with four TDs obtained from the transformation of the SD I- Q signal, the inter- domain contrastive losses are depicted in Fig. 6. The multi- domain joint contrastive loss function under the "I- Q single- centering" strategy can be expressed as  
+
+\[\mathcal{L}_K = \eta_1\mathcal{L}_{intra} + \sum_{t = 2}^K\eta_t\mathcal{L}_{inter}^{V_s,V_t} \quad (13)\]  
+
+where \(\eta_{1},\eta_{2}\dots \eta_{K}\) is the weighting coefficient for the loss functions between the SD and each TD, and \(\sum_{t = 1}^{K}\eta_{t} = 1\)  
+
+Furthermore, the intra- domain contrast similarity is determined by the construction of individual positive and negative samples. Eq. (11) indicates that minimizing \(\mathcal{L}_{intra}\) involves dispersing individual signals in the feature space. In unsupervised training, where class labels are not available, the proxy task of individual identification aims to separate similar signals in the feature space, even if they belong to the same modulation class.  
+
+We call this phenomenon as "Over- learning of intra- domain representations". In downstream tasks such as modulation recognition, challenges is posed for linearly classifying different instances of the same class. By selecting the I- Q SD as the center domain, the inter- domain negative samples from the other \(K - 1\) transformed domains exhibit relatively lower contrast similarities compared to the intra- domain negative samples. As a result, their distributions in the feature space will be further separated from the SD samples, as illustrated in Fig. 3. "I- Q single- centering", which effectively amplifies the distinctiveness of samples in the feature space while striking a balance between computational efficiency and operational effectiveness.  
+
+2) Domain attention module: As mentioned above, when extending MAC to multiple representation domains, MAC should distinguish which feature vectors obtained from different representation domains provide the most helpful information for AMR; otherwise, the final classification module may not work due to the much-confused information MAC bringing in. In other words, the task of domain selection, which was previously performed at a signal level, is now shifted to a feature level.  
+
+![](images/Figure_7.jpg)
+
+<center>Fig. 7: DA module for attention inference. </center>  
+
+We propose DA module that utilizes inter- domain relationships of features and extracts information about the importance of representation domains in the input feature map. Specifically, DA can infer attention weights for each feature vector, allowing subsequent modulation- based classification using domain- weighted feature vectors, illustrated in Fig. 7. Firstly, the set of feature vectors \(\nu :\{\nu_{s},\nu_{1},\dots ,\nu_{K}\}\) , derived from different representation domains, serves as the raw input \(\nu_{s},\nu_{1},\dots ,\nu_{K}\in R^{1\times L}\) for DA, where \(L\) represents the length of the feature vectors. DA performs two distinct fusion operations to obtain consolidated features \(\nu_{coh1}\in\) \(R^{1\times (K + 1)L},\nu_{coh2}\in R^{(K + 1)\times L}\)  
+
+\[\begin{array}{rl} & {\nu_{coh1} = \mathcal{J}(\nu_s,\nu_1,\dots ,\nu_K),\mathrm{s.t.}\nu_{coh1}(1,n + (k + 1)\times L) = \nu_k(n)}\\ & {\nu_{coh2} = \mathcal{J}(\nu_s,\nu_1,\dots ,\nu_K),\mathrm{s.t.}\nu_{coh2}(k + 1,n) = \nu_k(n)} \end{array} \quad (14)\]  
+
+where \(\mathcal{J}\) represents the concatenate operation, Subsequently, DA applies global average pooling to \(\nu_{coh2}\) , squeezing the features from different representation domains to generate \(\nu_{sq}\in R^{1\times (K + 1)}\) . Then, \(\nu_{sq}\) is then passed through a \(1\times 1\) conv layer to map it to representation domain weight scores \(\gamma :[\gamma_{s},\gamma_{1},\dots ,\gamma_{K}]\) , highlighting the importance of each domain. Finally, the representation domain weight scores \(\nu_{att}\) can be obtained through vector multiplication \(\otimes\) between \(\gamma\) and \(\nu_{coh1}\) . The entire process can be represented as  
+
+\[\nu_{att} = \nu_{coh1}\otimes \sigma (\mathrm{cov}^{1\times 1}(AvgPool(\nu_{coh2}))) \quad (15)\]  
+
+where \(\sigma\) represents the sigmoid activation function. As a result, \(\nu_{att}\in R^{1\times (K + 1)L}\) is capable of disregarding redundant information across multiple representation domains, ensuring that the final modulation classification employs the most suitable representation domain features. DA achieves the selection of signal representation domain at the feature level, thereby significantly reducing reliance on prior information and expert experience.  
+
+In conclusion, the UAMR framework we propose, based on multi- representation domain attentive contrastive learning, is depicted in Alg. 1.  
+
+## V. PERFORMANCE EVALUATION AND ANALYSIS  
+
+In this section, we evaluate the effectiveness of the proposed unsupervised learning framework. Firstly, we provide the training details of the two publicly available datasets, as well as the parameter settings for training. Subsequently, we compare the performance of MAC with existing unsupervised and supervised AMR methods, with a particular focus on the generalization performance. Finally, we present the recognition results and feature visualizations.
+
+<--- Page Split --->
+
+# Algorithm 1: MAC Algorithm for UAMR Task  
+
+Input: SD I- Q Training data \(\{x^{i}(n)\}_{i = 1}^{N}\) Training iterations \(\mathcal{I}\) , Initial learning rate \(lr\) , Momentum update parameters \(\rho\) , Feature dictionary size \(k_{m}\) , Temperature coefficients \(\mu\) ,  
+
+Output: The optimal parameters \(f_{s / t}^{*}, f_{A / B}^{*}\)  
+
+1 Obtain transform domain dataset \(V_{TD} = \{V_{1}, V_{2}, \ldots V_{M}\}\)  
+
+2 Randomly initialized CNN parameters \(f_{s / t}, f_{A / B}\)  
+
+3 for epoch \(= 1,2,\dots ,I\) do  
+
+4 for batch in \(N\) do  
+
+5 Randomly select mini- batch \(N_{b}\) sample from the SD and TD datasets  
+
+6 Extract feature \(q^{i}_{s / t}, q^{i}_{A / B}\)  
+
+7 Calculate multi- domain comparative loss \(\mathcal{L}_{K}\) by Eq. 13  
+
+8 Compute the backpropagation error by  
+
+9 \(\frac{\partial \mathcal{L}_{K}}{\partial x_{n}} = \eta_{1}\frac{\partial \mathcal{L}_{intra}}{\partial x_{n}} +\sum_{t = 1}^{K - 1}\eta_{t}\frac{\partial \mathcal{L}_{inter}^{V_{S},V_{t}}}{\partial x_{n}}\)  
+
+10 Update feature dictionary by Eq. 6  
+
+11 Update the parameters by  
+
+12 \(f^{*} = f - lr\cdot (\eta_{1}\frac{\partial\mathcal{L}_{intra}}{\partial x_{n}} +\sum_{t = 1}^{K - 1}\eta_{t}\frac{\partial\mathcal{L}_{inter}^{V_{S},V_{t}}}{\partial x_{n}})\)  
+
+13 end  
+
+14 end  
+
+### A. Dataset introduction  
+
+The RML series dataset, developed by O'Shea et al. [35]. using GNU Radio, has emerged as a widely adopted benchmark dataset in numerous research studies. Among these datasets, the RML2016.10A dataset stands out, comprising a total of 220,000 signal samples. This dataset encompasses 11 distinct modulation types, namely 8PSK, AM- DSB, AM- SSB, BPSK, CPFSK, GFSK, PAW4, QAM16, QAM64, QPSK, and WBFM. Each modulation type is further characterized by 20 different SNR levels, spanning from - 20 dB to 18 dB with a 2 dB increment.  
+
+Each sample in the RML dataset is composed of two channels, I- channal and Q- channal, representing the in- phase and quadrature components. These samples have a fixed length of 128. Notably, the dataset generation process incorporates various common channel effects typically encountered in wireless systems. These effects include frequency offset, phase offset, sampling rate offset, multipath fading, and additive white noise. By simulating these propagation characteristics, the dataset accurately captures the challenges posed by wireless signal transmission in realistic and complex environments.  
+
+The dataset RML2016.10B consists of 1.2 million signal samples, maintaining consistency with RML2016.10A in terms of SNR distribution and sample length [6]. However, RML2016.10B differs from RML2016.10A by reducing the inclusion of AM- DSB modulation, resulting in a total of 10 modulation types.  
+
+### B. Experimental setup  
+
+When we conducted experiments, each dataset was split into three subsets in a ratio of 6:3:1 training set, testing set, and validation set. Specifically, for each modulation type and SNR, we randomly allocate 1000 signals, with 600 signals used for training and 300 signals for testing. Each normalized signal sample is then placed in a \(2 \times 128\) matrix, which serves as the input. Note that our method's effectiveness analysis and ablation validation were conducted on two datasets, namely RML2016.10A and RML2016.10B. Meanwhile, the models were trained on the RML2016.10A dataset and subsequently tested on the RML2016.10B dataset to assess the ability of generalization.  
+
+1) Unsupervised representation learning: In the unsupervised training phase, we conduct a total of 240 training epochs with a batch size of 256. The initial learning rate is 0.03, and after the first 120 epochs, the learning rate is reduced by a factor of 0.1 every 40 epochs. For calculating the contrastive loss, the temperature coefficient \(\mu\) is set to 0.07.  
+
+2) Linear evaluation: Following the paradigm of unsupervised learning [34], we adopt the approach of training only the two-layer linear classifier while keeping the encoder parameters frozen to evaluate the quality of representation learning. In the linear evaluation phase, we conduct a total of 80 training epochs with a batch size of 128. The initial learning rate is set to 0.01, and after the first 40 epochs, the learning rate is reduced by a factor of 0.2 every 10 epochs.  
+
+### C. Effects of hyperparameters and module ablation  
+
+In this section, we discuss the impact of hyperparameters as well as some key modules of MAC for ablation. The symbols for the variants are as follows  
+
+1) MAC-MT4: Multi-representation domain attentive contrastive learning framework as shown in Fig.3. 
+2) MC-MT4: MAC-MT4 without the domain attention module. 
+3) SRC: MAC-MT4 without the inter-domain contrastive learning module, which only learns signal representation through intra-domain contrastive learning. 
+4) TAC: MAC-MT4 without the intra-domain contrastive learning module, which only learns signal representation through inter-domain contrastive learning. 
+5) MAC-DX: A network structure similar to MAC-MT4, but only considering two representation domains. Four combinations, with MAC-D1\~MAC-D4 representing transformation domain combinations \(\{IQ, A\phi \}\) \(\{IQ, A f\}\) \(\{IQ, \mathcal{F}\}\) \(\{IQ, WT\}\) , respectively. The combination method of TAC-DX is similar to MAC-DX.  
+
+Prior to this, we demonstrate the effects of momentum update coefficient and feature dictionary stack size on the effectiveness of signal representation learning. We compared the recognition accuracy and training time of the proposed MAC- MT4 and representative MAC- D1 for 0dB signals on two datasets.
+
+<--- Page Split --->
+
+
+TABLE II ACCURACY \((\%)\) COMPARISON OF THE PROPOSED METHODS WITH DIFFERENT MOMENTUM VALUES ON THE RML2016.10A AND RML2016.10B DATASETS   
+
+<table><tr><td rowspan="2" colspan="2">Methods</td><td colspan="8">momentum ρ</td></tr><tr><td>0</td><td>0.1</td><td>0.3</td><td>0.5</td><td>0.7</td><td>0.9</td><td>0.99</td><td>0.999</td></tr><tr><td rowspan="2">RML2016.10A</td><td>MAC-D1</td><td>fail</td><td>70.32</td><td>80.78</td><td>81.01</td><td>81.14</td><td>83.16</td><td>80.19</td><td>80.04</td></tr><tr><td>MAC-MT4</td><td>fail</td><td>72.20</td><td>81.93</td><td>82.25</td><td>83.73</td><td>86.45</td><td>84.19</td><td>82.73</td></tr><tr><td rowspan="2">RML2016.10B</td><td>MRC-D1</td><td>fail</td><td>57.32</td><td>59.51</td><td>78.68</td><td>80.23</td><td>82.71</td><td>80.61</td><td>79.82</td></tr><tr><td>MAC-MT4</td><td>fail</td><td>59.09</td><td>61.51</td><td>81.72</td><td>84.34</td><td>88.04</td><td>86.78</td><td>84.31</td></tr></table>  
+
+![](images/Figure_8.jpg)
+
+<center>Fig. 8: Performance comparison of the proposed method with different domain stack sizes on the RML2016.10A and RML2016.10B datasets. (a) MAC-D1 on RML2016.10A, (b) MAC-MT4 on RML2016.10A, (c) MAC-D1 on RML2016.10B, (d) MAC-MT4 on RML2016.10B. </center>  
+
+Table II illustrates the impact of momentum update coefficients on the consistency of features within the range of 0 to 0.999. When \(\rho = 0.9\) both MAC- MT4 and MAC- D1 achieve optimal performance on two datasets, indicating that a moderately slow update of the key encoder is beneficial. This can be attributed to the fact that rapid updates of encoder parameters (i.e., too small coefficients) lead to the loss of consistency between consecutive iterations of features within the dictionary over time. Conversely, slow updates (i.e., too large coefficients) result in significant distribution differences among features in different dictionaries; at the extreme of no momentum ( \(\rho = 0\) ), the training loss oscillates and fails to converge. These results support our motivation to build a consistent dictionary.  
+
+Notably, the proposed method outperforms RML2016.10B on the RML2016.10A dataset when using a smaller momentum update coefficient \((\rho < 0.7)\) . This can be attributed to the smaller sample size of the RML2016.10A dataset, where individual identification- based proxy tasks are relatively easy to accomplish in unsupervised training, thereby requiring less consistency in sample features. Furthermore, the momentum update strategy does not introduce any additional trainable parameters.  
+
+Fig. 8 illustrates the influence of \(k_{m}\) on the effectiveness of signal representation learning. In general, the accuracy of identification benefits from a larger \(k_{m}\) , akin to the concept of a memory bank. The inclusion of a greater number of negative sample features in the field of comparison facilitates the learning of signal representation. However, excessive negative samples not only prolong training time but also increase the difficulty of contrastive learning.  
+
+The results indicate that the improvement in accuracy becomes negligible compared to the additional computational resources when the number of negative samples exceeds  
+
+![](images/Figure_9.jpg)
+
+<center>Fig. 9: Validation comparative loss curves of unsupervised training on the RML2016.10A dataset(a). Linear evaluation validation loss on ablation of different modules(b). \(V_{1},V_{2},V_{3},V_{4}\) Representing the combination of transformation domains \(\{A\phi \} ,\{A f\} ,\{\mathcal{F}\} ,\{W T\}\) separately. </center>  
+
+16,384. The proposed method achieves the optimal trade- off between accuracy and training time on the RML2016.10A and RML2016.10B datasets when \(k_{m} = 8,192\) and 16,384, respectively. Building upon these findings, we will conduct subsequent experiments based on the aforementioned hyperparameters.  
+
+As mentioned in IV- D, the different representation domains serve as different perspectives of the same modulation type, where the sample from SD and TD can alternate as contrastive query vectors. Fig. 9 (a) shows the contrastive loss curves between different representation domains according to Fig. 6 on the validation set in training MAC- MT4. The four groups of contrastive loss curves consistently decrease and converge as the unsupervised training epoch goes on. This indicates that MAC can simultaneously complete the task of positive sample screening in four representation domains. \(\mathcal{L}_{s - t}^{V_{s},V_{2}}\) converge to nearly the minimum value. This is attributed to the locally scaled representation domains \(\{W T\}\) are obtained from the
+
+<--- Page Split --->
+
+
+TABLE III COMPARISON ACCURACY \((\%)\) OF ABLATION OF VARIOUS MODULES IN MAC-BASED UAMR AT O-18DB ON THE RML2016.10A DATASET. IN COLUMN "SD", \(\nu \times\) DENOTES WHETHER SOURCE DOMAIN CONTRASTIVE LEARNING WAS EMPLOYED. COLUMN \(\Delta\) DENOTES BOOSTING ON MAC-MT4   
+
+<table><tr><td>Methods</td><td>SD</td><td>0dB</td><td>2dB</td><td>4dB</td><td>6dB</td><td>8dB</td><td>10dB</td><td>12dB</td><td>14dB</td><td>16dB</td><td>18dB</td><td>Σ</td><td>Δ(↑%)</td></tr><tr><td rowspan="2">MAC-D1(IQ,Aφ)</td><td>✓</td><td>83.16</td><td>80.77</td><td>81.77</td><td>80.72</td><td>82.11</td><td>81.81</td><td>79.89</td><td>82.89</td><td>82.35</td><td>82.18</td><td>81.58</td><td>3.80</td></tr><tr><td>×</td><td>80.27</td><td>78.34</td><td>80.58</td><td>80.54</td><td>81.23</td><td>81.04</td><td>80.12</td><td>81.42</td><td>81.11</td><td>81.04</td><td>80.56</td><td>4.82</td></tr><tr><td rowspan="2">MAC-D2(IQ,Af)</td><td>✓</td><td>81.68</td><td>82.87</td><td>77.48</td><td>82.45</td><td>80.41</td><td>83.54</td><td>79.28</td><td>78.64</td><td>77.24</td><td>76.74</td><td>80.03</td><td>5.35</td></tr><tr><td>×</td><td>80.87</td><td>81.46</td><td>78.23</td><td>83.45</td><td>78.93</td><td>80.21</td><td>79.85</td><td>78.57</td><td>77.76</td><td>74.45</td><td>79.37</td><td>6.01</td></tr><tr><td rowspan="2">MAC-D3(IQ, F)</td><td>✓</td><td>85.45</td><td>81.05</td><td>82.37</td><td>83.09</td><td>87.35</td><td>84.09</td><td>83.13</td><td>83.34</td><td>81.34</td><td>82.34</td><td>83.35</td><td>2.03</td></tr><tr><td>×</td><td>82.57</td><td>80.14</td><td>81.23</td><td>82.09</td><td>86.23</td><td>83.38</td><td>83.11</td><td>83.16</td><td>81.02</td><td>81.35</td><td>82.42</td><td>2.96</td></tr><tr><td rowspan="2">MAC-D4(IQ, WT)</td><td>✓</td><td>84.68</td><td>83.20</td><td>86.86</td><td>84.04</td><td>78.54</td><td>81.42</td><td>79.54</td><td>78.97</td><td>80.51</td><td>79.52</td><td>81.72</td><td>3.66</td></tr><tr><td>×</td><td>82.35</td><td>82.94</td><td>85.63</td><td>83.95</td><td>77.45</td><td>81.34</td><td>79.74</td><td>79.53</td><td>79.04</td><td>79.25</td><td>81.12</td><td>4.26</td></tr><tr><td>SRC</td><td>✓</td><td>73.31</td><td>72.09</td><td>74.43</td><td>73.92</td><td>75.62</td><td>74.76</td><td>73.12</td><td>74.43</td><td>73.32</td><td>72.38</td><td>73.63</td><td>11.75</td></tr><tr><td>TAC-MT4</td><td>×</td><td>84.23</td><td>85.34</td><td>83.32</td><td>85.25</td><td>87.84</td><td>85.23</td><td>83.1</td><td>84.39</td><td>82.93</td><td>82.25</td><td>84.38</td><td>1.01</td></tr><tr><td>MC-MT4</td><td>✓</td><td>82.42</td><td>83.56</td><td>82.86</td><td>84.75</td><td>84.23</td><td>83.86</td><td>79.23</td><td>82.32</td><td>81.17</td><td>82.56</td><td>82.69</td><td>2.69</td></tr><tr><td>MAC-MT4</td><td>✓</td><td>86.45</td><td>87.22</td><td>86.59</td><td>86.59</td><td>88.86</td><td>87.41</td><td>86.43</td><td>86.31</td><td>85.12</td><td>84.84</td><td>85.39</td><td>-</td></tr></table>  
+
+SD through wavelet transformation, resulting in high similarity in overall waveform trends that facilitate effective contrastive learning by the network. Benefiting from the "I- Q singlecentering" strategy, \(\mathcal{L}_{s - t}\) with SD samples as query vectors reaches the comparatively better solution than \(\mathcal{L}_{t - s}\)  
+
+Fig. 9 (b) demonstrates the convergence of the loss function for MAC- MT4, MC- MT4, and TAC during the linear evaluation stage. TAC- MT4, which lacks the intra- domain contrastive learning, only converges to a local minimum. Due to the presence of DA, MAC- MT4 outperforms MC- MT4 and achieves the comparatively best solution.  
+
+Subsequently, a detailed analysis will be undertaken to assess the impact of each representation domain's ablation and the specific contributions made by SD representation learning and DA to MAC.  
+
+As described in IV- A, we conducted ablation experiments on intra- domain and inter- domain contrastive learning, as well as the domain attention mechanism, comparing the classification performance of MAC- MT4, MAC- MT4, SRC, TAC, and MAC- DX on two datasets versus SNR.  
+
+The results on the RML2016.10A and RML2016.10B datasets, as shown in Table III and IV, respectively, indicate that overall, the recognition accuracy is higher on the RML2016.10B dataset due to its larger sample size. The performances for both datasets demonstrate that MAC- MT4 is the most effective among all SNRs. Consistent with the analysis in Fig. 9 (b), the method of combining different domains and source domains under the MAC framework (MAC- DX) significantly outperforms SRC in terms of testing accuracy. Compared to SRC, the accuracy of MAC- MT4 improved by \(11.75\%\) on the RML2016.10A dataset and \(12.93\%\) on the RML2016.10B dataset. This confirms the effectiveness of the MAC unsupervised framework, where inter- domain contrastive learning can comprehensively utilize information from both SD and TDs.  
+
+Using only two representation domains in MAC- DX results in lower classification accuracy compared to MACMT4. Notably, MAC- D4 demonstrates superior performance in low SNRs, which benefits from the noise reduction effect of wavelet transformations. The rapid fluctuations in instan  
+
+taneous frequency pose a challenge for the encoder in terms of feature learning. Consequently, this leads to a relatively lower accuracy in the case of MAC- D2. This highlights the advantages of integrating multi- representation domains to effectively explore information across different domains.  
+
+The confusion matrices for the proposed MAC- MT4 on the RML2016.10A and RML2016.10B datasets are shown in Fig. 10 at \(\mathrm{SNR} = 0\mathrm{dB}\) and \(8\mathrm{dB}\) . The proposed MAC- MT4 demonstrates satisfactory discriminability for the challenging recognition problem of QAM16 and QAM64, which has been a major challenge for most existing AMR methods [19][41]. Additionally, through the DA module, the MAC framework effectively reduces confusion between 8PSK, AM- DSB, and QPSK signals. These modulation types exhibit significant distinguishability in constellation space and instantaneous amplitude representation, which can be appropriately captured by MAC. However, differentiating between AM- DSB and WBFM poses some difficulties. Due to the strong spectral similarity between these two types of signals [36], WBFM also has periods of audio silence [18].  
+
+As detailed in IV- C, SD representation learning is crucial for preserving the characteristics of the SD and distinguishing amplified samples within the feature space. For a more straightforward visualization of the impact of source domain representation learning on feature vectors, we compute the density distribution of intra- class similarity \(\mathcal{P}_{\mathrm{intra - class}}\) and inter- class similarity \(\mathcal{P}_{\mathrm{inter - class}}\) for modulation signal classes. We employ the cosine distance as the standard metric for measuring similarity, denoted as  
+
+\[\mathcal{P}_{\mathrm{intra - class}} = \sum_{l = 1}^{L}\mathcal{P}_{l}^{\mathrm{id}} = \sum_{l = 1}^{L}\sum_{i = 1}^{N}\sum_{v_{i}^{id - 1}}^{v_{i}^{id - 1}\cdot v_{i}^{id - 1}}\frac{v_{i}^{id}}{v_{i}^{id - 1}} \quad (16)\]  
+
+\[\mathcal{P}_{\mathrm{inter - class}} = \sum_{l = 1}^{L}\mathcal{P}_{l}^{\mathrm{id}} = \sum_{l = 1}^{L}\sum_{i = 1}^{N}\sum_{i_{s} = 1}^{N_{s}}\frac{v_{i}^{id}}{v_{i}^{id - 1}\cdot v_{i}^{id - 1}}\frac{v_{i}^{is}}{v_{i}^{id - 1}} \quad (17)\]  
+
+where, \(\mathcal{P}_{l}^{\mathrm{id - class}}\) and \(\mathcal{P}_{l}^{\mathrm{inter - class}}\) represent the intra- class and inter- class similarities of the \(l\) - th class of signals, \(N_{s}\) stands for the number of inter- class sampled samples, and \(v_{i}^{id}\)
+
+<--- Page Split --->
+
+
+TABLE IV COMPARISON ACCURACY \((\%)\) OF ABLATION OF VARIOUS MODULES IN MAC-BASED UAMR AT O-18DB ON THE RML2016.10B DATASET. IN COLUMN "SD", \(\nu \times\) DENOTES WHETHER SOURCE DOMAIN CONTRASTIVE LEARNING WAS EMPLOYED. COLUMN \(\Delta\) DENOTES BOOSTING ON MAC-MT4   
+
+<table><tr><td>Methods</td><td>SD</td><td>0dB</td><td>2dB</td><td>4dB</td><td>6dB</td><td>8dB</td><td>10dB</td><td>12dB</td><td>14dB</td><td>16dB</td><td>18dB</td><td>E</td><td>Δ(↑%)</td></tr><tr><td rowspan="2">MAC-D1(IQ,Aφ)</td><td>✓</td><td>82.71</td><td>86.57</td><td>86.06</td><td>86.83</td><td>88.09</td><td>86.05</td><td>84.03</td><td>82.15</td><td>86.09</td><td>88.46</td><td>85.70</td><td>5.01</td></tr><tr><td>×</td><td>81.23</td><td>85.45</td><td>83.25</td><td>85.90</td><td>86.34</td><td>83.31</td><td>83.45</td><td>82.16</td><td>85.39</td><td>84.46</td><td>84.09</td><td>6.62</td></tr><tr><td rowspan="2">MAC-D2(IQ,Af)</td><td>✓</td><td>84.26</td><td>86.59</td><td>85.86</td><td>88.14</td><td>88.78</td><td>87.57</td><td>88.72</td><td>88.44</td><td>85.33</td><td>85.01</td><td>86.87</td><td>3.84</td></tr><tr><td>×</td><td>82.26</td><td>84.37</td><td>84.92</td><td>86.17</td><td>84.56</td><td>86.43</td><td>86.35</td><td>87.75</td><td>81.62</td><td>80.04</td><td>84.45</td><td>6.27</td></tr><tr><td rowspan="2">MAC-D3(IQ,FT)</td><td>✓</td><td>85.12</td><td>84.81</td><td>88.16</td><td>88.47</td><td>89.84</td><td>87.36</td><td>89.63</td><td>87.97</td><td>88.37</td><td>87.48</td><td>87.72</td><td>2.99</td></tr><tr><td>×</td><td>84.32</td><td>84.16</td><td>86.47</td><td>87.72</td><td>86.93</td><td>85.45</td><td>84.61</td><td>84.93</td><td>83.46</td><td>85.27</td><td>85.33</td><td>5.38</td></tr><tr><td rowspan="2">MAC-D4(IQ,WT)</td><td>✓</td><td>85.28</td><td>87.99</td><td>87.57</td><td>89.14</td><td>88.42</td><td>88.61</td><td>84.09</td><td>82.27</td><td>82.29</td><td>82.35</td><td>85.80</td><td>5.38</td></tr><tr><td>×</td><td>84.53</td><td>86.81</td><td>86.66</td><td>87.72</td><td>88.10</td><td>85.45</td><td>80.24</td><td>79.92</td><td>80.21</td><td>79.88</td><td>85.70</td><td>5.01</td></tr><tr><td>SRC</td><td>✓</td><td>76.67</td><td>78.91</td><td>76.10</td><td>78.32</td><td>77.76</td><td>74.65</td><td>78.65</td><td>79.34</td><td>80.12</td><td>77.34</td><td>77.79</td><td>12.93</td></tr><tr><td>TAC-MT4</td><td>×</td><td>84.23</td><td>85.34</td><td>83.32</td><td>85.25</td><td>87.84</td><td>85.23</td><td>83.1</td><td>84.39</td><td>82.93</td><td>82.25</td><td>84.38</td><td>1.01</td></tr><tr><td>MC-MT4</td><td>✓</td><td>84.57</td><td>87.43</td><td>88.49</td><td>87.92</td><td>90.11</td><td>89.04</td><td>88.72</td><td>89.13</td><td>89.60</td><td>89.42</td><td>88.44</td><td>2.64</td></tr><tr><td>MAC-MT4</td><td>✓</td><td>88.04</td><td>89.88</td><td>91.17</td><td>91.71</td><td>91.67</td><td>90.87</td><td>90.41</td><td>91.12</td><td>91.04</td><td>91.21</td><td>90.71</td><td>-</td></tr></table>  
+
+![](images/Figure_10.jpg)
+
+<center>Fig. 10: The confusion matrix of the proposed MAC-MT4 at SNR=0dB (1) and 8dB (2) on RML2016.10A (a) and RML2016.10B (b) datasets. </center>  
+
+![](images/Figure_11.jpg)
+
+<center>Fig. 11: Distribution of intra-class (a) and inter-class (b) similarity density of MAC-MT4 and TAC-MT4. </center>  
+
+represent the feature vector of the \(i\) - th sample of the \(l\) - th class signal.  
+
+Pleasant contrastive learning results should maximize the intra- class sample similarity while minimizing the inter- class similarity. We define \(N_{s} = N\) as the number of inter- class samples used for inter- class similarity calculations. As depicted in Fig. 11, with the addition of intra- domain contrastive learning, intra- class sample similarity is increased, while inter- class sample similarity is decreased. Consequently, SD representation learning amplifies the distinctiveness in the signal feature space.  
+
+As shown in Table III and IV. It's worth noting that MCT4, lacking attention guidance, achieves lower performance compared to MAC- MT4. MC- MT4 has limited capability  
+
+to filter out irrelevant information and emphasize relevant information among signals from multi- representation domains. In the subsequent analysis, we will delve into a detailed display of the effectiveness of DA module in selecting signal representation domains at the feature level.  
+
+In summary, the extensive incorporation of multi- representation domains in MAC- MT4 leads to superior classification performance. Intra- domain contrastive learning assists MAC in preserving robust SD features, and the DA module within the MAC framework plays a pivotal role. Effective domain attention weights aid in selecting the most suitable representation domain forms at the feature level, laying a strong foundation for the final recognition.  
+
+### D. Intuitive demonstration of the feature-level representation domain selection of MAC  
+
+The intuitive effectiveness of MAC on feature- level representation domain selection is demonstrated in this section. Fig. 12 illustrates this with an example using five different representation domains and their respective normalized attention weight vectors for 10 modulation types from the RML2016.10B dataset at SNR=0dB. In each subplot, the normalized attention scores obtained by the DA are displayed in the order of domains as \(\{IQ\} ,\{A\varphi \} ,\{Af\} ,\{\mathcal{F}\} ,\{WT\}\) on the left. Simultaneously, the five different representation domain forms, including the source domain, are shown on the right.
+
+<--- Page Split --->
+![](images/Figure_12.jpg)
+
+<center>Fig. 12: Intuitive demonstrations of the feature-level representation domain selection of MAC-MT4. A sampled signal of SNR=0 dB is taken as an example for each modulation. In each subfigure, the normalized attention vectors \(\hat{\gamma}\) are shown on the left, and signal waveform with attention distribution of MAC is shown on the right side. (a) 8PSK. (b) AM-DSB. (c) BPSK. (d) CPFSK. (e) GFSK. (f) PAM4. (g) 16QAM. (h) 64QAM. (i) QPSK. (j) WBFM. </center>
+
+<--- Page Split --->
+
+
+TABLE V COMPARISON OF ACCURACY BETWEEN MAC-MT4 AND UNSUPERVISED ALGORITHM AT 0-18DB ON THE RML2016.10A DATASET. COLUMN \(\Delta\) DENOTES BOOSTING ON MAC-MT4   
+
+<table><tr><td>Methods</td><td>0dB</td><td>2dB</td><td>4dB</td><td>6dB</td><td>8dB</td><td>10dB</td><td>12dB</td><td>14dB</td><td>16dB</td><td>18dB</td><td>Δ (↑%)</td></tr><tr><td>SAE[37]</td><td>58.93</td><td>61.02</td><td>62.21</td><td>61.73</td><td>62.32</td><td>62.87</td><td>63.43</td><td>62.23</td><td>61.23</td><td>62.54</td><td>61.85</td></tr><tr><td>Simsiam[38]</td><td>61.36</td><td>67.77</td><td>63.32</td><td>64.54</td><td>66.51</td><td>65.32</td><td>64.32</td><td>65.68</td><td>64.74</td><td>62.53</td><td>64.60</td></tr><tr><td>MoCoV1[34]</td><td>68.32</td><td>69.77</td><td>65.34</td><td>64.64</td><td>65.73</td><td>67.23</td><td>63.42</td><td>62.21</td><td>62.56</td><td>63.19</td><td>65.24</td></tr><tr><td>MoCoV2[39]</td><td>77.68</td><td>78.33</td><td>78.35</td><td>79.34</td><td>78.34</td><td>79.92</td><td>77.35</td><td>77.48</td><td>76.24</td><td>77.16</td><td>78.01</td></tr><tr><td>CPC[24]</td><td>81.68</td><td>85.05</td><td>84.82</td><td>82.42</td><td>83.56</td><td>84.24</td><td>81.56</td><td>83.27</td><td>80.75</td><td>81.63</td><td>82.89</td></tr><tr><td>MAC-MT4</td><td>86.45</td><td>87.22</td><td>86.59</td><td>86.49</td><td>88.86</td><td>87.41</td><td>86.43</td><td>86.31</td><td>85.12</td><td>84.84</td><td>86.58</td></tr></table>  
+
+![](images/Figure_13.jpg)
+
+<center>Fig. 13: Recognition performance comparison of existing unsupervised frameworks and the proposed MAC-MT4. </center>  
+
+The color of the signal waveforms indicates the areas of focus by the network. The colored blocks below the waveforms represent the attention scores \(\hat{\gamma} \colon [\hat{\gamma}_s, \hat{\gamma}_1, \dots , \hat{\gamma}_K]\) for the respective representation domains that have a decisive impact on the final modulation classification.  
+
+Comparing the visual attention weights to the modulation signal types, MAC typically makes the correct feature domain selection by assigning higher attention weights to the appropriate domains. PSK- wise and QAM- wise signals exhibit robust constellation modulation characteristics. As shown in Fig. 12 (a),(c),(g- h), MAC assigns higher weights to the constellation space representation domain. For AM- DSB, due to its nonconstant envelope characteristics, as shown in Fig. 12 (b), MAC shows a noticeable attention to instantaneous amplitude information. Similar correct selections are observed for CPFSK and GFSK signals, as these frequency modulation signals have better discrimination in the frequency representation domain and instantaneous frequency. In the case of WBFM signals, modulation signals are derived from actual audio streams, resulting in a relatively uniform attention distribution due to silent periods in the audio. Proper signal representation selection ensures correct classification in subsequent modules. Therefore, MAC correctly chooses the transformation domains for signal preprocessing at the feature level and emphasizes the feature vectors of the appropriate representation domains for different modulation types in the final classification module, effectively improving the performance of UAMR.   
+
+### E. Comparison with unsupervised frameworks  
+
+In this section, we conducted a comparative analysis of our proposed framework with several previous unsupervised learning frameworks. The frameworks included in the comparison were SAE [37], MoCo [34], SimSiam [38], MoCoV2 [39], and CPC [24]. The results, presented in Table V, clearly demonstrate that our MAC- MT4 model outperforms the previous UAMR models in terms of accuracy. This observation indicates that the contrastive unsupervised learning approach exhibits superior capabilities in extracting meaningful representations compared to the simpler generative unsupervised sparse autoencoders.  
+
+The proposed MAC- MT4 framework not only surpasses existing popular unsupervised algorithms in the computer vision field but also achieves superior results in the context of AMR. Fig. 13 illustrates the accuracy curves of various methods at all SNRs, clearly demonstrating MAC- MT4's consistent outperformance over the selected unsupervised algorithms. The comprehensive utilization of multi- domain features in MAC- MT4 contributes to its improved accuracy, indicating that crucial modulation information in wireless signals resides in multiple representation domains within high- dimensional space. By effectively leveraging this multi- domain information, we can capture discriminative features underlying the signals and achieve enhanced classification accuracy.  
+
+Significantly, we maintained consistency in hyperparameters such as \(k_m, \rho\) across MAC- MT4, MoCo, and MoCoV2. Additionally, in all comparative experiments except for SAE, we utilized the same CNN as the feature extractor to ensure fair performance comparison among unsupervised frameworks with similar feature extraction capabilities. In summary, our proposed MAC framework currently demonstrates the most promising classification performance in UAMR.  
+
+### F. Generalization ability  
+
+The inability of an AMR method to accurately classify modulations arises when it fails to identify the fundamental AMR characteristics within its training set. In order to thoroughly investigate the network's generalization ability, our experiment is designed to ensure clear demarcation between training and testing phases by employing distinct datasets. In each method, the corresponding neural network trained in RML2016.10A
+
+<--- Page Split --->
+
+
+TABLE VI COMPARISON OF ACCURACY BETWEEN MAC-BASED UAMR AND UNSUPERVISED ALGORITHM AT 0-18DB ON THE RML2016.10B DATASET. COLUMN \(\Delta\) DENOTES BOOSTING ON MAC-MT4   
+
+<table><tr><td>Methods</td><td>0dB</td><td>2dB</td><td>4dB</td><td>6dB</td><td>8dB</td><td>10dB</td><td>12dB</td><td>14dB</td><td>16dB</td><td>18dB</td><td>E</td><td>Δ(↑%)</td></tr><tr><td>I-Q CNN[35]</td><td>62.26</td><td>69.96</td><td>69.14</td><td>68.04</td><td>70.01</td><td>62.65</td><td>62.35</td><td>61.02</td><td>62.42</td><td>63.25</td><td>65.11</td><td>25.09</td></tr><tr><td>ResNet[40]</td><td>84.32</td><td>84.75</td><td>86.12</td><td>86.76</td><td>87.64</td><td>88.82</td><td>87.53</td><td>87.61</td><td>88.13</td><td>88.19</td><td>86.98</td><td>3.21</td></tr><tr><td>CLDNN[41]</td><td>69.27</td><td>69.16</td><td>72.91</td><td>67.12</td><td>65.59</td><td>66.48</td><td>68.62</td><td>67.45</td><td>69.56</td><td>65.87</td><td>68.20</td><td>22.00</td></tr><tr><td>CLDNN2[40]</td><td>75.62</td><td>77.72</td><td>78.92</td><td>79.45</td><td>82.12</td><td>81.27</td><td>81.26</td><td>79.90</td><td>79.23</td><td>81.25</td><td>79.67</td><td>10.53</td></tr><tr><td>LSTM[17]</td><td>77.67</td><td>82.51</td><td>83.79</td><td>84.13</td><td>84.04</td><td>83.91</td><td>84.33</td><td>83.86</td><td>83.46</td><td>83.67</td><td>83.13</td><td>7.06</td></tr><tr><td>MCLDNN[19]</td><td>86.12</td><td>88.12</td><td>89.37</td><td>90.05</td><td>90.08</td><td>89.33</td><td>90.10</td><td>90.07</td><td>88.46</td><td>89.95</td><td>89.16</td><td>1.03</td></tr><tr><td>PET-CGDNN[42]</td><td>63.57</td><td>67.83</td><td>71.51</td><td>74.03</td><td>74.09</td><td>73.96</td><td>74.68</td><td>74.44</td><td>74.52</td><td>73.97</td><td>72.26</td><td>17.94</td></tr><tr><td>MAC-D1</td><td>85.45</td><td>82.93</td><td>85.84</td><td>90.65</td><td>89.27</td><td>88.51</td><td>85.34</td><td>83.21</td><td>82.34</td><td>85.83</td><td>85.93</td><td>4.26</td></tr><tr><td>MAC-MT4</td><td>87.07</td><td>89.74</td><td>90.09</td><td>90.71</td><td>91.47</td><td>90.61</td><td>90.12</td><td>91.56</td><td>89.89</td><td>90.78</td><td>90.20</td><td>-</td></tr></table>  
+
+![](images/Figure_14.jpg)
+
+<center>Fig. 14: The confusion matrix of the proposed MAC-MT4 generalization experiment at \(\mathrm{SNR} = 0\mathrm{dB}\) (a), 8dB (b) </center>  
+
+will be tested in RML2016.10B to verify the generalization abilities of the model.  
+
+The contrastive methods are described as follows  
+
+1) I-Q CNN[35]: Signals are the simplest and most intuitive representation of the baseband signal, obtained by sampling the I-Q component. Using 1-D CNN to treat the I-Q component as two channels of the signal for feature extraction and classification. 
+2) ResNet[40]: Implementing AMR for baseband I-Q signals using CNN networks with residual structure connections. 
+3) CLDNN[41]: The AMR method based on I-Q signals is implemented using Convolutional long short-term deep neural network (CLDNN). 
+4) CLDNN2[40]: Another CLDNN model with no bypass layer connections. 
+5) LSTM[17]: Convert the I-Q signal into amplitude and phase, and input it into a model using two layers LSTM to achieve AMR. 
+6) MCLDNN[19]: The AMR method integrates one-dimensional (1D) convolutional, two-dimensional (2D) convolutional and long short-term memory (LSTM) layers. 
+7) PET-CGDNN[42]: An effective hybrid AMR model based on phase parameter estimation and transformation with I-Q signal as input.  
+
+It can be seen that an AMR method can no longer classify modulations well if this method cannot find the essential AMR in its training set.  
+
+Considering the results in Table VI, most of the AMR methods based on IQ signals have shown poor performance in generalization accuracy.  
+
+The ResNet architecture, incorporating multiple layers of residual structure connections, effectively mitigates overfitting on the training dataset, thereby preserving an accuracy of \(86.98\%\) on the generalization dataset. MCLDNN exploits the complementary information from I- Q multi- channel, I channel, and Q channel data to extract robust signal features, resulting in an accuracy of \(89.16\%\) . The proposed MAC- MT4, has achieved the best performance and its accuracies are over \(91\%\) when the \(\mathrm{SNR} = 8\mathrm{dB}\) . This demonstrates the strong AMR generalization ability of MAC- MT4. The possible reason is as follows. Firstly, during unsupervised training, MAC- MT4 does not establish a direct mapping between signal samples and class labels but discretizes the feature vectors of the samples in the sample space. This enables MAC- MT4 to avoid overfitting samples in a single dataset. Secondly, the utilization of multi- domain information assists MAC- MT4 in identifying the distinctive features of signals in different representation domains. Most importantly, the proposed MAC model selects relevant domain information through domain attention mechanisms to emphasize key representations. For PSK and QAM signals in particular, the constellation space representation domain is a 2D statistical distribution diagram result of symbol values of a signal on the I- Q plane, and its shape, number, and array of constellations are generally unchanged, even when the transmission symbols of the same modulation are ordered differently in different datasets. These explicit features to represent modulations are not difficult to find by MAC.  
+
+The confusion matrices in Fig. 14 depict the performance of MAC- MT4 on the generalization task at \(\mathrm{SNR} = 0\mathrm{dB}\) and 8dB. Overall, the diagonal elements of the confusion matrices are significantly clear, and the classification results for each signal type are similar to those shown in Fig. 10. This indicates that MAC- MT4 maintains robust feature extraction capabilities and achieves satisfactory classification performance when trained and tested on two different datasets.  
+
+To assess the effectiveness of MAC in achieving favorable generalization performance, we evaluate the quality of features extracted by both supervised and unsupervised model encoders. The distribution of feature vectors in the feature space serves as a reliable indicator of the signal representation
+
+<--- Page Split --->
+![](images/Figure_15.jpg)
+
+<center>Fig. 15: Distribution of similarity ratio \(\mathcal{R}\) density of supervised frameworks and the proposed framework. (a) RML2016.10A trained; RML2016.10A tested. (b) RML2016.10A trained; RML2016.10B tested. </center>  
+
+quality. In this regard, we introduce the similarity ratio \(\mathcal{R}\) which provides a comprehensive assessment of both intra- class and inter- class distributions, which can be expressed as  
+
+\[\mathcal{R} = \frac{1}{L}\sum_{l = 1}^{L}\frac{\mathcal{P}^{l}}{\mathcal{P}^{l_{inter - class}}} \quad (18)\]  
+
+A higher similarity ratio between intra- class and inter- class indicates that the features within the same class are more tightly clustered, which is beneficial for subsequent classification. Fig. 15 illustrates the distribution of the proposed unsupervised method and a supervised model with the same backbone on the generalization task. In Fig. 15 (a), when the training and testing data belong to the same dataset, the density distribution of the unsupervised model is similar to the supervised model. However, in Fig. 15 (b), when tested with signals that are not in the same dataset as the ones used for training, the similarity ratio of the supervised model peaks around \(\mathcal{R} = 1\) . This suggests that some signals have similar intra- class similarity \(\mathcal{P}_{intra - class}\) and inter- class similarity \(\mathcal{P}_{inter - class}\) , posing significant challenges for subsequent classification. In contrast, the proposed unsupervised model exhibits a higher similarity ratio, indicating that MAC- MT4 can learn more robust signal representations for new datasets.  
+
+### G. Feature visualization  
+
+In this section, we visualize and analyze the effectiveness of unsupervised representation learning in the proposed MAC framework. We utilize T- Distributed Stochastic Neighbor Embedding (t- SNE [43]) to map the high- dimensional feature vectors extracted by MAC- MT4 to a two- dimensional space for visualization. t- SNE calculates the similarity between data points in the high- dimensional space and constructs a probability distribution in the two- dimensional space based on this similarity information. By overlaying the clustering results with their original class labels, we can assess the quality of unsupervised representation learning. Important to note that the clustering process is performed without any annotated information. We visualize the feature projections at different SNRs(- 8dB, 0dB, 8dB, 12dB) to observe the clustering patterns and assess the effectiveness of unsupervised representation learning in capturing the underlying structure of the data.  
+
+We observe the entire process of unsupervised training in Fig. 16. It shows the clustering of feature vectors of modulation signals in the feature space after training 240 epochs. The signals are clustered into multiple groups, with better clustering performance observed when the SNR>0dB. Notably, distinguishing between QPSK and 8PSK, 16QAM and 64QAM, and WBFM and AM- DSB signals proves to be relatively challenging, consistent with the classification results shown in the confusion matrix. Although 16QAM and 64QAM signals are not completely separated in the feature space, they achieve good classification results during linear evaluation. This can be attributed to the use of high- dimensional features extracted by the encoder in the linear evaluation, rather than relying solely on the features focused by the projection layer. When SNR=- 8dB, the signals cannot be well separated in the feature space due to the strong influence of noise. However, it is still possible to observe that different signal classes tend to cluster in different directions in the high- dimensional space. From feature visualization perspective, the proposed MAC framework demonstrates the ability to perform unsupervised learning of signal representations using data augmentation and domain- transformed signals, without requiring any labeled information. These learned representations can then be utilized for classification tasks.  
+
+## VI. CONCLUSION  
+
+The paper presents a novel unsupervised framework, MAC- based UAMR, for wireless signal. MAC leverages unlabeled signal samples to generate pseudo- labels. Creating positive and negative sample pairs using signal multi- representation domains and data augmentation, signal representation learning is performed self- supervised. Specifically, the DA module allocates suitable attention to multi- representation domains, facilitating the selection of the optimal signal representation domain. Subsequently, the encoder parameters are frozen, and the classification head is trained to assess the efficacy of representation learning. The result on two public datasets highlight the impressive unsupervised learning capability and interpretability of the MAC framework. It effectively reduces the disparity with supervised models in terms of classification results and exhibits robust generalization performance.  
+
+For future work, we plan to optimize the representation learning process by considering multiple similarity measurement methods. Quantitative metrics to assess the extent of unsupervised representation learning need to excavate. Most importantly, unsupervised signal representation learning is not confined to a specific feature task. Our objective is to leverage MAC for transferring across multiple downstream tasks, such as modulation recognition, estimation of key signal parameters, SNR estimation, and communication signal behavior recognition.  
+
+## REFERENCES  
+
+[1] R. Ding, F. Zhou, Q. Wu, C. Dong, Z. Han, and O. A. Dobre, "Data and Knowledge Dual- Driven Automatic Modulation Classification for 6G Wireless Communications," IEEE Transactions on Wireless Communications, pp. 1- 1, 2023.
+
+<--- Page Split --->
+![](images/Figure_16.jpg)
+
+<center>Fig. 16: Feature visualization results for MAC-MT4 at different SNRs and training epochs of RML2016.10A dataset. (a) epoch=1. (b) epoch=50. (c) epoch=100. (d) epoch=150. (e) epoch=240. I SNR=8dB. II SNR=8dB. III SNR=8dB. IV SNR=12dB. </center>  
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+
+<--- Page Split --->

preprint/preprint__c920c18058ab46f53e638e8412b5e57517bdfe1939a4e9e3a569ed18158055db/images_list.json

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+[
+  {
+    "type": "image",
+    "img_path": "images/Figure_1.jpg",
+    "caption": "Fig. 1 Monensin induces the translocation of ATG8 to the tonoplast. a The impact of different concentrations of monensin on the subcellular localization of YFP-ATG8e. 5-day-old YFP-ATG8e transgenic seedlings were treated with different concentrations of monensin (0, 5, 10, 20, 40 μM) in 1/2MS liquid medium for 1 h, followed by confocal microscopy observation. Scale bar, 20 μm. b Time series analysis of the dynamics of GFP-ATG8a in response to monensin (20 μM). Time is presented in minutes. Scale bar, 10 μm. c-g Colocalization analyses between ATG8 and the tonoplast marker VAMP711-mCherry (c), the late endosome marker Rab7-GFP (d), the early endosome marker YFP-ARA7 (e), the TGN marker VHA-a1-RFP (f), as well as the cis-Golgi marker GFP-SYP32 (g). Scale bars in c-g, 20 μm. h Quantification of the colocalization ratios shown in c-g. The Pearson",
+    "footnote": [],
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+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_2.jpg",
+    "caption": "Fig. 2 Translocation of ATG8 to tonoplast requires the ATG conjugation system. a",
+    "footnote": [],
+    "bbox": [
+      [
+        147,
+        88,
+        850,
+        545
+      ]
+    ],
+    "page_idx": 21
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_3.jpg",
+    "caption": "Fig. 3 NADPH oxidase-derived ROS and V-ATPase are required for ATG8 translocation to the tonoplast. a Detection of ROS generation after monensin treatment. 5-day-old mCherry-ATG8f seedlings were subjected to monensin treatment at a concentration of \\(20\\mu \\mathrm{M}\\) . The ROS-sensitive dye H2DCF-DA (1 \\(\\mu \\mathrm{M}\\) ) was incubated 10 min prior to confocal imaging. The images were shown with LUT pseudocolor scale (Rainbow RGB). Scale bar, \\(50\\mu \\mathrm{m}\\) . b The ROS scavenger ascorbic acid (AsA) reduced GFP-ATG8a response to monensin. The left schematic diagram illustrated the timing of addition of AsA and the subsequent monensin treatment. Scale bar, \\(20\\mu \\mathrm{m}\\) . c Treatment with",
+    "footnote": [],
+    "bbox": [
+      [
+        144,
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+        847,
+        680
+      ]
+    ],
+    "page_idx": 23
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_4.jpg",
+    "caption": "Fig. 4 ATG8 facilitates the intralumenal vesicles formation in vacuoles. a 3D projection of GFP-ATG8a and tonoplast marker Vamp711-mCherry after monensin treatment. Arrows indicated representative intralumenal vesicles. Scale bar, \\(20 \\mu \\mathrm{m}\\) . b Representative electron microscopic images illustrated the morphological changes in the vacuole following a 1 h treatment with monensin. Invaginating vesicles are denoted by purple triangles. Scale bars, \\(1 \\mu \\mathrm{m}\\) . c Electron tomography analysis of the 3D organization",
+    "footnote": [],
+    "bbox": [
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+      ]
+    ],
+    "page_idx": 25
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_0.jpg",
+    "caption": "Fig. S1 The effect of different ionophores on the subcellular localization of GFP-ATG8a. a An overview of the chemical structures of monensin sodium, nigericin sodium, and salinomycin sodium. b The formation of membrane-like structures of GFP-ATG8a in response to three ionophores. 5-day-old GFP-ATG8a transgenic seedlings were treated with monensin, nigericin, and salinomycin at a concentration of \\(20\\mu M\\) for 1 hour, followed by confocal microscopy observation. Scale bar, \\(20\\mu m\\) . Similar confocal imaging results were obtained in at least six individual roots with three replicates.",
+    "footnote": [],
+    "bbox": [
+      [
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+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_1.jpg",
+    "caption": "Fig. S2 The effects of monensin treatment on different ATG8 isoforms. 5-day-old fluorescent proteins-labeled ATG8 (ATG8a to ATG8i) transgenic seedlings were treated with \\(20\\mu \\mathrm{M}\\) monensin for 1 hour, followed by confocal microscopy observation. Scale bar, \\(20\\mu \\mathrm{m}\\) . Similar confocal imaging results were obtained in at least six individual roots with three replicates.",
+    "footnote": [],
+    "bbox": [
+      [
+        147,
+        90,
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+      ]
+    ],
+    "page_idx": 28
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_2.jpg",
+    "caption": "Fig. S3 Monensin treatment caused Golgi apparatus swelling. a A large number of vesicular structures accumulated in the cytoplasm after treatment with monensin. Five-day-old seedlings were treated for 1 h in a solution containing \\(0.2\\%\\) ethanol (Control) or 20 \\(\\mu M\\) monensin, followed by excision of the root tip for high-pressure freeze-fixation. Abbreviation: CW, cell wall; ER, endoplasmic reticulum; M, mitochondria; N, nucleus; P, plastid; MVB, multi-vesicular body. Similar electron microscopic images were observed in at least 5 different root tip samples. b Electron tomography analysis of the 3D organization of a representative fragmented Golgi apparatus. The red dashed box indicated the reconstructed region. Four representative image planes (N = 11, 50, 100, and 149) were given in the middle region. 3D model reconstructed from the tomography were presented on the right. Scale bars, \\(1 \\mu m\\) .",
+    "footnote": [],
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+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_3.jpg",
+    "caption": "Fig. S4 Characterization of vha-a2 vha-a3 double mutant. a Defective of V-ATPase resulted in the accumulation of mCherry-ATG8f punctate structures within the vacuoles.",
+    "footnote": [],
+    "bbox": [
+      [
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+    "page_idx": 30
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_4.jpg",
+    "caption": "Fig. S5 ATG16, ATG5, and ATG7 did not respond to monensin treatment. Five-day-old YFP-ATG16, ATG5-GFP, and ATG7-GFP transgenic seedlings were treated with \\(0.2\\%\\) ethanol (control) or \\(20\\mu \\mathrm{M}\\) monensin for \\(1\\mathrm{h}\\) , followed by confocal observation. Scale bars, \\(20\\mu \\mathrm{m}\\) . Similar confocal imaging results were obtained in at least six individual roots with three replicates.",
+    "footnote": [],
+    "bbox": [
+      [
+        145,
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+    "page_idx": 31
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+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_5.jpg",
+    "caption": "Fig. S6 A model highlighting the distinction between canonical autophagy and",
+    "footnote": [],
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+    "page_idx": 32
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_6.jpg",
+    "caption": "Fig. S7 Unprocessed western blots and DNA gel.",
+    "footnote": [],
+    "bbox": [
+      [
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preprint/preprint__c920c18058ab46f53e638e8412b5e57517bdfe1939a4e9e3a569ed18158055db/preprint__c920c18058ab46f53e638e8412b5e57517bdfe1939a4e9e3a569ed18158055db.mmd

@@ -0,0 +1,344 @@
+
+# ATG8ylation facilitates an ESCRT-independent vacuolar membrane invagination in plants  
+
+Xuanang Zheng  
+
+Guangdong Provincial Key Laboratory of Biotechnology for Plant Development, School of Life Sciences, South China Normal University  
+
+Juncai Ma  
+
+Chinese University of Hong Kong https://orcid.org/0000- 0002- 5693- 1117  
+
+Jing Li  
+
+School of Life Sciences, Centre for Cell & Developmental Biology and State Key Laboratory of Agrobiotechnology, The Chinese University of Hong Kong https://orcid.org/0000- 0002- 4060- 1754  
+
+Siyu Chen  
+
+MOE Key Laboratory & Guangdong Provincial Key Laboratory of Laser Life Science, College of Biophotonics, South China Normal University  
+
+Jun Luo  
+
+South China Normal University  
+
+Jianxiong Wu  
+
+South China Normal University  
+
+Kaiyan Zhang  
+
+The Chinese University of Hong Kong  
+
+Chang- lian Peng  
+
+South China Normal University  
+
+Yonglun Zeng  
+
+South China Botanical Garden, Chinese Academy of Sciences https://orcid.org/0000- 0002- 9512- 6487  
+
+Byung- Ho Kang  
+
+Chinese University of Hong Kong https://orcid.org/0000- 0002- 4299- 2170  
+
+Caiji Gao  
+
+Guangdong Provincial Key Laboratory of Biotechnology for Plant Development, School of Life Sciences, South China Normal University https://orcid.org/0000- 0003- 3958- 4499  
+
+Jun Zhou  
+
+zhou.jun@scnu.edu.cn  
+
+South China Normal University https://orcid.org/0000- 0001- 9655- 6588
+
+<--- Page Split --->
+
+## Keywords:  
+
+Posted Date: February 2nd, 2024  
+
+DOI: https://doi.org/10.21203/rs.3.rs- 3878363/v1  
+
+License: © This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License  
+
+Additional Declarations: There is NO Competing Interest.  
+
+Version of Record: A version of this preprint was published at Nature Communications on July 18th, 2025. See the published version at https://doi.org/10.1038/s41467- 025- 62084- 3.
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+1 ATG8ylation facilitates an ESCRT-independent vacuolar membrane 2 invagination in plants 3 Xuanang Zheng1,4, Juncai Ma2,4, Jing Li2, Siyu Chen1, Jun Luo1, Jianxiong Wu1, Kaiyan 4 Zhang2, Changlian Peng1, Yonglun Zeng3, Byung-Ho Kang2, Caiji Gao1, Jun Zhou1 5 1 Guangdong Provincial Key Laboratory of Biotechnology for Plant Development, School 6 of Life Sciences; MOE Key Laboratory & Guangdong Provincial Key Laboratory of Laser 7 Life Science, College of Biophotonics, South China Normal University, Guangzhou, China 8 2 School of Life Sciences, Centre for Cell & Developmental Biology and State Key 9 Laboratory of Agrobiotechnology, The Chinese University of Hong Kong, Shatin, New 10 Territories, Hong Kong, China 11 3 State Key Laboratory of Plant Diversity and Specialty Crops, South China Botanical 12 Garden, Chinese Academy of Sciences, Guangzhou, China 13 4 These authors contributed equally to this work 14 Correspondence: zhoujun@scnu.edu.cn (J.Z.); gaocaiji@m.scnu.edu.cn (C.G.); 15 bkang@cuhk.edu.hk (B.K.)
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+## Abstract  
+
+ATG8- family proteins have been found to be incorporated into single- membrane structures, a process referred to as non- canonical autophagy. While several physiological roles of non- canonical conjugation of ATG8 (ATG8ylation) have been established, the specific functions of ATG8 on single membrane remain largely elusive. Here, we demonstrate that ionophores induce conjugation of ATG8 to vacuolar membrane to promote invagination in Arabidopsis. Upon monensin treatment, ATG8 is rapidly translocated to the vacuolar membrane, which is reliant on the ATG conjugation system rather than upstream autophagic regulators such as ATG1, ATG9, and phosphoinositide 3- kinase (PI3K). Moreover, inhibiting reactive oxygen species (ROS) generation or V- ATPase activity greatly impedes the targeting of ATG8 to the vacuolar membrane. Intriguingly, the recruitment of ATG8 to the tonoplast exhibits a pronounced enhancement of invagination and fosters the formation of intraluminal vesicles within the vacuoles. Further analyses elucidate that the topological remodeling of the vacuolar membrane is achieved in a ESCRT machinery- independent manner. Collectively, this study reveals a previously unrecognized role of ATG8ylation in driving the topological transformation of vacuolar membranes in plants.
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+## Main  
+
+Autophagy is an evolutionarily conserved mechanism that removes damaged organelles and protein aggregates to maintain cellular homeostasis. Over the past few decades, ground- breaking studies have uncovered autophagy- related genes (ATG) and molecular details of autophagy \(^{1,2}\) . Among them, the ATG8- family proteins serve as critical components of the autophagic machinery, exerting influence in numerous facets, including cargo selection, phagophore expansion, autophagosome closure, and fusion with vacuole/lysosome \(^{3,4}\) . Interestingly, emerging lines of evidence demonstrate that ATG8 can also be conjugated with various single- membrane structures, such as the Golgi apparatus \(^{5,6}\) , phagosome \(^{7- 9}\) , endosome \(^{10}\) and lysosome \(^{11}\) , leading to alternative pathways collectively known as non- canonical autophagy. This covalent lipidation of ATG8, termed 'ATG8ylation', has recently garnered attention as a putative membrane stress signal \(^{12}\) , displaying broad functional significance in the immune response \(^{7,8,13}\) , antigen presentation \(^{14}\) , cancer and neurodegeneration \(^{15}\) . In plants, despite recent studies have revealed the translocation of ATG8 to swollen Golgi cisternae to aid its reassembly after heat stress \(^{5,16}\) , our understanding as to non- canonical autophagy and roles of ATG8ylation in the pathway remains limited.  
+
+Recent investigations from non- plant systems have made significant advances in elucidating the regulatory mechanisms of non- canonical autophagy. Generally, the vacuolar- type ATPase (V- ATPase) has been found to directly recruit ATG16L1 (ATG16 in plants) to mediate lipidation of ATG8- family proteins to single membrane structures \(^{6- 8,17}\) . Deletion of the C- terminal WD40 domain or a single point mutation (K490A) in ATG16L1 impairs its functionality specifically in non- canonical autophagy, while exerting no influence on macroautophagy \(^{17,18}\) . In agreement with this, the inhibition of V- ATPase using Bafilomycin A1 disrupts the conjugation of ATG8 to single membrane structures. Thus, the V- ATPase- ATG16L1 axis is characterized as a universal mechanism governing non- canonical autophagy \(^{8,18,19}\) . V- ATPase is a highly conserved proton pump among eukaryotes responsible for acidification in various endomembrane compartments such as endosomes and vacuoles/lysosomes \(^{20}\) . Isoforms of the subunit a in the membrane- integral
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+V0 subcomplex dictate the diverse subcellular localization of the V- ATPase. For example, VHA- a1 targets the V- ATPase to the trans- Golgi network (TGN)/early endosomes, while VHA- a2 and VHA- a3 are localized to the tonoplast in Arabidopsis \(^{21}\) . Currently, the role of V- ATPase in regulating non- canonical autophagy in plants remain largely unexplored.  
+
+One of the critical functions of ATG8 is the recognition and binding of cargoes/receptors, primarily facilitated through the interaction of ATG8- interacting motifs (AIMs) with the AIMs docking site (ADS) on ATG8 proteins \(^{22}\) . From the topological orientation, the incorporation of ATG8 proteins on the single- membrane vesicles seems to take place solely on their side facing the cytosol. In this context, it is speculated that ATG8 on these single- membrane structures is unlikely to sequester cargoes from the cytosol as it does in classical autophagosomes \(^{23}\) . However, the specific functions associated with the non- canonical conjugation of ATG8 have not been clearly established. In this study, we demonstrated that ionophores promoted rapid translocation of ATG8 to the tonoplast, which remarkably enhanced vacuolar membrane invagination. In addition, the formation of ATG8- positive intraluminal vesicles in the vacuole was not relied on the ESCRT machinery. Our research unveiled new functionalities of ATG8 in influencing membrane curvature, providing a model for further investigation into the diverse roles of ATG8 in single membrane structures in plants.  
+
+## Results  
+
+## Ionophores induce conjugation of ATG8 to tonoplast  
+
+In a previous study, we found that ATG8- family proteins concentrate to swollen Golgi stacks following acute heat stress \(^{5}\) . This finding prompted us to investigate whether the disruption of the Golgi could induce a similar response. We conducted a screening of several chemicals including brefeldin A, concanamycin A (ConcA), and monensin, which are known to disrupt the Golgi structure \(^{24, 25}\) . Upon treatment with monensin at concentrations exceeding 10 μM, we discerned membranous structures exhibiting YFP- ATG8e fluorescence (Fig. 1a). We then examined the pattern changes of ATG8 in response to other carboxylic ionophores (i.e., nigericin and salinomycin). These ionophores share
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+similar molecular structures (Fig. S1a), and their carboxyl and hydroxyl groups facilitate the formation of electrically neutral zwitterionic complexes with cations<sup>26</sup>. The resulting chelate complexes exhibit lipid solubility, enabling their diffusion across biological membranes for mediating ion exchange<sup>26</sup>. Intriguingly, localization of GFP- ATG8a on membranous structures matching those after monensin treatment was also observed by incubation with either nigericin or salinomycin (Fig. S1b). Next, taken monensin as an example, the dynamics of ATG8 was characterized by time- lapse confocal imaging. As shown in Fig. 1b, treatment with monensin rapidly induced subcellular alterations in GFP- ATG8a, with obvious membrane- like signal observed within 20 min. Moreover, we assessed the subcellular localization variations among different ATG8 isoforms, and interestingly, all ATG8 isoforms (ATG8a to ATG8i) displayed a comparable response to monensin, forming similar membrane- like structures (Fig. S2).  
+
+To figure out the subcellular location of ATG8 following monensin treatment, we generated double transgenic lines of ATG8 with different organelle markers. Upon monensin treatment, the fluorescent signals of ATG8 exhibited good colocalization with Vamp711- mCherry (tonoplast) as well as Rab7- GFP (late endosome), while no significant colocalization was observed with other endomembrane markers, including YFP- ARA7 (early endosome), VHA- a1- RFP (TGN) and GFP- SYP32 (cis- Golgi) (Fig. 1c- h). It is noteworthy that monensin treatment caused intracellular aggregations of both VHA- a1- RFP and GFP- SYP32 (Fig. 1f- g). Such aggregates were further characterized as clusters of dilated vesicles derived from the Golgi/TGN complexes by transmission electron microscopy (TEM) (Fig. S3a). By conducting three- dimensional (3D) electron tomography analysis, we were able to discern residual Golgi cisternae that remain partially undeformed, in direct proximity to the swollen vesicles (Fig. S3b). However, no ATG8 was associated with the swollen Golgi membrane unlike plant cells challenged by acute heat stress<sup>5</sup>. These results indicated that ATG8 selectively incorporated into the vacuolar membrane following treatment with monensin.  
+
+## ATG8 targeted to tonoplast relies on the ATG conjugation system  
+
+In canonical autophagy, several core complexes such as the ATG1 complex, ATG9 vesicles,
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+and phosphoinositide 3- kinase (PI3K) complex synergistically regulate the formation of autophagosomes<sup>2</sup>. To test whether these upstream regulators were involved in the conjugation of ATG8 to tonoplast, we evaluated the subcellular location of GFP- ATG8a in atg1abct, atg11- 1, and atg9- 4 mutants. Unexpectedly, after treatment with monensin, an obvious vacuolar membrane signal can still be observed in these mutant lines (Fig. 2a, b). Similarly, inhibition of PI3K activity with wortmannin did not prevent monensin- induced translocation of ATG8 to vacuolar membranes (Fig. 2b). Therefore, the core upstream autophagy regulators, including ATG1, ATG11, ATG9, and PI3K, appear to be dispensable for the targeting of ATG8 to the tonoplast.  
+
+The C- terminal cleavage of ATG8 at a conserved glycine residue by the cysteine protease ATG4 is a prerequisite for lipidation<sup>27</sup>. Using YFP- ATG8a(G132A) x mCherry- ATG8f double transgenic plants, we analyzed the impact of point mutation of ATG4 recognition site on ATG8 localization. Noteworthily, in contrast to mCherry- ATG8f, the recruitment of YFP- ATG8a(G132A) to the tonoplast was completely abolished upon monensin treatment (Fig. 2c). Next, we evaluated alterations in the localization of ATG8 in mutants defective in ATG conjugation system, specifically atg5- 1, atg7- 2, and atg16- c1. Monensin treatment did not affect the cytosolic distribution of ATG8 in atg5- 1, atg7- 2, or atg16- c1 mutants (Fig. 2d). Furthermore, the application of monensin significantly enhanced the lipidation level of ATG8 in the Col- 0 and atg11- 1 mutants, while no such increase was observed in atg5- 1 and atg16- c1 mutants (Fig. 2e, f). Collectively, these results indicate that the ATG conjugation system is critical for the targeting of ATG8 to vacuolar membranes.  
+
+## Reactive oxygen species and V-ATPase are required for ATG8 translocation to tonoplast  
+
+Previous studies have shown that cells accumulate a significant amount of reactive oxygen species (ROS) under monensin treatment<sup>28</sup>. To investigate the potential involvement of ROS in monensin- induced targeting of ATG8 to the tonoplast, we assessed ROS generation using a cell- permeant indicator H2DCFDA. Accompanied by the translocation of mCherry- ATG8f to the vacuolar membrane, a robust burst of ROS was observed in the root cells (Fig. 3a). Notably, the exogenous application of ascorbic acid (AsA), which
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+eliminates ROS<sup>29</sup>, resulted in a great reduction in ATG8 binding to the tonoplast followed by monensin treatment (Fig. 3b). Interestingly, pretreatment with diphenyleneiodonium (DPI), an inhibitor of NADPH oxidase<sup>30</sup>, markedly attenuated the recruitment of GFP- ATG8a to the vacuolar membrane (Fig. 3c), indicating the requirement of NADPH oxidase- derived ROS for ATG8 conjugation to the tonoplast upon monensin treatment.  
+
+In mammalian cells, V- ATPase is considered as a universal regulator for the conjugation of ATG8- family proteins to single membranes<sup>8, 19</sup>. To test whether the V- ATPase was also involved in ATG8 targeting to the tonoplast, we firstly investigated the subcellular localization of GFP- ATG8a in the presence ConcA, a specific inhibitor of V- ATPase<sup>31</sup>. As shown in Fig. 3d, the localization of GFP- ATG8a to vacuolar membranes was completely blocked by ConcA. Correspondingly, the treatment with ConcA resulted in a significant reduction in the lipidation form of ATG8 following monensin treatment (Fig. 3e,f). Next, ATG8 targeting to tonoplast was studied in the vha- a2 vha- a3 double mutant, which lacks the tonoplast- localized V- ATPase<sup>32, 33</sup>. Under normal physiological conditions, a large amount of mCherry- ATG8f punctate structures were observed within the vacuoles of the elongation regions of vha- a2 vha- a3 mutants (Fig. S4a). This phenomenon is likely attributed to vacuolar alkalization resulting from the deficiency of V- ATPase<sup>32</sup>, which subsequently leads to reduced protease activities. Noteworthily, in comparison to wild- type Col- 0 plants, the vha- a2 vha- a3 mutant failed to exhibit the conjugation of mCherry- ATG8f to vacuolar membranes after treatment with monensin (Fig. 3g,h). Taken together, these results demonstrated the essential requirement of both NADPH oxidase- derived ROS and V- ATPase for the incorporation of ATG8 into vacuolar membranes, resembling the mechanisms observed in non- canonical autophagy processes in mammalian cells<sup>8</sup>.  
+
+## ATG8 enhances the invagination of vacuolar membranes  
+
+To gain insights into the potential roles of ATG8 in tonoplast dynamics, we examined vacuolar morphology using GFP- ATG8a x Vamp711- mCherry double transgenic plants. After monensin treatment, massive vesicles labeled with both GFP- ATG8a and Vamp711- mCherry appeared in the vacuoles, some of which were attached to the vacuolar membrane, while others were randomly distributed within the vacuolar lumen (Fig. 4a). To
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+further obtain the ultrastructure of the vacuoles, we subjected seedlings treated with monensin to high- pressure freeze fixation for TEM analysis. Interestingly, after monensin treatment, numerous micrometer- sized vesicles containing cytoplasmic components accumulated inside the vacuole (Fig. 4b). Further analysis using 3D electron tomography revealed that these vesicles, formed by invaginations of the vacuolar membrane, not only exhibited spherical shapes but also included some large tubular structures (Fig. 4c, Supplementary Video 1). It is worth mentioning that some of these vesicles also contained organelles such as mitochondria and endoplasmic reticulum (Fig. 4c). Additionally, the time- lapse confocal imaging further showed that the vacuolar membrane was highly dynamic, with masses of invagination occurring (Fig. 4d, Supplementary Video 2). By contrast, inhibition of GFP- ATG8a targeting to vacuolar membranes by application with ConcA obviously decreased the vacuolar invaginations (Fig. 4e). Consistently, a reduction in vacuolar membrane invaginations was also observed in atg5- 1 mutant (Fig. 4f), indicating that the incorporation of ATG8 facilitates the invagination of tonoplast.  
+
+It is well characterized that the endosomal sorting complexes required for transport (ESCRT) plays crucial roles in membrane curvature and the final fission process<sup>34</sup>. To determine whether ESCRT was involved in formatting intraluminal vesicles, we investigated the subcellular location of FYVE domain protein required for endosomal sorting 1 (FREE1), a plant- specific ESCRT component that regulates the closure of autophagosomes via direct interaction with ATG8<sup>4</sup>. Intriguingly, GFP- FREE1 did not localize to the vacuolar membrane as clearly as mCherry- ATG8f after treatment with monensin (Fig. 4g). To further figure out the impact of monensin on the vacuolar morphology in free1 mutants, we introduced YFP- ATG8e into heterozygous T- DNA insertional mutants free1(+/-) and screened the albino seedlings (i.e. the homozygous free1(- /- )<sup>34</sup>) to conduct subsequent confocal analyses. The time- lapse imaging showed that some small vesicles were still generated and closely associated with the vacuolar membrane in the free1(- /-) mutant (Fig. 4h, Supplementary Video 3). Notably, these vesicles exhibited a smaller size within the vacuolar lumen compared to the wild- type counterparts, which may be attributed to the extensive fragmentation of vacuoles in the
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+free1(- /-) mutant<sup>34</sup>. The reduced volume of the smaller vacuole may limit the size of the invaginated vesicles. Collectively, these results indicated that the ATG8- mediated invagination of the vacuolar membrane may operate independently of ESCRT functionality.  
+
+## Discussion  
+
+In the process of canonical autophagy, ATG8 performs diverse and essential functions, encompassing cargo recognition and binding, membrane tethering and extension, as well as autophagosome closure and maturation<sup>2, 4, 8</sup>. However, recent investigations have unveiled an intriguing aspect wherein ATG8 demonstrates the ability to associate with single- membrane structures independently of the classical upstream regulatory factors involved in autophagy<sup>5, 7- 9, 11, 18</sup>. Recruitment of ATG8 onto single- membrane vesicles is generally believed to result in eventual degradation<sup>23</sup>. Currently, the specific roles played by ATG8 in these single- membrane structures remain largely unknown. In this study, we have elucidated that the conjugation of ATG8 to vacuolar membranes, induced by ionophores, actively promoted invagination and the formation of intraluminal vesicles. These findings provide valuable insights into the molecular activities exercised by ATG8 in regulating membrane dynamics and morphology.  
+
+In mammalian cells, the V- ATPase is generally considered to be a universal regulator of non- canonical autophagy<sup>8, 19</sup>. It recruits ATG16 to assemble into a functional E3 complex (known as the ATG12- ATG5- ATG16 complex), which catalyzes the lipidation of ATG8 on single membranes. In consistent, our pharmacological and genetic studies demonstrated that inhibiting V- ATPase significantly impeded the targeting of ATG8 to tonoplast (Fig. 3d,h). This finding suggested that plants share a common mechanism with animals for inducing non- canonical autophagy. In Arabidopsis, the V- ATPase exhibits dual subcellular localization, which is regulated by distinct isoforms of the subunit a. VHA- a1 directs it to the TGN/EE compartments, while VHA- a2 and VHA- a3 are predominantly localized to the tonoplast<sup>20, 21</sup>. Notably, monensin treatment resulted in the disruption of TGN/EE morphology, leading to the formation of vesicular structures with a bubble- like appearance (Fig. 1f and Fig. S3). However, this cellular perturbation did not elicit the translocation of ATG8 to the swollen TGN/EE membrane (Fig. 1f). Conversely, our previous investigations
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+unveiled that extremely high temperatures can evoke the translocation of ATG8 to the dilated Golgi apparatus rather than the vacuolar membrane<sup>5</sup>. Thus, although both the TGN and tonoplast harbor V- ATPase, they are possibly governed by discrete regulatory mechanisms. Such regulatory diversification may facilitate the selective targeting of ATG8 towards distinct single- membrane organelles under disparate environmental stimuli conditions.  
+
+Membrane curvature exerts a substantial influence on the structural configuration of the cell membrane, contributing significantly to its overall shape and organization. In vitro reconstitution investigations employing purified proteins and synthetic giant unilamellar vesicles have provided valuable insights into the multifaceted membrane- associated functionalities facilitated by ATG8 conjugation, such as tethering, hemi- fusion, tubulation, perturbation, and in/out- bud<sup>35- 38</sup>. The direction of membrane curvature induced by the covalent anchorage of ATG8 is predominantly determined by the difference in the membrane area between the outer and inner layers of the lipid bilayer<sup>35, 36</sup>. It is noteworthy that ATG8 conjugation is inadequate to initiate membrane invagination. Instead, it relies on the recruitment of other proteins within the ATG conjugation system, including ATG3, ATG7, and ATG12- ATG5- ATG16, to provide the necessary driving force for the induction of in- bud formation<sup>35</sup>. However, under monensin treatment, the subcellular localization of ATG16, ATG5, and ATG7 to the vacuolar membrane was not observed (Fig. S5), suggesting the potential involvement of other proteins in orchestrating the membrane scaffold organization. Notably, recent findings demonstrate that ATG8 can directly interact with the ESCRT component FREE1 to participate in the closure of autophagosomes<sup>4</sup>. However, in the presence of monensin, FREE1 was not recruited to the vacuolar membrane by ATG8, and the formation of invaginated vesicles was still observed in the vacuoles of free1(- /-) mutant, albeit smaller in size (Fig. 4g,h). Therefore, we speculate that ESCRT may not directly participate in ATG8- mediated vacuolar membrane invagination. Nevertheless, it is noteworthy that the intraluminal vesicles in the free1(- /-) mutant exhibited a prolonged adherence to the vacuolar membrane (Fig. 4h). This suggested a potential reliance on ESCRT- mediated scission processes for the detachment of invaginated vesicles from the
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+vacuolar membrane. Undoubtedly, further experimental evidences are required to substantiate this hypothesis.  
+
+ATG8 shares structural and modification similarities with ubiquitin, as both molecules undergo sequential enzymatic reactions involving E1, E2, and E3 enzymes. However, their respective targets differ, with ubiquitin primarily marking proteins and ATG8 specifically targeting membranes. Like the role of ubiquitination as a general signal for protein degradation, mounting evidence suggests that ATG8ylation also serves as a signaling mechanism in response to membrane stress events<sup>12</sup>. Ionophores disrupt membrane ion permeability, resulting in the inability of the vacuolar membrane to maintain a normal proton gradient<sup>26</sup>. Concurrently, this process triggers a burst of ROS, which could potentially induce oxidative damage to the membrane lipids (Fig. 3a). In this context, ATG8-mediated vacuolar membrane invagination may assist in the clearance of damaged membranes, thereby counteracting osmotic stress caused by monensin. In the future, it will be of interest to assess and quantify the damages inflicted on vacuolar membrane lipids, which would contribute to better understanding of the functional consequences of ATG8ylation.  
+
+Collectively, our results presented a non- canonical autophagic function of ATG8 in the field of plants. Under monensin treatment, ATG8 conjugation to tonoplast is rely on the ATG conjugation system rather than the upstream autophagic regulators. The association of ATG8 exerts a pronounced influence on membrane curvature, actively promoting invagination processes and facilitating the subsequent development of intraluminal vesicles within the vacuoles (Fig. S6). This study broadened the scope of understanding regarding the diverse functions of the core autophagy protein ATG8 in plant cells, extending beyond its canonical role in autophagy.
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+## Methods  
+
+## Plant materials and growth conditions  
+
+The autophagy mutants including atg5- 139, atg7- 239, atg16- c15 and atg11- 140, as well as the vha- a2 vha- a33 double mutants were described previously. The single transgenic plants GFP- ATG8a41, mCherry- ATG8f42, YFP- ATG8b/c/d/e/g/h/i5, YFP- ATG16s, ATG5- GFP5, ATG7- GFP5, GFP- ATG8a/atg1abcf41, GFP- ATG8a/atg5- 15, YFP- ATG8e/atg7- 25, GFP- ATG8a/atg9- 441, GFP- ATG8a/atg11- 140, GFP- ATG8a/atg16- c15 and GFP- FREE134 were reported previously. The double transgenic plants YFP- ATG8a(G132A) x mCherry- ATG8f5, GFP- ATG8a x Vamp711- mCherry5, Rab7- GFP x mCherry- ATG8f5, YFP- ARA7 x mCherry- ATG8f5, GFP- ATG8a x VHA- a1- RFP5, GFP- SYP32 x mCherry- ATG8f5 were described previously. The GFP- FREE1 x mCherry- ATG8f, mCherry- ATG8f/vha- a2 vha- a3 and Vamp711- mCherry/atg5- 1 were obtained by cross- pollination, and the homozygous mutant backgrounds were verified by PCR (Fig. S4b). ATG7- GFP was cloned into the pCAMBIA1300 vector, and the transgenic plant was generated through floral dip. The seeds were surface- sterilized with 70% (v/v) ethanol containing 0.05% Triton X- 100 and then sown on 1/2 Murashige and Skoog (MS) plates. After being kept at 4°C for 48 h, the plates were transferred to a culture chamber maintained at 22°C with a photoperiod of 16 h light and 8 h dark, and cultivate for 5 d for subsequent experiments.  
+
+## Chemical treatment  
+
+The ionophores including monensin sodium salt (MCE, #HY- N0150), salinomycin sodium salt (MCE, #HY- 17439), and nigericin sodium salt (MCE, #HY- 100381) were prepared as 10 mM stock solutions in ethanol and stored at - 20°C. The 5- day- old seedlings were immersed in liquid 1/2MS medium containing 0.2% ethanol (control) or 20 μM monensin for 1 h, and then the plant materials were subjected to confocal imaging. The treatment of salinomycin and nigericin is the same as monensin. ConcA (MCE, #HY- N1724) and wortmannin (MCE, #HY- 10197) stock solutions were prepared at concentrations of 1 mM and 16.5 mM, respectively, in DMSO and stored at - 20°C. ConcA (1 μM) or wortmannin (16.5 μM) was pre- incubated for 10 min and then added with 20 μM monensin for 1 h, followed by confocal imaging. For the ROS detection, a 1 μM concentration of the ROS
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+sensitive dye H2DCFDA (MCE, #HY- D0940) was incubated in darkness for 10 min prior to confocal imaging. L- Ascorbic acid sodium salt (MCE, #HY- B0166A) was freshly prepared in 1/2MS and added 1 h before monensin treatment. DPI (MCE, #HY- 100965) was prepared as 10 mM stock solutions in DMSO and added 0.5 h before monensin treatment.  
+
+## ATG8 lipidation assay  
+
+Briefly, 0.2 g of 5- day- old Col- 0, atg5- 1, atg7- 2, atg11- 1, and atg16- c1 seedlings, with or without \(20 \mu \mathrm{M}\) monensin treatment for 1h, were grounded thoroughly in pre- cooled mortar with 1.5 ml of membrane buffer (40 mM HEPES, 1 mM EDTA, 10 mM KCl, 0.4 M Sucrose, pH 7.4) on ice. The crude lysates were collected in 2 ml tubes, then centrifuged at 1000xg for 10 min to remove large cell fragments. The supernatants were transferred and mixed with loading buffer (250 mM Tris- HCl, pH 6.8, 10% (w/v) SDS, 0.5%(w/v) Bromophenol blue, 50% (v/v) Glycerol, 5% (v/v) \(\beta\) - Mercaptoethanol), and boiled at 95 °C for 10 min. The protein solution was subjected to 12% SDS- PAGE and immunoblotted with anti- ATG8 antibody (Agrisera, #AS14 2769). Uncropped western blots are available in supplementary files (Fig. S7).  
+
+## TEM analysis  
+
+The TEM assay was performed following our previously established protocols<sup>43, 44</sup>. Briefly, 5- d- old seedlings were germinated on 1/2 MS plate and then treated with or without \(20 \mu \mathrm{M}\) monensin in liquid 1/2 MS before dissecting. For high- pressure freezing, the root tips were collected and immediately frozen with a high- pressure freezer (EM ICE, Leica). For freeze substitution, the root tips were substituted with 2% osmium tetroxide in anhydrous acetone and maintained at \(- 80 ^{\circ} \mathrm{C}\) for 24 hours using an AFS2 temperature- controlling system (Leica). Subsequently, the samples were subjected to three washes with precooled acetone and gradually warmed to room temperature over a period of 60 h. Infiltration with increasing concentrations of EPON resin mix (50% Epon resin monomer, 15% dodecenyl succinic anhydride, and 35% nadic methyl anhydride) was carried out at room temperature. The root tips were then transferred into tin foil molds and polymerized by curing at \(60^{\circ} \mathrm{C}\) for 2 days. The embedded samples were sectioned into 90 nm- thick slices using an ultramicrotome (Leica UC7). Micrographs were acquired using a transmission electron
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+microscope (Hitachi H- 7650) operating at 80 kV, coupled with a charge- coupled device (CCD) camera.  
+
+## 3D electron tomography  
+
+Electron tomography was conducted using a 200 kV Tecnai F20 electron microscope (FEI Company) following previously established procedures<sup>45</sup>. Briefly, the tilt images were obtained from 250- nm- thick sections across a range of \(- 60^{\circ}\) to \(60^{\circ}\) , with \(1.5^{\circ}\) increments, while the grid was rotated by \(90^{\circ}\) for the collection of the other axis of the tilt image stack. Dual- axis tomograms were generated by utilizing pairs of image stacks with the etomo program of the IMOD software (v.4.11.25). The contours of vacuolar membranes and intraluminal vesicles were manually delineated and subsequently meshed using the 3dmod program within the IMOD software suite.  
+
+## Confocal imaging and image processing  
+
+The confocal images were acquired using the Zeiss LSM880 laser scanning confocal system with 63X/1.4 NA or 40X/1.4 NA oil objective. The excitation and emission wavelengths for YFP, GFP and H2DCFDA were 488 nm and 500- 550 nm, respectively. For mCherry and RFP, the excitation and emission wavelengths were 561 nm and 570- 650 nm, respectively. For dual- channel scanning, the "line" scanning mode was used. The images from different channels were exported separately using ZEN2.5 (blue edition) for further analysis. The co- localization analysis was performed using the PSC plugin in Image J software (NIH).  
+
+## Quantification and statistical analysis  
+
+All experiments were repeated at least three times with consistent results. The co- localization ratio and western band intensities were quantified using Image J software (NIH). Charting and statistical analysis were performed using GraphPad Prism 8 software. The \(P\) values were determined with two- tailed unpaired Student's \(t\) - tests, and the asterisks represent significance levels (ns, not significant; \(*P < 0.05\) ; \(***P < 0.001\) ).  
+
+## Acknowledgements  
+
+We appreciate Prof. Zhenhua Zhang (Hunan Agricultural University) for providing us with
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+the vha- a2 vha- a3 double mutants. This work was supported by grants from the National Natural Science Foundation of China (32061160467, 31870171) and Fok Ying- Tong Education Foundation for Young Teachers in the Higher Education Institutions of China (171014) to C.G., the National Science Foundation of China (31600288) and the Basic Research Program of Guangzhou (202201010508) to J.Z., and Hong Kong Research Grant Council (GRF14113921, GRF14121019, GRF14109222, N_CUHK462/22, and C4002- 20W) to B- H.K. We would like to acknowledge the Open Fund of MOE Key Laboratory of Laser life Science and Institute of Laser Life Science.  
+
+## Competing interests  
+
+The authors declare no competing interests.  
+
+## Contributions  
+
+J.Z., J.M., and C.G. designed the experiments. X.Z., J.M., J.Li, S.C., J.Luo, J.W., K.Z., and J.Z. performed the experiments. X.Z., J.M., Y.Z., B- H.K., C.G., and J.Z. analyzed the data. J.M., J.Li., K.Z., and B- H.K. contributed to the TEM analysis. J.Z., X.Z., J.M., C.P., Y.Z., B- H.K., and C.G. wrote and edited the manuscript. All authors reviewed the manuscript.  
+
+## References  
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+1. Noda, N.N. & Inagaki, F. Mechanisms of Autophagy. Annu Rev Biophys 44, 101-122 (2015).  
+2. Li, H. et al. Shedding Light on the Role of Phosphorylation in Plant Autophagy. FEBS Lett 596, 2172-2185 (2022).  
+3. Johansen, T. & Lamark, T. Selective Autophagy: ATG8 Family Proteins, LIR Motifs and Cargo Receptors. J Mol Biol 432, 80-103 (2020).  
+4. Zeng, Y. et al. The plant unique ESCRT component FREE1 regulates autophagosome closure. Nat Commun 14, 1768 (2023).  
+5. Zhou, J. et al. A non-canonical role of ATG8 in Golgi recovery from heat stress in plants. Nat Plants 9, 749-765 (2023).  
+6. Gao, Y. et al. Golgi-associated LC3 lipidation requires V-ATPase in noncanonical autophagy. Cell Death & Disease 7, e2330-e2330 (2016).  
+7. Xu, Y. et al. A Bacterial Effector Reveals the V-ATPase-ATG16L1 Axis that Initiates Xenophagy. Cell 178, 552-566 e520 (2019).  
+8. Hooper, K.M. et al. V-ATPase is a universal regulator of LC3-associated phagocytosis and non-canonical autophagy. J Cell Biol 221 (2022).  
+9. Durgan, J. et al. Non-canonical autophagy drives alternative ATG8 conjugation to phosphatidylserine. Mol Cell 81, 2031-2040 e2038 (2021).  
+10. Jia, M. et al. Noncanonical ATG8-ABS3 interaction controls senescence in plants.
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+<--- Page Split --->
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+410 Nat Plants 5, 212- 224 (2019). 411 11. Cross, J. et al. Lysosome damage triggers direct ATG8 conjugation and ATG2 engagement via non- canonical autophagy. J Cell Biol 222 (2023). 412 Kumar, S., Jia, J., & Deretic, V. Atg8ylation as a general membrane stress and remodeling response. Cell Stress 5, 128- 142. (2021). 413 13. Wang, Y. et al. Non- canonical autophagy functions of ATG16L1 in epithelial cells limit lethal infection by influenza A virus. EMBO J 40, e105543 (2021). 414 14. Romao, S. et al. Autophagy proteins stabilize pathogen- containing phagosomes for prolonged MHC II antigen processing. J Cell Biol 203, 757- 766 (2013). 415 Heckmann, B.L. et al. LC3- Associated Endocytosis Facilitates beta- Amyloid Clearance and Mitigates Neurodegeneration in Murine Alzheimer's Disease. Cell 178, 536- 551 e514 (2019). 416 Zheng, X., Chen, S., Gao, C. & Zhou, J. An emerging role of non- canonical conjugation of ATG8 proteins in plant response to heat stress. Autophagy, 1- 3. 417 Fletcher, K. et al. The WD40 domain of ATG16L1 is required for its non- canonical role in lipidation of LC3 at single membranes. EMBO J 37 (2018). 418 Fischer, T.D., Wang, C., Padman, B.S., Lazarou, M. & Youle, R.J. STING induces LC3B lipidation onto single- membrane vesicles via the V- ATPase and ATG16L1- WD40 domain. J Cell Biol 219 (2020). 419 Durgan, J., & Florey, O. Many roads lead to CASM: Diverse stimuli of noncanonical autophagy share a unifying molecular mechanism. Sci Adv 8, eabo1274 (2022). 420 Schumacher, K. & Krebs, M. The V- ATPase: small cargo, large effects. Curr Opin Plant Biol 13, 724- 730 (2010). 421 Lupanga, U. et al. The Arabidopsis V- ATPase is localized to the TGN/EE via a seed plant- specific motif. Elife 9 (2020). 422 Stephani, M. & Dagdas, Y. Plant Selective Autophagy- Still an Uncharted Territory With a Lot of Hidden Gems. J Mol Biol 432, 63- 79 (2020). 423 Nieto- Torres, J.L., Leidal, A.M., Debnath, J. & Hansen, M. Beyond Autophagy: The Expanding Roles of ATG8 Proteins. Trends Biochem Sci 46, 673- 686 (2021). 424 Ritzenthaler, C. et al. Reevaluation of the effects of brefeldin A on plant cells using tobacco Bright Yellow 2 cells expressing Golgi- targeted green fluorescent protein and COP1 antisera. Plant Cell 14, 237- 261 (2002). 425 Zhang, G. F., Driouich, A., & Staehelin, L. A. Effect of monensin on plant Golgi: re- examination of the monensin- induced changes in cisternal architecture and functional activities of the Golgi apparatus of sycamore suspension- cultured cells. J. Cell Sci. 104, 819- 831 (1993). 426 Painter, G. R., & Pressman, B. C. Dynamic aspects of ionophore mediated membrane transport. Host Guest Complex Chemistry II, 83- 110 (2005). 427 Yoshimoto, K. et al. Processing of ATG8s, Ubiquitin- Like Proteins, and Their Deconjugation by ATG4s Are Essential for Plant Autophagy. Plant Cell 16, 2967- 2983 (2004). 428 Charvat, R.A. & Arrizabalaga, G. Oxidative stress generated during monensin treatment contributes to altered Toxoplasma gondii mitochondrial function. Sci Rep 6, 22997 (2016).
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+29. Yu, Y. et al. Ascorbic Acid Integrates the Antagonistic Modulation of Ethylene and Abscisic Acid in the Accumulation of Reactive Oxygen Species. Plant Physiol 179, 1861-1875 (2019).
+30. Zhou, J., Sun, A. & Xing, D. Modulation of cellular redox status by thiamine-activated NADPH oxidase confers Arabidopsis resistance to Sclerotinia sclerotiorum. J Exp Bot 64, 3261-3272 (2013).
+31. Yu, J. & Zhou, J. Vacuolar accumulation and colocalization is not a proper criterion for cytoplasmic soluble proteins undergoing selective autophagy. Plant Signal Behav 16, 1932319 (2021).
+32. Krebs, M. et al. Arabidopsis V-ATPase activity at the tonoplast is required for efficient nutrient storage but not for sodium accumulation. Proc Natl Acad Sci U S A 107, 3251-3256 (2010).
+33. Liang, G., Song, H., Xiao, Y. & Zhang, Z. Ammonium Accumulation Caused by Reduced Tonoplast V-ATPase Activity in Arabidopsis thaliana. Int J Mol Sci 22 (2020).
+34. Gao, C. et al. A Unique Plant ESCRT Component, FREE1, Regulates Multivesicular Body Protein Sorting and Plant Growth. Curr Biol 24, 2556-2563 (2014).
+35. Alam, J.M. et al. Complete set of the Atg8-E1-E2-E3 conjugation machinery forms an interaction web that mediates membrane shaping. Nat Struct Mol Biol (2023).
+36. Maruyama, T. et al. Membrane perturbation by lipidated Atg8 underlies autophagosome biogenesis. Nat Struct Mol Biol 28, 583-593 (2021).
+37. Nakatogawa, H., Ichimura, Y. & Ohsumi, Y. Atg8, a Ubiquitin-like Protein Required for Autophagosome Formation, Mediates Membrane Tethering and Hemifusion. Cell 130, 165-178 (2007).
+38. Wang, X. et al. Membrane Morphology Is Actively Transformed by Covalent Binding of the Protein Atg8 to PE-Lipids. PLoS ONE 9 (2014).
+39. Yin, R. et al. Up-regulation of autophagy by low concentration of salicylic acid delays methyl jasmonate-induced leaf senescence. Sci Rep 10, 11472 (2020).
+40. Li, F., Chung, T. & Viestra, R.D. AUTOPHAGY-RELATED11 plays a critical role in general autophagy- and senescence-induced mitophagy in Arabidopsis. Plant Cell 26, 788-807 (2014).
+41. Huang, X. et al. Genetic Analyses of the Arabidopsis ATG1 Kinase Complex Reveal Both Kinase-Dependent and Independent Autophagic Routes during Fixed-Carbon Starvation. Plant Cell 31, 2973-2995 (2019).
+42. Zhuang, X. et al. A BAR-domain protein SH3P2, which binds to phosphatidylinositol 3-phosphate and ATG8, regulates autophagosome formation in Arabidopsis. Plant Cell 25, 4596-4615 (2013).
+43. Kang, B.H. Electron microscopy and high-pressure freezing of Arabidopsis. Methods Cell Biol 96, 259-283 (2010).
+44. Ma, J. et al. Friendly mediates membrane depolarization-induced mitophagy in Arabidopsis. Curr Biol 31, 1931-1944 (2021).
+45. Toyooka, K. & Kang, B.H. Reconstructing plant cells in 3D by serial section electron tomography. Methods Mol Biol 1080, 159-170 (2014).
+
+<--- Page Split --->
+![](images/Figure_1.jpg)
+
+<center>Fig. 1 Monensin induces the translocation of ATG8 to the tonoplast. a The impact of different concentrations of monensin on the subcellular localization of YFP-ATG8e. 5-day-old YFP-ATG8e transgenic seedlings were treated with different concentrations of monensin (0, 5, 10, 20, 40 μM) in 1/2MS liquid medium for 1 h, followed by confocal microscopy observation. Scale bar, 20 μm. b Time series analysis of the dynamics of GFP-ATG8a in response to monensin (20 μM). Time is presented in minutes. Scale bar, 10 μm. c-g Colocalization analyses between ATG8 and the tonoplast marker VAMP711-mCherry (c), the late endosome marker Rab7-GFP (d), the early endosome marker YFP-ARA7 (e), the TGN marker VHA-a1-RFP (f), as well as the cis-Golgi marker GFP-SYP32 (g). Scale bars in c-g, 20 μm. h Quantification of the colocalization ratios shown in c-g. The Pearson </center>
+
+<--- Page Split --->
+
+correlation (PSC) coefficient was analyzed by ImageJ with the PSC colocalization plugin. The data represent means ± s.d. \(n = 6\) confocal images ( \(112.5 \mu m \times 112.5 \mu m\) ) of individual roots. Similar confocal imaging results were obtained from at least six individual roots, with three replicates.
+
+<--- Page Split --->
+![](images/Figure_2.jpg)
+
+<center>Fig. 2 Translocation of ATG8 to tonoplast requires the ATG conjugation system. a </center>  
+
+The impact of monensin on the subcellular localization of GFP- ATG8a in ATG1 complex mutants. b The impact of mutation of ATG9 or inhibition of PI3K activity on the subcellular localization of GFP- ATG8a under monensin treatment. c Analysis of the impact of ATG4 on the subcellular localization of YFP- ATG8a. d Effect of mutation in ATG5, ATG7, and ATG16 genes on the subcellular localization of ATG8 under monensin treatment. 5- day- old GFP- ATG8a/atg1abct, GFP- ATG8a/atg11- 1, GFP- ATG8a/atg9- 4, GFP- ATG8a/atg5- 1, YFP- ATG8e/atg7- 2 and YFP- ATG8a(G132A) x mCherry- ATG8f double transgenic seedlings were treated with \(20\mu \mathrm{M}\) monensin for 1 hour, followed by confocal microscopy observation. Wortmannin (16.5 \(\mu \mathrm{M}\) ) was pre- incubated for 10 minutes and then added with \(20\mu \mathrm{M}\) monensin for 1 hour, followed by confocal imaging. Scale bars in a- d, \(20\mu \mathrm{m}\) . Similar confocal imaging results were obtained in at least six individual roots with three replicates. e- h The impact of monensin on ATG8 lipidation in wild- type Col- 0 and autophagy mutants
+
+<--- Page Split --->
+
+including atg11- 1, atg7- 2, atg5- 1 and atg16- c1. The ratios \((n = 3)\) between the lipidation form ATG8 and actin was quantified with ImageJ (f and h). Asterisk indicated unknown band. Mon, Monensin. Data are mean ± s.d. Significance analysis using unpaired twosided Student's \(t\) - test. The immunoblotting assays were independently replicated three times with consistent results.
+
+<--- Page Split --->
+![](images/Figure_3.jpg)
+
+<center>Fig. 3 NADPH oxidase-derived ROS and V-ATPase are required for ATG8 translocation to the tonoplast. a Detection of ROS generation after monensin treatment. 5-day-old mCherry-ATG8f seedlings were subjected to monensin treatment at a concentration of \(20\mu \mathrm{M}\) . The ROS-sensitive dye H2DCF-DA (1 \(\mu \mathrm{M}\) ) was incubated 10 min prior to confocal imaging. The images were shown with LUT pseudocolor scale (Rainbow RGB). Scale bar, \(50\mu \mathrm{m}\) . b The ROS scavenger ascorbic acid (AsA) reduced GFP-ATG8a response to monensin. The left schematic diagram illustrated the timing of addition of AsA and the subsequent monensin treatment. Scale bar, \(20\mu \mathrm{m}\) . c Treatment with </center>
+
+<--- Page Split --->
+
+diphenyleneiodonium chloride (DPI) inhibited GFP- ATG8a translocation to the tonoplast. The schematic diagram on the left illustrated the timing of DPI addition and the subsequent monensin treatment. Scale bar, \(20 \mu \mathrm{m}\) . d Pretreatment of ConcA inhibited the translocation of GFP- ATG8a to tonoplast. Scale bar, \(20 \mu \mathrm{m}\) . e Western blotting analysis of the effect of ConcA on the ATG8 lipidation. f Statistical analysis of the ratio of lipidation form ATG8 to ATG8 in (e). g A schematic diagram showing the structure of V- ATPase. The subunit a isoforms VHA- a2 and VHA- a3 are specifically located at vacuolar membranes. h Monensin- induced the translocation of GFP- ATG8a to tonoplast was abolished in vha- a2vha- a3 double mutant. Scale bar, \(20 \mu \mathrm{m}\) . Similar confocal imaging results were obtained in at least six individual roots with three replicates.
+
+<--- Page Split --->
+![](images/Figure_4.jpg)
+
+<center>Fig. 4 ATG8 facilitates the intralumenal vesicles formation in vacuoles. a 3D projection of GFP-ATG8a and tonoplast marker Vamp711-mCherry after monensin treatment. Arrows indicated representative intralumenal vesicles. Scale bar, \(20 \mu \mathrm{m}\) . b Representative electron microscopic images illustrated the morphological changes in the vacuole following a 1 h treatment with monensin. Invaginating vesicles are denoted by purple triangles. Scale bars, \(1 \mu \mathrm{m}\) . c Electron tomography analysis of the 3D organization </center>
+
+<--- Page Split --->
+
+of vacuole after monensin treatment for 1 h. Purple triangles in the individual slices indicated the presence of invaginating vesicles. 3D models reconstructed from the tomography were presented on the right. Scale bars, 1 μm. d Time-series analysis of the ATG8- positive vesicles invaginated from the vacuolar membrane. A representative invaginating vesicle was indicated by the arrowhead. Scale bar, 10 μm. e Time-series analysis of the effect of ConcA on ATG8- positive vesicles invaginated from the vacuolar membrane. Scale bar, 10 μm. f Time-series analysis of the vacuolar membrane invagination in atg5- 1 mutant upon monensin treatment. Scale bar, 10 μm. g Analysis of the subcellular location of GFP- FREE1 before and after monensin treatment. Scale bar, 20 μm. h Time-series analysis of the invagination of ATG8- positive vesicles in free1(- /-) mutant. The pink arrows indicated a vesicle that adhered inside the vacuolar membrane; white arrows indicated invaginated vesicles. Scale bar, 10 μm. Similar confocal imaging results were obtained in at least six individual roots with three replicates.
+
+<--- Page Split --->
+![](images/Figure_unknown_0.jpg)
+
+<center>Fig. S1 The effect of different ionophores on the subcellular localization of GFP-ATG8a. a An overview of the chemical structures of monensin sodium, nigericin sodium, and salinomycin sodium. b The formation of membrane-like structures of GFP-ATG8a in response to three ionophores. 5-day-old GFP-ATG8a transgenic seedlings were treated with monensin, nigericin, and salinomycin at a concentration of \(20\mu M\) for 1 hour, followed by confocal microscopy observation. Scale bar, \(20\mu m\) . Similar confocal imaging results were obtained in at least six individual roots with three replicates. </center>
+
+<--- Page Split --->
+![](images/Figure_unknown_1.jpg)
+
+<center>Fig. S2 The effects of monensin treatment on different ATG8 isoforms. 5-day-old fluorescent proteins-labeled ATG8 (ATG8a to ATG8i) transgenic seedlings were treated with \(20\mu \mathrm{M}\) monensin for 1 hour, followed by confocal microscopy observation. Scale bar, \(20\mu \mathrm{m}\) . Similar confocal imaging results were obtained in at least six individual roots with three replicates. </center>
+
+<--- Page Split --->
+![](images/Figure_unknown_2.jpg)
+
+<center>Fig. S3 Monensin treatment caused Golgi apparatus swelling. a A large number of vesicular structures accumulated in the cytoplasm after treatment with monensin. Five-day-old seedlings were treated for 1 h in a solution containing \(0.2\%\) ethanol (Control) or 20 \(\mu M\) monensin, followed by excision of the root tip for high-pressure freeze-fixation. Abbreviation: CW, cell wall; ER, endoplasmic reticulum; M, mitochondria; N, nucleus; P, plastid; MVB, multi-vesicular body. Similar electron microscopic images were observed in at least 5 different root tip samples. b Electron tomography analysis of the 3D organization of a representative fragmented Golgi apparatus. The red dashed box indicated the reconstructed region. Four representative image planes (N = 11, 50, 100, and 149) were given in the middle region. 3D model reconstructed from the tomography were presented on the right. Scale bars, \(1 \mu m\) . </center>
+
+<--- Page Split --->
+![](images/Figure_unknown_3.jpg)
+
+<center>Fig. S4 Characterization of vha-a2 vha-a3 double mutant. a Defective of V-ATPase resulted in the accumulation of mCherry-ATG8f punctate structures within the vacuoles. </center>  
+
+Confocal imaging was directly performed on 5- day- old transgenic seedlings. Scale bar, 20 \(\mu \mathrm{m}\) . b Validation of the homozygous vha- a2 vha- a3 mutants with PCR. The primer sequence: VHA- a2- LP, ACCTCTGGCTCAAAATTGTCC; VHA- a2- RP, TCCACATGAATATAGCCCAG; VHA- a3- LP, TGGAAATGAGAAGCATGGATC; VHA- a3- RP, ATTGGGTCCATTTTGAAAAGC; LBb1.3, ATTTTGCCGATTTCGGAAC.
+
+<--- Page Split --->
+![](images/Figure_unknown_4.jpg)
+
+<center>Fig. S5 ATG16, ATG5, and ATG7 did not respond to monensin treatment. Five-day-old YFP-ATG16, ATG5-GFP, and ATG7-GFP transgenic seedlings were treated with \(0.2\%\) ethanol (control) or \(20\mu \mathrm{M}\) monensin for \(1\mathrm{h}\) , followed by confocal observation. Scale bars, \(20\mu \mathrm{m}\) . Similar confocal imaging results were obtained in at least six individual roots with three replicates. </center>
+
+<--- Page Split --->
+![](images/Figure_unknown_5.jpg)
+
+<center>Fig. S6 A model highlighting the distinction between canonical autophagy and </center>  
+
+monensin- induced non- canonical autophagy. In canonical autophagy, the formation of autophagosomes is regulated by coordinated interactions among upstream autophagy factors such as the ATG1 complex, PI3K complex, and ATG9 vesicles. ATG8 is lipidated by the ATG conjugation system and conjugates to the phagophore, aiding in its elongation and closure to form mature autophagosomes. Subsequently, these autophagosomes fuse with the vacuolar membrane, delivering the inclusions for degradation. In contrast, in monensin- induced non- canonical autophagy, the targeting of ATG8 to the vacuolar membrane does not depend on upstream autophagy factors. V- ATPase may recruit ATG12- ATG5- ATG16, similar to the model observed in animals, to catalyze the conjugation of ATG8 to the vacuolar membrane. ATG8 facilitates membrane curvature on the tonoplast and mediates the formation of invaginated vesicles. The ESCRT machinery is potentially involved in the final scission to allow the vesicles to drop into the lumen of the vacuole.
+
+<--- Page Split --->
+![](images/Figure_unknown_6.jpg)
+
+<center>Fig. S7 Unprocessed western blots and DNA gel. </center>  
+
+637  
+
+Supplementary Video 1 3D electron tomography analysis of the invagination of tonoplast after treatment with monensin for 1 h.  
+
+Supplementary Video 2 Time- lapse confocal imaging of the formation process of invaginated vesicles with GFP- ATG8a x Vamp711- mCherry transgenic plants.  
+
+Supplementary Video 3 Time- lapse observation of the dynamic of invaginated vesicles in the free1(- /-) mutant.
+
+<--- Page Split --->
+
+## Supplementary Files  
+
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+SupplementaryVideo1. mov  SupplementaryVideo2. avi  SupplementaryVideo3. avi
+
+<--- Page Split --->

preprint/preprint__c920c18058ab46f53e638e8412b5e57517bdfe1939a4e9e3a569ed18158055db/preprint__c920c18058ab46f53e638e8412b5e57517bdfe1939a4e9e3a569ed18158055db_det.mmd

@@ -0,0 +1,428 @@
+<|ref|>title<|/ref|><|det|>[[42, 106, 844, 175]]<|/det|>
+# ATG8ylation facilitates an ESCRT-independent vacuolar membrane invagination in plants  
+
+<|ref|>text<|/ref|><|det|>[[42, 195, 189, 214]]<|/det|>
+Xuanang Zheng  
+
+<|ref|>text<|/ref|><|det|>[[42, 217, 951, 260]]<|/det|>
+Guangdong Provincial Key Laboratory of Biotechnology for Plant Development, School of Life Sciences, South China Normal University  
+
+<|ref|>text<|/ref|><|det|>[[42, 266, 141, 284]]<|/det|>
+Juncai Ma  
+
+<|ref|>text<|/ref|><|det|>[[52, 287, 701, 306]]<|/det|>
+Chinese University of Hong Kong https://orcid.org/0000- 0002- 5693- 1117  
+
+<|ref|>text<|/ref|><|det|>[[42, 312, 105, 330]]<|/det|>
+Jing Li  
+
+<|ref|>text<|/ref|><|det|>[[42, 333, 901, 376]]<|/det|>
+School of Life Sciences, Centre for Cell & Developmental Biology and State Key Laboratory of Agrobiotechnology, The Chinese University of Hong Kong https://orcid.org/0000- 0002- 4060- 1754  
+
+<|ref|>text<|/ref|><|det|>[[42, 380, 133, 398]]<|/det|>
+Siyu Chen  
+
+<|ref|>text<|/ref|><|det|>[[42, 401, 870, 443]]<|/det|>
+MOE Key Laboratory & Guangdong Provincial Key Laboratory of Laser Life Science, College of Biophotonics, South China Normal University  
+
+<|ref|>text<|/ref|><|det|>[[42, 449, 125, 467]]<|/det|>
+Jun Luo  
+
+<|ref|>text<|/ref|><|det|>[[52, 471, 323, 490]]<|/det|>
+South China Normal University  
+
+<|ref|>text<|/ref|><|det|>[[42, 495, 125, 513]]<|/det|>
+Jianxiong Wu  
+
+<|ref|>text<|/ref|><|det|>[[52, 517, 323, 536]]<|/det|>
+South China Normal University  
+
+<|ref|>text<|/ref|><|det|>[[42, 542, 164, 560]]<|/det|>
+Kaiyan Zhang  
+
+<|ref|>text<|/ref|><|det|>[[52, 564, 380, 583]]<|/det|>
+The Chinese University of Hong Kong  
+
+<|ref|>text<|/ref|><|det|>[[42, 588, 188, 607]]<|/det|>
+Chang- lian Peng  
+
+<|ref|>text<|/ref|><|det|>[[52, 610, 323, 628]]<|/det|>
+South China Normal University  
+
+<|ref|>text<|/ref|><|det|>[[42, 634, 164, 653]]<|/det|>
+Yonglun Zeng  
+
+<|ref|>text<|/ref|><|det|>[[52, 655, 945, 676]]<|/det|>
+South China Botanical Garden, Chinese Academy of Sciences https://orcid.org/0000- 0002- 9512- 6487  
+
+<|ref|>text<|/ref|><|det|>[[42, 681, 182, 700]]<|/det|>
+Byung- Ho Kang  
+
+<|ref|>text<|/ref|><|det|>[[52, 702, 701, 722]]<|/det|>
+Chinese University of Hong Kong https://orcid.org/0000- 0002- 4299- 2170  
+
+<|ref|>text<|/ref|><|det|>[[42, 727, 122, 745]]<|/det|>
+Caiji Gao  
+
+<|ref|>text<|/ref|><|det|>[[42, 748, 950, 791]]<|/det|>
+Guangdong Provincial Key Laboratory of Biotechnology for Plant Development, School of Life Sciences, South China Normal University https://orcid.org/0000- 0003- 3958- 4499  
+
+<|ref|>text<|/ref|><|det|>[[42, 796, 128, 814]]<|/det|>
+Jun Zhou  
+
+<|ref|>text<|/ref|><|det|>[[52, 823, 267, 841]]<|/det|>
+zhou.jun@scnu.edu.cn  
+
+<|ref|>text<|/ref|><|det|>[[52, 868, 682, 888]]<|/det|>
+South China Normal University https://orcid.org/0000- 0001- 9655- 6588
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[44, 45, 137, 64]]<|/det|>
+## Keywords:  
+
+<|ref|>text<|/ref|><|det|>[[44, 83, 330, 102]]<|/det|>
+Posted Date: February 2nd, 2024  
+
+<|ref|>text<|/ref|><|det|>[[44, 121, 475, 141]]<|/det|>
+DOI: https://doi.org/10.21203/rs.3.rs- 3878363/v1  
+
+<|ref|>text<|/ref|><|det|>[[42, 158, 914, 202]]<|/det|>
+License: © This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License  
+
+<|ref|>text<|/ref|><|det|>[[42, 219, 535, 239]]<|/det|>
+Additional Declarations: There is NO Competing Interest.  
+
+<|ref|>text<|/ref|><|det|>[[42, 274, 911, 317]]<|/det|>
+Version of Record: A version of this preprint was published at Nature Communications on July 18th, 2025. See the published version at https://doi.org/10.1038/s41467- 025- 62084- 3.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[103, 95, 852, 556]]<|/det|>
+1 ATG8ylation facilitates an ESCRT-independent vacuolar membrane 2 invagination in plants 3 Xuanang Zheng1,4, Juncai Ma2,4, Jing Li2, Siyu Chen1, Jun Luo1, Jianxiong Wu1, Kaiyan 4 Zhang2, Changlian Peng1, Yonglun Zeng3, Byung-Ho Kang2, Caiji Gao1, Jun Zhou1 5 1 Guangdong Provincial Key Laboratory of Biotechnology for Plant Development, School 6 of Life Sciences; MOE Key Laboratory & Guangdong Provincial Key Laboratory of Laser 7 Life Science, College of Biophotonics, South China Normal University, Guangzhou, China 8 2 School of Life Sciences, Centre for Cell & Developmental Biology and State Key 9 Laboratory of Agrobiotechnology, The Chinese University of Hong Kong, Shatin, New 10 Territories, Hong Kong, China 11 3 State Key Laboratory of Plant Diversity and Specialty Crops, South China Botanical 12 Garden, Chinese Academy of Sciences, Guangzhou, China 13 4 These authors contributed equally to this work 14 Correspondence: zhoujun@scnu.edu.cn (J.Z.); gaocaiji@m.scnu.edu.cn (C.G.); 15 bkang@cuhk.edu.hk (B.K.)
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[147, 91, 224, 106]]<|/det|>
+## Abstract  
+
+<|ref|>text<|/ref|><|det|>[[144, 125, 853, 540]]<|/det|>
+ATG8- family proteins have been found to be incorporated into single- membrane structures, a process referred to as non- canonical autophagy. While several physiological roles of non- canonical conjugation of ATG8 (ATG8ylation) have been established, the specific functions of ATG8 on single membrane remain largely elusive. Here, we demonstrate that ionophores induce conjugation of ATG8 to vacuolar membrane to promote invagination in Arabidopsis. Upon monensin treatment, ATG8 is rapidly translocated to the vacuolar membrane, which is reliant on the ATG conjugation system rather than upstream autophagic regulators such as ATG1, ATG9, and phosphoinositide 3- kinase (PI3K). Moreover, inhibiting reactive oxygen species (ROS) generation or V- ATPase activity greatly impedes the targeting of ATG8 to the vacuolar membrane. Intriguingly, the recruitment of ATG8 to the tonoplast exhibits a pronounced enhancement of invagination and fosters the formation of intraluminal vesicles within the vacuoles. Further analyses elucidate that the topological remodeling of the vacuolar membrane is achieved in a ESCRT machinery- independent manner. Collectively, this study reveals a previously unrecognized role of ATG8ylation in driving the topological transformation of vacuolar membranes in plants.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[148, 91, 192, 106]]<|/det|>
+## Main  
+
+<|ref|>text<|/ref|><|det|>[[145, 125, 852, 561]]<|/det|>
+Autophagy is an evolutionarily conserved mechanism that removes damaged organelles and protein aggregates to maintain cellular homeostasis. Over the past few decades, ground- breaking studies have uncovered autophagy- related genes (ATG) and molecular details of autophagy \(^{1,2}\) . Among them, the ATG8- family proteins serve as critical components of the autophagic machinery, exerting influence in numerous facets, including cargo selection, phagophore expansion, autophagosome closure, and fusion with vacuole/lysosome \(^{3,4}\) . Interestingly, emerging lines of evidence demonstrate that ATG8 can also be conjugated with various single- membrane structures, such as the Golgi apparatus \(^{5,6}\) , phagosome \(^{7- 9}\) , endosome \(^{10}\) and lysosome \(^{11}\) , leading to alternative pathways collectively known as non- canonical autophagy. This covalent lipidation of ATG8, termed 'ATG8ylation', has recently garnered attention as a putative membrane stress signal \(^{12}\) , displaying broad functional significance in the immune response \(^{7,8,13}\) , antigen presentation \(^{14}\) , cancer and neurodegeneration \(^{15}\) . In plants, despite recent studies have revealed the translocation of ATG8 to swollen Golgi cisternae to aid its reassembly after heat stress \(^{5,16}\) , our understanding as to non- canonical autophagy and roles of ATG8ylation in the pathway remains limited.  
+
+<|ref|>text<|/ref|><|det|>[[145, 580, 852, 905]]<|/det|>
+Recent investigations from non- plant systems have made significant advances in elucidating the regulatory mechanisms of non- canonical autophagy. Generally, the vacuolar- type ATPase (V- ATPase) has been found to directly recruit ATG16L1 (ATG16 in plants) to mediate lipidation of ATG8- family proteins to single membrane structures \(^{6- 8,17}\) . Deletion of the C- terminal WD40 domain or a single point mutation (K490A) in ATG16L1 impairs its functionality specifically in non- canonical autophagy, while exerting no influence on macroautophagy \(^{17,18}\) . In agreement with this, the inhibition of V- ATPase using Bafilomycin A1 disrupts the conjugation of ATG8 to single membrane structures. Thus, the V- ATPase- ATG16L1 axis is characterized as a universal mechanism governing non- canonical autophagy \(^{8,18,19}\) . V- ATPase is a highly conserved proton pump among eukaryotes responsible for acidification in various endomembrane compartments such as endosomes and vacuoles/lysosomes \(^{20}\) . Isoforms of the subunit a in the membrane- integral
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[144, 88, 852, 193]]<|/det|>
+V0 subcomplex dictate the diverse subcellular localization of the V- ATPase. For example, VHA- a1 targets the V- ATPase to the trans- Golgi network (TGN)/early endosomes, while VHA- a2 and VHA- a3 are localized to the tonoplast in Arabidopsis \(^{21}\) . Currently, the role of V- ATPase in regulating non- canonical autophagy in plants remain largely unexplored.  
+
+<|ref|>text<|/ref|><|det|>[[144, 208, 852, 590]]<|/det|>
+One of the critical functions of ATG8 is the recognition and binding of cargoes/receptors, primarily facilitated through the interaction of ATG8- interacting motifs (AIMs) with the AIMs docking site (ADS) on ATG8 proteins \(^{22}\) . From the topological orientation, the incorporation of ATG8 proteins on the single- membrane vesicles seems to take place solely on their side facing the cytosol. In this context, it is speculated that ATG8 on these single- membrane structures is unlikely to sequester cargoes from the cytosol as it does in classical autophagosomes \(^{23}\) . However, the specific functions associated with the non- canonical conjugation of ATG8 have not been clearly established. In this study, we demonstrated that ionophores promoted rapid translocation of ATG8 to the tonoplast, which remarkably enhanced vacuolar membrane invagination. In addition, the formation of ATG8- positive intraluminal vesicles in the vacuole was not relied on the ESCRT machinery. Our research unveiled new functionalities of ATG8 in influencing membrane curvature, providing a model for further investigation into the diverse roles of ATG8 in single membrane structures in plants.  
+
+<|ref|>sub_title<|/ref|><|det|>[[148, 609, 215, 624]]<|/det|>
+## Results  
+
+<|ref|>sub_title<|/ref|><|det|>[[147, 645, 592, 663]]<|/det|>
+## Ionophores induce conjugation of ATG8 to tonoplast  
+
+<|ref|>text<|/ref|><|det|>[[144, 680, 852, 895]]<|/det|>
+In a previous study, we found that ATG8- family proteins concentrate to swollen Golgi stacks following acute heat stress \(^{5}\) . This finding prompted us to investigate whether the disruption of the Golgi could induce a similar response. We conducted a screening of several chemicals including brefeldin A, concanamycin A (ConcA), and monensin, which are known to disrupt the Golgi structure \(^{24, 25}\) . Upon treatment with monensin at concentrations exceeding 10 μM, we discerned membranous structures exhibiting YFP- ATG8e fluorescence (Fig. 1a). We then examined the pattern changes of ATG8 in response to other carboxylic ionophores (i.e., nigericin and salinomycin). These ionophores share
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[144, 88, 852, 415]]<|/det|>
+similar molecular structures (Fig. S1a), and their carboxyl and hydroxyl groups facilitate the formation of electrically neutral zwitterionic complexes with cations<sup>26</sup>. The resulting chelate complexes exhibit lipid solubility, enabling their diffusion across biological membranes for mediating ion exchange<sup>26</sup>. Intriguingly, localization of GFP- ATG8a on membranous structures matching those after monensin treatment was also observed by incubation with either nigericin or salinomycin (Fig. S1b). Next, taken monensin as an example, the dynamics of ATG8 was characterized by time- lapse confocal imaging. As shown in Fig. 1b, treatment with monensin rapidly induced subcellular alterations in GFP- ATG8a, with obvious membrane- like signal observed within 20 min. Moreover, we assessed the subcellular localization variations among different ATG8 isoforms, and interestingly, all ATG8 isoforms (ATG8a to ATG8i) displayed a comparable response to monensin, forming similar membrane- like structures (Fig. S2).  
+
+<|ref|>text<|/ref|><|det|>[[144, 431, 852, 839]]<|/det|>
+To figure out the subcellular location of ATG8 following monensin treatment, we generated double transgenic lines of ATG8 with different organelle markers. Upon monensin treatment, the fluorescent signals of ATG8 exhibited good colocalization with Vamp711- mCherry (tonoplast) as well as Rab7- GFP (late endosome), while no significant colocalization was observed with other endomembrane markers, including YFP- ARA7 (early endosome), VHA- a1- RFP (TGN) and GFP- SYP32 (cis- Golgi) (Fig. 1c- h). It is noteworthy that monensin treatment caused intracellular aggregations of both VHA- a1- RFP and GFP- SYP32 (Fig. 1f- g). Such aggregates were further characterized as clusters of dilated vesicles derived from the Golgi/TGN complexes by transmission electron microscopy (TEM) (Fig. S3a). By conducting three- dimensional (3D) electron tomography analysis, we were able to discern residual Golgi cisternae that remain partially undeformed, in direct proximity to the swollen vesicles (Fig. S3b). However, no ATG8 was associated with the swollen Golgi membrane unlike plant cells challenged by acute heat stress<sup>5</sup>. These results indicated that ATG8 selectively incorporated into the vacuolar membrane following treatment with monensin.  
+
+<|ref|>sub_title<|/ref|><|det|>[[145, 859, 697, 877]]<|/det|>
+## ATG8 targeted to tonoplast relies on the ATG conjugation system  
+
+<|ref|>text<|/ref|><|det|>[[144, 895, 852, 913]]<|/det|>
+In canonical autophagy, several core complexes such as the ATG1 complex, ATG9 vesicles,
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[144, 88, 852, 330]]<|/det|>
+and phosphoinositide 3- kinase (PI3K) complex synergistically regulate the formation of autophagosomes<sup>2</sup>. To test whether these upstream regulators were involved in the conjugation of ATG8 to tonoplast, we evaluated the subcellular location of GFP- ATG8a in atg1abct, atg11- 1, and atg9- 4 mutants. Unexpectedly, after treatment with monensin, an obvious vacuolar membrane signal can still be observed in these mutant lines (Fig. 2a, b). Similarly, inhibition of PI3K activity with wortmannin did not prevent monensin- induced translocation of ATG8 to vacuolar membranes (Fig. 2b). Therefore, the core upstream autophagy regulators, including ATG1, ATG11, ATG9, and PI3K, appear to be dispensable for the targeting of ATG8 to the tonoplast.  
+
+<|ref|>text<|/ref|><|det|>[[144, 348, 852, 673]]<|/det|>
+The C- terminal cleavage of ATG8 at a conserved glycine residue by the cysteine protease ATG4 is a prerequisite for lipidation<sup>27</sup>. Using YFP- ATG8a(G132A) x mCherry- ATG8f double transgenic plants, we analyzed the impact of point mutation of ATG4 recognition site on ATG8 localization. Noteworthily, in contrast to mCherry- ATG8f, the recruitment of YFP- ATG8a(G132A) to the tonoplast was completely abolished upon monensin treatment (Fig. 2c). Next, we evaluated alterations in the localization of ATG8 in mutants defective in ATG conjugation system, specifically atg5- 1, atg7- 2, and atg16- c1. Monensin treatment did not affect the cytosolic distribution of ATG8 in atg5- 1, atg7- 2, or atg16- c1 mutants (Fig. 2d). Furthermore, the application of monensin significantly enhanced the lipidation level of ATG8 in the Col- 0 and atg11- 1 mutants, while no such increase was observed in atg5- 1 and atg16- c1 mutants (Fig. 2e, f). Collectively, these results indicate that the ATG conjugation system is critical for the targeting of ATG8 to vacuolar membranes.  
+
+<|ref|>sub_title<|/ref|><|det|>[[145, 691, 850, 736]]<|/det|>
+## Reactive oxygen species and V-ATPase are required for ATG8 translocation to tonoplast  
+
+<|ref|>text<|/ref|><|det|>[[144, 755, 852, 913]]<|/det|>
+Previous studies have shown that cells accumulate a significant amount of reactive oxygen species (ROS) under monensin treatment<sup>28</sup>. To investigate the potential involvement of ROS in monensin- induced targeting of ATG8 to the tonoplast, we assessed ROS generation using a cell- permeant indicator H2DCFDA. Accompanied by the translocation of mCherry- ATG8f to the vacuolar membrane, a robust burst of ROS was observed in the root cells (Fig. 3a). Notably, the exogenous application of ascorbic acid (AsA), which
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[144, 88, 852, 219]]<|/det|>
+eliminates ROS<sup>29</sup>, resulted in a great reduction in ATG8 binding to the tonoplast followed by monensin treatment (Fig. 3b). Interestingly, pretreatment with diphenyleneiodonium (DPI), an inhibitor of NADPH oxidase<sup>30</sup>, markedly attenuated the recruitment of GFP- ATG8a to the vacuolar membrane (Fig. 3c), indicating the requirement of NADPH oxidase- derived ROS for ATG8 conjugation to the tonoplast upon monensin treatment.  
+
+<|ref|>text<|/ref|><|det|>[[144, 236, 852, 728]]<|/det|>
+In mammalian cells, V- ATPase is considered as a universal regulator for the conjugation of ATG8- family proteins to single membranes<sup>8, 19</sup>. To test whether the V- ATPase was also involved in ATG8 targeting to the tonoplast, we firstly investigated the subcellular localization of GFP- ATG8a in the presence ConcA, a specific inhibitor of V- ATPase<sup>31</sup>. As shown in Fig. 3d, the localization of GFP- ATG8a to vacuolar membranes was completely blocked by ConcA. Correspondingly, the treatment with ConcA resulted in a significant reduction in the lipidation form of ATG8 following monensin treatment (Fig. 3e,f). Next, ATG8 targeting to tonoplast was studied in the vha- a2 vha- a3 double mutant, which lacks the tonoplast- localized V- ATPase<sup>32, 33</sup>. Under normal physiological conditions, a large amount of mCherry- ATG8f punctate structures were observed within the vacuoles of the elongation regions of vha- a2 vha- a3 mutants (Fig. S4a). This phenomenon is likely attributed to vacuolar alkalization resulting from the deficiency of V- ATPase<sup>32</sup>, which subsequently leads to reduced protease activities. Noteworthily, in comparison to wild- type Col- 0 plants, the vha- a2 vha- a3 mutant failed to exhibit the conjugation of mCherry- ATG8f to vacuolar membranes after treatment with monensin (Fig. 3g,h). Taken together, these results demonstrated the essential requirement of both NADPH oxidase- derived ROS and V- ATPase for the incorporation of ATG8 into vacuolar membranes, resembling the mechanisms observed in non- canonical autophagy processes in mammalian cells<sup>8</sup>.  
+
+<|ref|>sub_title<|/ref|><|det|>[[147, 747, 625, 764]]<|/det|>
+## ATG8 enhances the invagination of vacuolar membranes  
+
+<|ref|>text<|/ref|><|det|>[[147, 784, 852, 913]]<|/det|>
+To gain insights into the potential roles of ATG8 in tonoplast dynamics, we examined vacuolar morphology using GFP- ATG8a x Vamp711- mCherry double transgenic plants. After monensin treatment, massive vesicles labeled with both GFP- ATG8a and Vamp711- mCherry appeared in the vacuoles, some of which were attached to the vacuolar membrane, while others were randomly distributed within the vacuolar lumen (Fig. 4a). To
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[144, 88, 852, 470]]<|/det|>
+further obtain the ultrastructure of the vacuoles, we subjected seedlings treated with monensin to high- pressure freeze fixation for TEM analysis. Interestingly, after monensin treatment, numerous micrometer- sized vesicles containing cytoplasmic components accumulated inside the vacuole (Fig. 4b). Further analysis using 3D electron tomography revealed that these vesicles, formed by invaginations of the vacuolar membrane, not only exhibited spherical shapes but also included some large tubular structures (Fig. 4c, Supplementary Video 1). It is worth mentioning that some of these vesicles also contained organelles such as mitochondria and endoplasmic reticulum (Fig. 4c). Additionally, the time- lapse confocal imaging further showed that the vacuolar membrane was highly dynamic, with masses of invagination occurring (Fig. 4d, Supplementary Video 2). By contrast, inhibition of GFP- ATG8a targeting to vacuolar membranes by application with ConcA obviously decreased the vacuolar invaginations (Fig. 4e). Consistently, a reduction in vacuolar membrane invaginations was also observed in atg5- 1 mutant (Fig. 4f), indicating that the incorporation of ATG8 facilitates the invagination of tonoplast.  
+
+<|ref|>text<|/ref|><|det|>[[144, 487, 852, 896]]<|/det|>
+It is well characterized that the endosomal sorting complexes required for transport (ESCRT) plays crucial roles in membrane curvature and the final fission process<sup>34</sup>. To determine whether ESCRT was involved in formatting intraluminal vesicles, we investigated the subcellular location of FYVE domain protein required for endosomal sorting 1 (FREE1), a plant- specific ESCRT component that regulates the closure of autophagosomes via direct interaction with ATG8<sup>4</sup>. Intriguingly, GFP- FREE1 did not localize to the vacuolar membrane as clearly as mCherry- ATG8f after treatment with monensin (Fig. 4g). To further figure out the impact of monensin on the vacuolar morphology in free1 mutants, we introduced YFP- ATG8e into heterozygous T- DNA insertional mutants free1(+/-) and screened the albino seedlings (i.e. the homozygous free1(- /- )<sup>34</sup>) to conduct subsequent confocal analyses. The time- lapse imaging showed that some small vesicles were still generated and closely associated with the vacuolar membrane in the free1(- /-) mutant (Fig. 4h, Supplementary Video 3). Notably, these vesicles exhibited a smaller size within the vacuolar lumen compared to the wild- type counterparts, which may be attributed to the extensive fragmentation of vacuoles in the
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[145, 89, 851, 164]]<|/det|>
+free1(- /-) mutant<sup>34</sup>. The reduced volume of the smaller vacuole may limit the size of the invaginated vesicles. Collectively, these results indicated that the ATG8- mediated invagination of the vacuolar membrane may operate independently of ESCRT functionality.  
+
+<|ref|>sub_title<|/ref|><|det|>[[147, 183, 245, 199]]<|/det|>
+## Discussion  
+
+<|ref|>text<|/ref|><|det|>[[144, 218, 852, 543]]<|/det|>
+In the process of canonical autophagy, ATG8 performs diverse and essential functions, encompassing cargo recognition and binding, membrane tethering and extension, as well as autophagosome closure and maturation<sup>2, 4, 8</sup>. However, recent investigations have unveiled an intriguing aspect wherein ATG8 demonstrates the ability to associate with single- membrane structures independently of the classical upstream regulatory factors involved in autophagy<sup>5, 7- 9, 11, 18</sup>. Recruitment of ATG8 onto single- membrane vesicles is generally believed to result in eventual degradation<sup>23</sup>. Currently, the specific roles played by ATG8 in these single- membrane structures remain largely unknown. In this study, we have elucidated that the conjugation of ATG8 to vacuolar membranes, induced by ionophores, actively promoted invagination and the formation of intraluminal vesicles. These findings provide valuable insights into the molecular activities exercised by ATG8 in regulating membrane dynamics and morphology.  
+
+<|ref|>text<|/ref|><|det|>[[144, 561, 853, 914]]<|/det|>
+In mammalian cells, the V- ATPase is generally considered to be a universal regulator of non- canonical autophagy<sup>8, 19</sup>. It recruits ATG16 to assemble into a functional E3 complex (known as the ATG12- ATG5- ATG16 complex), which catalyzes the lipidation of ATG8 on single membranes. In consistent, our pharmacological and genetic studies demonstrated that inhibiting V- ATPase significantly impeded the targeting of ATG8 to tonoplast (Fig. 3d,h). This finding suggested that plants share a common mechanism with animals for inducing non- canonical autophagy. In Arabidopsis, the V- ATPase exhibits dual subcellular localization, which is regulated by distinct isoforms of the subunit a. VHA- a1 directs it to the TGN/EE compartments, while VHA- a2 and VHA- a3 are predominantly localized to the tonoplast<sup>20, 21</sup>. Notably, monensin treatment resulted in the disruption of TGN/EE morphology, leading to the formation of vesicular structures with a bubble- like appearance (Fig. 1f and Fig. S3). However, this cellular perturbation did not elicit the translocation of ATG8 to the swollen TGN/EE membrane (Fig. 1f). Conversely, our previous investigations
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[144, 90, 852, 247]]<|/det|>
+unveiled that extremely high temperatures can evoke the translocation of ATG8 to the dilated Golgi apparatus rather than the vacuolar membrane<sup>5</sup>. Thus, although both the TGN and tonoplast harbor V- ATPase, they are possibly governed by discrete regulatory mechanisms. Such regulatory diversification may facilitate the selective targeting of ATG8 towards distinct single- membrane organelles under disparate environmental stimuli conditions.  
+
+<|ref|>text<|/ref|><|det|>[[144, 262, 852, 899]]<|/det|>
+Membrane curvature exerts a substantial influence on the structural configuration of the cell membrane, contributing significantly to its overall shape and organization. In vitro reconstitution investigations employing purified proteins and synthetic giant unilamellar vesicles have provided valuable insights into the multifaceted membrane- associated functionalities facilitated by ATG8 conjugation, such as tethering, hemi- fusion, tubulation, perturbation, and in/out- bud<sup>35- 38</sup>. The direction of membrane curvature induced by the covalent anchorage of ATG8 is predominantly determined by the difference in the membrane area between the outer and inner layers of the lipid bilayer<sup>35, 36</sup>. It is noteworthy that ATG8 conjugation is inadequate to initiate membrane invagination. Instead, it relies on the recruitment of other proteins within the ATG conjugation system, including ATG3, ATG7, and ATG12- ATG5- ATG16, to provide the necessary driving force for the induction of in- bud formation<sup>35</sup>. However, under monensin treatment, the subcellular localization of ATG16, ATG5, and ATG7 to the vacuolar membrane was not observed (Fig. S5), suggesting the potential involvement of other proteins in orchestrating the membrane scaffold organization. Notably, recent findings demonstrate that ATG8 can directly interact with the ESCRT component FREE1 to participate in the closure of autophagosomes<sup>4</sup>. However, in the presence of monensin, FREE1 was not recruited to the vacuolar membrane by ATG8, and the formation of invaginated vesicles was still observed in the vacuoles of free1(- /-) mutant, albeit smaller in size (Fig. 4g,h). Therefore, we speculate that ESCRT may not directly participate in ATG8- mediated vacuolar membrane invagination. Nevertheless, it is noteworthy that the intraluminal vesicles in the free1(- /-) mutant exhibited a prolonged adherence to the vacuolar membrane (Fig. 4h). This suggested a potential reliance on ESCRT- mediated scission processes for the detachment of invaginated vesicles from the
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[144, 90, 850, 135]]<|/det|>
+vacuolar membrane. Undoubtedly, further experimental evidences are required to substantiate this hypothesis.  
+
+<|ref|>text<|/ref|><|det|>[[144, 153, 852, 504]]<|/det|>
+ATG8 shares structural and modification similarities with ubiquitin, as both molecules undergo sequential enzymatic reactions involving E1, E2, and E3 enzymes. However, their respective targets differ, with ubiquitin primarily marking proteins and ATG8 specifically targeting membranes. Like the role of ubiquitination as a general signal for protein degradation, mounting evidence suggests that ATG8ylation also serves as a signaling mechanism in response to membrane stress events<sup>12</sup>. Ionophores disrupt membrane ion permeability, resulting in the inability of the vacuolar membrane to maintain a normal proton gradient<sup>26</sup>. Concurrently, this process triggers a burst of ROS, which could potentially induce oxidative damage to the membrane lipids (Fig. 3a). In this context, ATG8-mediated vacuolar membrane invagination may assist in the clearance of damaged membranes, thereby counteracting osmotic stress caused by monensin. In the future, it will be of interest to assess and quantify the damages inflicted on vacuolar membrane lipids, which would contribute to better understanding of the functional consequences of ATG8ylation.  
+
+<|ref|>text<|/ref|><|det|>[[144, 523, 852, 737]]<|/det|>
+Collectively, our results presented a non- canonical autophagic function of ATG8 in the field of plants. Under monensin treatment, ATG8 conjugation to tonoplast is rely on the ATG conjugation system rather than the upstream autophagic regulators. The association of ATG8 exerts a pronounced influence on membrane curvature, actively promoting invagination processes and facilitating the subsequent development of intraluminal vesicles within the vacuoles (Fig. S6). This study broadened the scope of understanding regarding the diverse functions of the core autophagy protein ATG8 in plant cells, extending beyond its canonical role in autophagy.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[147, 90, 223, 106]]<|/det|>
+## Methods  
+
+<|ref|>sub_title<|/ref|><|det|>[[147, 127, 470, 144]]<|/det|>
+## Plant materials and growth conditions  
+
+<|ref|>text<|/ref|><|det|>[[145, 152, 852, 590]]<|/det|>
+The autophagy mutants including atg5- 139, atg7- 239, atg16- c15 and atg11- 140, as well as the vha- a2 vha- a33 double mutants were described previously. The single transgenic plants GFP- ATG8a41, mCherry- ATG8f42, YFP- ATG8b/c/d/e/g/h/i5, YFP- ATG16s, ATG5- GFP5, ATG7- GFP5, GFP- ATG8a/atg1abcf41, GFP- ATG8a/atg5- 15, YFP- ATG8e/atg7- 25, GFP- ATG8a/atg9- 441, GFP- ATG8a/atg11- 140, GFP- ATG8a/atg16- c15 and GFP- FREE134 were reported previously. The double transgenic plants YFP- ATG8a(G132A) x mCherry- ATG8f5, GFP- ATG8a x Vamp711- mCherry5, Rab7- GFP x mCherry- ATG8f5, YFP- ARA7 x mCherry- ATG8f5, GFP- ATG8a x VHA- a1- RFP5, GFP- SYP32 x mCherry- ATG8f5 were described previously. The GFP- FREE1 x mCherry- ATG8f, mCherry- ATG8f/vha- a2 vha- a3 and Vamp711- mCherry/atg5- 1 were obtained by cross- pollination, and the homozygous mutant backgrounds were verified by PCR (Fig. S4b). ATG7- GFP was cloned into the pCAMBIA1300 vector, and the transgenic plant was generated through floral dip. The seeds were surface- sterilized with 70% (v/v) ethanol containing 0.05% Triton X- 100 and then sown on 1/2 Murashige and Skoog (MS) plates. After being kept at 4°C for 48 h, the plates were transferred to a culture chamber maintained at 22°C with a photoperiod of 16 h light and 8 h dark, and cultivate for 5 d for subsequent experiments.  
+
+<|ref|>sub_title<|/ref|><|det|>[[148, 608, 315, 624]]<|/det|>
+## Chemical treatment  
+
+<|ref|>text<|/ref|><|det|>[[145, 634, 852, 904]]<|/det|>
+The ionophores including monensin sodium salt (MCE, #HY- N0150), salinomycin sodium salt (MCE, #HY- 17439), and nigericin sodium salt (MCE, #HY- 100381) were prepared as 10 mM stock solutions in ethanol and stored at - 20°C. The 5- day- old seedlings were immersed in liquid 1/2MS medium containing 0.2% ethanol (control) or 20 μM monensin for 1 h, and then the plant materials were subjected to confocal imaging. The treatment of salinomycin and nigericin is the same as monensin. ConcA (MCE, #HY- N1724) and wortmannin (MCE, #HY- 10197) stock solutions were prepared at concentrations of 1 mM and 16.5 mM, respectively, in DMSO and stored at - 20°C. ConcA (1 μM) or wortmannin (16.5 μM) was pre- incubated for 10 min and then added with 20 μM monensin for 1 h, followed by confocal imaging. For the ROS detection, a 1 μM concentration of the ROS
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[144, 88, 852, 191]]<|/det|>
+sensitive dye H2DCFDA (MCE, #HY- D0940) was incubated in darkness for 10 min prior to confocal imaging. L- Ascorbic acid sodium salt (MCE, #HY- B0166A) was freshly prepared in 1/2MS and added 1 h before monensin treatment. DPI (MCE, #HY- 100965) was prepared as 10 mM stock solutions in DMSO and added 0.5 h before monensin treatment.  
+
+<|ref|>sub_title<|/ref|><|det|>[[148, 211, 335, 227]]<|/det|>
+## ATG8 lipidation assay  
+
+<|ref|>text<|/ref|><|det|>[[144, 237, 852, 506]]<|/det|>
+Briefly, 0.2 g of 5- day- old Col- 0, atg5- 1, atg7- 2, atg11- 1, and atg16- c1 seedlings, with or without \(20 \mu \mathrm{M}\) monensin treatment for 1h, were grounded thoroughly in pre- cooled mortar with 1.5 ml of membrane buffer (40 mM HEPES, 1 mM EDTA, 10 mM KCl, 0.4 M Sucrose, pH 7.4) on ice. The crude lysates were collected in 2 ml tubes, then centrifuged at 1000xg for 10 min to remove large cell fragments. The supernatants were transferred and mixed with loading buffer (250 mM Tris- HCl, pH 6.8, 10% (w/v) SDS, 0.5%(w/v) Bromophenol blue, 50% (v/v) Glycerol, 5% (v/v) \(\beta\) - Mercaptoethanol), and boiled at 95 °C for 10 min. The protein solution was subjected to 12% SDS- PAGE and immunoblotted with anti- ATG8 antibody (Agrisera, #AS14 2769). Uncropped western blots are available in supplementary files (Fig. S7).  
+
+<|ref|>sub_title<|/ref|><|det|>[[148, 525, 262, 541]]<|/det|>
+## TEM analysis  
+
+<|ref|>text<|/ref|><|det|>[[144, 551, 852, 905]]<|/det|>
+The TEM assay was performed following our previously established protocols<sup>43, 44</sup>. Briefly, 5- d- old seedlings were germinated on 1/2 MS plate and then treated with or without \(20 \mu \mathrm{M}\) monensin in liquid 1/2 MS before dissecting. For high- pressure freezing, the root tips were collected and immediately frozen with a high- pressure freezer (EM ICE, Leica). For freeze substitution, the root tips were substituted with 2% osmium tetroxide in anhydrous acetone and maintained at \(- 80 ^{\circ} \mathrm{C}\) for 24 hours using an AFS2 temperature- controlling system (Leica). Subsequently, the samples were subjected to three washes with precooled acetone and gradually warmed to room temperature over a period of 60 h. Infiltration with increasing concentrations of EPON resin mix (50% Epon resin monomer, 15% dodecenyl succinic anhydride, and 35% nadic methyl anhydride) was carried out at room temperature. The root tips were then transferred into tin foil molds and polymerized by curing at \(60^{\circ} \mathrm{C}\) for 2 days. The embedded samples were sectioned into 90 nm- thick slices using an ultramicrotome (Leica UC7). Micrographs were acquired using a transmission electron
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[147, 90, 850, 135]]<|/det|>
+microscope (Hitachi H- 7650) operating at 80 kV, coupled with a charge- coupled device (CCD) camera.  
+
+<|ref|>sub_title<|/ref|><|det|>[[148, 155, 355, 172]]<|/det|>
+## 3D electron tomography  
+
+<|ref|>text<|/ref|><|det|>[[147, 182, 852, 395]]<|/det|>
+Electron tomography was conducted using a 200 kV Tecnai F20 electron microscope (FEI Company) following previously established procedures<sup>45</sup>. Briefly, the tilt images were obtained from 250- nm- thick sections across a range of \(- 60^{\circ}\) to \(60^{\circ}\) , with \(1.5^{\circ}\) increments, while the grid was rotated by \(90^{\circ}\) for the collection of the other axis of the tilt image stack. Dual- axis tomograms were generated by utilizing pairs of image stacks with the etomo program of the IMOD software (v.4.11.25). The contours of vacuolar membranes and intraluminal vesicles were manually delineated and subsequently meshed using the 3dmod program within the IMOD software suite.  
+
+<|ref|>sub_title<|/ref|><|det|>[[148, 414, 491, 431]]<|/det|>
+## Confocal imaging and image processing  
+
+<|ref|>text<|/ref|><|det|>[[147, 441, 852, 654]]<|/det|>
+The confocal images were acquired using the Zeiss LSM880 laser scanning confocal system with 63X/1.4 NA or 40X/1.4 NA oil objective. The excitation and emission wavelengths for YFP, GFP and H2DCFDA were 488 nm and 500- 550 nm, respectively. For mCherry and RFP, the excitation and emission wavelengths were 561 nm and 570- 650 nm, respectively. For dual- channel scanning, the "line" scanning mode was used. The images from different channels were exported separately using ZEN2.5 (blue edition) for further analysis. The co- localization analysis was performed using the PSC plugin in Image J software (NIH).  
+
+<|ref|>sub_title<|/ref|><|det|>[[148, 673, 466, 690]]<|/det|>
+## Quantification and statistical analysis  
+
+<|ref|>text<|/ref|><|det|>[[147, 700, 852, 829]]<|/det|>
+All experiments were repeated at least three times with consistent results. The co- localization ratio and western band intensities were quantified using Image J software (NIH). Charting and statistical analysis were performed using GraphPad Prism 8 software. The \(P\) values were determined with two- tailed unpaired Student's \(t\) - tests, and the asterisks represent significance levels (ns, not significant; \(*P < 0.05\) ; \(***P < 0.001\) ).  
+
+<|ref|>sub_title<|/ref|><|det|>[[148, 849, 316, 865]]<|/det|>
+## Acknowledgements  
+
+<|ref|>text<|/ref|><|det|>[[147, 886, 850, 903]]<|/det|>
+We appreciate Prof. Zhenhua Zhang (Hunan Agricultural University) for providing us with
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[144, 89, 852, 301]]<|/det|>
+the vha- a2 vha- a3 double mutants. This work was supported by grants from the National Natural Science Foundation of China (32061160467, 31870171) and Fok Ying- Tong Education Foundation for Young Teachers in the Higher Education Institutions of China (171014) to C.G., the National Science Foundation of China (31600288) and the Basic Research Program of Guangzhou (202201010508) to J.Z., and Hong Kong Research Grant Council (GRF14113921, GRF14121019, GRF14109222, N_CUHK462/22, and C4002- 20W) to B- H.K. We would like to acknowledge the Open Fund of MOE Key Laboratory of Laser life Science and Institute of Laser Life Science.  
+
+<|ref|>sub_title<|/ref|><|det|>[[149, 322, 321, 338]]<|/det|>
+## Competing interests  
+
+<|ref|>text<|/ref|><|det|>[[149, 350, 494, 366]]<|/det|>
+The authors declare no competing interests.  
+
+<|ref|>sub_title<|/ref|><|det|>[[149, 387, 266, 403]]<|/det|>
+## Contributions  
+
+<|ref|>text<|/ref|><|det|>[[147, 414, 851, 515]]<|/det|>
+J.Z., J.M., and C.G. designed the experiments. X.Z., J.M., J.Li, S.C., J.Luo, J.W., K.Z., and J.Z. performed the experiments. X.Z., J.M., Y.Z., B- H.K., C.G., and J.Z. analyzed the data. J.M., J.Li., K.Z., and B- H.K. contributed to the TEM analysis. J.Z., X.Z., J.M., C.P., Y.Z., B- H.K., and C.G. wrote and edited the manuscript. All authors reviewed the manuscript.  
+
+<|ref|>sub_title<|/ref|><|det|>[[148, 535, 247, 551]]<|/det|>
+## References  
+
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+1. Noda, N.N. & Inagaki, F. Mechanisms of Autophagy. Annu Rev Biophys 44, 101-122 (2015).  
+2. Li, H. et al. Shedding Light on the Role of Phosphorylation in Plant Autophagy. FEBS Lett 596, 2172-2185 (2022).  
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+4. Zeng, Y. et al. The plant unique ESCRT component FREE1 regulates autophagosome closure. Nat Commun 14, 1768 (2023).  
+5. Zhou, J. et al. A non-canonical role of ATG8 in Golgi recovery from heat stress in plants. Nat Plants 9, 749-765 (2023).  
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+10. Jia, M. et al. Noncanonical ATG8-ABS3 interaction controls senescence in plants.
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+<--- Page Split --->
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+31. Yu, J. & Zhou, J. Vacuolar accumulation and colocalization is not a proper criterion for cytoplasmic soluble proteins undergoing selective autophagy. Plant Signal Behav 16, 1932319 (2021).
+32. Krebs, M. et al. Arabidopsis V-ATPase activity at the tonoplast is required for efficient nutrient storage but not for sodium accumulation. Proc Natl Acad Sci U S A 107, 3251-3256 (2010).
+33. Liang, G., Song, H., Xiao, Y. & Zhang, Z. Ammonium Accumulation Caused by Reduced Tonoplast V-ATPase Activity in Arabidopsis thaliana. Int J Mol Sci 22 (2020).
+34. Gao, C. et al. A Unique Plant ESCRT Component, FREE1, Regulates Multivesicular Body Protein Sorting and Plant Growth. Curr Biol 24, 2556-2563 (2014).
+35. Alam, J.M. et al. Complete set of the Atg8-E1-E2-E3 conjugation machinery forms an interaction web that mediates membrane shaping. Nat Struct Mol Biol (2023).
+36. Maruyama, T. et al. Membrane perturbation by lipidated Atg8 underlies autophagosome biogenesis. Nat Struct Mol Biol 28, 583-593 (2021).
+37. Nakatogawa, H., Ichimura, Y. & Ohsumi, Y. Atg8, a Ubiquitin-like Protein Required for Autophagosome Formation, Mediates Membrane Tethering and Hemifusion. Cell 130, 165-178 (2007).
+38. Wang, X. et al. Membrane Morphology Is Actively Transformed by Covalent Binding of the Protein Atg8 to PE-Lipids. PLoS ONE 9 (2014).
+39. Yin, R. et al. Up-regulation of autophagy by low concentration of salicylic acid delays methyl jasmonate-induced leaf senescence. Sci Rep 10, 11472 (2020).
+40. Li, F., Chung, T. & Viestra, R.D. AUTOPHAGY-RELATED11 plays a critical role in general autophagy- and senescence-induced mitophagy in Arabidopsis. Plant Cell 26, 788-807 (2014).
+41. Huang, X. et al. Genetic Analyses of the Arabidopsis ATG1 Kinase Complex Reveal Both Kinase-Dependent and Independent Autophagic Routes during Fixed-Carbon Starvation. Plant Cell 31, 2973-2995 (2019).
+42. Zhuang, X. et al. A BAR-domain protein SH3P2, which binds to phosphatidylinositol 3-phosphate and ATG8, regulates autophagosome formation in Arabidopsis. Plant Cell 25, 4596-4615 (2013).
+43. Kang, B.H. Electron microscopy and high-pressure freezing of Arabidopsis. Methods Cell Biol 96, 259-283 (2010).
+44. Ma, J. et al. Friendly mediates membrane depolarization-induced mitophagy in Arabidopsis. Curr Biol 31, 1931-1944 (2021).
+45. Toyooka, K. & Kang, B.H. Reconstructing plant cells in 3D by serial section electron tomography. Methods Mol Biol 1080, 159-170 (2014).
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[152, 90, 835, 636]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[145, 646, 852, 916]]<|/det|>
+<center>Fig. 1 Monensin induces the translocation of ATG8 to the tonoplast. a The impact of different concentrations of monensin on the subcellular localization of YFP-ATG8e. 5-day-old YFP-ATG8e transgenic seedlings were treated with different concentrations of monensin (0, 5, 10, 20, 40 μM) in 1/2MS liquid medium for 1 h, followed by confocal microscopy observation. Scale bar, 20 μm. b Time series analysis of the dynamics of GFP-ATG8a in response to monensin (20 μM). Time is presented in minutes. Scale bar, 10 μm. c-g Colocalization analyses between ATG8 and the tonoplast marker VAMP711-mCherry (c), the late endosome marker Rab7-GFP (d), the early endosome marker YFP-ARA7 (e), the TGN marker VHA-a1-RFP (f), as well as the cis-Golgi marker GFP-SYP32 (g). Scale bars in c-g, 20 μm. h Quantification of the colocalization ratios shown in c-g. The Pearson </center>
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[144, 88, 852, 196]]<|/det|>
+correlation (PSC) coefficient was analyzed by ImageJ with the PSC colocalization plugin. The data represent means ± s.d. \(n = 6\) confocal images ( \(112.5 \mu m \times 112.5 \mu m\) ) of individual roots. Similar confocal imaging results were obtained from at least six individual roots, with three replicates.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[147, 88, 850, 545]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[147, 555, 850, 579]]<|/det|>
+<center>Fig. 2 Translocation of ATG8 to tonoplast requires the ATG conjugation system. a </center>  
+
+<|ref|>text<|/ref|><|det|>[[145, 580, 852, 907]]<|/det|>
+The impact of monensin on the subcellular localization of GFP- ATG8a in ATG1 complex mutants. b The impact of mutation of ATG9 or inhibition of PI3K activity on the subcellular localization of GFP- ATG8a under monensin treatment. c Analysis of the impact of ATG4 on the subcellular localization of YFP- ATG8a. d Effect of mutation in ATG5, ATG7, and ATG16 genes on the subcellular localization of ATG8 under monensin treatment. 5- day- old GFP- ATG8a/atg1abct, GFP- ATG8a/atg11- 1, GFP- ATG8a/atg9- 4, GFP- ATG8a/atg5- 1, YFP- ATG8e/atg7- 2 and YFP- ATG8a(G132A) x mCherry- ATG8f double transgenic seedlings were treated with \(20\mu \mathrm{M}\) monensin for 1 hour, followed by confocal microscopy observation. Wortmannin (16.5 \(\mu \mathrm{M}\) ) was pre- incubated for 10 minutes and then added with \(20\mu \mathrm{M}\) monensin for 1 hour, followed by confocal imaging. Scale bars in a- d, \(20\mu \mathrm{m}\) . Similar confocal imaging results were obtained in at least six individual roots with three replicates. e- h The impact of monensin on ATG8 lipidation in wild- type Col- 0 and autophagy mutants
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[144, 88, 852, 222]]<|/det|>
+including atg11- 1, atg7- 2, atg5- 1 and atg16- c1. The ratios \((n = 3)\) between the lipidation form ATG8 and actin was quantified with ImageJ (f and h). Asterisk indicated unknown band. Mon, Monensin. Data are mean ± s.d. Significance analysis using unpaired twosided Student's \(t\) - test. The immunoblotting assays were independently replicated three times with consistent results.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[144, 87, 847, 680]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[145, 683, 850, 894]]<|/det|>
+<center>Fig. 3 NADPH oxidase-derived ROS and V-ATPase are required for ATG8 translocation to the tonoplast. a Detection of ROS generation after monensin treatment. 5-day-old mCherry-ATG8f seedlings were subjected to monensin treatment at a concentration of \(20\mu \mathrm{M}\) . The ROS-sensitive dye H2DCF-DA (1 \(\mu \mathrm{M}\) ) was incubated 10 min prior to confocal imaging. The images were shown with LUT pseudocolor scale (Rainbow RGB). Scale bar, \(50\mu \mathrm{m}\) . b The ROS scavenger ascorbic acid (AsA) reduced GFP-ATG8a response to monensin. The left schematic diagram illustrated the timing of addition of AsA and the subsequent monensin treatment. Scale bar, \(20\mu \mathrm{m}\) . c Treatment with </center>
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[144, 88, 852, 358]]<|/det|>
+diphenyleneiodonium chloride (DPI) inhibited GFP- ATG8a translocation to the tonoplast. The schematic diagram on the left illustrated the timing of DPI addition and the subsequent monensin treatment. Scale bar, \(20 \mu \mathrm{m}\) . d Pretreatment of ConcA inhibited the translocation of GFP- ATG8a to tonoplast. Scale bar, \(20 \mu \mathrm{m}\) . e Western blotting analysis of the effect of ConcA on the ATG8 lipidation. f Statistical analysis of the ratio of lipidation form ATG8 to ATG8 in (e). g A schematic diagram showing the structure of V- ATPase. The subunit a isoforms VHA- a2 and VHA- a3 are specifically located at vacuolar membranes. h Monensin- induced the translocation of GFP- ATG8a to tonoplast was abolished in vha- a2vha- a3 double mutant. Scale bar, \(20 \mu \mathrm{m}\) . Similar confocal imaging results were obtained in at least six individual roots with three replicates.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[148, 90, 845, 750]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[147, 757, 851, 914]]<|/det|>
+<center>Fig. 4 ATG8 facilitates the intralumenal vesicles formation in vacuoles. a 3D projection of GFP-ATG8a and tonoplast marker Vamp711-mCherry after monensin treatment. Arrows indicated representative intralumenal vesicles. Scale bar, \(20 \mu \mathrm{m}\) . b Representative electron microscopic images illustrated the morphological changes in the vacuole following a 1 h treatment with monensin. Invaginating vesicles are denoted by purple triangles. Scale bars, \(1 \mu \mathrm{m}\) . c Electron tomography analysis of the 3D organization </center>
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[144, 88, 853, 444]]<|/det|>
+of vacuole after monensin treatment for 1 h. Purple triangles in the individual slices indicated the presence of invaginating vesicles. 3D models reconstructed from the tomography were presented on the right. Scale bars, 1 μm. d Time-series analysis of the ATG8- positive vesicles invaginated from the vacuolar membrane. A representative invaginating vesicle was indicated by the arrowhead. Scale bar, 10 μm. e Time-series analysis of the effect of ConcA on ATG8- positive vesicles invaginated from the vacuolar membrane. Scale bar, 10 μm. f Time-series analysis of the vacuolar membrane invagination in atg5- 1 mutant upon monensin treatment. Scale bar, 10 μm. g Analysis of the subcellular location of GFP- FREE1 before and after monensin treatment. Scale bar, 20 μm. h Time-series analysis of the invagination of ATG8- positive vesicles in free1(- /-) mutant. The pink arrows indicated a vesicle that adhered inside the vacuolar membrane; white arrows indicated invaginated vesicles. Scale bar, 10 μm. Similar confocal imaging results were obtained in at least six individual roots with three replicates.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[145, 95, 847, 370]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[145, 386, 851, 570]]<|/det|>
+<center>Fig. S1 The effect of different ionophores on the subcellular localization of GFP-ATG8a. a An overview of the chemical structures of monensin sodium, nigericin sodium, and salinomycin sodium. b The formation of membrane-like structures of GFP-ATG8a in response to three ionophores. 5-day-old GFP-ATG8a transgenic seedlings were treated with monensin, nigericin, and salinomycin at a concentration of \(20\mu M\) for 1 hour, followed by confocal microscopy observation. Scale bar, \(20\mu m\) . Similar confocal imaging results were obtained in at least six individual roots with three replicates. </center>
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[147, 90, 846, 595]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[147, 609, 850, 737]]<|/det|>
+<center>Fig. S2 The effects of monensin treatment on different ATG8 isoforms. 5-day-old fluorescent proteins-labeled ATG8 (ATG8a to ATG8i) transgenic seedlings were treated with \(20\mu \mathrm{M}\) monensin for 1 hour, followed by confocal microscopy observation. Scale bar, \(20\mu \mathrm{m}\) . Similar confocal imaging results were obtained in at least six individual roots with three replicates. </center>
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[155, 90, 848, 504]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[145, 516, 852, 812]]<|/det|>
+<center>Fig. S3 Monensin treatment caused Golgi apparatus swelling. a A large number of vesicular structures accumulated in the cytoplasm after treatment with monensin. Five-day-old seedlings were treated for 1 h in a solution containing \(0.2\%\) ethanol (Control) or 20 \(\mu M\) monensin, followed by excision of the root tip for high-pressure freeze-fixation. Abbreviation: CW, cell wall; ER, endoplasmic reticulum; M, mitochondria; N, nucleus; P, plastid; MVB, multi-vesicular body. Similar electron microscopic images were observed in at least 5 different root tip samples. b Electron tomography analysis of the 3D organization of a representative fragmented Golgi apparatus. The red dashed box indicated the reconstructed region. Four representative image planes (N = 11, 50, 100, and 149) were given in the middle region. 3D model reconstructed from the tomography were presented on the right. Scale bars, \(1 \mu m\) . </center>
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[145, 88, 850, 265]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[145, 275, 852, 321]]<|/det|>
+<center>Fig. S4 Characterization of vha-a2 vha-a3 double mutant. a Defective of V-ATPase resulted in the accumulation of mCherry-ATG8f punctate structures within the vacuoles. </center>  
+
+<|ref|>text<|/ref|><|det|>[[145, 330, 852, 430]]<|/det|>
+Confocal imaging was directly performed on 5- day- old transgenic seedlings. Scale bar, 20 \(\mu \mathrm{m}\) . b Validation of the homozygous vha- a2 vha- a3 mutants with PCR. The primer sequence: VHA- a2- LP, ACCTCTGGCTCAAAATTGTCC; VHA- a2- RP, TCCACATGAATATAGCCCAG; VHA- a3- LP, TGGAAATGAGAAGCATGGATC; VHA- a3- RP, ATTGGGTCCATTTTGAAAAGC; LBb1.3, ATTTTGCCGATTTCGGAAC.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[145, 88, 847, 584]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[145, 590, 850, 715]]<|/det|>
+<center>Fig. S5 ATG16, ATG5, and ATG7 did not respond to monensin treatment. Five-day-old YFP-ATG16, ATG5-GFP, and ATG7-GFP transgenic seedlings were treated with \(0.2\%\) ethanol (control) or \(20\mu \mathrm{M}\) monensin for \(1\mathrm{h}\) , followed by confocal observation. Scale bars, \(20\mu \mathrm{m}\) . Similar confocal imaging results were obtained in at least six individual roots with three replicates. </center>
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[150, 84, 850, 303]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[147, 312, 852, 335]]<|/det|>
+<center>Fig. S6 A model highlighting the distinction between canonical autophagy and </center>  
+
+<|ref|>text<|/ref|><|det|>[[145, 343, 853, 666]]<|/det|>
+monensin- induced non- canonical autophagy. In canonical autophagy, the formation of autophagosomes is regulated by coordinated interactions among upstream autophagy factors such as the ATG1 complex, PI3K complex, and ATG9 vesicles. ATG8 is lipidated by the ATG conjugation system and conjugates to the phagophore, aiding in its elongation and closure to form mature autophagosomes. Subsequently, these autophagosomes fuse with the vacuolar membrane, delivering the inclusions for degradation. In contrast, in monensin- induced non- canonical autophagy, the targeting of ATG8 to the vacuolar membrane does not depend on upstream autophagy factors. V- ATPase may recruit ATG12- ATG5- ATG16, similar to the model observed in animals, to catalyze the conjugation of ATG8 to the vacuolar membrane. ATG8 facilitates membrane curvature on the tonoplast and mediates the formation of invaginated vesicles. The ESCRT machinery is potentially involved in the final scission to allow the vesicles to drop into the lumen of the vacuole.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[260, 81, 738, 512]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[145, 517, 559, 535]]<|/det|>
+<center>Fig. S7 Unprocessed western blots and DNA gel. </center>  
+
+<|ref|>text<|/ref|><|det|>[[145, 547, 175, 560]]<|/det|>
+637  
+
+<|ref|>text<|/ref|><|det|>[[145, 573, 778, 618]]<|/det|>
+Supplementary Video 1 3D electron tomography analysis of the invagination of tonoplast after treatment with monensin for 1 h.  
+
+<|ref|>text<|/ref|><|det|>[[145, 636, 790, 680]]<|/det|>
+Supplementary Video 2 Time- lapse confocal imaging of the formation process of invaginated vesicles with GFP- ATG8a x Vamp711- mCherry transgenic plants.  
+
+<|ref|>text<|/ref|><|det|>[[145, 700, 836, 746]]<|/det|>
+Supplementary Video 3 Time- lapse observation of the dynamic of invaginated vesicles in the free1(- /-) mutant.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[43, 43, 312, 71]]<|/det|>
+## Supplementary Files  
+
+<|ref|>text<|/ref|><|det|>[[43, 93, 768, 113]]<|/det|>
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+<|ref|>text<|/ref|><|det|>[[60, 131, 320, 203]]<|/det|>
+SupplementaryVideo1. mov  SupplementaryVideo2. avi  SupplementaryVideo3. avi
+
+<--- Page Split --->

preprint/preprint__c943e9f1be4e28206e9384d35f291fa956f8d435dc4d390d8891f4c83e74c83a/images_list.json

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+[
+  {
+    "type": "image",
+    "img_path": "images/Figure_1.jpg",
+    "caption": "Fig. 1 Illustration of the experimental setup. Laser pulses are focused by an \\(f / 2.3\\) off-axis parabola (OAP) onto thin plastic foil targets, thereby generating a plasma. Protons get accelerated in the plasma and propagate away from the foil. The kinetic energy distribution of the protons was measured by two Thomson parabola spectrometers (TPS15 and TPS45 positioned at \\(15^{\\circ}\\) and \\(45^{\\circ}\\) with respect to the laser propagation direction) and a time-of-flight detector (TOF31 positioned at \\(31^{\\circ}\\) ). The spatial proton beam profile was characterised either by an imaged scintillator screen or by a radio-chromic film stack (not shown). Laser light transmitted through the target was collected by a ceramic screen.",
+    "footnote": [],
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+    "page_idx": 4
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_2.jpg",
+    "caption": "Fig. 2 Plasma accelerator performance and scalability. a Maximum proton energy from Thomson spectrometer measurements in \\(15^{\\circ}\\) and \\(45^{\\circ}\\) direction (TPS15 and TPS45) sorted by transmitted laser light. b Maximum proton energies for different laser pulse energies \\(\\mathrm{E}_{\\mathrm{L}}\\) . The dotted lines represent proton energy scalings for better trend visualisation.",
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+  {
+    "type": "image",
+    "img_path": "images/Figure_3.jpg",
+    "caption": "Fig. 3 Beam parameters for selected high-energy shots. a TPS15 results (background substracted and normalised raw images), showing the zero deflection axis (zero) and parabolic traces from protons (p) and ions (C6+/O8+) for the five most energetic shots (labelled #1 – #5). b Corresponding particle spectra (solid lines) and maximum energies (squares) for TPS15 and TPS45 with errorbars indicating the energy uncertainty as defined by the projected pinhole size. The green arrow displays the maximum energy measured by the TOF in the \\(31^{\\circ}\\) direction. c Angular dose distribution from RCF measurements for a representative high energy shot. The dashed/dotted line shows the angular area used to generate the particle spectrum in d. e Proton beam profiles from scintillator measurements for two different absorber configurations (c.f. sketch) with spatially varying threshold energies (40 MeV, 80 MeV and 100 MeV respectively). There is a clear shift of the acceleration direction of the high energy protons towards the laser direction (smaller angles). The spectrometers axes are indicated by colored circles (TPS15-blue, TOF31-green, TPS45-orange), and grey areas indicate parts without data.",
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+  {
+    "type": "image",
+    "img_path": "images/Figure_4.jpg",
+    "caption": "Fig. 4 Simulation results revealing multiple acceleration contributions in different directions. a Proton emission distribution from 3D PIC simulation. Only protons in the central slice of \\(\\pm 1\\mu \\mathrm{m}\\) around the symmetry plane within a vertical emission range of \\(\\pm 3^{\\circ}\\) are considered. The spectral emission pattern in laser propagation direction clearly deviates from the target normal direction. b Simulated particle spectrum in \\(15^{\\circ}\\) and \\(45^{\\circ}\\) direction. c Relative contribution of different acceleration mechanisms ('thermal': diffuse sheath set up by thermal and recirculating electrons, 'prompt': \\(j\\times B\\) accelerated electron bunches, 'FSA': target front and bulk acceleration) to the energy gain of protons with a final energy of \\(80\\mathrm{MeV}\\) .",
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preprint/preprint__c96dc60f4328289900d60e0da1a11c9b44dab7ef660882dcb2a7edc7044843f2/preprint__c96dc60f4328289900d60e0da1a11c9b44dab7ef660882dcb2a7edc7044843f2.mmd

@@ -0,0 +1,334 @@
+
+# Laser-driven high-energy proton beams from cascaded acceleration regimes  
+
+Tim Ziegler  
+
+t.ziegler@hzdr.de  
+
+Helmholtz- Zentrum Dresden - Rossendorf, Dresden, 01328, Germany; Technische Universitat Dresden, Dresden, 01069, Germany https://orcid.org/0000- 0002- 3727- 7017  
+
+Ilja Gothel  
+
+Helmholtz- Zentrum Dresden - Rossendorf, Dresden, 01328, Germany; Technische Universitat Dresden, Dresden, 01069, Germany  
+
+Stefan Assenbaum  
+
+Helmholtz- Zentrum Dresden - Rossendorf, Dresden, 01328, Germany; Technische Universitat Dresden, Dresden, 01069, Germany  
+
+Constantin Bernert  
+
+Helmholtz- Zentrum Dresden - Rossendorf, Dresden, 01328, Germany; Technische Universitat Dresden, Dresden, 01069, Germany https://orcid.org/0000- 0003- 1739- 0159  
+
+Florian- Emanuel Brack  
+
+Helmholtz- Zentrum Dresden - Rossendorf, Dresden, 01328, Germany; Technische Universitat Dresden, Dresden, 01069, Germany https://orcid.org/0000- 0002- 9859- 2408  
+
+Thomas E. Cowan  
+
+Helmholtz- Zentrum Dresden - Rossendorf, Dresden, 01328, Germany; Technische Universitat Dresden, Dresden, 01069, Germany https://orcid.org/0000- 0002- 5845- 000X  
+
+Nicholas P. Dover  
+
+Kansai Photon Science Institute, National Institutes for Quantum Science and Technology, 8- 1- 7 Umemidai, Kizugawa, 619- 0215, Kyoto, Japan; The John Adams Institute for Accelerator Science, Blackett Laboratory, Imperial College London, London SW7 2AZ, United Kingdom https://orcid.org/0000- 0003- 0420- 3940  
+
+Lennart Gaus  
+
+Helmholtz- Zentrum Dresden - Rossendorf, Dresden, 01328, Germany; Technische Universitat Dresden, Dresden, 01069, Germany https://orcid.org/0000- 0002- 6914- 4083  
+
+Thomas Kluge  
+
+Helmholtz- Zentrum Dresden - Rossendorf, Dresden, 01328, Germany https://orcid.org/0000- 0003- 4861- 5584  
+
+Stephan Kraft
+
+<--- Page Split --->
+
+Helmholtz-Zentrum Dresden - Rossendorf, Dresden, 01328, Germany https://orcid.org/0000-0002-0638-6990 
+
+Florian Kroll 
+
+Helmholtz-Zentrum Dresden - Rossendorf, Dresden, 01328, Germany https://orcid.org/0000-0002-0275-9892 
+
+Josefine Metzkes-Ng 
+
+Helmholtz-Zentrum Dresden - Rossendorf, Dresden, 01328, Germany https://orcid.org/0000-0002-9556-0662 
+
+Mamiko Nishiuchi 
+
+Kansai Photon Science Institute, National Institutes for Quantum Science and Technology, 8-1-7
+Umemidai, Kizugawa, 619-0215, Kyoto, Japan 
+
+Irene Prencipe 
+
+Helmholtz-Zentrum Dresden - Rossendorf, Dresden, 01328, Germany 
+
+Thomas Püschel 
+
+Helmholtz-Zentrum Dresden - Rossendorf, Dresden, 01328, Germany https://orcid.org/0000-0002-4738-6436 
+
+Martin Rehwald 
+
+Helmholtz-Zentrum Dresden - Rossendorf, Dresden, 01328, Germany; Technische Universität Dresden,
+Dresden, 01069, Germany https://orcid.org/0000-0001-6200-6406 
+
+Marvin Reimold 
+
+Helmholtz-Zentrum Dresden - Rossendorf, Dresden, 01328, Germany; Technische Universität Dresden,
+Dresden, 01069, Germany https://orcid.org/0000-0003-4962-2153 
+
+Hans-Peter Schlenvoigt 
+
+Helmholtz-Zentrum Dresden - Rossendorf, Dresden, 01328, Germany https://orcid.org/0000-0003-4400-1315 
+
+Marvin Elias Paul Umlandt 
+
+Helmholtz-Zentrum Dresden - Rossendorf, Dresden, 01328, Germany; Technische Universität Dresden,
+Dresden, 01069, Germany https://orcid.org/0000-0001-7332-7395 
+
+Milenko Vescovi 
+
+Helmholtz-Zentrum Dresden - Rossendorf, Dresden, 01328, Germany 
+
+Ulrich Schramm 
+
+Helmholtz-Zentrum Dresden - Rossendorf, Dresden, 01328, Germany; Technische Universität Dresden,
+Dresden, 01069, Germany https://orcid.org/0000-0003-0390-7671 
+
+Karl Zeil 
+
+k.zeil@hzdr.de 
+
+Helmholtz-Zentrum Dresden - Rossendorf, Dresden, 01328, Germany https://orcid.org/0000-0003-
+3926-409X
+
+<--- Page Split --->
+
+## Physical Sciences - Article  
+
+# Keywords:  
+
+Posted Date: May 19th, 2023  
+
+DOI: https://doi.org/10.21203/rs.3.rs- 2841731/v1  
+
+License: © This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License  
+
+Additional Declarations: There is NO Competing Interest.  
+
+Version of Record: A version of this preprint was published at Nature Physics on May 13th, 2024. See the published version at https://doi.org/10.1038/s41567- 024- 02505- 0.
+
+<--- Page Split --->
+
+# Laser-driven high-energy proton beams from cascaded acceleration regimes  
+
+Tim Ziegler \(^{1,2*}\) , Ilja Göthel \(^{1,2}\) , Stefan Assenbaum \(^{1,2}\) , Constantin Bernert \(^{1,2}\) , Florian- Emanuel Brack \(^{1,2}\) , Thomas E. Cowan \(^{1,2}\) , Nicholas P. Dover \(^{3,4}\) , Lennart Gaus \(^{1,2}\) , Thomas Kluge \(^{1}\) , Stephan Kraft \(^{1}\) , Florian Kroll \(^{1}\) , Josefine Metzkes- Ng \(^{1}\) , Mamiko Nishiuchi \(^{3}\) , Irene Prencipe \(^{1}\) , Thomas Püschel \(^{1}\) , Martin Rehwald \(^{1,2}\) , Marvin Reimold \(^{1,2}\) , Hans- Peter Schlenvoigt \(^{1}\) , Marvin E. P. Umlandt \(^{1,2}\) , Milenko Vescovi \(^{1}\) , Ulrich Schramm \(^{1,2}\) and Karl Zeil \(^{1*}\) \(^{1}\) Helmholtz- Zentrum Dresden - Rossendorf, Dresden, 01328, Germany. \(^{2}\) Technische Universität Dresden, Dresden, 01069, Germany. \(^{3}\) Kansai Photon Science Institute, National Institutes for Quantum Science and Technology, 8- 1- 7 Umemidai, Kizugawa, 619- 0215, Kyoto, Japan. \(^{4}\) The John Adams Institute for Accelerator Science, Blackett Laboratory, Imperial College London, London SW7 2AZ, United Kingdom.  
+
+\*Corresponding author(s). E- mail(s): t.ziegler@hzdr.de; k.zeil@hzdr.de;  
+
+## Abstract  
+
+Laser- driven ion accelerators can deliver high- energy, high peak current beams from relativistic laser plasmas formed in solid- density materials [1, 2]. This innovative concept attracts a lot of attention for various multidisciplinary applications as a compact alternative to conventional accelerators [3]. However, achieving energy levels suitable for applications such as radiation therapy remains a challenge for laser- driven ion accelerators. Here, we report on experimental generation of plasma- accelerated proton beams with a spectrally separated high- energy component of up to \(150\mathrm{MeV}\) by irradiating solid- density plastic foil targets with ultrashort laser pulses from a repetitive Petawatt laser. Three- dimensional particle- in- cell simulations reveal that the observed beam parameters result from cascaded acceleration regimes that occur at the onset of relativistically induced transparency. The ultrashort pulse duration allows a rapid sequence of these regimes at highest intensity, enabling proton acceleration to unprecedented energy levels. Target transparency was identified to discriminate the high- performance domain of the acquired data set, making it a suitable feedback parameter for automated laser and target optimisation to enhance stability of plasma accelerators in the future. Ultimately, our results encourage further exploration and application of laser- driven plasmas as compact proton accelerators in the multi- \(100\mathrm{MeV}\) range.  
+
+Particle accelerators driven by high- intensity lasers have been an area of increasing interest over the last two decades, as they can produce beam parameters suitable for a wide range of applications in science, medicine, and industry. Of particular interest is the generation of pulsed, high- intensity multi- MeV ion  
+
+beams from relativistic plasmas created at laser irradiated solid- density foils. These laser- driven ion beams can be used for multidisciplinary applications, including radiation therapy [4], injectors for advanced accelerator concepts [5, 6], neutron production [7] or fast ignition in inertial confinement fusion [8].
+
+<--- Page Split --->
+
+A major focus in this research field is to increase the achievable proton energies, particularly beyond the \(100\mathrm{MeV}\) frontier. Historically, record proton energies were mainly reported from large- scale high- energy \((>100\mathrm{J})\) lasers with limited shot rate, irradiating micrometre thick foil targets and inducing acceleration via hot- electron- driven plasma expansion known as target normal sheath acceleration (TNSA) [9- 11]. For this mechanism, the maximum proton energy is mainly boosted by progressively increasing the laser energy coupled into the plasma [12]. Conceptually different acceleration mechanisms utilise field structures that drive protons in a more coherent manner to further increase achievable maximum energies [13- 17]. These advanced concepts enabled compact high- intensity lasers with ultrashort pulses to achieve comparable performance levels with significantly reduced laser energy (few J) and repetition rates relevant for practical applications [18- 20]. Recent experimental and theoretical results revealed that multiple acceleration mechanisms coexist during the laser- plasma interaction [21- 25] and the current energy record for laser- driven proton acceleration near- \(100\mathrm{MeV}\) was achieved by a hybrid combination of processes [23], albeit still using a high- energy laser.  
+
+Here we report experimental breakthrough results for plasma- accelerated proton beams featuring a spectrally separated high- energy component well exceeding \(100\mathrm{MeV}\) at application- relevant particle yields. Irradiating solid- density plastic foil targets with ultrashort laser pulses from a Petawatt laser enabled these results without the need for shot- rate limiting concepts such as cleaning of the temporal laser contrast (e.g. by plasma mirrors [26]) or specialized target treatment (e.g. [27, 28]). By matching the initial target thickness to the laser parameters, multiple shots under optimal conditions resulted in proton acceleration to energies beyond \(100\mathrm{MeV}\) . The preceding laser light heated the target, leading to its subsequent expansion and a near- critical plasma density profile. This permitted the laser main pulse to penetrate the initially opaque target and trigger proton acceleration via a cascade of different mechanisms, as confirmed by three- dimensional particle- in- cell (PIC) simulations. The transmitted laser light, which is linked to target transparency, proved to be an easily accessible control parameter for identifying the high- performance domain within the acquired dataset.  
+
+Previous research has shown that plasma- acceleration can be enhanced when the laser main pulse arrival coincides with the onset of target transparency [23, 25, 29- 34], making this a promising way to improve particle beam parameters such as energy and directionality. The moment where the initially opaque target becomes transparent to the laser is termed the onset of relativistically induced transparency (RIT) [35] and occurs when the plasma frequency drops below the laser frequency due to the relativistic mass increase of the electrons. Investigating plasma- acceleration at the onset of RIT first requires to identify the optimal interaction parameters for the specific laser used.  
+
+![](images/Figure_1.jpg)
+
+<center>Fig. 1 Illustration of the experimental setup. Laser pulses are focused by an \(f / 2.3\) off-axis parabola (OAP) onto thin plastic foil targets, thereby generating a plasma. Protons get accelerated in the plasma and propagate away from the foil. The kinetic energy distribution of the protons was measured by two Thomson parabola spectrometers (TPS15 and TPS45 positioned at \(15^{\circ}\) and \(45^{\circ}\) with respect to the laser propagation direction) and a time-of-flight detector (TOF31 positioned at \(31^{\circ}\) ). The spatial proton beam profile was characterised either by an imaged scintillator screen or by a radio-chromic film stack (not shown). Laser light transmitted through the target was collected by a ceramic screen. </center>   
+
+A dedicated pre- study was conducted, where the target thickness was varied over a wide range and the acceleration performance was compared to numerical simulations. An optimal target thickness between \(200 - 300\mathrm{nm}\) was determined, where electron expulsion from the target bulk due to RIT led to extremely localised space charge fields [25]. These results served as the basis for the present study.  
+
+A schematic of the experimental setup at the DRACO- PW [20, 36] laser is shown in Figure 1. Laser pulses (pulse duration \(\approx 30\mathrm{fs}\) ) are focused by an
+
+<--- Page Split --->
+
+f/2.3 parabola (peak intensity \(\approx 6.5 \times 10^{21} \mathrm{Wcm}^{- 2}\) ) onto plastic foils of \(250 \mathrm{nm} \pm 25 \mathrm{nm}\) thickness under oblique incidence \((50^{\circ})\) , allowing separation of different acceleration components and particle emission directions. A ceramic screen was used to measure the amount of laser light transmitted through the target, helping to analyse the interaction regime for each shot. The generated particle beam was characterised between laser propagation and target normal direction using multiple detectors based on different detection principles to provide robust measurement of the maximum energy (details in Methods). Thomson parabola spectrometers (TPS) positioned at \(15^{\circ}\) (TPS15) and \(45^{\circ}\) (TPS45) with respect to the laser propagation direction \((0^{\circ})\) , enabled the analysis of particle spectra with high energy resolution. A time- of- flight (TOF) detector complemented the maximum proton energy detection at \(31^{\circ}\) (TOF31). A scintillator- based beam profiler equipped with absorbers of different thicknesses at its front provided a spatial measurement of accelerated protons at discrete threshold energies. A slit in the central horizontal plane of the profiler allowed for the parallel operation of the TPS and TOF detectors. For selected shots, a stack of radiochromic films (RCF's) was inserted to provide an energy- resolved spatial dose distribution of the particle beam. Figure 2a displays the maximum proton energies as a function of transmitted laser light for TPS measurements in the two surveyed spatial directions. Best acceleration performance was observed at \(0.5\% - 3\%\) of transmitted laser light, corresponding to the onset of RIT. In this regime, highest proton energies were achieved in both directions, while higher or lower amounts of transmitted light led to weaker acceleration performance. The peak energy of the protons, as measured by the TPS, was \(150 \mathrm{MeV} \pm 15 \mathrm{MeV}\) at \(15^{\circ}\) and \(63 \mathrm{MeV} \pm 3 \mathrm{MeV}\) at \(45^{\circ}\) . Shots yielding \(>5\%\) transmission showed strongly reduced acceleration performance with maximum proton energies below \(25 \mathrm{MeV}\) in both TPS axes.  
+
+A comparison of the most energetic protons measured in the \(15^{\circ}\) and \(45^{\circ}\) direction for varied laser energies is shown in Figure 2b. A fundamental change in energy scaling for the different directions is evident within the investigated range. The maximum proton energies at \(15^{\circ}\) scale much faster with laser pulse energy than at \(45^{\circ}\) , indicating a changed acceleration scheme.  
+
+Figure 3a shows TPS15 readout images (background subtraction applied) for the five most energetic shots. The most notable observation is the spectral  
+
+![](images/Figure_2.jpg)
+
+<center>Fig. 2 Plasma accelerator performance and scalability. a Maximum proton energy from Thomson spectrometer measurements in \(15^{\circ}\) and \(45^{\circ}\) direction (TPS15 and TPS45) sorted by transmitted laser light. b Maximum proton energies for different laser pulse energies \(\mathrm{E}_{\mathrm{L}}\) . The dotted lines represent proton energy scalings for better trend visualisation. </center>  
+
+constriction of the separated high- energy feature in the proton traces. Figure 3b displays the analysed particle spectra for the corresponding shots. The TPS15 spectra (blue lines) feature a low- energy \((< 40 \mathrm{MeV})\) exponential and a separated high- energy \((\geq 100 \mathrm{MeV})\) component, while the TPS45 spectra (orange lines) consistently only exhibit an exponentially decaying component. TOF measurements at \(31^{\circ}\) show similarly high maximum proton energies as the TPS15.  
+
+An analysed RCF stack for a representative high- energy shot is shown in Figure 3c. The displayed angular dose distribution was derived from lineouts along the horizontal axis covering a vertical angle of \(6.5^{\circ}\) for each energy layer. The dose maximum of the \(35 \mathrm{MeV} - 60 \mathrm{MeV}\) layers of the stack is centered along \(45^{\circ}\) with a divergence of \(\pm 15^{\circ}\) , while energy layers \(>60 \mathrm{MeV}\) show almost no dose in this direction. In contrast, the detected dose at \(25^{\circ}\) exhibits a significant reduced divergence of \(\pm 3^{\circ}\) and persists until the last available layer at \(104 \mathrm{MeV}\) . The absolute particle spectra in Figure 3d were derived by deconvoluting
+
+<--- Page Split --->
+![](images/Figure_3.jpg)
+
+<center>Fig. 3 Beam parameters for selected high-energy shots. a TPS15 results (background substracted and normalised raw images), showing the zero deflection axis (zero) and parabolic traces from protons (p) and ions (C6+/O8+) for the five most energetic shots (labelled #1 – #5). b Corresponding particle spectra (solid lines) and maximum energies (squares) for TPS15 and TPS45 with errorbars indicating the energy uncertainty as defined by the projected pinhole size. The green arrow displays the maximum energy measured by the TOF in the \(31^{\circ}\) direction. c Angular dose distribution from RCF measurements for a representative high energy shot. The dashed/dotted line shows the angular area used to generate the particle spectrum in d. e Proton beam profiles from scintillator measurements for two different absorber configurations (c.f. sketch) with spatially varying threshold energies (40 MeV, 80 MeV and 100 MeV respectively). There is a clear shift of the acceleration direction of the high energy protons towards the laser direction (smaller angles). The spectrometers axes are indicated by colored circles (TPS15-blue, TOF31-green, TPS45-orange), and grey areas indicate parts without data. </center>  
+
+the depth- dose profile along the \(25^{\circ}\) and \(45^{\circ}\) directions (orange and blue squares). The obtained results are consistent with the TPS measurements.  
+
+Figure 3e shows images of the segmented proton beam profiler for the corresponding high- energy shots of Figure 3a and b. The detected signal behind the \(80\mathrm{MeV}\) and \(100\mathrm{MeV}\) threshold energy absorbers is consistent with the TPS measurements and indicates that the acceleration direction of the high- energy protons is shifted towards the laser propagation direction.  
+
+Concluding this section, the different detectors provided consistent experimental evidence that a laser- driven proton beam well exceeding \(100\mathrm{MeV}\) was produced in multiple shots. The proton beam comprises a medium- energy ( \(< 70\mathrm{MeV}\) ) broadband component and a spectrally and angularly separated high- energy ( \(>100\mathrm{MeV}\) ) component with reduced divergence. The observed beam parameters and the scaling behaviour of the two components can be associated with several known acceleration mechanisms.  
+
+Considering the extremely short effective acceleration duration provided by the ultrashort laser pulses, we anticipate a combination of different mechanisms [21, 22, 25].  
+
+To investigate these underlying acceleration mechanisms, we conducted a combination of hydrodynamic and PIC simulations using the laser and target parameters of the experiment. The influence of the preceding laser light on a \(270\mathrm{nm}\) thick plastic foil and the resulting expansion was simulated by a 2D hydrodynamic code. The simulation started \(67\mathrm{ps}\) before the arrival of the laser main pulse, when laser induced breakdown is known to occur for the target and temporal laser contrast conditions of this experiment [25, 37]. The results of this first simulation stage, ending \(1\mathrm{ps}\) prior to the laser main pulse, were used as input for a subsequent 3D PIC simulation, which studied the high- intensity interaction (details in Methods).  
+
+The simulated angular proton emission distribution in the horizontal plane and lineouts for the
+
+<--- Page Split --->
+![](images/Figure_4.jpg)
+
+<center>Fig. 4 Simulation results revealing multiple acceleration contributions in different directions. a Proton emission distribution from 3D PIC simulation. Only protons in the central slice of \(\pm 1\mu \mathrm{m}\) around the symmetry plane within a vertical emission range of \(\pm 3^{\circ}\) are considered. The spectral emission pattern in laser propagation direction clearly deviates from the target normal direction. b Simulated particle spectrum in \(15^{\circ}\) and \(45^{\circ}\) direction. c Relative contribution of different acceleration mechanisms ('thermal': diffuse sheath set up by thermal and recirculating electrons, 'prompt': \(j\times B\) accelerated electron bunches, 'FSA': target front and bulk acceleration) to the energy gain of protons with a final energy of \(80\mathrm{MeV}\) . </center>  
+
+experimentally surveyed directions ( \(15^{\circ}\) and \(45^{\circ}\) ) are shown in Figure 4a and b, respectively. The simulation results qualitatively agree with the experimental observations, including the energy level, the emission direction and the modulated spectral distribution of the most energetic particles (between \(0^{\circ} - 15^{\circ}\) ). Additionally, the amount of transmitted laser light \((\approx 4.5\%)\) indicates the onset of RIT.  
+
+To gain deeper insights into the acceleration dynamics during the laser- plasma interaction, a subset of protons was randomly selected upon initialisation. The trajectories of these protons were recorded and analysed to understand their individual acceleration based on the plasma density and electric field at each simulation time step. Protons with the highest final energies were initially located close to the target front and subjected to a cascade of multiple acceleration mechanisms.  
+
+When the relativistic laser pulse penetrates into the expanded plasma, it gets reflected near the relativistically critical density front \(n_{cr} = \gamma n_c\) where \(\gamma\) is the electron Lorentz factor and \(n_c\) the classical critical density which is defined by \(n_c = \epsilon_0 m_e \omega_L^2 / e^2\) , with vacuum permittivity \(\epsilon_0\) , electron mass \(m_e\) , angular laser frequency \(\omega_L\) and electron charge \(e\) . Electrons at \(n_{cr}\) are pushed into the target, thereby creating charge separation fields. These fields trigger different acceleration mechanisms such as hole- boring RPA [13, 18, 23], relativistic transparency front RPA [38] or collisionless shocks [39]. For the sake of simplicity, we refer to this acceleration component as front surface acceleration (FSA), which is mainly induced by the radiation pressure of the laser and is maintained until the expanding target undergoes RIT. Throughout the interaction with the plasma, the relativistic laser pulse directly generates electron bunches in forward direction through the oscillating \(j \times B\) term of the Lorentz force [40- 42], and thermal laser absorption mechanisms [43, 44]. The former, prompt electrons [17, 25] are directed, with narrow energy bandwidth and follow the laser oscillating field structure, while thermal and recirculating electrons generate a diffuse sheath field at the target rear. The occurrence of the characteristic oscillation of the acceleration field induced by the prompt electron component allows distinction between acceleration during the interaction with the ultrashort laser pulse at highest intensity and the effect of energy transfer within the diffuse sheath, which can occur on larger spatial and temporal scales.   
+
+Figure 4c shows the relative contributions of different acceleration mechanisms to the energy gain of protons that reach \(80\mathrm{MeV}\) by the end of the simulation. In laser propagation direction, the most energetic protons experienced a significant acceleration contribution due to the fields induced by the prompt electron bunches. In contrast, the fastest protons in the target
+
+<--- Page Split --->
+
+normal direction gained most of their energy within a TNSA phase in which they were injected with a relatively high velocity from the FSA component. The prompt electron contribution was almost negligible in this direction.  
+
+The simulation results reproduce the experimental trends, such as the observed energy level and the angular energy distribution of the protons. This demonstrates the effectiveness of ultrashort laser pulses for efficient and prompt energy transfer at highest intensity through a cascade of acceleration regimes. The specific interaction parameters for the ideal acceleration cascade could not yet be actively tailored. However, our findings serve as a starting point for future optimisation, diagnostic development, and investigation of scaling properties.  
+
+In conclusion, this study demonstrated the capability of laser- driven plasma accelerators to generate intense proton beams with a spectrally separated high- energy component at maximum energies well exceeding \(100\mathrm{MeV}\) . Multiple detectors based on different detection principles simultaneously confirmed the experimental results. This proof- of- principle demonstration marks an important milestone in the field of plasma accelerators, paving the way towards the use of laser- driven ion sources for various demanding applications. The results revealed that target transparency is a simple parameter to identify the high- performance domain, despite its sensitivity to subtle changes in the initial laser- target conditions. Using the transmitted laser light as an independent feedback parameter related to acceleration performance is ideal for future automated laser and target optimisation. In combination with the relatively high repetition rate \((\geq 1\mathrm{Hz})\) of ultrashort pulse lasers, this has the potential to enhance the stability of the acceleration cascade for practical applications. Simulations considering the full interaction from picosecond- long expansion to proton acceleration during the high- intensity laser pulse arrival, using hydrodynamic and PIC modelling respectively, revealed that a cascade of acceleration regimes is responsible for the observed beam parameters. The nature of the ultrashort pulse duration favors the rapid succession of acceleration processes at highest intensities. We believe that these circumstances enabled the realisation of the high proton energies which were not considered possible for this type of laser parameters at the time of the discovery of laser- driven ion acceleration.  
+
+## Methods  
+
+## Experimental setup  
+
+Experiments were performed with the DRACO- PW laser at Helmholtz- Zentrum Dresden- Rossendorf. DRACO- PW is a Ti:Sa laser system (central wavelength: \(810\mathrm{nm}\) ) with two chirped pulse amplification (CPA) stages, providing \(30\mathrm{fs}\) (full- width at half maximum, FWHM) laser pulses with a maximum energy of \(22.4\mathrm{J}\) on- target. The temporal pulse contrast was measured to be \(< 10^{- 12}\) at \(100\mathrm{ps}\) and \(< 10^{- 6}\) at \(10\mathrm{ps}\) (details reported in [20, 36]). Laser pulses (p- polarisation) were focused by an \(\mathrm{f} / 2.3\) off- axis parabola to a spot size of \(2.5\mu \mathrm{m}\) (FWHM) containing \(32\%\) of the total laser energy, yielding an estimated peak intensity of \(6.5\times 10^{21}\mathrm{Wcm}^{- 2}\) \((a_0\simeq 55)\) . The laser pulses were focussed under oblique incidence \((50^{\circ})\) on Formvar plastic foils \((\mathrm{C}_5\mathrm{H}_8\mathrm{O}_2\) \(\rho \approx 1.2\mathrm{gcm}^{- 3}\) \(n_e = 230n_c\) ) in a thickness range from \(\mathrm{d} = 210\mathrm{nm} - 270\mathrm{nm}\) . Fundamental laser light transmitted through the target was detected by a ceramic screen of size \(16\mathrm{cm}\times 16\mathrm{cm}\) placed \(\approx 33\mathrm{cm}\) away from the target, and imaged onto a bandpass filtered \((800\mathrm{nm}\pm 25\mathrm{nm})\) and calibrated CMOS detector.  
+
+## Particle diagnostic  
+
+Two Thomson parabola spectrometers (TPS) positioned at \(15^{\circ}\) and \(45^{\circ}\) with respect to the laser axis measured the proton and ion energy spectra. The minimal detectable proton energy of the TPS measurements was \(7\mathrm{MeV}\) . The energy resolution is dominated by the pinhole size (TPS15:1mm, TPS45: \(0.3\mathrm{mm}\) ) yielding an uncertainty better than \(\pm 4\% |\pm 10\%\) (c.f. errorbars in Figure 2) for a maximum proton energy of \(60\mathrm{MeV}|150\mathrm{MeV}\) respectively. Each TPS was equipped with a micro- channel plate (MCP) containing a phosphor screen that was imaged onto a CCD camera. The MCP response up to \(60\mathrm{MeV}\) was cross- calibrated to simultaneous measurements with a calibrated scintillator screen. To avoid any ambiguity in particle species identification, a \(3\mathrm{mm}\) thick aluminium plate was inserted just in front of the MCP to prevent other ion species from interfering with the detection of the most energetic protons. Scattering contribution induced by the pinhole and the aluminium plate on the energy resolution were calculated to be negligible.  
+
+Another particle detection method was realised by time- of- flight (TOF) measurements. Therefore a high- sensitivity avalanche photodetector (Menlo APD210, Si- detector, size: \(0.5\mathrm{mm}\) diameter, rise- time: \(500\mathrm{ps}\) )
+
+<--- Page Split --->
+
+was placed at a distance of \(\approx 4\mathrm{m}\) from the target at an angle of \(31^{\circ}\) with respect to the laser axis. Carbons and heavier ions were blocked by a \(2\mathrm{mm}\) copper plate just in front of the diode (threshold: \(34\mathrm{MeV}\) for protons, \(64\mathrm{MeVu}^{- 1}\) for carbons). Signal read- out was provided by a fast oscilloscope (Tektronix MSO64, \(6\mathrm{GHz}\) , \(25\mathrm{GSamples}\) per second). Due to the lower sensitivity of this detection method (in comparison to the TPS) the TOF is suitable to confirm the maximum energy level, but is unable to derive particle numbers for the highest energetic protons.  
+
+Spatially resolved particle detection was conducted with a proton beam profiler. A calibrated scintillator (DRZ High from MCI Optonix) of size \(100\mathrm{mm}\times 100\mathrm{mm}\) was positioned at a distance of \(87\mathrm{mm}\) from the target. The emitted luminescence light was captured by a bandpass filtered \((540\mathrm{nm}\pm 2\mathrm{nm})\) CCD camera. Separation between protons of different energy is achieved by filtering using absorbers of different thicknesses (absorber thickness - threshold energy: \(8\mathrm{mm}\) Al - \(42\mathrm{MeV}\) protons | \(78\mathrm{MeVu}^{- 1}\) carbons, \(25\mathrm{mm}\) Al - \(80\mathrm{MeV}\) protons | \(149\mathrm{MeVu}^{- 1}\) carbons, \(38\mathrm{mm}\) Al - \(102\mathrm{MeV}\) protons | \(190\mathrm{MeVu}^{- 1}\) carbons). A slit in the central horizontal plane of the scintillator allowed for the parallel operation of the TPS and TOF detectors.  
+
+For selected shots a radiochromic film (RCF) stack was placed \(55\mathrm{mm}\) behind the target, blocking all other particle diagnostics. Gafchromic EBT3 films with a size of \(100\mathrm{mm}\times 50\mathrm{mm}\) and a dose range from \(0.1\mathrm{Gy}\) to \(20\mathrm{Gy}\) interleaved with copper plates as absorber material were used. The angular proton dose distribution was derived from line- outs along the horizontal axis covering a vertical angle of \(6.5^{\circ}\) for each energy layer.  
+
+## Numerical simulations  
+
+Two different numerical codes were used to model the experiment. As a first stage, the FLASH code (v4.6.2) [45] was used in a 2D radially symmetric geometry with adaptive mesh refinement to perform a hydrodynamic simulation of the preceding laser light induced expansion of a \(270\mathrm{nm}\) Formvar foil. This simulation covered the time period from the onset of laser induced dielectric breakdown (around \(67\mathrm{ps}\) ) up to \(1\mathrm{ps}\) before the laser main pulse. The breakdown point was derived using the measured laser contrast [20] and optical probing studies of the laser- induced breakdown of Formvar foils following the approach described in [37, 46]. Tabulated equation- of- state was used in the simulations, generated using the  
+
+FEOS code [45]. The Lee- More conductivity and heat exchange were used. The resulting density profile from the hydrodynamic simulation was rotated around its axis of symmetry and used as initial input for a 3D PIC simulation, with densities below \(0.04n_c\) discarded. The final picosecond and main pulse interaction were modelled using the fully relativistic code PIConGPU (running on 900 A100- GPUs for \(35\mathrm{k}\) timesteps) [47]. The laser was focused to a Gaussian spot with \(w_0 = 2.14\mu \mathrm{m}\) on the front surface of the target in p- polarisation under oblique incidence \((45^{\circ})\) aiming at the center of the originally unexpanded foil. The temporal intensity profile was matched to measured data from [20] by fitting two exponential ramps and a \(30\mathrm{fs}\) - Gaussian with a peak \(a_0\) of about 50. A cell size of \(20\mathrm{nm}\) and one carbon and eight hydrogen macroparticles (thus, 13 electrons) per cell were initialised.  
+
+Acknowledgments. We thank the DRACO- PW operation team for their experiment support. This work was supported by Laserlab Europe V (PRISES, contract no. 871124) and the IMPULSE project (contract no. 871161). M.N. was supported by Kakenhi Grant No. 20H00140, Grant No. 21KK0049, Grant No. 22H00121, QST President's Strategic Grant (QST International Research Initiative (AAA98) and Creative Research (ABACS)).  
+
+## Declarations  
+
+Conflict of interests. The authors declare no competing interests.  
+
+Data availability. The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.  
+
+Code availability. All codes written for use in this study are available from the corresponding author on reasonable request.  
+
+Author contributions. T.Z., S.A., F.- E.B., L.G., S.K., F.K., J.M.- N., I.P., T.P., M.Reh., M.Rei., H.- P.S., M.E.P.U., M.V. and K.Z. set up and performed the experiment. T.Z. performed the analysis and interpretation of the experimental data with support from F.- E.B., F.K., M.Reh., M.E.P.U. and K.Z. I.G. performed and analysed the numerical simulations with support from N.D. and T.K. T.Z., I.G., T.K. and K.Z. interpreted the numerical simulation data. T.Z. and K.Z. wrote the manuscript. U.S. and K.Z. supervised
+
+<--- Page Split --->
+
+the project. All authors reviewed the manuscript and contributed to discussions.  
+
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+
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+<|ref|>title<|/ref|><|det|>[[44, 107, 816, 175]]<|/det|>
+# Laser-driven high-energy proton beams from cascaded acceleration regimes  
+
+<|ref|>text<|/ref|><|det|>[[44, 195, 144, 214]]<|/det|>
+Tim Ziegler  
+
+<|ref|>text<|/ref|><|det|>[[54, 222, 245, 240]]<|/det|>
+t.ziegler@hzdr.de  
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+Ilja Gothel  
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+Stefan Assenbaum  
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+Constantin Bernert  
+
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+Florian- Emanuel Brack  
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+Helmholtz- Zentrum Dresden - Rossendorf, Dresden, 01328, Germany; Technische Universitat Dresden, Dresden, 01069, Germany https://orcid.org/0000- 0002- 5845- 000X  
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+Stephan Kraft
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+<--- Page Split --->
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+Florian Kroll 
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+Kansai Photon Science Institute, National Institutes for Quantum Science and Technology, 8-1-7
+Umemidai, Kizugawa, 619-0215, Kyoto, Japan 
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+Irene Prencipe 
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+Thomas Püschel 
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+Dresden, 01069, Germany https://orcid.org/0000-0001-6200-6406 
+
+<|ref|>text<|/ref|><|det|>[[42, 486, 185, 504]]<|/det|>
+Marvin Reimold 
+
+<|ref|>text<|/ref|><|det|>[[42, 508, 936, 550]]<|/det|>
+Helmholtz-Zentrum Dresden - Rossendorf, Dresden, 01328, Germany; Technische Universität Dresden,
+Dresden, 01069, Germany https://orcid.org/0000-0003-4962-2153 
+
+<|ref|>text<|/ref|><|det|>[[42, 555, 252, 574]]<|/det|>
+Hans-Peter Schlenvoigt 
+
+<|ref|>text<|/ref|><|det|>[[42, 578, 916, 619]]<|/det|>
+Helmholtz-Zentrum Dresden - Rossendorf, Dresden, 01328, Germany https://orcid.org/0000-0003-4400-1315 
+
+<|ref|>text<|/ref|><|det|>[[42, 625, 277, 643]]<|/det|>
+Marvin Elias Paul Umlandt 
+
+<|ref|>text<|/ref|><|det|>[[42, 647, 936, 689]]<|/det|>
+Helmholtz-Zentrum Dresden - Rossendorf, Dresden, 01328, Germany; Technische Universität Dresden,
+Dresden, 01069, Germany https://orcid.org/0000-0001-7332-7395 
+
+<|ref|>text<|/ref|><|det|>[[42, 694, 191, 712]]<|/det|>
+Milenko Vescovi 
+
+<|ref|>text<|/ref|><|det|>[[52, 716, 652, 735]]<|/det|>
+Helmholtz-Zentrum Dresden - Rossendorf, Dresden, 01328, Germany 
+
+<|ref|>text<|/ref|><|det|>[[42, 740, 185, 758]]<|/det|>
+Ulrich Schramm 
+
+<|ref|>text<|/ref|><|det|>[[42, 762, 936, 804]]<|/det|>
+Helmholtz-Zentrum Dresden - Rossendorf, Dresden, 01328, Germany; Technische Universität Dresden,
+Dresden, 01069, Germany https://orcid.org/0000-0003-0390-7671 
+
+<|ref|>text<|/ref|><|det|>[[42, 810, 120, 827]]<|/det|>
+Karl Zeil 
+
+<|ref|>text<|/ref|><|det|>[[52, 837, 213, 854]]<|/det|>
+k.zeil@hzdr.de 
+
+<|ref|>text<|/ref|><|det|>[[42, 883, 916, 925]]<|/det|>
+Helmholtz-Zentrum Dresden - Rossendorf, Dresden, 01328, Germany https://orcid.org/0000-0003-
+3926-409X
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[44, 45, 275, 65]]<|/det|>
+## Physical Sciences - Article  
+
+<|ref|>title<|/ref|><|det|>[[44, 84, 135, 102]]<|/det|>
+# Keywords:  
+
+<|ref|>text<|/ref|><|det|>[[44, 120, 296, 140]]<|/det|>
+Posted Date: May 19th, 2023  
+
+<|ref|>text<|/ref|><|det|>[[44, 159, 475, 179]]<|/det|>
+DOI: https://doi.org/10.21203/rs.3.rs- 2841731/v1  
+
+<|ref|>text<|/ref|><|det|>[[42, 196, 914, 240]]<|/det|>
+License: © This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License  
+
+<|ref|>text<|/ref|><|det|>[[42, 257, 534, 277]]<|/det|>
+Additional Declarations: There is NO Competing Interest.  
+
+<|ref|>text<|/ref|><|det|>[[42, 312, 952, 355]]<|/det|>
+Version of Record: A version of this preprint was published at Nature Physics on May 13th, 2024. See the published version at https://doi.org/10.1038/s41567- 024- 02505- 0.
+
+<--- Page Split --->
+<|ref|>title<|/ref|><|det|>[[159, 138, 840, 195]]<|/det|>
+# Laser-driven high-energy proton beams from cascaded acceleration regimes  
+
+<|ref|>text<|/ref|><|det|>[[130, 218, 872, 456]]<|/det|>
+Tim Ziegler \(^{1,2*}\) , Ilja Göthel \(^{1,2}\) , Stefan Assenbaum \(^{1,2}\) , Constantin Bernert \(^{1,2}\) , Florian- Emanuel Brack \(^{1,2}\) , Thomas E. Cowan \(^{1,2}\) , Nicholas P. Dover \(^{3,4}\) , Lennart Gaus \(^{1,2}\) , Thomas Kluge \(^{1}\) , Stephan Kraft \(^{1}\) , Florian Kroll \(^{1}\) , Josefine Metzkes- Ng \(^{1}\) , Mamiko Nishiuchi \(^{3}\) , Irene Prencipe \(^{1}\) , Thomas Püschel \(^{1}\) , Martin Rehwald \(^{1,2}\) , Marvin Reimold \(^{1,2}\) , Hans- Peter Schlenvoigt \(^{1}\) , Marvin E. P. Umlandt \(^{1,2}\) , Milenko Vescovi \(^{1}\) , Ulrich Schramm \(^{1,2}\) and Karl Zeil \(^{1*}\) \(^{1}\) Helmholtz- Zentrum Dresden - Rossendorf, Dresden, 01328, Germany. \(^{2}\) Technische Universität Dresden, Dresden, 01069, Germany. \(^{3}\) Kansai Photon Science Institute, National Institutes for Quantum Science and Technology, 8- 1- 7 Umemidai, Kizugawa, 619- 0215, Kyoto, Japan. \(^{4}\) The John Adams Institute for Accelerator Science, Blackett Laboratory, Imperial College London, London SW7 2AZ, United Kingdom.  
+
+<|ref|>text<|/ref|><|det|>[[207, 490, 792, 510]]<|/det|>
+\*Corresponding author(s). E- mail(s): t.ziegler@hzdr.de; k.zeil@hzdr.de;  
+
+<|ref|>sub_title<|/ref|><|det|>[[468, 542, 531, 557]]<|/det|>
+## Abstract  
+
+<|ref|>text<|/ref|><|det|>[[127, 560, 873, 755]]<|/det|>
+Laser- driven ion accelerators can deliver high- energy, high peak current beams from relativistic laser plasmas formed in solid- density materials [1, 2]. This innovative concept attracts a lot of attention for various multidisciplinary applications as a compact alternative to conventional accelerators [3]. However, achieving energy levels suitable for applications such as radiation therapy remains a challenge for laser- driven ion accelerators. Here, we report on experimental generation of plasma- accelerated proton beams with a spectrally separated high- energy component of up to \(150\mathrm{MeV}\) by irradiating solid- density plastic foil targets with ultrashort laser pulses from a repetitive Petawatt laser. Three- dimensional particle- in- cell simulations reveal that the observed beam parameters result from cascaded acceleration regimes that occur at the onset of relativistically induced transparency. The ultrashort pulse duration allows a rapid sequence of these regimes at highest intensity, enabling proton acceleration to unprecedented energy levels. Target transparency was identified to discriminate the high- performance domain of the acquired data set, making it a suitable feedback parameter for automated laser and target optimisation to enhance stability of plasma accelerators in the future. Ultimately, our results encourage further exploration and application of laser- driven plasmas as compact proton accelerators in the multi- \(100\mathrm{MeV}\) range.  
+
+<|ref|>text<|/ref|><|det|>[[84, 802, 480, 901]]<|/det|>
+Particle accelerators driven by high- intensity lasers have been an area of increasing interest over the last two decades, as they can produce beam parameters suitable for a wide range of applications in science, medicine, and industry. Of particular interest is the generation of pulsed, high- intensity multi- MeV ion  
+
+<|ref|>text<|/ref|><|det|>[[519, 803, 915, 901]]<|/det|>
+beams from relativistic plasmas created at laser irradiated solid- density foils. These laser- driven ion beams can be used for multidisciplinary applications, including radiation therapy [4], injectors for advanced accelerator concepts [5, 6], neutron production [7] or fast ignition in inertial confinement fusion [8].
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[80, 74, 476, 480]]<|/det|>
+A major focus in this research field is to increase the achievable proton energies, particularly beyond the \(100\mathrm{MeV}\) frontier. Historically, record proton energies were mainly reported from large- scale high- energy \((>100\mathrm{J})\) lasers with limited shot rate, irradiating micrometre thick foil targets and inducing acceleration via hot- electron- driven plasma expansion known as target normal sheath acceleration (TNSA) [9- 11]. For this mechanism, the maximum proton energy is mainly boosted by progressively increasing the laser energy coupled into the plasma [12]. Conceptually different acceleration mechanisms utilise field structures that drive protons in a more coherent manner to further increase achievable maximum energies [13- 17]. These advanced concepts enabled compact high- intensity lasers with ultrashort pulses to achieve comparable performance levels with significantly reduced laser energy (few J) and repetition rates relevant for practical applications [18- 20]. Recent experimental and theoretical results revealed that multiple acceleration mechanisms coexist during the laser- plasma interaction [21- 25] and the current energy record for laser- driven proton acceleration near- \(100\mathrm{MeV}\) was achieved by a hybrid combination of processes [23], albeit still using a high- energy laser.  
+
+<|ref|>text<|/ref|><|det|>[[80, 481, 475, 853]]<|/det|>
+Here we report experimental breakthrough results for plasma- accelerated proton beams featuring a spectrally separated high- energy component well exceeding \(100\mathrm{MeV}\) at application- relevant particle yields. Irradiating solid- density plastic foil targets with ultrashort laser pulses from a Petawatt laser enabled these results without the need for shot- rate limiting concepts such as cleaning of the temporal laser contrast (e.g. by plasma mirrors [26]) or specialized target treatment (e.g. [27, 28]). By matching the initial target thickness to the laser parameters, multiple shots under optimal conditions resulted in proton acceleration to energies beyond \(100\mathrm{MeV}\) . The preceding laser light heated the target, leading to its subsequent expansion and a near- critical plasma density profile. This permitted the laser main pulse to penetrate the initially opaque target and trigger proton acceleration via a cascade of different mechanisms, as confirmed by three- dimensional particle- in- cell (PIC) simulations. The transmitted laser light, which is linked to target transparency, proved to be an easily accessible control parameter for identifying the high- performance domain within the acquired dataset.  
+
+<|ref|>text<|/ref|><|det|>[[80, 855, 475, 886], [519, 521, 912, 717]]<|/det|>
+Previous research has shown that plasma- acceleration can be enhanced when the laser main pulse arrival coincides with the onset of target transparency [23, 25, 29- 34], making this a promising way to improve particle beam parameters such as energy and directionality. The moment where the initially opaque target becomes transparent to the laser is termed the onset of relativistically induced transparency (RIT) [35] and occurs when the plasma frequency drops below the laser frequency due to the relativistic mass increase of the electrons. Investigating plasma- acceleration at the onset of RIT first requires to identify the optimal interaction parameters for the specific laser used.  
+
+<|ref|>image<|/ref|><|det|>[[530, 75, 896, 345]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[518, 359, 912, 501]]<|/det|>
+<center>Fig. 1 Illustration of the experimental setup. Laser pulses are focused by an \(f / 2.3\) off-axis parabola (OAP) onto thin plastic foil targets, thereby generating a plasma. Protons get accelerated in the plasma and propagate away from the foil. The kinetic energy distribution of the protons was measured by two Thomson parabola spectrometers (TPS15 and TPS45 positioned at \(15^{\circ}\) and \(45^{\circ}\) with respect to the laser propagation direction) and a time-of-flight detector (TOF31 positioned at \(31^{\circ}\) ). The spatial proton beam profile was characterised either by an imaged scintillator screen or by a radio-chromic film stack (not shown). Laser light transmitted through the target was collected by a ceramic screen. </center>   
+
+<|ref|>text<|/ref|><|det|>[[518, 718, 911, 846]]<|/det|>
+A dedicated pre- study was conducted, where the target thickness was varied over a wide range and the acceleration performance was compared to numerical simulations. An optimal target thickness between \(200 - 300\mathrm{nm}\) was determined, where electron expulsion from the target bulk due to RIT led to extremely localised space charge fields [25]. These results served as the basis for the present study.  
+
+<|ref|>text<|/ref|><|det|>[[518, 847, 911, 896]]<|/det|>
+A schematic of the experimental setup at the DRACO- PW [20, 36] laser is shown in Figure 1. Laser pulses (pulse duration \(\approx 30\mathrm{fs}\) ) are focused by an
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[82, 70, 481, 728]]<|/det|>
+f/2.3 parabola (peak intensity \(\approx 6.5 \times 10^{21} \mathrm{Wcm}^{- 2}\) ) onto plastic foils of \(250 \mathrm{nm} \pm 25 \mathrm{nm}\) thickness under oblique incidence \((50^{\circ})\) , allowing separation of different acceleration components and particle emission directions. A ceramic screen was used to measure the amount of laser light transmitted through the target, helping to analyse the interaction regime for each shot. The generated particle beam was characterised between laser propagation and target normal direction using multiple detectors based on different detection principles to provide robust measurement of the maximum energy (details in Methods). Thomson parabola spectrometers (TPS) positioned at \(15^{\circ}\) (TPS15) and \(45^{\circ}\) (TPS45) with respect to the laser propagation direction \((0^{\circ})\) , enabled the analysis of particle spectra with high energy resolution. A time- of- flight (TOF) detector complemented the maximum proton energy detection at \(31^{\circ}\) (TOF31). A scintillator- based beam profiler equipped with absorbers of different thicknesses at its front provided a spatial measurement of accelerated protons at discrete threshold energies. A slit in the central horizontal plane of the profiler allowed for the parallel operation of the TPS and TOF detectors. For selected shots, a stack of radiochromic films (RCF's) was inserted to provide an energy- resolved spatial dose distribution of the particle beam. Figure 2a displays the maximum proton energies as a function of transmitted laser light for TPS measurements in the two surveyed spatial directions. Best acceleration performance was observed at \(0.5\% - 3\%\) of transmitted laser light, corresponding to the onset of RIT. In this regime, highest proton energies were achieved in both directions, while higher or lower amounts of transmitted light led to weaker acceleration performance. The peak energy of the protons, as measured by the TPS, was \(150 \mathrm{MeV} \pm 15 \mathrm{MeV}\) at \(15^{\circ}\) and \(63 \mathrm{MeV} \pm 3 \mathrm{MeV}\) at \(45^{\circ}\) . Shots yielding \(>5\%\) transmission showed strongly reduced acceleration performance with maximum proton energies below \(25 \mathrm{MeV}\) in both TPS axes.  
+
+<|ref|>text<|/ref|><|det|>[[84, 725, 479, 853]]<|/det|>
+A comparison of the most energetic protons measured in the \(15^{\circ}\) and \(45^{\circ}\) direction for varied laser energies is shown in Figure 2b. A fundamental change in energy scaling for the different directions is evident within the investigated range. The maximum proton energies at \(15^{\circ}\) scale much faster with laser pulse energy than at \(45^{\circ}\) , indicating a changed acceleration scheme.  
+
+<|ref|>text<|/ref|><|det|>[[84, 854, 479, 903]]<|/det|>
+Figure 3a shows TPS15 readout images (background subtraction applied) for the five most energetic shots. The most notable observation is the spectral  
+
+<|ref|>image<|/ref|><|det|>[[536, 70, 890, 430]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[518, 437, 916, 514]]<|/det|>
+<center>Fig. 2 Plasma accelerator performance and scalability. a Maximum proton energy from Thomson spectrometer measurements in \(15^{\circ}\) and \(45^{\circ}\) direction (TPS15 and TPS45) sorted by transmitted laser light. b Maximum proton energies for different laser pulse energies \(\mathrm{E}_{\mathrm{L}}\) . The dotted lines represent proton energy scalings for better trend visualisation. </center>  
+
+<|ref|>text<|/ref|><|det|>[[519, 531, 915, 679]]<|/det|>
+constriction of the separated high- energy feature in the proton traces. Figure 3b displays the analysed particle spectra for the corresponding shots. The TPS15 spectra (blue lines) feature a low- energy \((< 40 \mathrm{MeV})\) exponential and a separated high- energy \((\geq 100 \mathrm{MeV})\) component, while the TPS45 spectra (orange lines) consistently only exhibit an exponentially decaying component. TOF measurements at \(31^{\circ}\) show similarly high maximum proton energies as the TPS15.  
+
+<|ref|>text<|/ref|><|det|>[[519, 680, 915, 875]]<|/det|>
+An analysed RCF stack for a representative high- energy shot is shown in Figure 3c. The displayed angular dose distribution was derived from lineouts along the horizontal axis covering a vertical angle of \(6.5^{\circ}\) for each energy layer. The dose maximum of the \(35 \mathrm{MeV} - 60 \mathrm{MeV}\) layers of the stack is centered along \(45^{\circ}\) with a divergence of \(\pm 15^{\circ}\) , while energy layers \(>60 \mathrm{MeV}\) show almost no dose in this direction. In contrast, the detected dose at \(25^{\circ}\) exhibits a significant reduced divergence of \(\pm 3^{\circ}\) and persists until the last available layer at \(104 \mathrm{MeV}\) . The absolute particle spectra in Figure 3d were derived by deconvoluting
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[78, 70, 914, 433]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[80, 439, 914, 556]]<|/det|>
+<center>Fig. 3 Beam parameters for selected high-energy shots. a TPS15 results (background substracted and normalised raw images), showing the zero deflection axis (zero) and parabolic traces from protons (p) and ions (C6+/O8+) for the five most energetic shots (labelled #1 – #5). b Corresponding particle spectra (solid lines) and maximum energies (squares) for TPS15 and TPS45 with errorbars indicating the energy uncertainty as defined by the projected pinhole size. The green arrow displays the maximum energy measured by the TOF in the \(31^{\circ}\) direction. c Angular dose distribution from RCF measurements for a representative high energy shot. The dashed/dotted line shows the angular area used to generate the particle spectrum in d. e Proton beam profiles from scintillator measurements for two different absorber configurations (c.f. sketch) with spatially varying threshold energies (40 MeV, 80 MeV and 100 MeV respectively). There is a clear shift of the acceleration direction of the high energy protons towards the laser direction (smaller angles). The spectrometers axes are indicated by colored circles (TPS15-blue, TOF31-green, TPS45-orange), and grey areas indicate parts without data. </center>  
+
+<|ref|>text<|/ref|><|det|>[[81, 576, 475, 623]]<|/det|>
+the depth- dose profile along the \(25^{\circ}\) and \(45^{\circ}\) directions (orange and blue squares). The obtained results are consistent with the TPS measurements.  
+
+<|ref|>text<|/ref|><|det|>[[81, 625, 476, 740]]<|/det|>
+Figure 3e shows images of the segmented proton beam profiler for the corresponding high- energy shots of Figure 3a and b. The detected signal behind the \(80\mathrm{MeV}\) and \(100\mathrm{MeV}\) threshold energy absorbers is consistent with the TPS measurements and indicates that the acceleration direction of the high- energy protons is shifted towards the laser propagation direction.  
+
+<|ref|>text<|/ref|><|det|>[[82, 741, 477, 902]]<|/det|>
+Concluding this section, the different detectors provided consistent experimental evidence that a laser- driven proton beam well exceeding \(100\mathrm{MeV}\) was produced in multiple shots. The proton beam comprises a medium- energy ( \(< 70\mathrm{MeV}\) ) broadband component and a spectrally and angularly separated high- energy ( \(>100\mathrm{MeV}\) ) component with reduced divergence. The observed beam parameters and the scaling behaviour of the two components can be associated with several known acceleration mechanisms.  
+
+<|ref|>text<|/ref|><|det|>[[515, 576, 911, 641]]<|/det|>
+Considering the extremely short effective acceleration duration provided by the ultrashort laser pulses, we anticipate a combination of different mechanisms [21, 22, 25].  
+
+<|ref|>text<|/ref|><|det|>[[516, 642, 911, 869]]<|/det|>
+To investigate these underlying acceleration mechanisms, we conducted a combination of hydrodynamic and PIC simulations using the laser and target parameters of the experiment. The influence of the preceding laser light on a \(270\mathrm{nm}\) thick plastic foil and the resulting expansion was simulated by a 2D hydrodynamic code. The simulation started \(67\mathrm{ps}\) before the arrival of the laser main pulse, when laser induced breakdown is known to occur for the target and temporal laser contrast conditions of this experiment [25, 37]. The results of this first simulation stage, ending \(1\mathrm{ps}\) prior to the laser main pulse, were used as input for a subsequent 3D PIC simulation, which studied the high- intensity interaction (details in Methods).  
+
+<|ref|>text<|/ref|><|det|>[[516, 870, 911, 902]]<|/det|>
+The simulated angular proton emission distribution in the horizontal plane and lineouts for the
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[172, 75, 820, 328]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[83, 339, 916, 418]]<|/det|>
+<center>Fig. 4 Simulation results revealing multiple acceleration contributions in different directions. a Proton emission distribution from 3D PIC simulation. Only protons in the central slice of \(\pm 1\mu \mathrm{m}\) around the symmetry plane within a vertical emission range of \(\pm 3^{\circ}\) are considered. The spectral emission pattern in laser propagation direction clearly deviates from the target normal direction. b Simulated particle spectrum in \(15^{\circ}\) and \(45^{\circ}\) direction. c Relative contribution of different acceleration mechanisms ('thermal': diffuse sheath set up by thermal and recirculating electrons, 'prompt': \(j\times B\) accelerated electron bunches, 'FSA': target front and bulk acceleration) to the energy gain of protons with a final energy of \(80\mathrm{MeV}\) . </center>  
+
+<|ref|>text<|/ref|><|det|>[[84, 438, 479, 568]]<|/det|>
+experimentally surveyed directions ( \(15^{\circ}\) and \(45^{\circ}\) ) are shown in Figure 4a and b, respectively. The simulation results qualitatively agree with the experimental observations, including the energy level, the emission direction and the modulated spectral distribution of the most energetic particles (between \(0^{\circ} - 15^{\circ}\) ). Additionally, the amount of transmitted laser light \((\approx 4.5\%)\) indicates the onset of RIT.  
+
+<|ref|>text<|/ref|><|det|>[[84, 570, 479, 730]]<|/det|>
+To gain deeper insights into the acceleration dynamics during the laser- plasma interaction, a subset of protons was randomly selected upon initialisation. The trajectories of these protons were recorded and analysed to understand their individual acceleration based on the plasma density and electric field at each simulation time step. Protons with the highest final energies were initially located close to the target front and subjected to a cascade of multiple acceleration mechanisms.  
+
+<|ref|>text<|/ref|><|det|>[[84, 732, 479, 894], [519, 439, 915, 780]]<|/det|>
+When the relativistic laser pulse penetrates into the expanded plasma, it gets reflected near the relativistically critical density front \(n_{cr} = \gamma n_c\) where \(\gamma\) is the electron Lorentz factor and \(n_c\) the classical critical density which is defined by \(n_c = \epsilon_0 m_e \omega_L^2 / e^2\) , with vacuum permittivity \(\epsilon_0\) , electron mass \(m_e\) , angular laser frequency \(\omega_L\) and electron charge \(e\) . Electrons at \(n_{cr}\) are pushed into the target, thereby creating charge separation fields. These fields trigger different acceleration mechanisms such as hole- boring RPA [13, 18, 23], relativistic transparency front RPA [38] or collisionless shocks [39]. For the sake of simplicity, we refer to this acceleration component as front surface acceleration (FSA), which is mainly induced by the radiation pressure of the laser and is maintained until the expanding target undergoes RIT. Throughout the interaction with the plasma, the relativistic laser pulse directly generates electron bunches in forward direction through the oscillating \(j \times B\) term of the Lorentz force [40- 42], and thermal laser absorption mechanisms [43, 44]. The former, prompt electrons [17, 25] are directed, with narrow energy bandwidth and follow the laser oscillating field structure, while thermal and recirculating electrons generate a diffuse sheath field at the target rear. The occurrence of the characteristic oscillation of the acceleration field induced by the prompt electron component allows distinction between acceleration during the interaction with the ultrashort laser pulse at highest intensity and the effect of energy transfer within the diffuse sheath, which can occur on larger spatial and temporal scales.   
+
+<|ref|>text<|/ref|><|det|>[[519, 781, 915, 894]]<|/det|>
+Figure 4c shows the relative contributions of different acceleration mechanisms to the energy gain of protons that reach \(80\mathrm{MeV}\) by the end of the simulation. In laser propagation direction, the most energetic protons experienced a significant acceleration contribution due to the fields induced by the prompt electron bunches. In contrast, the fastest protons in the target
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[81, 74, 476, 155]]<|/det|>
+normal direction gained most of their energy within a TNSA phase in which they were injected with a relatively high velocity from the FSA component. The prompt electron contribution was almost negligible in this direction.  
+
+<|ref|>text<|/ref|><|det|>[[81, 157, 476, 335]]<|/det|>
+The simulation results reproduce the experimental trends, such as the observed energy level and the angular energy distribution of the protons. This demonstrates the effectiveness of ultrashort laser pulses for efficient and prompt energy transfer at highest intensity through a cascade of acceleration regimes. The specific interaction parameters for the ideal acceleration cascade could not yet be actively tailored. However, our findings serve as a starting point for future optimisation, diagnostic development, and investigation of scaling properties.  
+
+<|ref|>text<|/ref|><|det|>[[80, 333, 476, 871]]<|/det|>
+In conclusion, this study demonstrated the capability of laser- driven plasma accelerators to generate intense proton beams with a spectrally separated high- energy component at maximum energies well exceeding \(100\mathrm{MeV}\) . Multiple detectors based on different detection principles simultaneously confirmed the experimental results. This proof- of- principle demonstration marks an important milestone in the field of plasma accelerators, paving the way towards the use of laser- driven ion sources for various demanding applications. The results revealed that target transparency is a simple parameter to identify the high- performance domain, despite its sensitivity to subtle changes in the initial laser- target conditions. Using the transmitted laser light as an independent feedback parameter related to acceleration performance is ideal for future automated laser and target optimisation. In combination with the relatively high repetition rate \((\geq 1\mathrm{Hz})\) of ultrashort pulse lasers, this has the potential to enhance the stability of the acceleration cascade for practical applications. Simulations considering the full interaction from picosecond- long expansion to proton acceleration during the high- intensity laser pulse arrival, using hydrodynamic and PIC modelling respectively, revealed that a cascade of acceleration regimes is responsible for the observed beam parameters. The nature of the ultrashort pulse duration favors the rapid succession of acceleration processes at highest intensities. We believe that these circumstances enabled the realisation of the high proton energies which were not considered possible for this type of laser parameters at the time of the discovery of laser- driven ion acceleration.  
+
+<|ref|>sub_title<|/ref|><|det|>[[516, 70, 613, 89]]<|/det|>
+## Methods  
+
+<|ref|>sub_title<|/ref|><|det|>[[516, 103, 670, 118]]<|/det|>
+## Experimental setup  
+
+<|ref|>text<|/ref|><|det|>[[515, 120, 912, 460]]<|/det|>
+Experiments were performed with the DRACO- PW laser at Helmholtz- Zentrum Dresden- Rossendorf. DRACO- PW is a Ti:Sa laser system (central wavelength: \(810\mathrm{nm}\) ) with two chirped pulse amplification (CPA) stages, providing \(30\mathrm{fs}\) (full- width at half maximum, FWHM) laser pulses with a maximum energy of \(22.4\mathrm{J}\) on- target. The temporal pulse contrast was measured to be \(< 10^{- 12}\) at \(100\mathrm{ps}\) and \(< 10^{- 6}\) at \(10\mathrm{ps}\) (details reported in [20, 36]). Laser pulses (p- polarisation) were focused by an \(\mathrm{f} / 2.3\) off- axis parabola to a spot size of \(2.5\mu \mathrm{m}\) (FWHM) containing \(32\%\) of the total laser energy, yielding an estimated peak intensity of \(6.5\times 10^{21}\mathrm{Wcm}^{- 2}\) \((a_0\simeq 55)\) . The laser pulses were focussed under oblique incidence \((50^{\circ})\) on Formvar plastic foils \((\mathrm{C}_5\mathrm{H}_8\mathrm{O}_2\) \(\rho \approx 1.2\mathrm{gcm}^{- 3}\) \(n_e = 230n_c\) ) in a thickness range from \(\mathrm{d} = 210\mathrm{nm} - 270\mathrm{nm}\) . Fundamental laser light transmitted through the target was detected by a ceramic screen of size \(16\mathrm{cm}\times 16\mathrm{cm}\) placed \(\approx 33\mathrm{cm}\) away from the target, and imaged onto a bandpass filtered \((800\mathrm{nm}\pm 25\mathrm{nm})\) and calibrated CMOS detector.  
+
+<|ref|>sub_title<|/ref|><|det|>[[515, 477, 662, 492]]<|/det|>
+## Particle diagnostic  
+
+<|ref|>text<|/ref|><|det|>[[515, 494, 911, 833]]<|/det|>
+Two Thomson parabola spectrometers (TPS) positioned at \(15^{\circ}\) and \(45^{\circ}\) with respect to the laser axis measured the proton and ion energy spectra. The minimal detectable proton energy of the TPS measurements was \(7\mathrm{MeV}\) . The energy resolution is dominated by the pinhole size (TPS15:1mm, TPS45: \(0.3\mathrm{mm}\) ) yielding an uncertainty better than \(\pm 4\% |\pm 10\%\) (c.f. errorbars in Figure 2) for a maximum proton energy of \(60\mathrm{MeV}|150\mathrm{MeV}\) respectively. Each TPS was equipped with a micro- channel plate (MCP) containing a phosphor screen that was imaged onto a CCD camera. The MCP response up to \(60\mathrm{MeV}\) was cross- calibrated to simultaneous measurements with a calibrated scintillator screen. To avoid any ambiguity in particle species identification, a \(3\mathrm{mm}\) thick aluminium plate was inserted just in front of the MCP to prevent other ion species from interfering with the detection of the most energetic protons. Scattering contribution induced by the pinhole and the aluminium plate on the energy resolution were calculated to be negligible.  
+
+<|ref|>text<|/ref|><|det|>[[515, 834, 911, 899]]<|/det|>
+Another particle detection method was realised by time- of- flight (TOF) measurements. Therefore a high- sensitivity avalanche photodetector (Menlo APD210, Si- detector, size: \(0.5\mathrm{mm}\) diameter, rise- time: \(500\mathrm{ps}\) )
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[84, 74, 479, 252]]<|/det|>
+was placed at a distance of \(\approx 4\mathrm{m}\) from the target at an angle of \(31^{\circ}\) with respect to the laser axis. Carbons and heavier ions were blocked by a \(2\mathrm{mm}\) copper plate just in front of the diode (threshold: \(34\mathrm{MeV}\) for protons, \(64\mathrm{MeVu}^{- 1}\) for carbons). Signal read- out was provided by a fast oscilloscope (Tektronix MSO64, \(6\mathrm{GHz}\) , \(25\mathrm{GSamples}\) per second). Due to the lower sensitivity of this detection method (in comparison to the TPS) the TOF is suitable to confirm the maximum energy level, but is unable to derive particle numbers for the highest energetic protons.  
+
+<|ref|>text<|/ref|><|det|>[[84, 253, 480, 495]]<|/det|>
+Spatially resolved particle detection was conducted with a proton beam profiler. A calibrated scintillator (DRZ High from MCI Optonix) of size \(100\mathrm{mm}\times 100\mathrm{mm}\) was positioned at a distance of \(87\mathrm{mm}\) from the target. The emitted luminescence light was captured by a bandpass filtered \((540\mathrm{nm}\pm 2\mathrm{nm})\) CCD camera. Separation between protons of different energy is achieved by filtering using absorbers of different thicknesses (absorber thickness - threshold energy: \(8\mathrm{mm}\) Al - \(42\mathrm{MeV}\) protons | \(78\mathrm{MeVu}^{- 1}\) carbons, \(25\mathrm{mm}\) Al - \(80\mathrm{MeV}\) protons | \(149\mathrm{MeVu}^{- 1}\) carbons, \(38\mathrm{mm}\) Al - \(102\mathrm{MeV}\) protons | \(190\mathrm{MeVu}^{- 1}\) carbons). A slit in the central horizontal plane of the scintillator allowed for the parallel operation of the TPS and TOF detectors.  
+
+<|ref|>text<|/ref|><|det|>[[84, 497, 479, 642]]<|/det|>
+For selected shots a radiochromic film (RCF) stack was placed \(55\mathrm{mm}\) behind the target, blocking all other particle diagnostics. Gafchromic EBT3 films with a size of \(100\mathrm{mm}\times 50\mathrm{mm}\) and a dose range from \(0.1\mathrm{Gy}\) to \(20\mathrm{Gy}\) interleaved with copper plates as absorber material were used. The angular proton dose distribution was derived from line- outs along the horizontal axis covering a vertical angle of \(6.5^{\circ}\) for each energy layer.  
+
+<|ref|>sub_title<|/ref|><|det|>[[85, 660, 262, 675]]<|/det|>
+## Numerical simulations  
+
+<|ref|>text<|/ref|><|det|>[[85, 677, 479, 902]]<|/det|>
+Two different numerical codes were used to model the experiment. As a first stage, the FLASH code (v4.6.2) [45] was used in a 2D radially symmetric geometry with adaptive mesh refinement to perform a hydrodynamic simulation of the preceding laser light induced expansion of a \(270\mathrm{nm}\) Formvar foil. This simulation covered the time period from the onset of laser induced dielectric breakdown (around \(67\mathrm{ps}\) ) up to \(1\mathrm{ps}\) before the laser main pulse. The breakdown point was derived using the measured laser contrast [20] and optical probing studies of the laser- induced breakdown of Formvar foils following the approach described in [37, 46]. Tabulated equation- of- state was used in the simulations, generated using the  
+
+<|ref|>text<|/ref|><|det|>[[519, 73, 914, 366]]<|/det|>
+FEOS code [45]. The Lee- More conductivity and heat exchange were used. The resulting density profile from the hydrodynamic simulation was rotated around its axis of symmetry and used as initial input for a 3D PIC simulation, with densities below \(0.04n_c\) discarded. The final picosecond and main pulse interaction were modelled using the fully relativistic code PIConGPU (running on 900 A100- GPUs for \(35\mathrm{k}\) timesteps) [47]. The laser was focused to a Gaussian spot with \(w_0 = 2.14\mu \mathrm{m}\) on the front surface of the target in p- polarisation under oblique incidence \((45^{\circ})\) aiming at the center of the originally unexpanded foil. The temporal intensity profile was matched to measured data from [20] by fitting two exponential ramps and a \(30\mathrm{fs}\) - Gaussian with a peak \(a_0\) of about 50. A cell size of \(20\mathrm{nm}\) and one carbon and eight hydrogen macroparticles (thus, 13 electrons) per cell were initialised.  
+
+<|ref|>text<|/ref|><|det|>[[519, 374, 914, 521]]<|/det|>
+Acknowledgments. We thank the DRACO- PW operation team for their experiment support. This work was supported by Laserlab Europe V (PRISES, contract no. 871124) and the IMPULSE project (contract no. 871161). M.N. was supported by Kakenhi Grant No. 20H00140, Grant No. 21KK0049, Grant No. 22H00121, QST President's Strategic Grant (QST International Research Initiative (AAA98) and Creative Research (ABACS)).  
+
+<|ref|>sub_title<|/ref|><|det|>[[519, 539, 658, 558]]<|/det|>
+## Declarations  
+
+<|ref|>text<|/ref|><|det|>[[519, 571, 913, 603]]<|/det|>
+Conflict of interests. The authors declare no competing interests.  
+
+<|ref|>text<|/ref|><|det|>[[519, 611, 914, 659]]<|/det|>
+Data availability. The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.  
+
+<|ref|>text<|/ref|><|det|>[[519, 668, 914, 715]]<|/det|>
+Code availability. All codes written for use in this study are available from the corresponding author on reasonable request.  
+
+<|ref|>text<|/ref|><|det|>[[519, 725, 914, 887]]<|/det|>
+Author contributions. T.Z., S.A., F.- E.B., L.G., S.K., F.K., J.M.- N., I.P., T.P., M.Reh., M.Rei., H.- P.S., M.E.P.U., M.V. and K.Z. set up and performed the experiment. T.Z. performed the analysis and interpretation of the experimental data with support from F.- E.B., F.K., M.Reh., M.E.P.U. and K.Z. I.G. performed and analysed the numerical simulations with support from N.D. and T.K. T.Z., I.G., T.K. and K.Z. interpreted the numerical simulation data. T.Z. and K.Z. wrote the manuscript. U.S. and K.Z. supervised
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[80, 73, 476, 106]]<|/det|>
+the project. All authors reviewed the manuscript and contributed to discussions.  
+
+<|ref|>sub_title<|/ref|><|det|>[[82, 124, 202, 144]]<|/det|>
+## References  
+
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+
+<--- Page Split --->

preprint/preprint__c9737008b18c23ba767d22e1ac78d292fdd130b60598596274e817b2ab868dca/images_list.json

@@ -0,0 +1,62 @@
+[
+  {
+    "type": "image",
+    "img_path": "images/Figure_1.jpg",
+    "caption": "Fig 1. | Enhanced freshwater input into the Arctic Ocean and freshwater exportation into the Labrador Sea. Changes (2091-2100 minus 2006-2015) in (a) equivalent sea ice thickness, (b) precipitation minus evaporation, and (c) river runoff in the Arctic in HighRes. (d) Surface ocean circulation in the Labrador Sea in HighRes. The shading shows climatology mixed layer depth in March. The 1000m, 2000m and 3000m isobaths are indicated by blue contours. The black box encloses the Labrador Sea region. LC is the Labrador Current. WGC is the West Greenland Current. Time series of upper-250 m freshwater flux into the Labrador Sea from (e) the west of Greenland across Davis Strait (solid line, negative values for freshwater input into the Labrador Sea) and Hudson Strait (dashed lines, positive values freshwater input into the Labrador Sea) and (f) from the east of Greenland. The thin lines in (e) and (f) show annual-mean freshwater flux. The thick lines represent 20-year running mean.",
+    "footnote": [],
+    "bbox": [
+      [
+        157,
+        100,
+        825,
+        444
+      ]
+    ],
+    "page_idx": 17
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_2.jpg",
+    "caption": "Fig 2. | Freshening of the Labrador Sea during the 21st century. Changes (2091-2100 minus 2006-2015) in sea surface salinity (SSS) in (a) HighRes and (c) LowRes. The black dashed line indicates AR7W line. (b, d) Same as (a) and (c) but for salinity change across AR7W line. The contour lines show velocity of currents cross AR7W with interval of \\(12\\mathrm{cm}\\mathrm{s}^{-1}\\) . The dashed (solid) lines represent currents out of (into) the Labrador Sea.",
+    "footnote": [],
+    "bbox": [
+      [
+        181,
+        100,
+        795,
+        505
+      ]
+    ],
+    "page_idx": 18
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_3.jpg",
+    "caption": "Fig 3. | Strengthening of the ocean stratification in the interior Labrador Sea. Time-averaged potential density ( \\(\\sigma\\) , with sea surface as reference pressure and minus \\(1000\\mathrm{kgm^{-3}}\\) ) profile in the interior Labrador Sea in (a) HighRes and (c) LowRes. Solid (dashed) lines indicate the mean within 2006-2015 (2091-2100). Strengthening of the upper-1000m ocean stratification \\((\\Delta N^2\\) , calculated as \\(g / \\sigma^{1000\\mathrm{m}}.({\\sigma^{1000\\mathrm{m}} - \\sigma^{0\\mathrm{m}}}) / 1000)\\) under global warming and the contributions due to temperature changes \\((\\Delta N_T^2)\\) , calculated as \\(-g\\alpha (T^{1000\\mathrm{m}} - T^{0\\mathrm{m}}) / 1000\\) , where \\(T\\) is potential temperature and \\(\\alpha\\) is the thermal expansion coefficient at \\(500\\mathrm{m}\\) , and the salinity changes \\((\\Delta N_S^2)\\) , calculated as \\(g\\beta (S^{1000\\mathrm{m}} - S^{0\\mathrm{m}}) / 1000\\) where \\(S\\) is salinity and \\(\\beta\\) is the haline contraction coefficient at \\(500\\mathrm{m}\\) , in (b) HighRes and (d) LowRes. Only regions in the Labrador Sea deeper than \\(2000\\mathrm{m}\\) are considered here.",
+    "footnote": [],
+    "bbox": [
+      [
+        166,
+        102,
+        790,
+        512
+      ]
+    ],
+    "page_idx": 19
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_4.jpg",
+    "caption": "Fig 4. | Weakening of Labrador Sea overturning and the AMOC. Time-averaged overturning across OSNAP West in (a) HighRes and (c) LowRes. Solid (dashed) lines indicate the mean within 2006-2015 (2091-2100). The normalized percentage change in the AMOC from 2006-2015 to 2091-2100 in (b) HighRes and (d) LowRes. Normalization uses the maximum AMOC value at \\(40^{\\circ}\\mathrm{N}\\) in 2006-2015 in each simulation. The AMOC is calculated in density space and then remapped into depth space using the zonal mean depth of each density layer.",
+    "footnote": [],
+    "bbox": [
+      [
+        161,
+        99,
+        825,
+        460
+      ]
+    ],
+    "page_idx": 20
+  }
+]

preprint/preprint__c9737008b18c23ba767d22e1ac78d292fdd130b60598596274e817b2ab868dca/preprint__c9737008b18c23ba767d22e1ac78d292fdd130b60598596274e817b2ab868dca.mmd

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+
+# Roles of the Labrador Current in the Atlantic Meridional Overturning Circulation responses to greenhouse warming  
+
+Xuan Shan  
+
+xuan.shan@whoi.edu  
+
+woods hole oceanographic institution https://orcid.org/0000- 0002- 4817- 9674  
+
+Shantong Sun  
+
+Laoshan Laboratory https://orcid.org/0000- 0002- 6932- 5589  
+
+Lixin Wu  
+
+Ocean University of China https://orcid.org/0000- 0002- 4694- 5531  
+
+Michael Spall  
+
+Woods Hole Oceanographic Institution  
+
+## Article  
+
+Keywords:  
+
+Posted Date: February 19th, 2024  
+
+DOI: https://doi.org/10.21203/rs.3.rs- 3950226/v1  
+
+License: © (T) This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License  
+
+Additional Declarations: There is NO Competing Interest.  
+
+Version of Record: A version of this preprint was published at Nature Communications on August 27th, 2024. See the published version at https://doi.org/10.1038/s41467- 024- 51449- 9.
+
+<--- Page Split --->
+
+2 Roles of the Labrador Current in the Atlantic Meridional Overturning Circulation responses to greenhouse warming  
+
+3 Xuan Shan \(^{1,2*}\) , Shantong Sun \(^{3*}\) , Lixin Wu \(^{3,1}\) , and Michael Spall \(^{2}\) \(^{1}\) Frontiers Science Center for Deep Ocean Multispheres and Earth System and Key Laboratory of Physical Oceanography, Ocean University of China, Qingdao, China \(^{2}\) Woods Hole Oceanographic Institution, Woods Hole, MA, USA \(^{3}\) Laoshan Laboratory, Qingdao, China
+
+<--- Page Split --->
+
+## Abstract  
+
+Anthropogenic warming is projected to enhance Arctic freshwater exportation into the Labrador Sea. This extra freshwater may weaken deep convections and contribute to the Atlantic Meridional Overturning Circulation (AMOC) decline. Here, by analyzing an unprecedented high- resolution climate model simulation for the 21st century, we show that the Labrador Current strongly restricts the lateral spread of freshwater from the Artic Ocean into the open ocean such that the freshwater input has a limited role in weakening the overturning circulation. In contrast, in the absence of a strong Labrador Current, the extra freshwater is allowed to spread into the interior region and eventually shut down deep convections in the Labrador Sea. Given that the Labrador Sea overturning makes a significant contribution to the AMOC in many climate models, our results suggest that the AMOC decline during the 21st century could be overestimated in these models due to the unresolved Labrador Current.
+
+<--- Page Split --->
+
+## Introduction  
+
+Increased freshwater supply to the Arctic Ocean in a warming climate makes the high- latitude regions susceptible to dramatic changes in ocean circulation. As anthropogenic warming continues in the 21st century, Arctic summer sea ice is likely to disappear in a few decades \(^{1,2}\) , increasing the Arctic freshwater storage. A stronger hydrological cycle in the atmosphere will also inject more freshwater into the Arctic through an increase in net precipitation and river runoff \(^{3,4}\) . Coupled climate models suggest that these extra freshwater sources to the Arctic will lead to a larger freshwater exportation to the subpolar North Atlantic in the 21st century \(^{5,6}\) . The additional freshwater will increase ocean stratification and potentially slow down the Atlantic Meridional Overturning Circulation (AMOC), with serious consequences for regional and global climates \(^{7 - 10}\) .  
+
+In this study, we focus on the influence of the extra freshwater from the Arctic on the ocean circulation in the Labrador Sea, a critical region for AMOC changes \(^{11 - 14}\) . Climate models consistently project a slowdown of the AMOC during the 21st century due to warming and freshening in the high- latitude North Atlantic \(^{15,16}\) . However, the overturning and deep convection responses to freshwater input are crucially impacted by the boundary current that typically circulates around open- ocean convection regions, where deep water forms. For example, there is significant freshwater input into the Weddell Sea, a key region for bottom water formation in the Southern Ocean, due to the melting of Antarctic ice sheet and sea ice. In the presence of a well- resolved Antarctic Slope Current, the extra freshwater largely stays on the shelf region as the slope current restricts the lateral spread of freshwater, with limited influence on open- ocean convection \(^{17}\) . The Labrador Current can also restrict the lateral exchange of freshwater between the shelf and open ocean \(^{18,19}\) . Thus, we hypothesize that, when the extra freshwater enters the Labrador Sea from the Arctic through the Canadian Arctic Archipelago \(^{20}\) , the Labrador Current restricts the freshwater from spreading into the open ocean and weakening the overturning circulation. Typical climate models for the Coupled Model Intercomparison Project (CMIP) of Intergovernmental Panel for Climate Change (IPCC) assessment report, mostly at \(1^{\circ}\) resolution, are unable to resolve the Labrador Current \(^{21}\) (Fig. S1), and thus could overestimate the overturning responses to the freshwater forcing due to anthropogenic warming \(^{22}\) .
+
+<--- Page Split --->
+
+Here, we study the role of the Labrador Current in regulating the overturning responses to an increased Arctic freshwater export in the Labrador Sea and its influence on AMOC changes in an unprecedented high- resolution coupled simulation over the 21st century (2006- 2100) under the high- emission scenario (RCP8.5). The simulation (HighRes) \(^{23}\) is conducted using the Community Earth System Model version 1 (CESM1), with a nominal horizontal resolution of \(0.1^{\circ}\) for the ocean, about \(6.5 \mathrm{km}\) in the Labrador Sea, and \(0.25^{\circ}\) for the atmosphere (see “CESM simulations” in “Method”). HighRes performs well in reproducing observations, including the Labrador Current (Fig. S1), the subpolar North Atlantic overturning (Fig. S2), and the North Atlantic sea surface temperature trend during the 20th century (Fig. S3), a footprint for AMOC weakening \(^{24}\) . These processes are often biased in coarse- resolution climate models (Fig. S1- 3). To quantify the role of the Labrador Current in regulating the overturning circulation changes, we also look at the overturning responses in a coarse- resolution counterpart of HighRes, LowRes, with a nominal \(1^{\circ}\) resolution as in most climate models in CMIP6. HighRes and LowRes differ from each other primarily in their horizontal resolutions. We show that the well- resolved Labrador Current in HighRes strongly restricts freshwater on the shelf and leads to a much weaker response in the Labrador Sea overturning circulation than LowRes, in which the Labrador Current is not resolved. Thus, we conclude that, without resolving the Labrador Current, coarse- resolution climate models may overestimate the AMOC decline during the 21st century.  
+
+## Results  
+
+## Increased Arctic freshwater exportation into the Labrador Sea  
+
+As in CMIP simulations \(^{5,6}\) , HighRes predicts a significant increase in freshwater input to the Arctic Ocean under anthropogenic warming (Fig. 1a- c). Under the RCP8.5 scenario in HighRes, the annual- mean sea ice volume decreases by \(99\%\) from 16,297 \(\mathrm{km^3}\) at 2006- 2015 to \(243 \mathrm{km^3}\) at the end of the 21st century; summer sea ice is completely lost in the 1960s. Net precipitation and river runoff also increases significantly due to a stronger atmospheric hydrological cycle by about \(161\%\) and \(39\%\) , respectively. The larger Arctic freshwater input will necessarily lead to an increased freshwater exportation into the subpolar North Atlantic, including the Labrador Sea.
+
+<--- Page Split --->
+
+We estimate the freshwater transport into the Labrador Sea from north across Davis Strait, from west across Hudson Strait, and from east by the West Greenland Current in HighRes (Fig. 1d). Annual- mean salinity in year 2006 is used as the reference salinity at each section (see "Freshwater flux" in "Method"). The increase in freshwater transport from Davis Strait is most significant, at a rate of about \(0.5\mathrm{mSv / year}\) over the 21st century (Fig. 1e). The freshwater transport across Hudson Strait also increases, but only at \(0.1\mathrm{mSv / year}\) (Fig. 1e). Both trends are statistically significant at the \(95\%\) confidence level (see "Statistical analysis" in "Method"). No significant trend appears in the freshwater transport coming from the east by the west Greenland Current (Fig. 1f). The freshwater pathway into the Labrador Sea is determined by several processes, including the Arctic circulation and the location of freshwater sources. The contrast in freshwater transport trends between the west and the east direction is likely related to the structure of freshwater increase in the Arctic Ocean in HighRes: freshwater content increases in the Canadian basin but decreases in the Eurasian basin (Fig. S4).  
+
+## Surface freshening confined to the western shelf by the Labrador Current  
+
+The extra freshwater transport into the Labrador Sea reduces sea surface salinity, but the freshening is mostly confined to the shelf close to Newfoundland and Labrador of Canada (Fig. 2a). The freshening on the shelf is about \(0.67\mathrm{psu}\) in 2091- 2100 relative to 2006- 2015. In contrast, in the interior Labrador Sea, where deep convection occurs (Fig. 1d), the surface freshening is only \(0.27\mathrm{psu}\) . We quantify the salinity change along the AR7W line. The freshening is most obvious in the upper \(150\mathrm{m}\) on the shelf (Fig. 2b). The exchange of freshwater between the shelf and the open ocean is strongly restricted by the narrow Labrador Current (Fig. 2b, Fig. S1), consistent with previous studies \(^{18,19}\) . The Labrador Current may also help flush the freshwater out into the North Atlantic Ocean, contributing to reducing the freshening effects. Coarse- resolution models (e.g., LowRes) are not able to resolve the Labrador Current, and thus may misrepresent the freshening due to increased freshwater input. Indeed, with similar freshwater transport increases in LowRes (Fig. S5), the surface freshening is almost uniformly in the Labrador Sea, with a \(1.52\mathrm{psu}\) decrease in the interior (Fig. 2c). The broader surface salinity decrease is related to the too weak and wide Labrador Current (Fig. 2d, Fig. S1), which allows freshwater to enter the interior Labrador Sea. Thus, we conclude that coarse- resolution climate models could overestimate the freshwater influence on the surface salinity change in the Labrador Sea.
+
+<--- Page Split --->
+
+The Labrador Current also regulates ocean stratification and mixed layer depth changes in the Labrador Sea due to surface freshening. We focus on the central Labrador Sea, deeper than 2000 m, where deep convections take place. Ocean stratification, quantified as the density difference between the sea surface and \(1\mathrm{km}\) depth divided by \(1\mathrm{km}\) , increases by \(91\%\) in 2091- 2100 relative to 2006- 2015 in HighRes. The strengthening is surface intensified and almost equally attributed to surface warming and freshening (Fig. 3a- b, Fig. S6). In contrast with HighRes, the upper- ocean stratification increases more dramatically in the 21st century by \(158\%\) in LowRes. The larger stratification increase in LowRes is due to a dramatic decrease of the surface density associated with the widespread surface freshening in the Labrador Sea (Fig. 3c- d, Fig. S6). Similar conclusions can be drawn for mixed layer depth (MLD) changes (Fig. S7). In HighRes, the March MLD in the central Labrador Sea decreases by \(56\%\) from \(430\mathrm{m}\) in 2006- 2015 to \(190\mathrm{m}\) in 2091- 2100. While in LowRes, the March MLD shoals by \(91\%\) from \(928\mathrm{m}\) to \(83\mathrm{m}\) during the same period. We note that the present- day MLD in LowRes is overestimated as in many coarse- resolution models \(^{25 - 27}\) . The results highlight the role of the Labrador Current in future ocean stratification changes in the Labrador Sea and suggest that coarse- resolution models may overestimate the stratification increase due to freshwater forcing.  
+
+## Response of the Labrador Sea overturning and the AMOC  
+
+Through its impacts on the surface freshening and stratification changes, the Labrador Current regulates the overturning circulation changes in a warming climate. The stratification increase will decrease deep water formation in the Labrador Sea and potentially contribute to the AMOC weakening during the 21st century. We quantify the Labrador Sea overturning at OSNAP West (Fig. 4a and d, see "OSNAP overturning streamfunction" in "Method"). The Labrador Sea overturning is weakened by about \(55\%\) in HighRes from 2006- 2015 to 2091- 2100, with a linear trend of - 5.7 Sv/century. In comparison, the weakening of the Labrador Sea overturning in LowRes is more substantial by about \(90\%\) from 2006- 2015 to 2091- 2100, with a linear trend of - 18 Sv/century. The deep convection in LowRes almost completely shuts down at the end of the 21st century. The much stronger weakening of the Labrador Sea overturning in LowRes can be attributed to the overly stratified ocean in the Labrador Sea. We
+
+<--- Page Split --->
+
+calculate the surface forced water mass transformation (SFWMT), a good indicator for the actual overturning<sup>13,14,28</sup>, using the surface buoyancy flux and surface density (see "Surface forced water mass transformation" in "Method" section). The SFWMT dominates the Labrador Sea overturning circulation as well as its changes during the 21st century (Fig. S8). Decomposing the SFWMT changes into contributions due to changes in the surface buoyancy flux and surface density stratification (see "Surface forced water mass transformation" in "Method"), we show that the differing Labrador Sea overturning responses between HighRes and LowRes are mainly due to changes in surface stratification (Fig. S8). The surface buoyancy flux is not significantly different between HighRes and LowRes at 98% confidence level (Fig. S9) and cannot explain their difference in the overturning changes.  
+
+The weakening of the Labrador Sea overturning circulation contributes to the AMOC decline during the 21st century. We calculate the North Atlantic overturning in density space and then remap it back to depth space following previous studies<sup>29,30</sup> (see "Density- space AMOC" in "Method"). Consistent with the Labrador Sea overturning circulation changes, the AMOC decline appears to be faster in LowRes (Fig. 4e and f) than HighRes (Fig. 4b and c). Overturning changes across OSNAP East, which dominates the North Atlantic overturning in observations, may also contribute to the faster AMOC decline in LowRes. However, the overturning across OSNAP East declines at a rate of - 12.2 Sv/century in LowRes and - 8.9 Sv/century in HighRes, with a smaller difference between these two simulations than OSNAP West (Fig. S10 and S11).  
+
+## Discussion  
+
+In this study, we highlight the role of the Labrador Current in regulating the Labrador Sea responses to increased freshwater input due to anthropogenic warming. The narrow Labrador Current strongly restricts the lateral exchange of freshwater between the continental shelf and open ocean. In the absence of this narrow boundary current, the extra freshwater input from the Arctic spreads into the open ocean and causes a much stronger increase in ocean stratification, leading to an overestimated weakening of the Labrador Sea overturning circulation. The impact of the Labrador Current in restricting lateral freshwater exchange might evolve as the climate continues to warm. HighRes
+
+<--- Page Split --->
+
+predicts a weakening of the Labrador Current due to surface wind changes (Fig. S12), suggesting a slightly diminishing role of the Labrador Current in the future climate. Nevertheless, given that the Labrador Sea overturning circulation makes a significant contribution to the AMOC in many climate models of coarse resolution \(^{25 - 27}\) , our results suggest that the AMOC weakening may be overestimated in these climate models \(^{22}\) .  
+
+With the advent of higher- resolution climate projections, we might expect more reliable and consistent climate predictions as compared to coarse- resolution ones. However, the dependence of the AMOC decline rate on model resolutions appears to be sensitive to the models being used. Consistent with CESM in this study, a slower AMOC decline rate at higher resolution in response to anthropogenic warming is simulated in GFDL models \(^{31}\) . But this is different from many HighResMIP simulations \(^{32}\) , most of which use NEMO as their ocean component \(^{33,34}\) and only partly resolve the boundary current at \(0.25^{\circ}\) resolution. The different results may also be related to the different length of simulations: HighResMIP models simulate years 2015- 2050, but most of the AMOC decline during the 21st century occurs post- \(2050^{15,35}\) . Therefore, high- resolution projections with various model configurations until 2100 are highly desired to have a more comprehensive understanding of the AMOC changes during the 21st century.  
+
+As anthropogenic warming continues, more freshwater is expected to enter the subpolar North Atlantic from the Greenland ice sheet melting and Arctic freshwater release. The extra freshwater input will necessarily interact with deep convection and cause a slowdown of the AMOC \(^{36 - 38}\) . However, our results suggest that future AMOC responses will be sensitive to how the extra freshwater input is distributed in the high- latitude region. To address this question, we need to monitor the freshwater sources and their exportation pathways through Arctic- subpolar North Atlantic gateways towards regions that could impact the AMOC. High- resolution models are also desired for a more accurate representation of freshwater transports associated with narrow boundary currents \(^{39 - 40}\) and oceanic eddies \(^{41 - 44}\) that are not resolved in coarse- resolution models.
+
+<--- Page Split --->
+
+## Methods  
+
+## CESM simulations  
+
+The simulations used in this paper were carried out by CESM1.3 at the International Laboratory for High- Resolution Earth System Prediction (iHESP) \(^{23}\) . CESM comprises the Community Atmosphere Model version 5 (CAM5), the Parallel Ocean Program version 2 (POP2), the Community Ice Code version 4 (CICE4), and the Community Land Model version 4 (CLM4). We make use of the configuration with high and low model horizontal resolutions. For HighRes, the resolutions of atmosphere, ocean and sea- ice components are \(0.25^{\circ}\) , \(0.1^{\circ}\) , and \(0.1^{\circ}\) , respectively. For LowRes, the nominal horizontal resolutions are \(1^{\circ}\) . The simulations we use were run under the representative concentration pathway 8.5 (RCP8.5) forcing from 2006 to 2100 in accordance with CMIP experimental protocol.  
+
+## Freshwater flux  
+
+The freshwater flux (FWF in unit of \(\mathrm{mSv} = 10^{- 3} \mathrm{~m}^{3} \mathrm{~s}^{- 1}\) ) is defined as follows  
+
+\[\mathrm{FWF}(x,y,z,t) = \nu (x,y,z,t)\cdot \frac{S_{\mathrm{ref}} - S(x,y,z,t)}{S_{\mathrm{ref}}} dA \quad (1)\]  
+
+where \(\nu\) is the cross- section velocity (in unit of \(\mathrm{m} \mathrm{s}^{- 1}\) ), \(S\) is the salinity (in unit of \(\mathrm{psu}\) ), \(S_{\mathrm{ref}}\) is the reference salinity which is set as the annual- mean salinity in 2006, as a function of longitude, latitude and depth, \(dA\) is the cross- section area at each grid point (in unit of \(\mathrm{m}^{2}\) ). We calculate the freshwater flux into the Labrador Sea by summing up the freshwater flux at each grid point along each section denoted in Figure 1d.  
+
+## Statistical analysis  
+
+The linear trends in freshwater transport and overturning circulation are calculated using least- square regression, with the statistical significance estimated using two- tailed Student's \(t\) - test.  
+
+## OSNAP overturning streamfunction  
+
+Dense waters that reside in the lower limb of the AMOC are produced mainly in the eastern subpolar North Atlantic (i.e., the Irminger and Iceland basins) in observations, and to a lesser extent, in the western subpolar North Atlantic (i.e., the Labrador Sea) \(^{45}\) . The strength of dense water formation can be measured by overturning across OSNAP West and OSNAP East in density space. In the main text, OSNAP overturning is
+
+<--- Page Split --->
+
+calculated in density space. Density referenced to \(2000\mathrm{- m}\) depth \((\sigma_{2})\) is used as the vertical coordinate (in unit of \(\mathrm{kgm^{- 3}}\) , after subtracting \(1000\mathrm{kgm^{- 3}}\) ). Volume fluxes are integrated from west to east and from higher to lower density.  
+
+## Surface forced water mass transformation  
+
+The overturning streamfunction in the subpolar North Atlantic and its variability are largely determined by the surface forced water mass transformation (SFWMT)13,14,28. In this paper we calculate the SFWMT (in units of \(\mathrm{Sv} = 10^{6}\mathrm{m}^{3}\mathrm{s}^{- 1}\) ) as a function of density referenced to \(2000\mathrm{- m}\) depth \(\sigma_{2}\) (in unit of \(\mathrm{kgm^{- 3}}\) , after subtracting \(1000\mathrm{kgm^{- 3}}\) ) by integrating the surface density flux \((B\) , in units of \(\mathrm{kg}\) seawater \(\mathrm{m}^{- 2}\mathrm{s}^{- 1}\) , defined as positive for ocean density increase) over surface density outcrop regions \((dA\) , in unit of \(\mathrm{m}^{2}\) ; corresponding to \(\sigma_{2}\) from \(\sigma_{2} - \Delta \sigma_{2} / 2\) to \(\sigma_{2} + \Delta \sigma_{2} / 2\) ) as follows  
+
+\[\mathrm{SFWMT}\big(\sigma_{2}\big) = \frac{1}{\Delta\sigma_{2}}\iint BdA \quad (2)\]  
+
+The density flux comprises heat and salt fluxes that referred to as \(B_{\mathrm{heat}}\) and \(B_{\mathrm{salt}}\) , respectively. The heat flux is  
+
+\[B_{\mathrm{heat}} = -\frac{\alpha}{C_p} Q \quad (3)\]  
+
+where \(\alpha\) is the thermal expansion coefficient (in unit of \(\mathrm{K}^{- 1}\) ), \(C_p\) is the specific heat capacity of seawater (in unit of \(\mathrm{Jkg^{- 1}K^{- 1}}\) ), \(Q\) is the surface net heat flux (in units of W \(\mathrm{m}^{- 2}\) , defined as positive for ocean heat gain), which is the sum of surface radiation and turbulent heat fluxes. The salt flux is  
+
+\[B_{\mathrm{salt}} = \beta \frac{S}{1 - S} F \quad (4)\]  
+
+where \(S\) is the sea surface salinity (in unit of \(\mathrm{msu} = 10^{- 3}\mathrm{psu}\) ), \(\beta\) is the haline contraction coefficient (in unit of \(\mathrm{msu}^{- 1}\) ), and \(F\) is virtual salt flux (in units of \(\mathrm{kg}\) freshwater \(\mathrm{m}^{- 2}\mathrm{s}^{- 1}\) , defined as positive for ocean salinity increase). Variations in SFWMT can be decomposed into contributions due to changes in surface density flux and surface density stratification. We calculate the latter (referred to as \(\mathrm{SFWMT}_{\mathrm{OCN}}\) ) in this paper by replacing the time- dependent surface density flux with the annual- mean surface density flux in 2006 in Eq. (2).  
+
+## Density-space AMOC
+
+<--- Page Split --->
+
+We calculate the AMOC in density space that better represents the overturning circulation at high latitudes. The AMOC streamfunction is defined as follows  
+
+\[\mathrm{AMOC}(y,\sigma ,t) = -\int_{z_{\mathrm{bot}}}^{0}\int_{x_{w}}^{x_{e}}H(\sigma '(x,y,z,t) - \sigma)v(x,y,z,t)dxdz \quad (5)\]  
+
+where \(H\) is the Heaviside function, \(\sigma\) ' represent the density field, \(x\) is longitude, \(y\) is latitude, \(z\) is depth, \(t\) is time, \(\sigma\) is the density at which the streamfunction is calculated, and \(v\) is the meridional velocity. The zonal integral is performed across the Atlantic Ocean from the western boundary \((x_{w})\) to the eastern boundary \((x_{e})\) , and the vertical integral is performed from the ocean bottom \((z_{\mathrm{bot}})\) to the sea surface. Density referenced to \(2000\mathrm{- m}\) depth \((\sigma_{2})\) is used as the vertical coordinate (in unit of \(\mathrm{kg m^{- 3}}\) , after subtracting \(1000\mathrm{kg m^{- 3}}\) ). We also remap the AMOC streamfunction in density space into depth space using the time- and zonally averaged depth of each density layer following previous studies \(^{29,30}\) .
+
+<--- Page Split --->
+
+## Acknowledgments  
+
+Funding: National Science Foundation Grant OPP- 2211691 (to M.S.), Ocean University of China Postdoctoral Fellowship for International Research (to X.S.)  
+
+## Author contributions  
+
+Conceptualization: Shantong Sun, Lixin Wu  Investigation: Xuan Shan  Visualization: Xuan Shan  Supervision: Shantong Sun, Lixin Wu  Writing—original draft: Xuan Shan  Writing—review & editing: Shantong Sun, Lixin Wu, Michael A. Spall  
+
+## Competing interests  
+
+Authors declare that they have no competing interests.  
+
+## Data availability  
+
+All data needed to evaluate the conclusions in the paper are present in the main text or the supplementary materials. The climate model simulations and observation data used in this study are publicly available and can be downloaded from the following websites: CESM model outputs (https://ihep.github.io/archive/products/ihep- products/data- release/DataRelease_Phase2. html or http://ihep.qnlm.ac), OSNAP overturning (https://www.o- snap.org/), Hadley Centre Sea Ice and Sea Surface Temperature data set (HadISST, https://www.metoffice.gov.uk/hadobs/hadisst/), and NOAA Extended Reconstructed SST V5 (ERSSTv5, https://psl.noaa.gov/data/gridded/data.noaa.ersst.v5.html).
+
+<--- Page Split --->
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+<--- Page Split --->
+
+Ocean Sci. 13, 609- 622 (2017). 27. Li, F. et al. Local and downstream relationships between Labrador Sea Water volume and North Atlantic Meridional Overturning Circulation variability. J. Clim. 32, 3883- 3898 (2019). 28. Jackson, L. C. & Petit, T. North Atlantic overturning and water mass transformation in CMIP6 models. Clim. Dyn. 60, 2871- 2891 (2023). 29. Xu, X., Rhines, P. B. & Chassignet, E. P. On mapping the diapycnal water mass transformation of the upper North Atlantic Ocean. J. Phys. Oceanogr. 48, 2233- 2258 (2018). 30. Rousselet, L., Cessi, P. & Forget, G. Routes of the upper branch of the Atlantic Meridional Overturning Circulation according to an ocean state estimate. Geophys. Res. Lett. 47, e2020GL089137 (2020). 31. Delworth, T. L. et al. Simulated climate and climate change in the GFDL CM2.5 high-resolution coupled climate model. J. Clim. 25, 2755- 2781 (2012). 32. Roberts, M. J. et al. Sensitivity of the Atlantic Meridional Overturning Circulation to model resolution in CMIP6 HighResMIP simulations and implications for future changes. J. Adv. Model. Earth Syst. 12, e2019MS002014 (2020). 33. Jackson, L. C. et al. Impact of ocean resolution and mean state on the rate of AMOC weakening. Clim. Dyn. 55, 1711- 1732 (2020). 34. Koenigk, T. et al. Deep mixed ocean volume in the Labrador Sea in HighResMIP models. Clim. Dyn. 57, 1895- 1918 (2021). 35. Cheng, W., Chiang, J. C. H. & Zhang, D. Atlantic Meridional Overturning Circulation (AMOC) in CMIP5 models: RCP and historical simulations. J. Clim. 26, 7187- 7197 (2013). 36. Rahmstorf, S. et al. Exceptional twentieth- century slowdown in Atlantic Ocean overturning circulation. Nat. Clim. Change 5, 475- 480 (2015). 37. Böning, C. W., Behrens, E., Biastoch, A., Getzlaff, K. & Bamber, J. L. Emerging impact of Greenland meltwater on deepwater formation in the North Atlantic Ocean. Nat. Geosci. 9, 523- 527 (2016). 38. Yang, Q. et al. Recent increases in Arctic freshwater flux affects Labrador Sea convection and Atlantic overturning circulation. Nat. Commun. 7, 10525 (2016). 39. Luo, H. et al. Oceanic transport of surface meltwater from the southern Greenland ice sheet. Nat. Geosci. 9, 528- 532 (2016). 40. Wang, H., Legg, S. & Hallberg, R. The effect of Arctic freshwater pathways on
+
+<--- Page Split --->
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+424 North Atlantic convection and the Atlantic Meridional Overturning Circulation. J. Clim. 31, 5165- 5188 (2018). 425 41. Schmidt, S. & Send, U. Origin and composition of seasonal Labrador Sea freshwater. J. Phys. Oceanogr. 37, 1445- 1454 (2007). 426 42. McGeehan, T. & Maslowski, W. Impact of shelf- basin freshwater transport on deep convection in the western Labrador Sea. J. Phys. Oceanogr. 41, 2187- 2210 (2011). 427 43. Weijer, W., Maltrud, M. E., Hecht, M. W., Dijkstra, H. A., & Kliphuis, M. A. Response of the Atlantic Ocean circulation to Greenland Ice Sheet melting in a strongly- eddying ocean model. Geophys. Res. Lett. 39, L09606 (2012). 428 44. Rieck, J. K., Böning, C. W. & Getzlaff, K. The nature of eddy kinetic energy in the Labrador Sea: Different types of mesoscale eddies, their temporal variability, and impact on deep convection. J. Phys. Oceanogr. 49, 2075- 2094 (2019). 429 45. Lozier, M. S. et al. A sea change in our view of overturning in the subpolar North Atlantic. Science 363, 516- 521 (2019).
+
+<--- Page Split --->
+![](images/Figure_1.jpg)
+
+<center>Fig 1. | Enhanced freshwater input into the Arctic Ocean and freshwater exportation into the Labrador Sea. Changes (2091-2100 minus 2006-2015) in (a) equivalent sea ice thickness, (b) precipitation minus evaporation, and (c) river runoff in the Arctic in HighRes. (d) Surface ocean circulation in the Labrador Sea in HighRes. The shading shows climatology mixed layer depth in March. The 1000m, 2000m and 3000m isobaths are indicated by blue contours. The black box encloses the Labrador Sea region. LC is the Labrador Current. WGC is the West Greenland Current. Time series of upper-250 m freshwater flux into the Labrador Sea from (e) the west of Greenland across Davis Strait (solid line, negative values for freshwater input into the Labrador Sea) and Hudson Strait (dashed lines, positive values freshwater input into the Labrador Sea) and (f) from the east of Greenland. The thin lines in (e) and (f) show annual-mean freshwater flux. The thick lines represent 20-year running mean. </center>
+
+<--- Page Split --->
+![](images/Figure_2.jpg)
+
+<center>Fig 2. | Freshening of the Labrador Sea during the 21st century. Changes (2091-2100 minus 2006-2015) in sea surface salinity (SSS) in (a) HighRes and (c) LowRes. The black dashed line indicates AR7W line. (b, d) Same as (a) and (c) but for salinity change across AR7W line. The contour lines show velocity of currents cross AR7W with interval of \(12\mathrm{cm}\mathrm{s}^{-1}\) . The dashed (solid) lines represent currents out of (into) the Labrador Sea. </center>
+
+<--- Page Split --->
+![](images/Figure_3.jpg)
+
+<center>Fig 3. | Strengthening of the ocean stratification in the interior Labrador Sea. Time-averaged potential density ( \(\sigma\) , with sea surface as reference pressure and minus \(1000\mathrm{kgm^{-3}}\) ) profile in the interior Labrador Sea in (a) HighRes and (c) LowRes. Solid (dashed) lines indicate the mean within 2006-2015 (2091-2100). Strengthening of the upper-1000m ocean stratification \((\Delta N^2\) , calculated as \(g / \sigma^{1000\mathrm{m}}.({\sigma^{1000\mathrm{m}} - \sigma^{0\mathrm{m}}}) / 1000)\) under global warming and the contributions due to temperature changes \((\Delta N_T^2)\) , calculated as \(-g\alpha (T^{1000\mathrm{m}} - T^{0\mathrm{m}}) / 1000\) , where \(T\) is potential temperature and \(\alpha\) is the thermal expansion coefficient at \(500\mathrm{m}\) , and the salinity changes \((\Delta N_S^2)\) , calculated as \(g\beta (S^{1000\mathrm{m}} - S^{0\mathrm{m}}) / 1000\) where \(S\) is salinity and \(\beta\) is the haline contraction coefficient at \(500\mathrm{m}\) , in (b) HighRes and (d) LowRes. Only regions in the Labrador Sea deeper than \(2000\mathrm{m}\) are considered here. </center>
+
+<--- Page Split --->
+![](images/Figure_4.jpg)
+
+<center>Fig 4. | Weakening of Labrador Sea overturning and the AMOC. Time-averaged overturning across OSNAP West in (a) HighRes and (c) LowRes. Solid (dashed) lines indicate the mean within 2006-2015 (2091-2100). The normalized percentage change in the AMOC from 2006-2015 to 2091-2100 in (b) HighRes and (d) LowRes. Normalization uses the maximum AMOC value at \(40^{\circ}\mathrm{N}\) in 2006-2015 in each simulation. The AMOC is calculated in density space and then remapped into depth space using the zonal mean depth of each density layer. </center>
+
+<--- Page Split --->
+
+## Supplementary Files  
+
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+SupplementaryInformation.pdf
+
+<--- Page Split --->

preprint/preprint__c9737008b18c23ba767d22e1ac78d292fdd130b60598596274e817b2ab868dca/preprint__c9737008b18c23ba767d22e1ac78d292fdd130b60598596274e817b2ab868dca_det.mmd

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+<|ref|>title<|/ref|><|det|>[[44, 108, 877, 210]]<|/det|>
+# Roles of the Labrador Current in the Atlantic Meridional Overturning Circulation responses to greenhouse warming  
+
+<|ref|>text<|/ref|><|det|>[[44, 230, 155, 247]]<|/det|>
+Xuan Shan  
+
+<|ref|>text<|/ref|><|det|>[[52, 257, 256, 273]]<|/det|>
+xuan.shan@whoi.edu  
+
+<|ref|>text<|/ref|><|det|>[[44, 303, 744, 323]]<|/det|>
+woods hole oceanographic institution https://orcid.org/0000- 0002- 4817- 9674  
+
+<|ref|>text<|/ref|><|det|>[[44, 328, 168, 345]]<|/det|>
+Shantong Sun  
+
+<|ref|>text<|/ref|><|det|>[[50, 350, 590, 368]]<|/det|>
+Laoshan Laboratory https://orcid.org/0000- 0002- 6932- 5589  
+
+<|ref|>text<|/ref|><|det|>[[44, 374, 121, 391]]<|/det|>
+Lixin Wu  
+
+<|ref|>text<|/ref|><|det|>[[50, 396, 638, 415]]<|/det|>
+Ocean University of China https://orcid.org/0000- 0002- 4694- 5531  
+
+<|ref|>text<|/ref|><|det|>[[44, 420, 164, 438]]<|/det|>
+Michael Spall  
+
+<|ref|>text<|/ref|><|det|>[[52, 443, 393, 461]]<|/det|>
+Woods Hole Oceanographic Institution  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 503, 103, 520]]<|/det|>
+## Article  
+
+<|ref|>text<|/ref|><|det|>[[44, 540, 137, 558]]<|/det|>
+Keywords:  
+
+<|ref|>text<|/ref|><|det|>[[44, 578, 336, 597]]<|/det|>
+Posted Date: February 19th, 2024  
+
+<|ref|>text<|/ref|><|det|>[[44, 616, 475, 635]]<|/det|>
+DOI: https://doi.org/10.21203/rs.3.rs- 3950226/v1  
+
+<|ref|>text<|/ref|><|det|>[[44, 653, 914, 696]]<|/det|>
+License: © (T) This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License  
+
+<|ref|>text<|/ref|><|det|>[[44, 714, 535, 733]]<|/det|>
+Additional Declarations: There is NO Competing Interest.  
+
+<|ref|>text<|/ref|><|det|>[[42, 770, 936, 813]]<|/det|>
+Version of Record: A version of this preprint was published at Nature Communications on August 27th, 2024. See the published version at https://doi.org/10.1038/s41467- 024- 51449- 9.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[115, 120, 833, 160]]<|/det|>
+2 Roles of the Labrador Current in the Atlantic Meridional Overturning Circulation responses to greenhouse warming  
+
+<|ref|>text<|/ref|><|det|>[[115, 180, 837, 300]]<|/det|>
+3 Xuan Shan \(^{1,2*}\) , Shantong Sun \(^{3*}\) , Lixin Wu \(^{3,1}\) , and Michael Spall \(^{2}\) \(^{1}\) Frontiers Science Center for Deep Ocean Multispheres and Earth System and Key Laboratory of Physical Oceanography, Ocean University of China, Qingdao, China \(^{2}\) Woods Hole Oceanographic Institution, Woods Hole, MA, USA \(^{3}\) Laoshan Laboratory, Qingdao, China
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[148, 86, 227, 101]]<|/det|>
+## Abstract  
+
+<|ref|>text<|/ref|><|det|>[[145, 108, 852, 397]]<|/det|>
+Anthropogenic warming is projected to enhance Arctic freshwater exportation into the Labrador Sea. This extra freshwater may weaken deep convections and contribute to the Atlantic Meridional Overturning Circulation (AMOC) decline. Here, by analyzing an unprecedented high- resolution climate model simulation for the 21st century, we show that the Labrador Current strongly restricts the lateral spread of freshwater from the Artic Ocean into the open ocean such that the freshwater input has a limited role in weakening the overturning circulation. In contrast, in the absence of a strong Labrador Current, the extra freshwater is allowed to spread into the interior region and eventually shut down deep convections in the Labrador Sea. Given that the Labrador Sea overturning makes a significant contribution to the AMOC in many climate models, our results suggest that the AMOC decline during the 21st century could be overestimated in these models due to the unresolved Labrador Current.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[148, 86, 261, 101]]<|/det|>
+## Introduction  
+
+<|ref|>text<|/ref|><|det|>[[145, 108, 852, 348]]<|/det|>
+Increased freshwater supply to the Arctic Ocean in a warming climate makes the high- latitude regions susceptible to dramatic changes in ocean circulation. As anthropogenic warming continues in the 21st century, Arctic summer sea ice is likely to disappear in a few decades \(^{1,2}\) , increasing the Arctic freshwater storage. A stronger hydrological cycle in the atmosphere will also inject more freshwater into the Arctic through an increase in net precipitation and river runoff \(^{3,4}\) . Coupled climate models suggest that these extra freshwater sources to the Arctic will lead to a larger freshwater exportation to the subpolar North Atlantic in the 21st century \(^{5,6}\) . The additional freshwater will increase ocean stratification and potentially slow down the Atlantic Meridional Overturning Circulation (AMOC), with serious consequences for regional and global climates \(^{7 - 10}\) .  
+
+<|ref|>text<|/ref|><|det|>[[145, 380, 852, 868]]<|/det|>
+In this study, we focus on the influence of the extra freshwater from the Arctic on the ocean circulation in the Labrador Sea, a critical region for AMOC changes \(^{11 - 14}\) . Climate models consistently project a slowdown of the AMOC during the 21st century due to warming and freshening in the high- latitude North Atlantic \(^{15,16}\) . However, the overturning and deep convection responses to freshwater input are crucially impacted by the boundary current that typically circulates around open- ocean convection regions, where deep water forms. For example, there is significant freshwater input into the Weddell Sea, a key region for bottom water formation in the Southern Ocean, due to the melting of Antarctic ice sheet and sea ice. In the presence of a well- resolved Antarctic Slope Current, the extra freshwater largely stays on the shelf region as the slope current restricts the lateral spread of freshwater, with limited influence on open- ocean convection \(^{17}\) . The Labrador Current can also restrict the lateral exchange of freshwater between the shelf and open ocean \(^{18,19}\) . Thus, we hypothesize that, when the extra freshwater enters the Labrador Sea from the Arctic through the Canadian Arctic Archipelago \(^{20}\) , the Labrador Current restricts the freshwater from spreading into the open ocean and weakening the overturning circulation. Typical climate models for the Coupled Model Intercomparison Project (CMIP) of Intergovernmental Panel for Climate Change (IPCC) assessment report, mostly at \(1^{\circ}\) resolution, are unable to resolve the Labrador Current \(^{21}\) (Fig. S1), and thus could overestimate the overturning responses to the freshwater forcing due to anthropogenic warming \(^{22}\) .
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[144, 84, 853, 570]]<|/det|>
+Here, we study the role of the Labrador Current in regulating the overturning responses to an increased Arctic freshwater export in the Labrador Sea and its influence on AMOC changes in an unprecedented high- resolution coupled simulation over the 21st century (2006- 2100) under the high- emission scenario (RCP8.5). The simulation (HighRes) \(^{23}\) is conducted using the Community Earth System Model version 1 (CESM1), with a nominal horizontal resolution of \(0.1^{\circ}\) for the ocean, about \(6.5 \mathrm{km}\) in the Labrador Sea, and \(0.25^{\circ}\) for the atmosphere (see “CESM simulations” in “Method”). HighRes performs well in reproducing observations, including the Labrador Current (Fig. S1), the subpolar North Atlantic overturning (Fig. S2), and the North Atlantic sea surface temperature trend during the 20th century (Fig. S3), a footprint for AMOC weakening \(^{24}\) . These processes are often biased in coarse- resolution climate models (Fig. S1- 3). To quantify the role of the Labrador Current in regulating the overturning circulation changes, we also look at the overturning responses in a coarse- resolution counterpart of HighRes, LowRes, with a nominal \(1^{\circ}\) resolution as in most climate models in CMIP6. HighRes and LowRes differ from each other primarily in their horizontal resolutions. We show that the well- resolved Labrador Current in HighRes strongly restricts freshwater on the shelf and leads to a much weaker response in the Labrador Sea overturning circulation than LowRes, in which the Labrador Current is not resolved. Thus, we conclude that, without resolving the Labrador Current, coarse- resolution climate models may overestimate the AMOC decline during the 21st century.  
+
+<|ref|>sub_title<|/ref|><|det|>[[148, 604, 214, 620]]<|/det|>
+## Results  
+
+<|ref|>sub_title<|/ref|><|det|>[[148, 628, 691, 645]]<|/det|>
+## Increased Arctic freshwater exportation into the Labrador Sea  
+
+<|ref|>text<|/ref|><|det|>[[147, 652, 852, 841]]<|/det|>
+As in CMIP simulations \(^{5,6}\) , HighRes predicts a significant increase in freshwater input to the Arctic Ocean under anthropogenic warming (Fig. 1a- c). Under the RCP8.5 scenario in HighRes, the annual- mean sea ice volume decreases by \(99\%\) from 16,297 \(\mathrm{km^3}\) at 2006- 2015 to \(243 \mathrm{km^3}\) at the end of the 21st century; summer sea ice is completely lost in the 1960s. Net precipitation and river runoff also increases significantly due to a stronger atmospheric hydrological cycle by about \(161\%\) and \(39\%\) , respectively. The larger Arctic freshwater input will necessarily lead to an increased freshwater exportation into the subpolar North Atlantic, including the Labrador Sea.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[144, 83, 852, 423]]<|/det|>
+We estimate the freshwater transport into the Labrador Sea from north across Davis Strait, from west across Hudson Strait, and from east by the West Greenland Current in HighRes (Fig. 1d). Annual- mean salinity in year 2006 is used as the reference salinity at each section (see "Freshwater flux" in "Method"). The increase in freshwater transport from Davis Strait is most significant, at a rate of about \(0.5\mathrm{mSv / year}\) over the 21st century (Fig. 1e). The freshwater transport across Hudson Strait also increases, but only at \(0.1\mathrm{mSv / year}\) (Fig. 1e). Both trends are statistically significant at the \(95\%\) confidence level (see "Statistical analysis" in "Method"). No significant trend appears in the freshwater transport coming from the east by the west Greenland Current (Fig. 1f). The freshwater pathway into the Labrador Sea is determined by several processes, including the Arctic circulation and the location of freshwater sources. The contrast in freshwater transport trends between the west and the east direction is likely related to the structure of freshwater increase in the Arctic Ocean in HighRes: freshwater content increases in the Canadian basin but decreases in the Eurasian basin (Fig. S4).  
+
+<|ref|>sub_title<|/ref|><|det|>[[145, 454, 787, 472]]<|/det|>
+## Surface freshening confined to the western shelf by the Labrador Current  
+
+<|ref|>text<|/ref|><|det|>[[144, 478, 852, 914]]<|/det|>
+The extra freshwater transport into the Labrador Sea reduces sea surface salinity, but the freshening is mostly confined to the shelf close to Newfoundland and Labrador of Canada (Fig. 2a). The freshening on the shelf is about \(0.67\mathrm{psu}\) in 2091- 2100 relative to 2006- 2015. In contrast, in the interior Labrador Sea, where deep convection occurs (Fig. 1d), the surface freshening is only \(0.27\mathrm{psu}\) . We quantify the salinity change along the AR7W line. The freshening is most obvious in the upper \(150\mathrm{m}\) on the shelf (Fig. 2b). The exchange of freshwater between the shelf and the open ocean is strongly restricted by the narrow Labrador Current (Fig. 2b, Fig. S1), consistent with previous studies \(^{18,19}\) . The Labrador Current may also help flush the freshwater out into the North Atlantic Ocean, contributing to reducing the freshening effects. Coarse- resolution models (e.g., LowRes) are not able to resolve the Labrador Current, and thus may misrepresent the freshening due to increased freshwater input. Indeed, with similar freshwater transport increases in LowRes (Fig. S5), the surface freshening is almost uniformly in the Labrador Sea, with a \(1.52\mathrm{psu}\) decrease in the interior (Fig. 2c). The broader surface salinity decrease is related to the too weak and wide Labrador Current (Fig. 2d, Fig. S1), which allows freshwater to enter the interior Labrador Sea. Thus, we conclude that coarse- resolution climate models could overestimate the freshwater influence on the surface salinity change in the Labrador Sea.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[144, 108, 852, 546]]<|/det|>
+The Labrador Current also regulates ocean stratification and mixed layer depth changes in the Labrador Sea due to surface freshening. We focus on the central Labrador Sea, deeper than 2000 m, where deep convections take place. Ocean stratification, quantified as the density difference between the sea surface and \(1\mathrm{km}\) depth divided by \(1\mathrm{km}\) , increases by \(91\%\) in 2091- 2100 relative to 2006- 2015 in HighRes. The strengthening is surface intensified and almost equally attributed to surface warming and freshening (Fig. 3a- b, Fig. S6). In contrast with HighRes, the upper- ocean stratification increases more dramatically in the 21st century by \(158\%\) in LowRes. The larger stratification increase in LowRes is due to a dramatic decrease of the surface density associated with the widespread surface freshening in the Labrador Sea (Fig. 3c- d, Fig. S6). Similar conclusions can be drawn for mixed layer depth (MLD) changes (Fig. S7). In HighRes, the March MLD in the central Labrador Sea decreases by \(56\%\) from \(430\mathrm{m}\) in 2006- 2015 to \(190\mathrm{m}\) in 2091- 2100. While in LowRes, the March MLD shoals by \(91\%\) from \(928\mathrm{m}\) to \(83\mathrm{m}\) during the same period. We note that the present- day MLD in LowRes is overestimated as in many coarse- resolution models \(^{25 - 27}\) . The results highlight the role of the Labrador Current in future ocean stratification changes in the Labrador Sea and suggest that coarse- resolution models may overestimate the stratification increase due to freshwater forcing.  
+
+<|ref|>sub_title<|/ref|><|det|>[[147, 579, 656, 597]]<|/det|>
+## Response of the Labrador Sea overturning and the AMOC  
+
+<|ref|>text<|/ref|><|det|>[[144, 603, 866, 892]]<|/det|>
+Through its impacts on the surface freshening and stratification changes, the Labrador Current regulates the overturning circulation changes in a warming climate. The stratification increase will decrease deep water formation in the Labrador Sea and potentially contribute to the AMOC weakening during the 21st century. We quantify the Labrador Sea overturning at OSNAP West (Fig. 4a and d, see "OSNAP overturning streamfunction" in "Method"). The Labrador Sea overturning is weakened by about \(55\%\) in HighRes from 2006- 2015 to 2091- 2100, with a linear trend of - 5.7 Sv/century. In comparison, the weakening of the Labrador Sea overturning in LowRes is more substantial by about \(90\%\) from 2006- 2015 to 2091- 2100, with a linear trend of - 18 Sv/century. The deep convection in LowRes almost completely shuts down at the end of the 21st century. The much stronger weakening of the Labrador Sea overturning in LowRes can be attributed to the overly stratified ocean in the Labrador Sea. We
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[144, 83, 852, 348]]<|/det|>
+calculate the surface forced water mass transformation (SFWMT), a good indicator for the actual overturning<sup>13,14,28</sup>, using the surface buoyancy flux and surface density (see "Surface forced water mass transformation" in "Method" section). The SFWMT dominates the Labrador Sea overturning circulation as well as its changes during the 21st century (Fig. S8). Decomposing the SFWMT changes into contributions due to changes in the surface buoyancy flux and surface density stratification (see "Surface forced water mass transformation" in "Method"), we show that the differing Labrador Sea overturning responses between HighRes and LowRes are mainly due to changes in surface stratification (Fig. S8). The surface buoyancy flux is not significantly different between HighRes and LowRes at 98% confidence level (Fig. S9) and cannot explain their difference in the overturning changes.  
+
+<|ref|>text<|/ref|><|det|>[[144, 377, 852, 644]]<|/det|>
+The weakening of the Labrador Sea overturning circulation contributes to the AMOC decline during the 21st century. We calculate the North Atlantic overturning in density space and then remap it back to depth space following previous studies<sup>29,30</sup> (see "Density- space AMOC" in "Method"). Consistent with the Labrador Sea overturning circulation changes, the AMOC decline appears to be faster in LowRes (Fig. 4e and f) than HighRes (Fig. 4b and c). Overturning changes across OSNAP East, which dominates the North Atlantic overturning in observations, may also contribute to the faster AMOC decline in LowRes. However, the overturning across OSNAP East declines at a rate of - 12.2 Sv/century in LowRes and - 8.9 Sv/century in HighRes, with a smaller difference between these two simulations than OSNAP West (Fig. S10 and S11).  
+
+<|ref|>sub_title<|/ref|><|det|>[[148, 678, 242, 694]]<|/det|>
+## Discussion  
+
+<|ref|>text<|/ref|><|det|>[[144, 701, 852, 892]]<|/det|>
+In this study, we highlight the role of the Labrador Current in regulating the Labrador Sea responses to increased freshwater input due to anthropogenic warming. The narrow Labrador Current strongly restricts the lateral exchange of freshwater between the continental shelf and open ocean. In the absence of this narrow boundary current, the extra freshwater input from the Arctic spreads into the open ocean and causes a much stronger increase in ocean stratification, leading to an overestimated weakening of the Labrador Sea overturning circulation. The impact of the Labrador Current in restricting lateral freshwater exchange might evolve as the climate continues to warm. HighRes
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[144, 83, 852, 201]]<|/det|>
+predicts a weakening of the Labrador Current due to surface wind changes (Fig. S12), suggesting a slightly diminishing role of the Labrador Current in the future climate. Nevertheless, given that the Labrador Sea overturning circulation makes a significant contribution to the AMOC in many climate models of coarse resolution \(^{25 - 27}\) , our results suggest that the AMOC weakening may be overestimated in these climate models \(^{22}\) .  
+
+<|ref|>text<|/ref|><|det|>[[144, 231, 852, 520]]<|/det|>
+With the advent of higher- resolution climate projections, we might expect more reliable and consistent climate predictions as compared to coarse- resolution ones. However, the dependence of the AMOC decline rate on model resolutions appears to be sensitive to the models being used. Consistent with CESM in this study, a slower AMOC decline rate at higher resolution in response to anthropogenic warming is simulated in GFDL models \(^{31}\) . But this is different from many HighResMIP simulations \(^{32}\) , most of which use NEMO as their ocean component \(^{33,34}\) and only partly resolve the boundary current at \(0.25^{\circ}\) resolution. The different results may also be related to the different length of simulations: HighResMIP models simulate years 2015- 2050, but most of the AMOC decline during the 21st century occurs post- \(2050^{15,35}\) . Therefore, high- resolution projections with various model configurations until 2100 are highly desired to have a more comprehensive understanding of the AMOC changes during the 21st century.  
+
+<|ref|>text<|/ref|><|det|>[[144, 550, 852, 790]]<|/det|>
+As anthropogenic warming continues, more freshwater is expected to enter the subpolar North Atlantic from the Greenland ice sheet melting and Arctic freshwater release. The extra freshwater input will necessarily interact with deep convection and cause a slowdown of the AMOC \(^{36 - 38}\) . However, our results suggest that future AMOC responses will be sensitive to how the extra freshwater input is distributed in the high- latitude region. To address this question, we need to monitor the freshwater sources and their exportation pathways through Arctic- subpolar North Atlantic gateways towards regions that could impact the AMOC. High- resolution models are also desired for a more accurate representation of freshwater transports associated with narrow boundary currents \(^{39 - 40}\) and oceanic eddies \(^{41 - 44}\) that are not resolved in coarse- resolution models.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[148, 85, 227, 101]]<|/det|>
+## Methods  
+
+<|ref|>sub_title<|/ref|><|det|>[[148, 109, 314, 126]]<|/det|>
+## CESM simulations  
+
+<|ref|>text<|/ref|><|det|>[[147, 133, 852, 374]]<|/det|>
+The simulations used in this paper were carried out by CESM1.3 at the International Laboratory for High- Resolution Earth System Prediction (iHESP) \(^{23}\) . CESM comprises the Community Atmosphere Model version 5 (CAM5), the Parallel Ocean Program version 2 (POP2), the Community Ice Code version 4 (CICE4), and the Community Land Model version 4 (CLM4). We make use of the configuration with high and low model horizontal resolutions. For HighRes, the resolutions of atmosphere, ocean and sea- ice components are \(0.25^{\circ}\) , \(0.1^{\circ}\) , and \(0.1^{\circ}\) , respectively. For LowRes, the nominal horizontal resolutions are \(1^{\circ}\) . The simulations we use were run under the representative concentration pathway 8.5 (RCP8.5) forcing from 2006 to 2100 in accordance with CMIP experimental protocol.  
+
+<|ref|>sub_title<|/ref|><|det|>[[148, 404, 288, 420]]<|/det|>
+## Freshwater flux  
+
+<|ref|>text<|/ref|><|det|>[[148, 427, 761, 446]]<|/det|>
+The freshwater flux (FWF in unit of \(\mathrm{mSv} = 10^{- 3} \mathrm{~m}^{3} \mathrm{~s}^{- 1}\) ) is defined as follows  
+
+<|ref|>equation<|/ref|><|det|>[[250, 448, 848, 494]]<|/det|>
+\[\mathrm{FWF}(x,y,z,t) = \nu (x,y,z,t)\cdot \frac{S_{\mathrm{ref}} - S(x,y,z,t)}{S_{\mathrm{ref}}} dA \quad (1)\]  
+
+<|ref|>text<|/ref|><|det|>[[147, 500, 851, 618]]<|/det|>
+where \(\nu\) is the cross- section velocity (in unit of \(\mathrm{m} \mathrm{s}^{- 1}\) ), \(S\) is the salinity (in unit of \(\mathrm{psu}\) ), \(S_{\mathrm{ref}}\) is the reference salinity which is set as the annual- mean salinity in 2006, as a function of longitude, latitude and depth, \(dA\) is the cross- section area at each grid point (in unit of \(\mathrm{m}^{2}\) ). We calculate the freshwater flux into the Labrador Sea by summing up the freshwater flux at each grid point along each section denoted in Figure 1d.  
+
+<|ref|>sub_title<|/ref|><|det|>[[148, 650, 310, 666]]<|/det|>
+## Statistical analysis  
+
+<|ref|>text<|/ref|><|det|>[[147, 673, 850, 740]]<|/det|>
+The linear trends in freshwater transport and overturning circulation are calculated using least- square regression, with the statistical significance estimated using two- tailed Student's \(t\) - test.  
+
+<|ref|>sub_title<|/ref|><|det|>[[148, 772, 462, 790]]<|/det|>
+## OSNAP overturning streamfunction  
+
+<|ref|>text<|/ref|><|det|>[[147, 797, 851, 912]]<|/det|>
+Dense waters that reside in the lower limb of the AMOC are produced mainly in the eastern subpolar North Atlantic (i.e., the Irminger and Iceland basins) in observations, and to a lesser extent, in the western subpolar North Atlantic (i.e., the Labrador Sea) \(^{45}\) . The strength of dense water formation can be measured by overturning across OSNAP West and OSNAP East in density space. In the main text, OSNAP overturning is
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[147, 84, 851, 154]]<|/det|>
+calculated in density space. Density referenced to \(2000\mathrm{- m}\) depth \((\sigma_{2})\) is used as the vertical coordinate (in unit of \(\mathrm{kgm^{- 3}}\) , after subtracting \(1000\mathrm{kgm^{- 3}}\) ). Volume fluxes are integrated from west to east and from higher to lower density.  
+
+<|ref|>sub_title<|/ref|><|det|>[[147, 185, 515, 202]]<|/det|>
+## Surface forced water mass transformation  
+
+<|ref|>text<|/ref|><|det|>[[147, 208, 852, 379]]<|/det|>
+The overturning streamfunction in the subpolar North Atlantic and its variability are largely determined by the surface forced water mass transformation (SFWMT)13,14,28. In this paper we calculate the SFWMT (in units of \(\mathrm{Sv} = 10^{6}\mathrm{m}^{3}\mathrm{s}^{- 1}\) ) as a function of density referenced to \(2000\mathrm{- m}\) depth \(\sigma_{2}\) (in unit of \(\mathrm{kgm^{- 3}}\) , after subtracting \(1000\mathrm{kgm^{- 3}}\) ) by integrating the surface density flux \((B\) , in units of \(\mathrm{kg}\) seawater \(\mathrm{m}^{- 2}\mathrm{s}^{- 1}\) , defined as positive for ocean density increase) over surface density outcrop regions \((dA\) , in unit of \(\mathrm{m}^{2}\) ; corresponding to \(\sigma_{2}\) from \(\sigma_{2} - \Delta \sigma_{2} / 2\) to \(\sigma_{2} + \Delta \sigma_{2} / 2\) ) as follows  
+
+<|ref|>equation<|/ref|><|det|>[[366, 379, 855, 421]]<|/det|>
+\[\mathrm{SFWMT}\big(\sigma_{2}\big) = \frac{1}{\Delta\sigma_{2}}\iint BdA \quad (2)\]  
+
+<|ref|>text<|/ref|><|det|>[[147, 430, 850, 472]]<|/det|>
+The density flux comprises heat and salt fluxes that referred to as \(B_{\mathrm{heat}}\) and \(B_{\mathrm{salt}}\) , respectively. The heat flux is  
+
+<|ref|>equation<|/ref|><|det|>[[407, 475, 848, 515]]<|/det|>
+\[B_{\mathrm{heat}} = -\frac{\alpha}{C_p} Q \quad (3)\]  
+
+<|ref|>text<|/ref|><|det|>[[147, 520, 851, 612]]<|/det|>
+where \(\alpha\) is the thermal expansion coefficient (in unit of \(\mathrm{K}^{- 1}\) ), \(C_p\) is the specific heat capacity of seawater (in unit of \(\mathrm{Jkg^{- 1}K^{- 1}}\) ), \(Q\) is the surface net heat flux (in units of W \(\mathrm{m}^{- 2}\) , defined as positive for ocean heat gain), which is the sum of surface radiation and turbulent heat fluxes. The salt flux is  
+
+<|ref|>equation<|/ref|><|det|>[[410, 616, 855, 653]]<|/det|>
+\[B_{\mathrm{salt}} = \beta \frac{S}{1 - S} F \quad (4)\]  
+
+<|ref|>text<|/ref|><|det|>[[147, 658, 852, 825]]<|/det|>
+where \(S\) is the sea surface salinity (in unit of \(\mathrm{msu} = 10^{- 3}\mathrm{psu}\) ), \(\beta\) is the haline contraction coefficient (in unit of \(\mathrm{msu}^{- 1}\) ), and \(F\) is virtual salt flux (in units of \(\mathrm{kg}\) freshwater \(\mathrm{m}^{- 2}\mathrm{s}^{- 1}\) , defined as positive for ocean salinity increase). Variations in SFWMT can be decomposed into contributions due to changes in surface density flux and surface density stratification. We calculate the latter (referred to as \(\mathrm{SFWMT}_{\mathrm{OCN}}\) ) in this paper by replacing the time- dependent surface density flux with the annual- mean surface density flux in 2006 in Eq. (2).  
+
+<|ref|>sub_title<|/ref|><|det|>[[147, 855, 338, 872]]<|/det|>
+## Density-space AMOC
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[145, 83, 850, 127]]<|/det|>
+We calculate the AMOC in density space that better represents the overturning circulation at high latitudes. The AMOC streamfunction is defined as follows  
+
+<|ref|>equation<|/ref|><|det|>[[180, 129, 848, 184]]<|/det|>
+\[\mathrm{AMOC}(y,\sigma ,t) = -\int_{z_{\mathrm{bot}}}^{0}\int_{x_{w}}^{x_{e}}H(\sigma '(x,y,z,t) - \sigma)v(x,y,z,t)dxdz \quad (5)\]  
+
+<|ref|>text<|/ref|><|det|>[[145, 190, 852, 410]]<|/det|>
+where \(H\) is the Heaviside function, \(\sigma\) ' represent the density field, \(x\) is longitude, \(y\) is latitude, \(z\) is depth, \(t\) is time, \(\sigma\) is the density at which the streamfunction is calculated, and \(v\) is the meridional velocity. The zonal integral is performed across the Atlantic Ocean from the western boundary \((x_{w})\) to the eastern boundary \((x_{e})\) , and the vertical integral is performed from the ocean bottom \((z_{\mathrm{bot}})\) to the sea surface. Density referenced to \(2000\mathrm{- m}\) depth \((\sigma_{2})\) is used as the vertical coordinate (in unit of \(\mathrm{kg m^{- 3}}\) , after subtracting \(1000\mathrm{kg m^{- 3}}\) ). We also remap the AMOC streamfunction in density space into depth space using the time- and zonally averaged depth of each density layer following previous studies \(^{29,30}\) .
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[149, 86, 308, 101]]<|/det|>
+## Acknowledgments  
+
+<|ref|>text<|/ref|><|det|>[[147, 104, 850, 140]]<|/det|>
+Funding: National Science Foundation Grant OPP- 2211691 (to M.S.), Ocean University of China Postdoctoral Fellowship for International Research (to X.S.)  
+
+<|ref|>sub_title<|/ref|><|det|>[[149, 161, 334, 176]]<|/det|>
+## Author contributions  
+
+<|ref|>text<|/ref|><|det|>[[147, 179, 725, 289]]<|/det|>
+Conceptualization: Shantong Sun, Lixin Wu  Investigation: Xuan Shan  Visualization: Xuan Shan  Supervision: Shantong Sun, Lixin Wu  Writing—original draft: Xuan Shan  Writing—review & editing: Shantong Sun, Lixin Wu, Michael A. Spall  
+
+<|ref|>sub_title<|/ref|><|det|>[[148, 309, 323, 325]]<|/det|>
+## Competing interests  
+
+<|ref|>text<|/ref|><|det|>[[148, 327, 589, 344]]<|/det|>
+Authors declare that they have no competing interests.  
+
+<|ref|>sub_title<|/ref|><|det|>[[148, 363, 293, 379]]<|/det|>
+## Data availability  
+
+<|ref|>text<|/ref|><|det|>[[147, 382, 850, 550]]<|/det|>
+All data needed to evaluate the conclusions in the paper are present in the main text or the supplementary materials. The climate model simulations and observation data used in this study are publicly available and can be downloaded from the following websites: CESM model outputs (https://ihep.github.io/archive/products/ihep- products/data- release/DataRelease_Phase2. html or http://ihep.qnlm.ac), OSNAP overturning (https://www.o- snap.org/), Hadley Centre Sea Ice and Sea Surface Temperature data set (HadISST, https://www.metoffice.gov.uk/hadobs/hadisst/), and NOAA Extended Reconstructed SST V5 (ERSSTv5, https://psl.noaa.gov/data/gridded/data.noaa.ersst.v5.html).
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[90, 68, 855, 920]]<|/det|>
+Reference1. Notz, D. & Community, S. Arctic sea ice in CMIP6. Geophys. Res. Lett. 47, e2019GL086749 (2020).2. Kim, Y.- H., Min, S.- K., Gillett, N. P., Notz, D. & Malinina, E. Observationally- constrained projections of an ice- free Arctic even under a low emission scenario. Nat. Commun. 14, 3139 (2023).3. Bintanja, R. & Selten, F. M. Future increases in Arctic precipitation linked to local evaporation and sea- ice retreat. Nature 509, 479- 482 (2014).4. Vihma, T. et al. The atmospheric role in the Arctic water cycle: A review on processes, past and future changes, and their impacts. J. Geophys. Res. Biogeosci.121, 586- 620 (2016).5. Haine, T. W. N. et al. Arctic freshwater export: Status, mechanisms, and prospects. Glob. Planet. Change 125, 13- 35 (2015).6. Wang, Q. et al. A Review of Arctic- Subarctic Ocean linkages: past changes, mechanisms, and future projections. Ocean- Land- Atmos. Res. 2, 0013 (2023).7. Vellinga, M. & Wood, R. A. Global climatic impacts of a collapse of the Atlantic thermohaline circulation. Clim. Change 54, 251- 267 (2002).8. Cheng, W., Bitz, C. M. & Chiang, J. C. H. Adjustment of the global climate to an abrupt slowdown of the Atlantic meridional overturning circulation in Geophysical Monograph Series (American Geophysical Union, Washington D. C. 2007), Vol. 173, pp. 295.9. Woollings, T., Gregory, J. M., Pinto, J. G., Reyers, M. & Brayshaw, D. J. Response of the North Atlantic storm track to climate change shaped by ocean- atmosphere coupling. Nat. Geosci. 5, 313- 317 (2012).10. Bellomo, K., Angeloni, M., Corti, S. & Von Hardenberg, J. Future climate change shaped by inter- model differences in Atlantic meridional overturning circulation response. Nat. Commun. 12, 3659 (2021).11. Jackson, L. C., Peterson, K. A., Roberts, C. D. & Wood, R. A. Recent slowing of Atlantic overturning circulation as a recovery from earlier strengthening. Nat. Geosci. 9, 518- 522 (2016).12. Thornalley, D. J. R. et al. Anomalously weak Labrador Sea convection and Atlantic overturning during the past 150 years. Nature 556, 227- 230 (2018).13. Yeager, S. et al. An outsized role for the Labrador Sea in the multidecadal variability of the Atlantic overturning circulation. Sci. Adv. 7, eabh3592 (2021).
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+14. Oldenburg, D., Wills, R. C. J., Armour, K. C., Thompson, L. & Jackson, L. C. Mechanisms of low-frequency variability in North Atlantic ocean heat transport and AMOC. J. Clim. 34, 4733-4755 (2021).  
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+15. Weijer, W., Cheng, W., Garuba, O. A., Hu, A., & Nadiga, B. T. CMIP6 models predict significant 21st century decline of the Atlantic Meridional Overturning Circulation. Geophys. Res. Lett. 47, e2019GL086075 (2020).  
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+16. Climate Change 2021: The Physical Science Basis. Working Group I Contribution to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change, eds. Masson-Delmotte, V., et al., Cambridge Univ. Press (2023).  
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+17. Lockwood, J. W., Dufour, C. O., Griffies, S. M. & Winton, M. On the role of the Antarctic slope front on the occurrence of the Weddell Sea polynya under climate change. J. Clim. 34, 2529-2548 (2021).  
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+18. Myers, P. G. Impact of freshwater from the Canadian Arctic Archipelago on Labrador Sea Water formation. Geophys. Res. Lett. 32, 2004GL022082 (2005).  
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+19. Houssais, M.-N. & Herbaut C. Atmospheric forcing on the Canadian Arctic Archipelago freshwater outflow and implications for the Labrador Sea variability, J. Geophys. Res. 116, C00D02 (2011).  
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+20. Zhang, J. et al. Labrador Sea freshening linked to Beaufort Gyre freshwater release. Nat. Commun. 12, 1229 (2021).  
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+21. Talandier, C. Improvements of simulated Western North Atlantic current system and impacts on the AMOC. Ocean Model. 76, 1-19 (2014).  
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+22. He, F. & Clark P. U. Freshwater forcing of the Atlantic Meridional Overturning Circulation revisited. Nat. Clim. Chang. 12, 449-454 (2022).  
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+23. Chang, P. et al. An unprecedented set of high-resolution earth system simulations for understanding multiscale interactions in climate variability and change. J. Adv. Model. Earth Syst. 12, e2020MS002298 (2020).  
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+24. Caesar, L., Rahmstorf, S., Robinson, A., Feulner, G. & Saba, V. Observed fingerprint of a weakening Atlantic Ocean overturning circulation. Nature 556, 191-196 (2018).  
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+25. Danabasoglu, D. et al. North Atlantic simulations in Coordinated Ocean-ice Reference Experiments phase II (CORE-II). Part I: Mean states. Ocean Model. 73, 76-107 (2014).  
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+Ocean Sci. 13, 609- 622 (2017). 27. Li, F. et al. Local and downstream relationships between Labrador Sea Water volume and North Atlantic Meridional Overturning Circulation variability. J. Clim. 32, 3883- 3898 (2019). 28. Jackson, L. C. & Petit, T. North Atlantic overturning and water mass transformation in CMIP6 models. Clim. Dyn. 60, 2871- 2891 (2023). 29. Xu, X., Rhines, P. B. & Chassignet, E. P. On mapping the diapycnal water mass transformation of the upper North Atlantic Ocean. J. Phys. Oceanogr. 48, 2233- 2258 (2018). 30. Rousselet, L., Cessi, P. & Forget, G. Routes of the upper branch of the Atlantic Meridional Overturning Circulation according to an ocean state estimate. Geophys. Res. Lett. 47, e2020GL089137 (2020). 31. Delworth, T. L. et al. Simulated climate and climate change in the GFDL CM2.5 high-resolution coupled climate model. J. Clim. 25, 2755- 2781 (2012). 32. Roberts, M. J. et al. Sensitivity of the Atlantic Meridional Overturning Circulation to model resolution in CMIP6 HighResMIP simulations and implications for future changes. J. Adv. Model. Earth Syst. 12, e2019MS002014 (2020). 33. Jackson, L. C. et al. Impact of ocean resolution and mean state on the rate of AMOC weakening. Clim. Dyn. 55, 1711- 1732 (2020). 34. Koenigk, T. et al. Deep mixed ocean volume in the Labrador Sea in HighResMIP models. Clim. Dyn. 57, 1895- 1918 (2021). 35. Cheng, W., Chiang, J. C. H. & Zhang, D. Atlantic Meridional Overturning Circulation (AMOC) in CMIP5 models: RCP and historical simulations. J. Clim. 26, 7187- 7197 (2013). 36. Rahmstorf, S. et al. Exceptional twentieth- century slowdown in Atlantic Ocean overturning circulation. Nat. Clim. Change 5, 475- 480 (2015). 37. Böning, C. W., Behrens, E., Biastoch, A., Getzlaff, K. & Bamber, J. L. Emerging impact of Greenland meltwater on deepwater formation in the North Atlantic Ocean. Nat. Geosci. 9, 523- 527 (2016). 38. Yang, Q. et al. Recent increases in Arctic freshwater flux affects Labrador Sea convection and Atlantic overturning circulation. Nat. Commun. 7, 10525 (2016). 39. Luo, H. et al. Oceanic transport of surface meltwater from the southern Greenland ice sheet. Nat. Geosci. 9, 528- 532 (2016). 40. Wang, H., Legg, S. & Hallberg, R. The effect of Arctic freshwater pathways on
+
+<--- Page Split --->
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+424 North Atlantic convection and the Atlantic Meridional Overturning Circulation. J. Clim. 31, 5165- 5188 (2018). 425 41. Schmidt, S. & Send, U. Origin and composition of seasonal Labrador Sea freshwater. J. Phys. Oceanogr. 37, 1445- 1454 (2007). 426 42. McGeehan, T. & Maslowski, W. Impact of shelf- basin freshwater transport on deep convection in the western Labrador Sea. J. Phys. Oceanogr. 41, 2187- 2210 (2011). 427 43. Weijer, W., Maltrud, M. E., Hecht, M. W., Dijkstra, H. A., & Kliphuis, M. A. Response of the Atlantic Ocean circulation to Greenland Ice Sheet melting in a strongly- eddying ocean model. Geophys. Res. Lett. 39, L09606 (2012). 428 44. Rieck, J. K., Böning, C. W. & Getzlaff, K. The nature of eddy kinetic energy in the Labrador Sea: Different types of mesoscale eddies, their temporal variability, and impact on deep convection. J. Phys. Oceanogr. 49, 2075- 2094 (2019). 429 45. Lozier, M. S. et al. A sea change in our view of overturning in the subpolar North Atlantic. Science 363, 516- 521 (2019).
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[157, 100, 825, 444]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[147, 457, 850, 660]]<|/det|>
+<center>Fig 1. | Enhanced freshwater input into the Arctic Ocean and freshwater exportation into the Labrador Sea. Changes (2091-2100 minus 2006-2015) in (a) equivalent sea ice thickness, (b) precipitation minus evaporation, and (c) river runoff in the Arctic in HighRes. (d) Surface ocean circulation in the Labrador Sea in HighRes. The shading shows climatology mixed layer depth in March. The 1000m, 2000m and 3000m isobaths are indicated by blue contours. The black box encloses the Labrador Sea region. LC is the Labrador Current. WGC is the West Greenland Current. Time series of upper-250 m freshwater flux into the Labrador Sea from (e) the west of Greenland across Davis Strait (solid line, negative values for freshwater input into the Labrador Sea) and Hudson Strait (dashed lines, positive values freshwater input into the Labrador Sea) and (f) from the east of Greenland. The thin lines in (e) and (f) show annual-mean freshwater flux. The thick lines represent 20-year running mean. </center>
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[181, 100, 795, 505]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[147, 512, 851, 606]]<|/det|>
+<center>Fig 2. | Freshening of the Labrador Sea during the 21st century. Changes (2091-2100 minus 2006-2015) in sea surface salinity (SSS) in (a) HighRes and (c) LowRes. The black dashed line indicates AR7W line. (b, d) Same as (a) and (c) but for salinity change across AR7W line. The contour lines show velocity of currents cross AR7W with interval of \(12\mathrm{cm}\mathrm{s}^{-1}\) . The dashed (solid) lines represent currents out of (into) the Labrador Sea. </center>
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[166, 102, 790, 512]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[147, 531, 851, 696]]<|/det|>
+<center>Fig 3. | Strengthening of the ocean stratification in the interior Labrador Sea. Time-averaged potential density ( \(\sigma\) , with sea surface as reference pressure and minus \(1000\mathrm{kgm^{-3}}\) ) profile in the interior Labrador Sea in (a) HighRes and (c) LowRes. Solid (dashed) lines indicate the mean within 2006-2015 (2091-2100). Strengthening of the upper-1000m ocean stratification \((\Delta N^2\) , calculated as \(g / \sigma^{1000\mathrm{m}}.({\sigma^{1000\mathrm{m}} - \sigma^{0\mathrm{m}}}) / 1000)\) under global warming and the contributions due to temperature changes \((\Delta N_T^2)\) , calculated as \(-g\alpha (T^{1000\mathrm{m}} - T^{0\mathrm{m}}) / 1000\) , where \(T\) is potential temperature and \(\alpha\) is the thermal expansion coefficient at \(500\mathrm{m}\) , and the salinity changes \((\Delta N_S^2)\) , calculated as \(g\beta (S^{1000\mathrm{m}} - S^{0\mathrm{m}}) / 1000\) where \(S\) is salinity and \(\beta\) is the haline contraction coefficient at \(500\mathrm{m}\) , in (b) HighRes and (d) LowRes. Only regions in the Labrador Sea deeper than \(2000\mathrm{m}\) are considered here. </center>
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[161, 99, 825, 460]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[147, 475, 850, 589]]<|/det|>
+<center>Fig 4. | Weakening of Labrador Sea overturning and the AMOC. Time-averaged overturning across OSNAP West in (a) HighRes and (c) LowRes. Solid (dashed) lines indicate the mean within 2006-2015 (2091-2100). The normalized percentage change in the AMOC from 2006-2015 to 2091-2100 in (b) HighRes and (d) LowRes. Normalization uses the maximum AMOC value at \(40^{\circ}\mathrm{N}\) in 2006-2015 in each simulation. The AMOC is calculated in density space and then remapped into depth space using the zonal mean depth of each density layer. </center>
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[43, 42, 312, 70]]<|/det|>
+## Supplementary Files  
+
+<|ref|>text<|/ref|><|det|>[[43, 92, 768, 112]]<|/det|>
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+<|ref|>text<|/ref|><|det|>[[60, 130, 353, 149]]<|/det|>
+SupplementaryInformation.pdf
+
+<--- Page Split --->

preprint/preprint__c97fae2081b3c70a4db079c3b13b5d4001b9db983346912d2d2d2d08573f4a53/images_list.json

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+    "caption": "Fig. 1 Single-cell landscape of the SF components. a Overview of SF workflow. OA, osteoarthritis; RA, rheumatoid arthritis; s, single sample; p, paired samples. b Eight main clusters across 62,334 cells on a t-distributed stochastic neighbor embedding (tSNE) visualization. BT, before treatment; AT, after treatment. c Dot plot showing the normalized expression level of the cell type-specific marker genes across SF clusters. d Relative percentage of different cell components in SF across patients. The horizontal coordinates indicate the cell proportions, the vertical coordinates indicate",
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+  {
+    "type": "image",
+    "img_path": "images/Figure_2.jpg",
+    "caption": "Fig. 2 Overview of the expression profile of SF cell clusters. a Expression dot plot of well-established RA-related genes in the main cell clusters among different groups of samples. b Expression of JAK1, JAK2, and TNF in macrophage and T cell clusters among different groups. \\(p\\) -values were calculated by the two-sided Wilcoxon test. ns \\(p > 0.05\\) , \\(*p < 0.05\\) , \\(**p < 0.01\\) , \\(***p < 0.001\\) , \\(****p < 0.0001\\) . Ada: adalimumab; Tof: tofacitinib. c Feature plot for the number of differentially expressed genes (DEGs) calculated by the two-sided Wilcoxon test. d Volcano plot of DEGs in macrophages. \\(p\\) -values were calculated by the two-sided Wilcoxon test. N.S., \\(p > 1\\times 10^{-10}\\) , Sig, \\(p < 1\\times 10^{-1}\\)",
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+    "type": "image",
+    "img_path": "images/Figure_3.jpg",
+    "caption": "Fig. 3 Profile and function of \\(SPP1^{+} / S100A12^{+}\\) macrophages. a tSNE plot of macrophage subclusters. b Heatmap of the marker gene expression for each macrophage subtype. c Histogram of the macrophage subclusters proportion in each patient. d The proportion of \\(SPP1^{+} / S100A12^{+}\\) macrophages across groups. \\(p\\) -values were calculated by the two-sided Wilcoxon test among OA-BT \\((n = 3)\\) , RA-BT \\((n = 6)\\) , and RA-AT \\((n = 6)\\) . e Correlation of \\(SPP1^{+}\\) macrophage proportion with DAS28. f The",
+    "footnote": [],
+    "bbox": [
+      [
+        152,
+        88,
+        843,
+        750
+      ]
+    ],
+    "page_idx": 43
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_4.jpg",
+    "caption": "Fig. 4 Expression characteristics and evolution trajectory of SPP1+ and S100A12+ macrophages. a Heatmap of the monocyte, M1, and M2 enrichment scores in macrophage subclusters. b Different M1 signature scores in SPP1+/S100A12+ macrophages. \\(p\\) -values were calculated by the two-sided Wilcoxon",
+    "footnote": [],
+    "bbox": [
+      [
+        150,
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+      ]
+    ],
+    "page_idx": 45
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_5.jpg",
+    "caption": "Fig. 5 Landscape of T cell subclusters in SF from RA patients. a tSNE plot for T cell subclusters. b Expression of markers genes for each T cell subcluster. c-d Proportion of CXCL13+CD4+ T in samples with scRNA-seq (n = 3 for OA-BT, n = 6 for RA-BT, n = 6 for RA-AT) and deconvolution score of CXCL13+CD4+ T in samples with bulk sequencing (n = 5 for OA-BT, n = 14 for RA-BT, n = 10 for RA-AT), respectively. p-values were calculated by the two-sided Wilcoxon test. e Deconvolution score of CXCL13+CD4+ T in published bulk data with synovial tissue (GSE12021, n = 10 for OA, n = 12 for RA; Zhang et al, n = 15 for OA, n = 9 for RA). p-values were calculated by",
+    "footnote": [],
+    "bbox": [
+      [
+        153,
+        80,
+        852,
+        692
+      ]
+    ],
+    "page_idx": 47
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_6.jpg",
+    "caption": "Fig. 6 Characteristics of pathogenic T cell subclusters. a The number of DEGs in each T cell subcluster among different samples. \\(p\\) -values were calculated by the twosided Wilcoxon test. b Positively enriched GSEA pathways in RA-BT group. c Heatmap of hallmarker for each T cell subcluster. d Activity of hallmarker pathways. \\(p\\) -values were calculated by the two-sided Wilcoxon test. ns \\(p > 0.05\\) , \\(^{**}p < 0.01\\) , \\(^{***}p < 0.0001\\) .",
+    "footnote": [],
+    "bbox": [
+      [
+        147,
+        80,
+        850,
+        770
+      ]
+    ],
+    "page_idx": 49
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_7.jpg",
+    "caption": "Fig. 7 Communications between pathogenic macrophage and T cell subclusters.",
+    "footnote": [],
+    "bbox": [
+      [
+        150,
+        90,
+        844,
+        545
+      ]
+    ],
+    "page_idx": 51
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_8.jpg",
+    "caption": "Fig. 8 Signature construction and validation. a-b Diagnostic signature score of inhouse/public scRNA-seq and bulk data, respectively. \\(p\\) -values were calculated by the two-sided Wilcoxon test. c Pearson's correlation analysis between severity signature scores and DAS28 in inhouse/public scRNA-seq data and inhouse bulk data. d Different prognostic signature scores in ACR20_Y and ACR20_N in inhouse scRNA data and bulk data. \\*\\*\\* \\(p < 0.0001\\) .",
+    "footnote": [],
+    "bbox": [
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+        337
+      ]
+    ],
+    "page_idx": 52
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_9.jpg",
+    "caption": "Fig. 9 Graph summary of the pathogenic cell subtypes in SF from RA. Ada, adalimumab; Tof, tofacitinib.",
+    "footnote": [],
+    "bbox": [
+      [
+        156,
+        98,
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+    "page_idx": 53
+  }
+]

preprint/preprint__c999646ce158e6162152ca469a47961a985dfd1cd4d348a07672f1401d98483a/images_list.json

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+[
+  {
+    "type": "image",
+    "img_path": "images/Figure_1.jpg",
+    "caption": "Fig. 1 | Amorphization of the hafnium-based oxides. a, Schematic drawing for the structure evolution from fluorite \\(\\mathrm{HfO_2}\\) to perovskite \\(\\mathrm{AHfO_3}\\) , where the \\(\\mathrm{HfO_2}\\) is drawn in normal coordinates of \\(< 100>\\) ( \\(a\\) axis), \\(< 010>\\) ( \\(b\\) axis), and \\(< 001>\\) ( \\(c\\) axis) while the \\(\\mathrm{AHfO_3}\\) is drawn in the coordinates of \\(< 110>\\) ( \\(a\\) axis), \\(< 1\\bar{1} 0>\\) ( \\(b\\) axis), and \\(< 001>\\) ( \\(c\\) axis). b, Amorphous regions of the Ba-Hf-O, Sr-Hf-O, and Ca-Hf-O systems, respectively, as functions of the difference in ionic radii between \\(A^{2 + }\\) and \\(\\mathrm{Hf^{4 + }}\\) ( \\(\\mathrm{r}_A - \\mathrm{r}_{\\mathrm{Hf}}\\) ) and the tolerance factor of \\(\\mathrm{AHfO_3}\\) . c, XRD patterns of Ba-substituted \\(\\mathrm{HfO_2}\\) ( \\(\\mathrm{BHO_x}\\) ) thin films with increasing concentration from 0 to \\(50\\%\\) . The # and \\* symbols denote Bragg",
+    "footnote": [],
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+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_2.jpg",
+    "caption": "Fig. 2 | Short-range structure of the amorphous BHO film. The Fourier transformed EXAFS data \\(\\left(|\\chi (R)|\\right)\\) of Hf \\(L_{\\mathrm{III}}\\) edge for BHO12 film, in which the imaginary part of \\(|\\chi (R)|\\) is also shown for clarity. The inset is the EXAFS spectrum of BHO12-RT film for comparison. The bule dashed, orange dotted, and black solid lines are fits to \\(P2_{1} / c\\) , \\(Pca2_{1}\\) , and \\(P2_{1} / c + Pca2_{1}\\) symmetries, respectively. The fitting window is \\(R = 1.0 \\sim 4.0\\) Å.",
+    "footnote": [],
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+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_3.jpg",
+    "caption": "Fig. 3 | Dielectric energy storage of BHO thin-film capacitors. a, \\(P - E\\) hysteresis loops of Pt/BHO/LSMO capacitors measured at \\(10\\mathrm{kHz}\\) . b, Two-parameter Weibull distribution analysis of breakdown strengths over 12 capacitors for each Ba concentration. c, Statistical \\(E_{\\mathrm{b}}\\) and (d) Weibull modulus \\(\\beta\\) extracted from (b) plotted as a function of Ba concentration. Here, \\(\\beta\\) is the slope of \\(\\ln [- \\ln (1 - p)]\\) vs. \\(\\ln E_{\\mathrm{b}}\\) , where \\(p = i / (n + 1)\\) ( \\(n\\) is the total number of samples and \\(i\\) is the \\(i\\) th sample). e, Energy storage density \\((U_{\\mathrm{rec}})\\) and efficiency \\((\\eta)\\) of the BHO capacitors calculated from \\(P - E\\) loops. The data points are averaged over 12 capacitors for each Ba concentration.",
+    "footnote": [],
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+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_4.jpg",
+    "caption": "Fig. 4 | Reliability of BHO dielectric capacitors. Energy storage density \\((U_{\\mathrm{rec}})\\) and efficiency \\((\\eta)\\) of BHO0, BHO02, BHO12, and BHO50 capacitors as functions of (a) electric field, (b) temperature (measured at \\(0.7 E_{\\mathrm{b}}\\) ), and (c) charging-discharging cycles (measured at \\(0.6 E_{\\mathrm{b}}\\) ), respectively.",
+    "footnote": [],
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preprint/preprint__c999646ce158e6162152ca469a47961a985dfd1cd4d348a07672f1401d98483a/preprint__c999646ce158e6162152ca469a47961a985dfd1cd4d348a07672f1401d98483a.mmd

@@ -0,0 +1,292 @@
+
+# Structure-evolution-designed amorphous oxides for dielectric energy storage  
+
+Yahui Yu Qingdao University  
+
+Qing Zhang Shandong University  
+
+Zhiyu Xu Qingdao University  
+
+Weijie Zheng College of Physics and Center for Marine Observation and Communications, Qingdao University  
+
+Jibo Xu Qingdao University  
+
+Zhongnan Xi Nanjing University  
+
+Lin Zhu Nanjing University  
+
+Chunyan Ding Qingdao University  
+
+Yanqiang Cao Nanjing University of Science and Technology  
+
+Chunyan Zheng Qingdao University  
+
+Yalin Qin Qingdao University  
+
+Shandong Li Qingdao University https://orcid.org/0000- 0001- 8105- 7612  
+
+Ai- Dong Li Nanjing University  
+
+Di Wu Nanjing University https://orcid.org/0000- 0003- 3619- 1411  
+
+Karin Rabe Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854  
+
+Xiaohui Liu Shandong University  
+
+Zheng Wen ( zwen@qdu.edu.cn )
+
+<--- Page Split --->
+
+## Letter  
+
+## Keywords:  
+
+Posted Date: February 6th, 2023  
+
+DOI: https://doi.org/10.21203/rs.3.rs- 2486944/v1  
+
+License: © This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License  
+
+Additional Declarations: There is NO Competing Interest.  
+
+Version of Record: A version of this preprint was published at Nature Communications on May 25th, 2023. See the published version at https://doi.org/10.1038/s41467- 023- 38847- 1.
+
+<--- Page Split --->
+
+Structure- evolution- designed amorphous oxides for dielectric energy storage  
+
+Yahui Yu, \(^{1,3\dagger}\) Qing Zhang, \(^{2\dagger}\) Zhiyu Xu, \(^{1,3\dagger}\) Weijie Zheng, \(^{1,3}\) Jibo Xu, \(^{1,3}\) Zhongnan Xi, \(^{4}\) Lin Zhu, \(^{4}\) Chunyan Ding, \(^{1,3}\) Yanqiang Cao, \(^{5}\) Chunyan Zheng, \(^{1}\) Yalin Qin, \(^{1}\) Shandong Li, \(^{3}\) Aidong Li, \(^{4}\) Di Wu, \(^{4}\) Karin M. Rabe, \(^{6}\) Xiaohui Liu, \(^{2\ast}\) and Zheng Wen \(^{1,3\ast}\) \(^{1}\) College of Physics, Qingdao University, Qingdao 266071, China \(^{2}\) School of Physics, Shandong University, Ji'nan 250100, China \(^{3}\) College of Electronics and Information, Qingdao University, Qingdao 266071, China \(^{4}\) National Laboratory of Solid- State Microstructures, Department of Materials Science and Engineering, Jiangsu Key Laboratory of Artificial Functional Materials and Collaborative Innovation Center for Advanced Materials, Nanjing University, Nanjing 210093, China \(^{5}\) Institute of Micro- nano Photonics and Quantum Manipulation, School of Science, Nanjing University of Science and Technology, Nanjing 210094, China \(^{6}\) Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854, USA \(^{+}\) These authors contributed equally in this work. \*Corresponding author. Email: zwen@qdu.edu.cn (Z.W.) and liuxiaohui@sdu.edu.cn (X.L.)
+
+<--- Page Split --->
+
+Dielectric capacitors are fundamental for electric power systems due to the fast charging/discharging rate and high- power density.\(^{[1,2]}\) Recently, rapidly increased demands of miniaturization and integration continuously challenge energy storage density of dielectric capacitors, especially for that could be compatible with the complementary metal- oxide- semiconductor (CMOS) technology, for developing energy- autonomous systems and implantable/wearable electronics, where high- \(\kappa\) capacitors become increasingly desirable in the next- generation applications.\(^{[3- 5]}\) However, their recoverable energy storage densities ( \(U_{\mathrm{rec}}\) ) are low in emerging capacitive energy storage materials. Here, by structure evolution between fluorite \(\mathrm{HfO_2}\) and perovskite hafnate who have similar metal sublattices, we create an amorphous hafnium- based oxide that exhibits a giant \(U_{\mathrm{rec}}\) of \(\sim 155\) \(\mathrm{J / cm^3}\) with an efficiency \((\eta)\) of \(87\%\) , which is record- high in high- \(\kappa\) materials and state- of- the- art in dielectric energy storage (Supplementary Fig. S1 and Table S1). The improved energy density is owing to the strong structure disordering in both short and long ranges induced by oxygen instability in between the two energetically- favorable crystalline forms. As a result, the carrier avalanche is impeded and an ultrahigh breakdown strength \((E_{\mathrm{b}})\) up to \(12 \mathrm{MV / cm}\) is achieved, which, accompanying with a large permittivity \((\epsilon_{\mathrm{r}})\) , remarkably enhances the dielectric energy storage. Our study provides a new and widely applicable playground for designing high- performance dielectric energy storage with the strategy exploring the boundary among different categories of materials.  
+
+Dielectric capacitors store energy in the form of electrostatic field \((E)\) against electric displacement \((D\) , or polarization \(P\) ), which is regulated by essential material characters, the \(\epsilon_{\mathrm{r}}\) and \(E_{\mathrm{b}}\) , of the dielectric layers.\(^{[1,2]}\) The primary performance parameter \(U_{\mathrm{rec}}\) can be calculated by \(\int_{P_{\mathrm{r}}}^{P_{\mathrm{m}}} E d P\) , according to the \(P\) - \(E\) hysteresis loop,
+
+<--- Page Split --->
+
+which formulates the discharging upon \(E\) from the remanent polarization \((P_{\mathrm{r}})\) to the maximum polarization \((P_{\mathrm{m}})\) before breakdown (Supplementary Fig. S2). Noting that the hysteresis area is the energy loss \((U_{\mathrm{loss}})\) during a charging- discharging cycle. The \(\eta\) is written as \(U_{\mathrm{rec}} / (U_{\mathrm{rec}} + U_{\mathrm{loss}})\) . For ideally linear dielectrics, the \(U_{\mathrm{rec}}\) is simplified to \(\frac{1}{2}\epsilon_0\epsilon_{\mathrm{r}}E_{\mathrm{b}}^2\) ( \(\epsilon_0\) : the vacuum permittivity). Therefore, a high- performance dielectric capacitor should hold both large \(\epsilon_{\mathrm{r}}\) and high \(E_{\mathrm{b}}\) , simultaneously. Moreover, the increase of \(E_{\mathrm{b}}\) would be more efficient to improve the energy storage density due to the square dependence. However, \(E_{\mathrm{b}}\) is usually restricted by \(\epsilon_{\mathrm{r}}\) in most dielectric materials, following a negative power law of \(E_{\mathrm{b}}\propto \epsilon_{\mathrm{r}}^{-\alpha}\) .[1,6,7] For example, perovskite oxides, such as SrTiO3, BaTiO3, and Pb(Zr,Ti)O3, have large \(\epsilon_{\mathrm{r}}\) of a few hundred but low \(E_{\mathrm{b}}\) of only \(1.0 \sim 3.0 \mathrm{MV / cm}\) in general.[1,6,7] For that have high breakdown strengths (>5.0 MV/cm), like polymers and dielectric glasses, their low \(\epsilon_{\mathrm{r}}\) limit energy densities.[2,8,9] How to overcome the negative correlation by increasing \(E_{\mathrm{b}}\) in large- permittivity materials is key to enhance the energy storage performance. Most recently, by introducing local disorders, such as grain boundaries, ionic defects, amorphous fractions, and interfacial layers, improved \(E_{\mathrm{b}}\) of 4.5, 5.92, 6.35, and 8.75 MV/cm have been achieved in \((\mathrm{Ba_0.7Ca_0.3}) \mathrm{TiO_3 / Ba(Zr_0.2Ti_0.8)O_3}\) multilayers, ion- bombarded \(\mathrm{Pb(Mg_{1 / 3}Nb_{2 / 3})O_3 - PbTiO_3}\) , high- entropy \((\mathrm{Bi_{3.25}La_{0.75})(Ti_{3 - 3x}Zr_xHf_xSn_x)O_{12}}\) , and nano- grained \(\mathrm{BaTiO_3}\) , respectively, generating state- of- the- art energy storage densities (Supplementary Table S1).[10- 19] However, in the rapidly developed field of high- \(\kappa\) capacitors, their breakdown strengths are still low relative to the well- optimized perovskite- based capacitors,[3,20] limiting the energy densities for developing microelectronic energy devices.  
+
+Here, we propose a new structure strategy to achieve an ultrahigh \(E_{\mathrm{b}}\) of \(\sim 12\) MV/cm, which is far beyond the restriction of permittivity (Supplementary Fig. S3) and
+
+<--- Page Split --->
+
+yields remarkably improved \(U_{\mathrm{rec}}\) of \(\sim 155 \mathrm{J / cm}^3\) , in an amorphous hafnium- based oxide designed by bridging fluorite \(\mathrm{HfO_2}\) and perovskite \(\mathrm{AHfO_3}\) (where \(A\) is a divalent ion). As depicted in Fig. 1a, although they are classified into different categories of crystals, the \(\mathrm{HfO_2}\) and \(\mathrm{AHfO_3}\) share similar face- centered metal sublattices. The difference is the stoichiometric ratio and lattice sites of oxygen ions. In fluorite structure, the molar ratio of oxygen to metal is 2:1 and the eight oxygen ions occupy the interstitial sites of \(\mathrm{Hf}\) tetrahedrons to support the \(\mathrm{Hf}\) metal frame. For perovskite, the oxygen/metal molar ratio is reduced to 1.5:1 and the \(\mathrm{Hf / A}\) metal frame is stabilized by six oxygen ions that take the connection- line sites of two same metal ions, such as \(\mathrm{Hf^{4 + } - Hf^{4 + }}\) and \(A^{2 + } - A^{2 + }\) . Therefore, we can evolve the lattice from the fluorite to the perovskite by reducing oxygen stoichiometric ratio through substituting \(\mathrm{Hf^{4 + }}\) with \(A^{2 + }\) , in which the oxygen ions move from the interstitial to the connection- line sites to stabilize the metal frames. However, during the structure evolution, the oxygen ions may be instable at either the interstitial or the connection- line sites. Such an oxygen instability dramatically distorts the \(\mathrm{Hf / A}\) metal frames and eventually results in the collapse of long- range periodicities for both the fluorite and the perovskite when the substitution concentration is proper. The amorphous structure is thus formed with strong disordering. Meanwhile, the structure similarity also facilitates the maintaining of \(\mathrm{Hf - O}\) bonding, which is the main contribution of electronic and ionic displacements for dielectric polarizability, when the long- range lattice ordering is absent. The large \(\epsilon_{\mathrm{r}}\) of the parent high- \(\kappa\) \(\mathrm{HfO_2}\) and \(\mathrm{AHfO_3}\) could thus be inherited by the amorphous structure.
+
+<--- Page Split --->
+![](images/Figure_1.jpg)
+
+<center>Fig. 1 | Amorphization of the hafnium-based oxides. a, Schematic drawing for the structure evolution from fluorite \(\mathrm{HfO_2}\) to perovskite \(\mathrm{AHfO_3}\) , where the \(\mathrm{HfO_2}\) is drawn in normal coordinates of \(< 100>\) ( \(a\) axis), \(< 010>\) ( \(b\) axis), and \(< 001>\) ( \(c\) axis) while the \(\mathrm{AHfO_3}\) is drawn in the coordinates of \(< 110>\) ( \(a\) axis), \(< 1\bar{1} 0>\) ( \(b\) axis), and \(< 001>\) ( \(c\) axis). b, Amorphous regions of the Ba-Hf-O, Sr-Hf-O, and Ca-Hf-O systems, respectively, as functions of the difference in ionic radii between \(A^{2 + }\) and \(\mathrm{Hf^{4 + }}\) ( \(\mathrm{r}_A - \mathrm{r}_{\mathrm{Hf}}\) ) and the tolerance factor of \(\mathrm{AHfO_3}\) . c, XRD patterns of Ba-substituted \(\mathrm{HfO_2}\) ( \(\mathrm{BHO_x}\) ) thin films with increasing concentration from 0 to \(50\%\) . The # and \* symbols denote Bragg </center>
+
+<--- Page Split --->
+
+reflections from STO substrate and epitaxial LSMO electrode, respectively. The purple and red dashed lines indicate Bragg reflections from fluorite ( \(m\) - and \(o\) - phases) and perovskite structures, respectively. STEM characterizations of the BHO50 (d), BHO12 (e), and BHO02 (f) heterostructures, where the left panels are high-resolution HAADF images with fast Fourier transform patterns shown in the insets and the right panels are element distributions of Hf, La, and Ba mapped by electron energy loss spectroscopy, respectively. \(\mathbf{g}\) , Formation energy of oxygen vacancy \([E^{\mathrm{f}}(V_0)]\) at the first nearest-neighbor (NN) site as a function of the substitution concentration. \(\mathbf{h}\) , \(E^{\mathrm{f}}(V_0)\) at different nearest-neighbor sites for the Ba concentration of 1/32. The inset depicts the lattice structure.  
+
+Alkaline- earth metals are adopted as the substitution ions \((A^{2 + })\) to drive the structure evolution (Fig. 1b) and the substituted HfO₂ thin films are deposited on SrTiO₃ (STO) substrates buffered with epitaxial (La₀.₆₇, Sr₀.₃₃)MnO₃ (LSMO) as bottom electrodes by pulsed laser deposition. X- ray diffraction (XRD) and scanning transmission electron microscopy (STEM) are employed to characterize the microstructures. Fig. 1c demonstrates XRD patterns of the Ba- substituted HfO₂/LSMO/STO heterostructures (abbr. BHOₓ, where \(x\) is the substitution concentration in percentage). The XRD for Sr- and Ca- substituted HfO₂ thin films are shown in Supplementary Fig. S4 and S5, respectively.  
+
+For low concentration of \(x \leq 4\%\) , the Ba- Hf- O system is in fluorite structure, in which the BHO0 thin film exhibits monoclinic \((m)\) phase with a diffraction peak for the (- 111)ₘ reflection observed at \(2\theta = 28^{\circ}\) while the BHO02 and BHO04 show the coexistence of \(m\) - and orthorhombic \((o)\) phases because of the substitution- induced lattice strains, as evidenced by the presence of (111)₀ reflection at \(2\theta = 30^{\circ}\) .[21,22] Fig. 1f demonstrate atomic- resolution high- angle annular dark- field (HAADF) images of the
+
+<--- Page Split --->
+
+fluorite lattices, in which the fast Fourier transform of the BHO02 layer exhibits ordered diffraction spots. In addition, the element mappings of Hf, La, and Ba indicate a sharp interface between BHO and LSMO layers.  
+
+When \(x \geq 6\%\) , the structure evolution takes place, in which the Bragg reflections from the fluorite structure are quenched and no new diffraction peaks emerge in the BHO06 \~ BHO15 thin films. Further characterization by the HAADF imaging indicates that there are no nanograins observed in the representative BHO12 layer (Fig. 1e). The fast Fourier transform is a ring- shaped pattern. These results suggest the formation of amorphous structure. More information about the BHO12/LSMO/STO heterostructure over a large scale is shown in Supplementary Fig. S6. The amorphization is understood by performing first- principles calculation on the oxygen stability, manifested by the formation energy of oxygen vacancy \([E^{f}(V_{O})]\) . Note that the amorphous state is formed in a high- temperature crystallizing process of the Ba- Hf- O system (see Methods). The HfO\(_{2}\) should have a high symmetry, like the cubic phase.\(^{[22,23]}\) Fig. 1g demonstrates the \(E^{f}(V_{O})\) at the \(1^{\text{st}}\) nearest- neighbor interstitial sites of Hf tetrahedrons in the cubic HfO\(_{2}\) as a function of substitution concentration. As shown, \(E^{f}(V_{O})\) is as high as \(+8.0 \text{eV}\) in the undoped HfO\(_{2}\) , comparable with the previous reported values,\(^{[24]}\) but sharply lowered to \(-2.5 \text{eV}\) when one in \(32 \text{Hf}^{4 + }\) ions are replaced by Ba\(^{2 + }\) . With increasing concentration, \(E^{f}(V_{O})\) keeps negative around \(-2.0 \text{eV}\) . These suggest that oxygen ions are no longer favorable at the interstitial sites near the substituted Ba\(^{2 + }\) and oxygen vacancies (V\(_{OS}\) ) are formed to maintain the electric neutrality. In addition, not only the \(1^{\text{st}}\) nearest- neighbor site but also the \(2^{\text{nd}}\) , \(3^{\text{rd}}\) , and \(4^{\text{th}}\) nearest- neighbor sites are all instable for oxygen ions even there are only \(1 / 32 \text{Hf}^{4 + }\) ions are replaced (Fig. 1h), which may be due to the strong lattice distortion induced by the large difference in ionic radii between Ba\(^{2 + }\) (1.35 Å) and Hf\(^{4 + }\) (0.71 Å). Therefore, Ba substitution can efficiently
+
+<--- Page Split --->
+
+reduce the oxygen stoichiometric ratio of \(\mathrm{HfO_2}\) . At a proper substitution region, e.g., \(4\%\) \(< x< 20\%\) in Fig. 1c, the number of oxygen ions is too less to support the fluorite Hf metal frame and the Ba- Hf- O system collapses into an amorphous state since the instability of oxygen ions destroy the long- range fluorite periodicity while the perovskite structure isn't formed yet in this oxygen/metal molar ratio.  
+
+The oxygen instability is characterized by X- ray photoelectron spectroscopy (XPS). As shown in Supplementary Fig. S7, the \(V_{\mathrm{OS}}\) increase with increasing \(x\) from \(0\%\) to \(12\%\) , indicating the reduction of oxygen stoichiometric ratio. However, with further increasing the Ba concentration, \(V_{\mathrm{OS}}\) are decreased in the \(\mathrm{BHO20}\) and become negligible in the \(\mathrm{BHO50}\) (i.e., the \(\mathrm{BaHfO_3}\) ). These suggest that, as the oxygen/metal molar ratio is further reduced, the \(\mathrm{Ba/Hf}\) metal frame evolves to the perovskite type that requires less oxygen ions to be stabilized. It is also consistent with the XRD patterns. When the Ba concentration is increased to \(x \geq 20\%\) , two diffraction peaks along with the \((00l)\) reflections of STO emerge and become stronger from \(\mathrm{BHO20}\) to \(\mathrm{BHO50}\) . The epitaxy of perovskite \(\mathrm{BHO50}\) on LSMO/STO is also observed in the HAADF image in Fig. 1d.  
+
+In Fig. 1g, we also show the \(E^{\mathrm{f}}(V_{\mathrm{O}})\) of Sr- and Ca- substituted \(\mathrm{HfO_2}\) , which are - 1.8 and - 1.1 eV at the concentration of 1/32, respectively, higher than that of the Ba- Hf- O system. The decrease of oxygen instability may be due to the smaller difference in ionic radii between \(A^{2 + }\) ( \(\mathrm{Sr^{2 + }}\) : 1.12 Å; \(\mathrm{Ca^{2 + }}\) : 0.99 Å) and \(\mathrm{Hf^{4 + }}\) . It is also consistent with the structure evolution shown in XRD patterns, in which the Sr- Hf- O and Ca- Hf- O systems need higher substitution concentrations to induce the amorphous structures in \(23\% \leq x \leq 30\%\) and \(33\% \leq x \leq 36\%\) , respectively (Supplementary Fig. S4 and S5), compared with the Ba- Hf- O. The amorphization behaviors are summarized in Fig. 1b. As shown, in the \(A\) - Hf- O system both width and location of amorphous region could be controlled
+
+<--- Page Split --->
+
+by the substituted ion through the difference in ionic radius \(\left(\mathrm{r}_A - \mathrm{r}_{\mathrm{Hf}}\right)\) and the tolerance factor of the formed perovskite \(A\mathrm{HfO}_3\) , calculated by \(\frac{\sqrt{2}\left(\mathrm{r}_{\mathrm{Hf}} + \mathrm{r}_{\mathrm{O}}\right)}{\mathrm{r}_A + \mathrm{r}_{\mathrm{O}}}\) .  
+
+![](images/Figure_2.jpg)
+
+<center>Fig. 2 | Short-range structure of the amorphous BHO film. The Fourier transformed EXAFS data \(\left(|\chi (R)|\right)\) of Hf \(L_{\mathrm{III}}\) edge for BHO12 film, in which the imaginary part of \(|\chi (R)|\) is also shown for clarity. The inset is the EXAFS spectrum of BHO12-RT film for comparison. The bule dashed, orange dotted, and black solid lines are fits to \(P2_{1} / c\) , \(Pca2_{1}\) , and \(P2_{1} / c + Pca2_{1}\) symmetries, respectively. The fitting window is \(R = 1.0 \sim 4.0\) Å. </center>  
+
+Short- range ordering of the designed amorphous structure is characterized by extended X- ray absorption fine- structure spectroscopy (EXAFS). Fig. 2 demonstrates the Fourier transformed EXAFS data \(\left(|\chi (R)|\right)\) of Hf \(L_{\mathrm{III}}\) edge for the representative BHO12 film, where \(R\) denotes the radial distance. Previous studies have shown that amorphous \(\mathrm{HfO}_2\) films are always monoclinic in local structure with the best fit to the \(P2_{1} / c\) symmetry. [25- 28] For comparison, we deposited an amorphous \(12\%\) Ba- substituted \(\mathrm{HfO}_2\) at room temperature (BHO12- RT), which also exhibits the short- range \(P2_{1} / c\) symmetry (the inset), in agreement with the reported results. However, the best fit to
+
+<--- Page Split --->
+
+the energetically- favorable phase of bulk \(\mathrm{HfO_2}\) suggests that the Ba substitution doesn't yield pronounced structure distortion on the BHO12- RT film, which can be explained by more stable oxygen ions in the conventionally amorphous structure (Supplementary Fig. S8).  
+
+Following the scattering paths used in BHO12- RT, the \(P2_{1} / c\) symmetry cannot give a good fit to the BHO12 film mainly because of the two distinguished oscillations in \(2.2 \mathrm{\AA} < R < 3.5 \mathrm{\AA}\) . A better fit can be found in orthorhombic \(Pca2_{1}\) symmetry and the best is achieved by combining the \(Pca2_{1}\) and \(P2_{1} / c\) , which is reasonable since, before the collapse of long- range fluorite periodicity, the Ba- Hf- O system has experienced an orthorhombic distortion. Similar two- phase coexistence has also been observed in the EXAFS spectrum of crystalline \(\mathrm{Hf_{0.46}Zr_{0.54}O_2}\) films.[28] Therefore, the observation of pronounced \(Pca2_{1}\) symmetry in Fig. 2 suggests that the Ba substitution- induced lattice distortion can be preserved in the short- range structure of BHO12, which isn't fully- relaxed like the unannealed BHO12- RT counterpart. Based on the fitting, the coordination information can be extracted (see Supplementary Text 1 for details). The BHO12 exhibits a Hf- O bond length of \(2.07 \sim 2.09 \mathrm{\AA}\) , which is shorter than that of the BHO12- RT and the previously reported amorphous \(\mathrm{HfO_2}\) , as well as the average Hf- O interatomic distance of crystalline \(\mathrm{HfO_2}\) ( \(\sim 2.14 \mathrm{\AA}\) ),[23,26,27] indicating a higher density. More importantly, due to the coexistence of \(Pca2_{1}\) and \(P2_{1} / c\) symmetries, the BHO12 shows a strong short- range disordering, in which the disorder (Debye- Waller) factor is as large as \(\sim 0.011\) , higher than both the unannealed one and the amorphous \(\mathrm{HfO_2}\) in literature.[25- 27] These structure characters are beneficial to achieve high breakdown strengths.
+
+<--- Page Split --->
+![](images/Figure_3.jpg)
+
+<center>Fig. 3 | Dielectric energy storage of BHO thin-film capacitors. a, \(P - E\) hysteresis loops of Pt/BHO/LSMO capacitors measured at \(10\mathrm{kHz}\) . b, Two-parameter Weibull distribution analysis of breakdown strengths over 12 capacitors for each Ba concentration. c, Statistical \(E_{\mathrm{b}}\) and (d) Weibull modulus \(\beta\) extracted from (b) plotted as a function of Ba concentration. Here, \(\beta\) is the slope of \(\ln [- \ln (1 - p)]\) vs. \(\ln E_{\mathrm{b}}\) , where \(p = i / (n + 1)\) ( \(n\) is the total number of samples and \(i\) is the \(i\) th sample). e, Energy storage density \((U_{\mathrm{rec}})\) and efficiency \((\eta)\) of the BHO capacitors calculated from \(P - E\) loops. The data points are averaged over 12 capacitors for each Ba concentration. </center>  
+
+Pt is adopted as top electrodes for fabricating dielectric capacitors. Fig. 3a shows \(P - E\) hysteresis loops of the Pt/BHO/LSMO capacitors and the corresponding Weibull distributions of breakdown strengths are plotted in Fig. 3b. Without Ba substitution, the BHO0 is a linear dielectric with the statistical \(E_{\mathrm{b}}\) of \(\sim 4.2\mathrm{MV / cm}\) (Fig. 3c), in agreement with the values reported previously in similar \(\mathrm{HfO_2}\) thin films. \(^{[3,29]}\) The calculated \(U_{\mathrm{rec}}\) is only \(\sim 22.4\mathrm{J / cm^3}\) (Fig. 3e) due to the low \(E_{\mathrm{b}}\) and \(P_{\mathrm{m}}\) . With Ba substitution, the polar \(o\) - phase is induced and a typical ferroelectric hysteresis loop is observed in the BHO02 capacitor. \(U_{\mathrm{rec}}\) is increased to \(\sim 32\mathrm{J / cm^3}\) but the strong hysteresis feature results in a large \(U_{\mathrm{loss}}\) and thus a low \(\eta\) of \(\sim 37\%\) . Similar phenomena are also observed in the
+
+<--- Page Split --->
+
+BHO04 capacitor.  
+
+Above \(x = 6\%\) , the Ba- Hf- O system evolves into amorphous state. The hysteresis behaviors become very weak and hence the \(\eta\) is increased to above \(85\%\) (Fig. 3e). The \(U_{\mathrm{rec}}\) is also substantially increased. It increases to \(\sim 100 \mathrm{J / cm^3}\) in the BHO08 and reaches a maximum value of \(\sim 155 \mathrm{J / cm^3}\) in the BHO12. In the BHO15, the \(U_{\mathrm{rec}}\) is relatively decreased but still maintains a large value above \(120 \mathrm{J / cm^3}\) . The giant energy densities are obviously owing to the dramatically improved breakdown strengths in the amorphous capacitors (Fig. 3c). For example, the BHO12, its \(E_{\mathrm{b}}\) can be as high as \(\sim 12 \mathrm{MV / cm}\) , about three times of that of the crystalline BHO0, yielding a large \(P_{\mathrm{m}}\) of \(\sim 30 \mu \mathrm{C / cm^2}\) . In addition, the amorphous BHO also exhibit large Weibull modulus \(\beta\) , indicating good reproducibility over different samples. However, when \(x\) further increases to above \(20\%\) , the perovskite \(\mathrm{BaHfO_3}\) is crystallized and \(E_{\mathrm{b}}\) is decreased to less than \(7.0 \mathrm{MV / cm}\) , resulting in low \(U_{\mathrm{rec}}\) of \(50 \sim 65 \mathrm{J / cm^3}\) in the BHO20 \(\sim\) BHO50 capacitors.  
+
+Overall, Fig. 3 indicates the critical role of breakdown strength for enhancing energy storage density. In dielectric capacitors, the breakdown usually takes place within a short period of time ( \(< 1.0 \mathrm{ms}\) ) and results from the electronic and/or the avalanche mechanisms.[1,2] Considering that the BHO thin films have similar bandgaps of \(\sim 5.0 \mathrm{eV}\) (Supplementary Fig. S9),[30,31] the electronic breakdown that is due to the activation of electrons from the valence band to the conduction band by \(E\) can be excluded. The improved \(E_{\mathrm{b}}\) is thus ascribed to the suppression of avalanche effect. First, the amorphous BHO is formed in the structure evolution by oxygen instability, which exhibits a strong disordering not only due to the collapse of fluorite and perovskite periodicities in long range but also the coexistence of \(Pca2_1\) and \(P2_1 / c\) symmetries in short range. Second, the high- temperature annealing but non- crystallization gives the
+
+<--- Page Split --->
+
+BHO a higher density than the reported crystalline/amorphous HfO<sub>2</sub> and the unannealed counterpart (e.g., the BHO12-RT, showing an \(E_{\mathrm{b}}\) of \(\sim 3.64 \mathrm{MV / cm}\) and a low \(U_{\mathrm{rec}}\) of \(\sim 10.4 \mathrm{J / cm}^3\) , Supplementary Fig. S10). In this highly- disordered and dense matrix, the carrier transport is dramatically scattered from one lattice to the other, which suppresses the ionizing collision effect with atoms and hence impedes the carrier avalanche for dielectric breakdown. One can thus find that the amorphous BHO12 capacitor exhibits a negligible dependence of \(E_{\mathrm{b}}\) upon film thickness \((d)\) whereas the \(E_{\mathrm{b}}\) of crystalline BHO0, BHO02, and BHO50 capacitors decrease with increasing \(d\) , following an empirical formula \(E_{\mathrm{b}} \propto d^{-\beta}\) \((0.12 < \beta < 0.29)\) (Supplementary Fig. S11).<sup>[1,32]</sup> In addition, in the amorphous structure, the bonding of Hf- O could be well maintained for contributing the dielectric polarizability and a large \(\epsilon_{\mathrm{r}}\) is obtained in the BHO12 (also in the amorphous state of Sr- Hf- O and Ca- Hf- O systems), which is even higher than that of the crystalline BHO0 at high frequency (Supplementary Fig. S12). Therefore, the ultrahigh breakdown strength that is achieved without the trade- off of permittivity gives rise to the remarkably improved energy densities in the amorphous structure.  
+
+![](images/Figure_4.jpg)
+
+<center>Fig. 4 | Reliability of BHO dielectric capacitors. Energy storage density \((U_{\mathrm{rec}})\) and efficiency \((\eta)\) of BHO0, BHO02, BHO12, and BHO50 capacitors as functions of (a) electric field, (b) temperature (measured at \(0.7 E_{\mathrm{b}}\) ), and (c) charging-discharging cycles (measured at \(0.6 E_{\mathrm{b}}\) ), respectively. </center>  
+
+Device reliability of the amorphous BHO12 capacitor is demonstrated in Fig. 4,
+
+<--- Page Split --->
+
+by comparing with the crystalline BHO0, BHO02, and BHO50. Fig. 4a plots the \(U_{\mathrm{rec}}\) and \(\eta\) as a function of \(E\) . The BHO12 capacitor exhibits a parabolic- like increase of \(U_{\mathrm{rec}}\) to \(155\mathrm{J / cm}^3\) with small variation in \(\eta\) up to \(12\mathrm{MV / cm}\) . However, in the BHO0, BHO02, and BHO50 capacitors, the dielectric breakdown occurs before \(6.0\mathrm{MV / cm}\) , impeding the increase of \(U_{\mathrm{rec}}\) . Corresponding \(P\) - \(E\) loops are shown in Supplementary Fig. S13 for clarity. Owing to the improved breakdown strength, the BHO12 exhibits much higher energy densities in high- temperature and charging/discharging cycling measurements. As shown in Fig. 4b, the amorphous BHO12 holds a similar temperature stability with that of the crystalline BHO0 and BHO50 but exhibits a more than 2 times higher \(U_{\mathrm{rec}}\) of \(\sim 80\mathrm{J / cm}^3\) ( \(\eta = 84\%\) ) at \(400\mathrm{K}\) . In Fig. 4c, the BHO12 exhibits optimized energy storage properties up to \(5\times 10^6\) charging/discharging cycles with a large \(U_{\mathrm{rec}}\) of \(\sim 56\) \(\mathrm{J / cm}^3\) and a \(\eta\) of \(\sim 90\%\) at \(7.2\mathrm{MV / cm}\) .  
+
+In summary, this study has provided a new playground for dielectric energy storage, which could be widely applicable by the additional experiments on Sr- Hf- O and Ca- Hf- O systems where very high \(E_{\mathrm{b}}\) and \(U_{\mathrm{rec}}\) are also observed (Supplementary Fig. S1). In addition, the dependence of structure evolution on the intrinsic material parameters of the \(\mathrm{HfO_2}\) and the series of alkaline- earth perovskites (Fig. 1b) suggests that the amorphization method could be highly controllable for material design. Besides, from a practical point of view, the amorphous hafnium- based oxide, which is high- \(\kappa\) but shows ultrahigh \(E_{\mathrm{b}}\) comparable to the \(\mathrm{SiO_2}\) (Supplementary Fig. 3), would be promising in a broad spectrum. Especially, it has great potential to be compatible with the current CMOS techniques for developing advanced electronic devices that require high breakdown strengths.[33- 35] More generally, the proposed structure- design strategy may also open a new perspective for exploring new functionalities in the boundary among different categories of materials.
+
+<--- Page Split --->
+
+## References  
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+2. Palneedi, H., Peddigari, M., Hwang, G.-T., Jeong, D.-Y. & Ryu, J. High-performance dielectric ceramic films for energy storage capacitors: progress and outlook. Adv. Func. Mater. 28, 1803665 (2018).  
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+9. Barshaw, E. J. et al. High energy density (HED) biaxially-oriented poly-propylene (BOPP) capacitors for pulse power applications. IEEE Trans. Magnet. 43, 223-225
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+14. Zhu, H. et al. Achieving a record-high capacitive energy density on Si with columnar nanograined ferroelectric films. ACS Appl. Mater. Interfaces 14, 7805-7813 (2022).  
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+16. Sun, Z. et al. Ultrahigh energy storage performance of lead-free oxide multilayer film capacitors via interface engineering. Adv. Mater. 29, 1604427 (2017).  
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+18. Hu, T.-Y. et al. Realizing high energy density and efficiency simultaneously via sub-grain modification in lead-free dielectric films. Nano Energy 98, 107313 (2022).  
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+19. Xie, J. et al. Achieving ultrahigh energy storage performance in bismuth magnesium titanate film capacitors via amorphous-structure engineering. J. Mater. Chem. C 7, 13632 (2019).
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+20. Reklaitis, I. et al. A comparative study on atomic layer deposited oxide film morphology and their electrical breakdown. Surf. Coat. Tech. 399, 126123 (2020).  
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+21. Schroeder, U. et al. Lanthanum-doped hafnium oxide: a robust ferroelectric material. Inorg. Chem. 57, 2752-2765 (2018).  
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+22. Schroeder, U., Park, M. H., Mikolajick, T. & Hwang, C. S. The fundamentals and applications of ferroelectric HfO₂. Nat. Rev. Mater. 7, 653-669 (2022).  
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+23. Gallington, L. C. et al. The structure of liquid and amorphous hafnia. Materials 10, 1290 (2017).  
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+24. Kaneta, C., Yamasaki, T. Oxygen-related defects in amorphous HfO₂ gate dielectrics. Microelectron. Eng. 84, 2370-2373 (2007).  
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+25. Lysaght, P. S. et al. Incipient amorphous-to-crystalline transition in HfO₂ as a function of thickness scaling and anneal temperature. J. Non-Crystal. Solids. 354, 399-403 (2008).  
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+26. Cho, D.-Y., Park, T. J., Na, K. D., Kim, J. H. & Hwang, C. S. Structural disorders in an amorphous HfO₂ film probed by X-ray absorption fine structure analysis. Phys. Rev. B 78, 132102 (2008).  
+
+27. Viennet, R. et al. XAFS atomistic insight of the oxygen gettering in Ti/HfO₂ based OxRRAM. Phys. Rev. Mater. 2, 055002 (2018).  
+
+28. Sahiner, M. A. et al. Identification of structural phases in ferroelectric hafnium zirconium oxide by density-functional-theory-assisted EXAFS analysis. Appl. Phys. Lett. 118, 092903 (2021).  
+
+29. Zhang, L. et al. ALD preparation of high-\(k\) HfO₂ thin films with enhanced energy density and efficient electrostatic energy storage. RSC Adv. 7, 8388-8393 (2017).  
+
+30. Yim, K. et al. Novel high-\(k\) dielectrics for next-generation electronic devices screened by automated ab initio calculations. NPG Asia Mater. 7, e190 (2015).
+
+<--- Page Split --->
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+31. Perevalov, T. V. et al. Atomic and electronic structure of amorphous and crystalline hafnium oxide: X-ray photoelectron spectroscopy and density functional calculations.  
+
+J. Appl. Phys. 101, 053704 (2007).  
+
+32. Zhao, L. & Liu, C. L. Review and mechanism of the thickness effect of solid dielectrics. Nanomaterials 10, 2473 (2020).  
+
+33. Palumbo, F. et al. A review on dielectric breakdown in thin dielectrics: silicon dioxide, high-\(k\), and layered dielectrics. Adv. Func. Mater. 30, 1900657 (2020).  
+
+34. Ceresoli, D. & Vanderbilt, D. Structural and dielectric properties of amorphous \(\mathrm{ZrO_2}\) and \(\mathrm{HfO_2}\) . Phys. Rev. B 74, 125108 (2006).  
+
+35. Luo, X. & Demkov, A. A. Structure, thermodynamics, and crystallization of amorphous hafnia. J. Appl. Phys. 118, 124105 (2015).
+
+<--- Page Split --->
+
+## Methods  
+
+Device preparation. The \(A\) - Hf- O thin films and LSMO electrodes were grown on (001) single- crystalline STO substrates by pulsed laser deposition using a KrF excimer laser (Coherent COMPexPro 201). The LSMO thin films were deposited at a laser energy density of \(\sim 3.0 \mathrm{J / cm^2}\) with a repetition rate of \(2 \mathrm{Hz}\) , keeping the substrate at \(973 \mathrm{K}\) and the oxygen pressure at \(0.2 \mathrm{mbar}\) . The \(A\) - Hf- O thin films were deposited with \(2.6 \mathrm{J / cm^2}\) laser energy density at \(4 \mathrm{Hz}\) repetition, keeping the substrate temperature at \(873 \mathrm{K}\) and the \(\mathrm{O_2}\) pressure at \(0.1 \mathrm{mbar}\) . After the deposition, the \(A\) - Hf- O heterostructures were annealed at \(973 \mathrm{K}\) for 1 hour in flowing \(\mathrm{O_2}\) . Pt top electrodes of \(\sim 30 \mu \mathrm{m}\) in diameter and \(\sim 50 \mathrm{nm}\) in thickness were deposited on the surface of \(A\) - Hf- O heterostructures by sputtering with a shadow mask to form the thin- film capacitors.  
+
+First- principles calculation. Density- functional theory (DFT) calculations are performed using Quantum ESPRESSO. The exchange and correlation effects are treated within the generalized gradient approximation (GGA) of Perdew- Burke- Ernzerhof (PBE). The Brillouin zone is sampled with \(6 \times 6 \times 6\) Monkhorst- Pack k- point meshes for the conventional unit cell of \(\mathrm{HfO_2}\) which is reduced reciprocally for larger supercells. The electronic wave functions are expanded in a plane- wave basis set limited by a cut- off energy of \(900 \mathrm{eV}\) . The atomic positions and lattice parameters are optimized until the force on each atom is converges to less than \(1 \mathrm{meV / \AA}\) in all supercells.  
+
+As shown in the table below, the lattice parameters of the three phases of \(\mathrm{HfO_2}\) are calculated which agree well with the experimental results. In order to study the effects of alkaline- earth metal \(\mathrm{Ba^{2 + }}\) (or \(\mathrm{Sr^{2 + }}\) , \(\mathrm{Ca^{2 + }}\) ) doping on the structural stability of \(\mathrm{HfO_2}\) , we construct several supercells: \(1 \times 1 \times 1\) , \(\sqrt{2} \times \sqrt{2} \times 1\) , \(\sqrt{2} \times \sqrt{2} \approx 2\) , and \(2 \times 2 \times 2\) unit cells which include 4, 8, 16 and \(32 \mathrm{Hf^{4 + }}\) ions respectively. With one \(\mathrm{Hf^{4 + }}\)
+
+<--- Page Split --->
+
+substituted by one alkaline-earth metal ion, we could simulate different doping concentrations of 1/4, 1/8, 1/16 and 1/32.  
+
+The oxygen vacancy formation energy is defined by \(E^{f}(V_{O}) = E_{\mathrm{defect}} - E_{\mathrm{pure}} + \mu_{0}\) . In our calculation, \(E_{\mathrm{defect}}\) is the total energy of a supercell containing a \(\mathrm{Ba}^{2 + }\) (or \(\mathrm{Sr}^{2 + }\) , \(\mathrm{Ca}^{2 + }\) ) ion and an oxygen vacancy; \(E_{\mathrm{pure}}\) is the total energy for the equivalent supercell substituted with a \(\mathrm{Ba}^{2 + }\) (or \(\mathrm{Sr}^{2 + }\) , \(\mathrm{Ca}^{2 + }\) ) ion, and \(\mu_{0}\) is the chemical potential of oxygen atom \((\mu_{0} = \mu_{O_{2}} / 2)\) .  
+
+The structural parameters of the monoclinic, orthorhombic and cubic phase of \(\mathrm{HfO_2}\) .  
+
+<table><tr><td></td><td>Calculation</td><td>Experiment [36-39]</td></tr><tr><td>Monoclinic</td><td></td><td></td></tr><tr><td>a</td><td>5.11Å</td><td>5.12Å</td></tr><tr><td>b</td><td>5.15Å</td><td>5.17Å</td></tr><tr><td>c</td><td>5.29Å</td><td>5.30Å</td></tr><tr><td>β</td><td>99.65°</td><td>99.20°</td></tr><tr><td>Orthorhombic</td><td></td><td></td></tr><tr><td>a</td><td>5.24Å</td><td>5.23Å</td></tr><tr><td>b</td><td>5.01Å</td><td>5.00Å</td></tr><tr><td>c</td><td>5.05Å</td><td>5.05Å</td></tr><tr><td>Cubic</td><td></td><td></td></tr><tr><td>a</td><td>5.04Å</td><td>5.08Å</td></tr></table>  
+
+Characterizations. XRD was performed on a Rigaku SmartLab diffractometer. The cross- sectional TEM specimens were prepared by focused ion beam (FIB, FEI Versa workstation) with a Ga ion source. The HAADF- STEM images were carried out at 200 kV by a JEOL ARM200CF microscope equipped with a cold field emission electron gun, an ASCOR probe corrector and a Gatan Quantum ER spectrometer. The Hf \(L_{\mathrm{III}}\) - edge x- ray adsorptions were measured on 150 nm- thick BHO films in fluorescence yield mode at room temperature at the BL14W1 beamline in the Shanghai Synchrotron Radiation Facility (SSRF). The EXAFS spectra were analyzed using FEFF6 code by Athena and Artemis packages.[40] XPS was performed on a Thermo ESCALAB 250 Xi, and the binding energy was calibrated by setting the C 1s at 284.6 eV. P- E hysteresis
+
+<--- Page Split --->
+
+loops were measured by a Radiant Premier II ferroelectric tester. Capacitances were recorded using an Agilent 4294A impedance analyzer. The testing pulses were applied to the Pt electrodes and the LSMO were always grounded.  
+
+## Data availability  
+
+The data supporting the findings of this study are available within the article and its Supplementary Information.  
+
+## References  
+
+36. J. Wang, H. P. Li, R. Stevens, Hafnia and hafnia-toughened ceramics. J. Mater. Sci. 27, 5397-5430 (1992).  
+
+37. D. M. Adams, S. Leonard, D. R. Russell, R. J. Cernik, X-ray diffraction study of Hafnia under high pressure using synchrotron radiation. J. Phys. Chem. Solids 52, 1181-1186 (1991).  
+
+38. D. W. Stacy, J. K. Johnstone, D. R. Wilder, Axial thermal expansion of HfO₂. J. Am. Ceram. Soc. 55, 482-483 (1972).  
+
+39. X. H. Sang, E. D. Grimley, T. Schenk, U. Schroeder, J. M. LeBeau, On the structural origins of ferroelectricity in HfO₂ thin films. Appl. Phys. Lett. 106, 162905 (2015).  
+
+40. B. Ravel, M. Newville, ATHENA, ARTEMIS, HEPHAESTUS: data analysis for X-ray absorption spectroscopy using IFEFFIT. J. Synchrotron Rad. 12, 537-541 (2005).  
+
+## Acknowledgements  
+
+This work was jointly sponsored by Natural Science Foundation of China (51872148 and 11974211), Natural Science Foundation of Shandong Province (ZR2020JQ03), the Taishan Scholar Program of Shandong Province (tsqn201812045), and Qilu Young Scholar Program of Shandong University.  
+
+## Author contributions  
+
+Z.W. and X.L. conceived this work and designed the experiments and calculations.
+
+<--- Page Split --->
+
+Q.Z. carried out the first-principles calculations. Y.Y., Z.Y.X., and W.Z. deposited the heterostructures, fabricated the capacitors, and measured the energy storage properties. Y.Y., Z.N.X., and J.X. collected the XRD data. C.D. measured the capacitances. L.Z. and Y.C. performed the XPS measurements. Z.W. performed the STEM and EXAFS analyses. Z.W., X.L., Y.Q., S.L., A.L., D.W. and K.M.R analyzed the experimental data and the first-principles calculation. Z.W., X.L., Y.Y., Q.Z. and K.M.R. wrote the manuscript. All authors discussed the data and contributed to the manuscript.  
+
+## Competing interests  
+
+The authors declare no competing interests.
+
+<--- Page Split --->
+
+## Supplementary Files  
+
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+SupplementaryMaterials.pdf
+
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+<|ref|>title<|/ref|><|det|>[[44, 108, 945, 177]]<|/det|>
+# Structure-evolution-designed amorphous oxides for dielectric energy storage  
+
+<|ref|>text<|/ref|><|det|>[[44, 196, 238, 238]]<|/det|>
+Yahui Yu Qingdao University  
+
+<|ref|>text<|/ref|><|det|>[[44, 244, 238, 284]]<|/det|>
+Qing Zhang Shandong University  
+
+<|ref|>text<|/ref|><|det|>[[44, 290, 222, 331]]<|/det|>
+Zhiyu Xu Qingdao University  
+
+<|ref|>text<|/ref|><|det|>[[44, 336, 884, 377]]<|/det|>
+Weijie Zheng College of Physics and Center for Marine Observation and Communications, Qingdao University  
+
+<|ref|>text<|/ref|><|det|>[[44, 382, 222, 423]]<|/det|>
+Jibo Xu Qingdao University  
+
+<|ref|>text<|/ref|><|det|>[[44, 428, 216, 469]]<|/det|>
+Zhongnan Xi Nanjing University  
+
+<|ref|>text<|/ref|><|det|>[[44, 475, 216, 515]]<|/det|>
+Lin Zhu Nanjing University  
+
+<|ref|>text<|/ref|><|det|>[[44, 521, 222, 561]]<|/det|>
+Chunyan Ding Qingdao University  
+
+<|ref|>text<|/ref|><|det|>[[44, 567, 455, 608]]<|/det|>
+Yanqiang Cao Nanjing University of Science and Technology  
+
+<|ref|>text<|/ref|><|det|>[[44, 614, 222, 654]]<|/det|>
+Chunyan Zheng Qingdao University  
+
+<|ref|>text<|/ref|><|det|>[[44, 660, 222, 700]]<|/det|>
+Yalin Qin Qingdao University  
+
+<|ref|>text<|/ref|><|det|>[[44, 706, 580, 747]]<|/det|>
+Shandong Li Qingdao University https://orcid.org/0000- 0001- 8105- 7612  
+
+<|ref|>text<|/ref|><|det|>[[44, 752, 216, 793]]<|/det|>
+Ai- Dong Li Nanjing University  
+
+<|ref|>text<|/ref|><|det|>[[44, 799, 571, 840]]<|/det|>
+Di Wu Nanjing University https://orcid.org/0000- 0003- 3619- 1411  
+
+<|ref|>text<|/ref|><|det|>[[44, 845, 835, 886]]<|/det|>
+Karin Rabe Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854  
+
+<|ref|>text<|/ref|><|det|>[[44, 891, 238, 931]]<|/det|>
+Xiaohui Liu Shandong University  
+
+<|ref|>text<|/ref|><|det|>[[44, 937, 360, 957]]<|/det|>
+Zheng Wen ( zwen@qdu.edu.cn )
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[44, 106, 97, 125]]<|/det|>
+## Letter  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 144, 137, 163]]<|/det|>
+## Keywords:  
+
+<|ref|>text<|/ref|><|det|>[[44, 181, 325, 201]]<|/det|>
+Posted Date: February 6th, 2023  
+
+<|ref|>text<|/ref|><|det|>[[44, 220, 474, 240]]<|/det|>
+DOI: https://doi.org/10.21203/rs.3.rs- 2486944/v1  
+
+<|ref|>text<|/ref|><|det|>[[44, 257, 910, 300]]<|/det|>
+License: © This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License  
+
+<|ref|>text<|/ref|><|det|>[[44, 317, 532, 338]]<|/det|>
+Additional Declarations: There is NO Competing Interest.  
+
+<|ref|>text<|/ref|><|det|>[[42, 372, 909, 417]]<|/det|>
+Version of Record: A version of this preprint was published at Nature Communications on May 25th, 2023. See the published version at https://doi.org/10.1038/s41467- 023- 38847- 1.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[147, 84, 849, 144]]<|/det|>
+Structure- evolution- designed amorphous oxides for dielectric energy storage  
+
+<|ref|>text<|/ref|><|det|>[[145, 155, 852, 688]]<|/det|>
+Yahui Yu, \(^{1,3\dagger}\) Qing Zhang, \(^{2\dagger}\) Zhiyu Xu, \(^{1,3\dagger}\) Weijie Zheng, \(^{1,3}\) Jibo Xu, \(^{1,3}\) Zhongnan Xi, \(^{4}\) Lin Zhu, \(^{4}\) Chunyan Ding, \(^{1,3}\) Yanqiang Cao, \(^{5}\) Chunyan Zheng, \(^{1}\) Yalin Qin, \(^{1}\) Shandong Li, \(^{3}\) Aidong Li, \(^{4}\) Di Wu, \(^{4}\) Karin M. Rabe, \(^{6}\) Xiaohui Liu, \(^{2\ast}\) and Zheng Wen \(^{1,3\ast}\) \(^{1}\) College of Physics, Qingdao University, Qingdao 266071, China \(^{2}\) School of Physics, Shandong University, Ji'nan 250100, China \(^{3}\) College of Electronics and Information, Qingdao University, Qingdao 266071, China \(^{4}\) National Laboratory of Solid- State Microstructures, Department of Materials Science and Engineering, Jiangsu Key Laboratory of Artificial Functional Materials and Collaborative Innovation Center for Advanced Materials, Nanjing University, Nanjing 210093, China \(^{5}\) Institute of Micro- nano Photonics and Quantum Manipulation, School of Science, Nanjing University of Science and Technology, Nanjing 210094, China \(^{6}\) Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854, USA \(^{+}\) These authors contributed equally in this work. \*Corresponding author. Email: zwen@qdu.edu.cn (Z.W.) and liuxiaohui@sdu.edu.cn (X.L.)
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[146, 78, 853, 767]]<|/det|>
+Dielectric capacitors are fundamental for electric power systems due to the fast charging/discharging rate and high- power density.\(^{[1,2]}\) Recently, rapidly increased demands of miniaturization and integration continuously challenge energy storage density of dielectric capacitors, especially for that could be compatible with the complementary metal- oxide- semiconductor (CMOS) technology, for developing energy- autonomous systems and implantable/wearable electronics, where high- \(\kappa\) capacitors become increasingly desirable in the next- generation applications.\(^{[3- 5]}\) However, their recoverable energy storage densities ( \(U_{\mathrm{rec}}\) ) are low in emerging capacitive energy storage materials. Here, by structure evolution between fluorite \(\mathrm{HfO_2}\) and perovskite hafnate who have similar metal sublattices, we create an amorphous hafnium- based oxide that exhibits a giant \(U_{\mathrm{rec}}\) of \(\sim 155\) \(\mathrm{J / cm^3}\) with an efficiency \((\eta)\) of \(87\%\) , which is record- high in high- \(\kappa\) materials and state- of- the- art in dielectric energy storage (Supplementary Fig. S1 and Table S1). The improved energy density is owing to the strong structure disordering in both short and long ranges induced by oxygen instability in between the two energetically- favorable crystalline forms. As a result, the carrier avalanche is impeded and an ultrahigh breakdown strength \((E_{\mathrm{b}})\) up to \(12 \mathrm{MV / cm}\) is achieved, which, accompanying with a large permittivity \((\epsilon_{\mathrm{r}})\) , remarkably enhances the dielectric energy storage. Our study provides a new and widely applicable playground for designing high- performance dielectric energy storage with the strategy exploring the boundary among different categories of materials.  
+
+<|ref|>text<|/ref|><|det|>[[147, 773, 852, 896]]<|/det|>
+Dielectric capacitors store energy in the form of electrostatic field \((E)\) against electric displacement \((D\) , or polarization \(P\) ), which is regulated by essential material characters, the \(\epsilon_{\mathrm{r}}\) and \(E_{\mathrm{b}}\) , of the dielectric layers.\(^{[1,2]}\) The primary performance parameter \(U_{\mathrm{rec}}\) can be calculated by \(\int_{P_{\mathrm{r}}}^{P_{\mathrm{m}}} E d P\) , according to the \(P\) - \(E\) hysteresis loop,
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[146, 80, 854, 838]]<|/det|>
+which formulates the discharging upon \(E\) from the remanent polarization \((P_{\mathrm{r}})\) to the maximum polarization \((P_{\mathrm{m}})\) before breakdown (Supplementary Fig. S2). Noting that the hysteresis area is the energy loss \((U_{\mathrm{loss}})\) during a charging- discharging cycle. The \(\eta\) is written as \(U_{\mathrm{rec}} / (U_{\mathrm{rec}} + U_{\mathrm{loss}})\) . For ideally linear dielectrics, the \(U_{\mathrm{rec}}\) is simplified to \(\frac{1}{2}\epsilon_0\epsilon_{\mathrm{r}}E_{\mathrm{b}}^2\) ( \(\epsilon_0\) : the vacuum permittivity). Therefore, a high- performance dielectric capacitor should hold both large \(\epsilon_{\mathrm{r}}\) and high \(E_{\mathrm{b}}\) , simultaneously. Moreover, the increase of \(E_{\mathrm{b}}\) would be more efficient to improve the energy storage density due to the square dependence. However, \(E_{\mathrm{b}}\) is usually restricted by \(\epsilon_{\mathrm{r}}\) in most dielectric materials, following a negative power law of \(E_{\mathrm{b}}\propto \epsilon_{\mathrm{r}}^{-\alpha}\) .[1,6,7] For example, perovskite oxides, such as SrTiO3, BaTiO3, and Pb(Zr,Ti)O3, have large \(\epsilon_{\mathrm{r}}\) of a few hundred but low \(E_{\mathrm{b}}\) of only \(1.0 \sim 3.0 \mathrm{MV / cm}\) in general.[1,6,7] For that have high breakdown strengths (>5.0 MV/cm), like polymers and dielectric glasses, their low \(\epsilon_{\mathrm{r}}\) limit energy densities.[2,8,9] How to overcome the negative correlation by increasing \(E_{\mathrm{b}}\) in large- permittivity materials is key to enhance the energy storage performance. Most recently, by introducing local disorders, such as grain boundaries, ionic defects, amorphous fractions, and interfacial layers, improved \(E_{\mathrm{b}}\) of 4.5, 5.92, 6.35, and 8.75 MV/cm have been achieved in \((\mathrm{Ba_0.7Ca_0.3}) \mathrm{TiO_3 / Ba(Zr_0.2Ti_0.8)O_3}\) multilayers, ion- bombarded \(\mathrm{Pb(Mg_{1 / 3}Nb_{2 / 3})O_3 - PbTiO_3}\) , high- entropy \((\mathrm{Bi_{3.25}La_{0.75})(Ti_{3 - 3x}Zr_xHf_xSn_x)O_{12}}\) , and nano- grained \(\mathrm{BaTiO_3}\) , respectively, generating state- of- the- art energy storage densities (Supplementary Table S1).[10- 19] However, in the rapidly developed field of high- \(\kappa\) capacitors, their breakdown strengths are still low relative to the well- optimized perovskite- based capacitors,[3,20] limiting the energy densities for developing microelectronic energy devices.  
+
+<|ref|>text<|/ref|><|det|>[[147, 849, 850, 901]]<|/det|>
+Here, we propose a new structure strategy to achieve an ultrahigh \(E_{\mathrm{b}}\) of \(\sim 12\) MV/cm, which is far beyond the restriction of permittivity (Supplementary Fig. S3) and
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[147, 80, 853, 760]]<|/det|>
+yields remarkably improved \(U_{\mathrm{rec}}\) of \(\sim 155 \mathrm{J / cm}^3\) , in an amorphous hafnium- based oxide designed by bridging fluorite \(\mathrm{HfO_2}\) and perovskite \(\mathrm{AHfO_3}\) (where \(A\) is a divalent ion). As depicted in Fig. 1a, although they are classified into different categories of crystals, the \(\mathrm{HfO_2}\) and \(\mathrm{AHfO_3}\) share similar face- centered metal sublattices. The difference is the stoichiometric ratio and lattice sites of oxygen ions. In fluorite structure, the molar ratio of oxygen to metal is 2:1 and the eight oxygen ions occupy the interstitial sites of \(\mathrm{Hf}\) tetrahedrons to support the \(\mathrm{Hf}\) metal frame. For perovskite, the oxygen/metal molar ratio is reduced to 1.5:1 and the \(\mathrm{Hf / A}\) metal frame is stabilized by six oxygen ions that take the connection- line sites of two same metal ions, such as \(\mathrm{Hf^{4 + } - Hf^{4 + }}\) and \(A^{2 + } - A^{2 + }\) . Therefore, we can evolve the lattice from the fluorite to the perovskite by reducing oxygen stoichiometric ratio through substituting \(\mathrm{Hf^{4 + }}\) with \(A^{2 + }\) , in which the oxygen ions move from the interstitial to the connection- line sites to stabilize the metal frames. However, during the structure evolution, the oxygen ions may be instable at either the interstitial or the connection- line sites. Such an oxygen instability dramatically distorts the \(\mathrm{Hf / A}\) metal frames and eventually results in the collapse of long- range periodicities for both the fluorite and the perovskite when the substitution concentration is proper. The amorphous structure is thus formed with strong disordering. Meanwhile, the structure similarity also facilitates the maintaining of \(\mathrm{Hf - O}\) bonding, which is the main contribution of electronic and ionic displacements for dielectric polarizability, when the long- range lattice ordering is absent. The large \(\epsilon_{\mathrm{r}}\) of the parent high- \(\kappa\) \(\mathrm{HfO_2}\) and \(\mathrm{AHfO_3}\) could thus be inherited by the amorphous structure.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[170, 80, 828, 633]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[147, 645, 852, 895]]<|/det|>
+<center>Fig. 1 | Amorphization of the hafnium-based oxides. a, Schematic drawing for the structure evolution from fluorite \(\mathrm{HfO_2}\) to perovskite \(\mathrm{AHfO_3}\) , where the \(\mathrm{HfO_2}\) is drawn in normal coordinates of \(< 100>\) ( \(a\) axis), \(< 010>\) ( \(b\) axis), and \(< 001>\) ( \(c\) axis) while the \(\mathrm{AHfO_3}\) is drawn in the coordinates of \(< 110>\) ( \(a\) axis), \(< 1\bar{1} 0>\) ( \(b\) axis), and \(< 001>\) ( \(c\) axis). b, Amorphous regions of the Ba-Hf-O, Sr-Hf-O, and Ca-Hf-O systems, respectively, as functions of the difference in ionic radii between \(A^{2 + }\) and \(\mathrm{Hf^{4 + }}\) ( \(\mathrm{r}_A - \mathrm{r}_{\mathrm{Hf}}\) ) and the tolerance factor of \(\mathrm{AHfO_3}\) . c, XRD patterns of Ba-substituted \(\mathrm{HfO_2}\) ( \(\mathrm{BHO_x}\) ) thin films with increasing concentration from 0 to \(50\%\) . The # and \* symbols denote Bragg </center>
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[147, 82, 852, 397]]<|/det|>
+reflections from STO substrate and epitaxial LSMO electrode, respectively. The purple and red dashed lines indicate Bragg reflections from fluorite ( \(m\) - and \(o\) - phases) and perovskite structures, respectively. STEM characterizations of the BHO50 (d), BHO12 (e), and BHO02 (f) heterostructures, where the left panels are high-resolution HAADF images with fast Fourier transform patterns shown in the insets and the right panels are element distributions of Hf, La, and Ba mapped by electron energy loss spectroscopy, respectively. \(\mathbf{g}\) , Formation energy of oxygen vacancy \([E^{\mathrm{f}}(V_0)]\) at the first nearest-neighbor (NN) site as a function of the substitution concentration. \(\mathbf{h}\) , \(E^{\mathrm{f}}(V_0)\) at different nearest-neighbor sites for the Ba concentration of 1/32. The inset depicts the lattice structure.  
+
+<|ref|>text<|/ref|><|det|>[[147, 410, 852, 693]]<|/det|>
+Alkaline- earth metals are adopted as the substitution ions \((A^{2 + })\) to drive the structure evolution (Fig. 1b) and the substituted HfO₂ thin films are deposited on SrTiO₃ (STO) substrates buffered with epitaxial (La₀.₆₇, Sr₀.₃₃)MnO₃ (LSMO) as bottom electrodes by pulsed laser deposition. X- ray diffraction (XRD) and scanning transmission electron microscopy (STEM) are employed to characterize the microstructures. Fig. 1c demonstrates XRD patterns of the Ba- substituted HfO₂/LSMO/STO heterostructures (abbr. BHOₓ, where \(x\) is the substitution concentration in percentage). The XRD for Sr- and Ca- substituted HfO₂ thin films are shown in Supplementary Fig. S4 and S5, respectively.  
+
+<|ref|>text<|/ref|><|det|>[[147, 706, 852, 888]]<|/det|>
+For low concentration of \(x \leq 4\%\) , the Ba- Hf- O system is in fluorite structure, in which the BHO0 thin film exhibits monoclinic \((m)\) phase with a diffraction peak for the (- 111)ₘ reflection observed at \(2\theta = 28^{\circ}\) while the BHO02 and BHO04 show the coexistence of \(m\) - and orthorhombic \((o)\) phases because of the substitution- induced lattice strains, as evidenced by the presence of (111)₀ reflection at \(2\theta = 30^{\circ}\) .[21,22] Fig. 1f demonstrate atomic- resolution high- angle annular dark- field (HAADF) images of the
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[147, 83, 851, 167]]<|/det|>
+fluorite lattices, in which the fast Fourier transform of the BHO02 layer exhibits ordered diffraction spots. In addition, the element mappings of Hf, La, and Ba indicate a sharp interface between BHO and LSMO layers.  
+
+<|ref|>text<|/ref|><|det|>[[146, 180, 853, 895]]<|/det|>
+When \(x \geq 6\%\) , the structure evolution takes place, in which the Bragg reflections from the fluorite structure are quenched and no new diffraction peaks emerge in the BHO06 \~ BHO15 thin films. Further characterization by the HAADF imaging indicates that there are no nanograins observed in the representative BHO12 layer (Fig. 1e). The fast Fourier transform is a ring- shaped pattern. These results suggest the formation of amorphous structure. More information about the BHO12/LSMO/STO heterostructure over a large scale is shown in Supplementary Fig. S6. The amorphization is understood by performing first- principles calculation on the oxygen stability, manifested by the formation energy of oxygen vacancy \([E^{f}(V_{O})]\) . Note that the amorphous state is formed in a high- temperature crystallizing process of the Ba- Hf- O system (see Methods). The HfO\(_{2}\) should have a high symmetry, like the cubic phase.\(^{[22,23]}\) Fig. 1g demonstrates the \(E^{f}(V_{O})\) at the \(1^{\text{st}}\) nearest- neighbor interstitial sites of Hf tetrahedrons in the cubic HfO\(_{2}\) as a function of substitution concentration. As shown, \(E^{f}(V_{O})\) is as high as \(+8.0 \text{eV}\) in the undoped HfO\(_{2}\) , comparable with the previous reported values,\(^{[24]}\) but sharply lowered to \(-2.5 \text{eV}\) when one in \(32 \text{Hf}^{4 + }\) ions are replaced by Ba\(^{2 + }\) . With increasing concentration, \(E^{f}(V_{O})\) keeps negative around \(-2.0 \text{eV}\) . These suggest that oxygen ions are no longer favorable at the interstitial sites near the substituted Ba\(^{2 + }\) and oxygen vacancies (V\(_{OS}\) ) are formed to maintain the electric neutrality. In addition, not only the \(1^{\text{st}}\) nearest- neighbor site but also the \(2^{\text{nd}}\) , \(3^{\text{rd}}\) , and \(4^{\text{th}}\) nearest- neighbor sites are all instable for oxygen ions even there are only \(1 / 32 \text{Hf}^{4 + }\) ions are replaced (Fig. 1h), which may be due to the strong lattice distortion induced by the large difference in ionic radii between Ba\(^{2 + }\) (1.35 Å) and Hf\(^{4 + }\) (0.71 Å). Therefore, Ba substitution can efficiently
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[147, 83, 852, 233]]<|/det|>
+reduce the oxygen stoichiometric ratio of \(\mathrm{HfO_2}\) . At a proper substitution region, e.g., \(4\%\) \(< x< 20\%\) in Fig. 1c, the number of oxygen ions is too less to support the fluorite Hf metal frame and the Ba- Hf- O system collapses into an amorphous state since the instability of oxygen ions destroy the long- range fluorite periodicity while the perovskite structure isn't formed yet in this oxygen/metal molar ratio.  
+
+<|ref|>text<|/ref|><|det|>[[147, 247, 852, 594]]<|/det|>
+The oxygen instability is characterized by X- ray photoelectron spectroscopy (XPS). As shown in Supplementary Fig. S7, the \(V_{\mathrm{OS}}\) increase with increasing \(x\) from \(0\%\) to \(12\%\) , indicating the reduction of oxygen stoichiometric ratio. However, with further increasing the Ba concentration, \(V_{\mathrm{OS}}\) are decreased in the \(\mathrm{BHO20}\) and become negligible in the \(\mathrm{BHO50}\) (i.e., the \(\mathrm{BaHfO_3}\) ). These suggest that, as the oxygen/metal molar ratio is further reduced, the \(\mathrm{Ba/Hf}\) metal frame evolves to the perovskite type that requires less oxygen ions to be stabilized. It is also consistent with the XRD patterns. When the Ba concentration is increased to \(x \geq 20\%\) , two diffraction peaks along with the \((00l)\) reflections of STO emerge and become stronger from \(\mathrm{BHO20}\) to \(\mathrm{BHO50}\) . The epitaxy of perovskite \(\mathrm{BHO50}\) on LSMO/STO is also observed in the HAADF image in Fig. 1d.  
+
+<|ref|>text<|/ref|><|det|>[[147, 607, 852, 889]]<|/det|>
+In Fig. 1g, we also show the \(E^{\mathrm{f}}(V_{\mathrm{O}})\) of Sr- and Ca- substituted \(\mathrm{HfO_2}\) , which are - 1.8 and - 1.1 eV at the concentration of 1/32, respectively, higher than that of the Ba- Hf- O system. The decrease of oxygen instability may be due to the smaller difference in ionic radii between \(A^{2 + }\) ( \(\mathrm{Sr^{2 + }}\) : 1.12 Å; \(\mathrm{Ca^{2 + }}\) : 0.99 Å) and \(\mathrm{Hf^{4 + }}\) . It is also consistent with the structure evolution shown in XRD patterns, in which the Sr- Hf- O and Ca- Hf- O systems need higher substitution concentrations to induce the amorphous structures in \(23\% \leq x \leq 30\%\) and \(33\% \leq x \leq 36\%\) , respectively (Supplementary Fig. S4 and S5), compared with the Ba- Hf- O. The amorphization behaviors are summarized in Fig. 1b. As shown, in the \(A\) - Hf- O system both width and location of amorphous region could be controlled
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[147, 83, 850, 149]]<|/det|>
+by the substituted ion through the difference in ionic radius \(\left(\mathrm{r}_A - \mathrm{r}_{\mathrm{Hf}}\right)\) and the tolerance factor of the formed perovskite \(A\mathrm{HfO}_3\) , calculated by \(\frac{\sqrt{2}\left(\mathrm{r}_{\mathrm{Hf}} + \mathrm{r}_{\mathrm{O}}\right)}{\mathrm{r}_A + \mathrm{r}_{\mathrm{O}}}\) .  
+
+<|ref|>image<|/ref|><|det|>[[262, 163, 737, 435]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[147, 453, 852, 635]]<|/det|>
+<center>Fig. 2 | Short-range structure of the amorphous BHO film. The Fourier transformed EXAFS data \(\left(|\chi (R)|\right)\) of Hf \(L_{\mathrm{III}}\) edge for BHO12 film, in which the imaginary part of \(|\chi (R)|\) is also shown for clarity. The inset is the EXAFS spectrum of BHO12-RT film for comparison. The bule dashed, orange dotted, and black solid lines are fits to \(P2_{1} / c\) , \(Pca2_{1}\) , and \(P2_{1} / c + Pca2_{1}\) symmetries, respectively. The fitting window is \(R = 1.0 \sim 4.0\) Å. </center>  
+
+<|ref|>text<|/ref|><|det|>[[147, 650, 852, 899]]<|/det|>
+Short- range ordering of the designed amorphous structure is characterized by extended X- ray absorption fine- structure spectroscopy (EXAFS). Fig. 2 demonstrates the Fourier transformed EXAFS data \(\left(|\chi (R)|\right)\) of Hf \(L_{\mathrm{III}}\) edge for the representative BHO12 film, where \(R\) denotes the radial distance. Previous studies have shown that amorphous \(\mathrm{HfO}_2\) films are always monoclinic in local structure with the best fit to the \(P2_{1} / c\) symmetry. [25- 28] For comparison, we deposited an amorphous \(12\%\) Ba- substituted \(\mathrm{HfO}_2\) at room temperature (BHO12- RT), which also exhibits the short- range \(P2_{1} / c\) symmetry (the inset), in agreement with the reported results. However, the best fit to
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[147, 83, 852, 201]]<|/det|>
+the energetically- favorable phase of bulk \(\mathrm{HfO_2}\) suggests that the Ba substitution doesn't yield pronounced structure distortion on the BHO12- RT film, which can be explained by more stable oxygen ions in the conventionally amorphous structure (Supplementary Fig. S8).  
+
+<|ref|>text<|/ref|><|det|>[[147, 211, 853, 828]]<|/det|>
+Following the scattering paths used in BHO12- RT, the \(P2_{1} / c\) symmetry cannot give a good fit to the BHO12 film mainly because of the two distinguished oscillations in \(2.2 \mathrm{\AA} < R < 3.5 \mathrm{\AA}\) . A better fit can be found in orthorhombic \(Pca2_{1}\) symmetry and the best is achieved by combining the \(Pca2_{1}\) and \(P2_{1} / c\) , which is reasonable since, before the collapse of long- range fluorite periodicity, the Ba- Hf- O system has experienced an orthorhombic distortion. Similar two- phase coexistence has also been observed in the EXAFS spectrum of crystalline \(\mathrm{Hf_{0.46}Zr_{0.54}O_2}\) films.[28] Therefore, the observation of pronounced \(Pca2_{1}\) symmetry in Fig. 2 suggests that the Ba substitution- induced lattice distortion can be preserved in the short- range structure of BHO12, which isn't fully- relaxed like the unannealed BHO12- RT counterpart. Based on the fitting, the coordination information can be extracted (see Supplementary Text 1 for details). The BHO12 exhibits a Hf- O bond length of \(2.07 \sim 2.09 \mathrm{\AA}\) , which is shorter than that of the BHO12- RT and the previously reported amorphous \(\mathrm{HfO_2}\) , as well as the average Hf- O interatomic distance of crystalline \(\mathrm{HfO_2}\) ( \(\sim 2.14 \mathrm{\AA}\) ),[23,26,27] indicating a higher density. More importantly, due to the coexistence of \(Pca2_{1}\) and \(P2_{1} / c\) symmetries, the BHO12 shows a strong short- range disordering, in which the disorder (Debye- Waller) factor is as large as \(\sim 0.011\) , higher than both the unannealed one and the amorphous \(\mathrm{HfO_2}\) in literature.[25- 27] These structure characters are beneficial to achieve high breakdown strengths.
+
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+<|ref|>image<|/ref|><|det|>[[160, 84, 835, 355]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[147, 369, 852, 617]]<|/det|>
+<center>Fig. 3 | Dielectric energy storage of BHO thin-film capacitors. a, \(P - E\) hysteresis loops of Pt/BHO/LSMO capacitors measured at \(10\mathrm{kHz}\) . b, Two-parameter Weibull distribution analysis of breakdown strengths over 12 capacitors for each Ba concentration. c, Statistical \(E_{\mathrm{b}}\) and (d) Weibull modulus \(\beta\) extracted from (b) plotted as a function of Ba concentration. Here, \(\beta\) is the slope of \(\ln [- \ln (1 - p)]\) vs. \(\ln E_{\mathrm{b}}\) , where \(p = i / (n + 1)\) ( \(n\) is the total number of samples and \(i\) is the \(i\) th sample). e, Energy storage density \((U_{\mathrm{rec}})\) and efficiency \((\eta)\) of the BHO capacitors calculated from \(P - E\) loops. The data points are averaged over 12 capacitors for each Ba concentration. </center>  
+
+<|ref|>text<|/ref|><|det|>[[147, 631, 852, 912]]<|/det|>
+Pt is adopted as top electrodes for fabricating dielectric capacitors. Fig. 3a shows \(P - E\) hysteresis loops of the Pt/BHO/LSMO capacitors and the corresponding Weibull distributions of breakdown strengths are plotted in Fig. 3b. Without Ba substitution, the BHO0 is a linear dielectric with the statistical \(E_{\mathrm{b}}\) of \(\sim 4.2\mathrm{MV / cm}\) (Fig. 3c), in agreement with the values reported previously in similar \(\mathrm{HfO_2}\) thin films. \(^{[3,29]}\) The calculated \(U_{\mathrm{rec}}\) is only \(\sim 22.4\mathrm{J / cm^3}\) (Fig. 3e) due to the low \(E_{\mathrm{b}}\) and \(P_{\mathrm{m}}\) . With Ba substitution, the polar \(o\) - phase is induced and a typical ferroelectric hysteresis loop is observed in the BHO02 capacitor. \(U_{\mathrm{rec}}\) is increased to \(\sim 32\mathrm{J / cm^3}\) but the strong hysteresis feature results in a large \(U_{\mathrm{loss}}\) and thus a low \(\eta\) of \(\sim 37\%\) . Similar phenomena are also observed in the
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[148, 85, 296, 101]]<|/det|>
+BHO04 capacitor.  
+
+<|ref|>text<|/ref|><|det|>[[147, 116, 853, 530]]<|/det|>
+Above \(x = 6\%\) , the Ba- Hf- O system evolves into amorphous state. The hysteresis behaviors become very weak and hence the \(\eta\) is increased to above \(85\%\) (Fig. 3e). The \(U_{\mathrm{rec}}\) is also substantially increased. It increases to \(\sim 100 \mathrm{J / cm^3}\) in the BHO08 and reaches a maximum value of \(\sim 155 \mathrm{J / cm^3}\) in the BHO12. In the BHO15, the \(U_{\mathrm{rec}}\) is relatively decreased but still maintains a large value above \(120 \mathrm{J / cm^3}\) . The giant energy densities are obviously owing to the dramatically improved breakdown strengths in the amorphous capacitors (Fig. 3c). For example, the BHO12, its \(E_{\mathrm{b}}\) can be as high as \(\sim 12 \mathrm{MV / cm}\) , about three times of that of the crystalline BHO0, yielding a large \(P_{\mathrm{m}}\) of \(\sim 30 \mu \mathrm{C / cm^2}\) . In addition, the amorphous BHO also exhibit large Weibull modulus \(\beta\) , indicating good reproducibility over different samples. However, when \(x\) further increases to above \(20\%\) , the perovskite \(\mathrm{BaHfO_3}\) is crystallized and \(E_{\mathrm{b}}\) is decreased to less than \(7.0 \mathrm{MV / cm}\) , resulting in low \(U_{\mathrm{rec}}\) of \(50 \sim 65 \mathrm{J / cm^3}\) in the BHO20 \(\sim\) BHO50 capacitors.  
+
+<|ref|>text<|/ref|><|det|>[[147, 542, 853, 890]]<|/det|>
+Overall, Fig. 3 indicates the critical role of breakdown strength for enhancing energy storage density. In dielectric capacitors, the breakdown usually takes place within a short period of time ( \(< 1.0 \mathrm{ms}\) ) and results from the electronic and/or the avalanche mechanisms.[1,2] Considering that the BHO thin films have similar bandgaps of \(\sim 5.0 \mathrm{eV}\) (Supplementary Fig. S9),[30,31] the electronic breakdown that is due to the activation of electrons from the valence band to the conduction band by \(E\) can be excluded. The improved \(E_{\mathrm{b}}\) is thus ascribed to the suppression of avalanche effect. First, the amorphous BHO is formed in the structure evolution by oxygen instability, which exhibits a strong disordering not only due to the collapse of fluorite and perovskite periodicities in long range but also the coexistence of \(Pca2_1\) and \(P2_1 / c\) symmetries in short range. Second, the high- temperature annealing but non- crystallization gives the
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[146, 80, 854, 565]]<|/det|>
+BHO a higher density than the reported crystalline/amorphous HfO<sub>2</sub> and the unannealed counterpart (e.g., the BHO12-RT, showing an \(E_{\mathrm{b}}\) of \(\sim 3.64 \mathrm{MV / cm}\) and a low \(U_{\mathrm{rec}}\) of \(\sim 10.4 \mathrm{J / cm}^3\) , Supplementary Fig. S10). In this highly- disordered and dense matrix, the carrier transport is dramatically scattered from one lattice to the other, which suppresses the ionizing collision effect with atoms and hence impedes the carrier avalanche for dielectric breakdown. One can thus find that the amorphous BHO12 capacitor exhibits a negligible dependence of \(E_{\mathrm{b}}\) upon film thickness \((d)\) whereas the \(E_{\mathrm{b}}\) of crystalline BHO0, BHO02, and BHO50 capacitors decrease with increasing \(d\) , following an empirical formula \(E_{\mathrm{b}} \propto d^{-\beta}\) \((0.12 < \beta < 0.29)\) (Supplementary Fig. S11).<sup>[1,32]</sup> In addition, in the amorphous structure, the bonding of Hf- O could be well maintained for contributing the dielectric polarizability and a large \(\epsilon_{\mathrm{r}}\) is obtained in the BHO12 (also in the amorphous state of Sr- Hf- O and Ca- Hf- O systems), which is even higher than that of the crystalline BHO0 at high frequency (Supplementary Fig. S12). Therefore, the ultrahigh breakdown strength that is achieved without the trade- off of permittivity gives rise to the remarkably improved energy densities in the amorphous structure.  
+
+<|ref|>image<|/ref|><|det|>[[168, 580, 840, 742]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[147, 758, 850, 873]]<|/det|>
+<center>Fig. 4 | Reliability of BHO dielectric capacitors. Energy storage density \((U_{\mathrm{rec}})\) and efficiency \((\eta)\) of BHO0, BHO02, BHO12, and BHO50 capacitors as functions of (a) electric field, (b) temperature (measured at \(0.7 E_{\mathrm{b}}\) ), and (c) charging-discharging cycles (measured at \(0.6 E_{\mathrm{b}}\) ), respectively. </center>  
+
+<|ref|>text<|/ref|><|det|>[[186, 888, 848, 907]]<|/det|>
+Device reliability of the amorphous BHO12 capacitor is demonstrated in Fig. 4,
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[147, 82, 853, 466]]<|/det|>
+by comparing with the crystalline BHO0, BHO02, and BHO50. Fig. 4a plots the \(U_{\mathrm{rec}}\) and \(\eta\) as a function of \(E\) . The BHO12 capacitor exhibits a parabolic- like increase of \(U_{\mathrm{rec}}\) to \(155\mathrm{J / cm}^3\) with small variation in \(\eta\) up to \(12\mathrm{MV / cm}\) . However, in the BHO0, BHO02, and BHO50 capacitors, the dielectric breakdown occurs before \(6.0\mathrm{MV / cm}\) , impeding the increase of \(U_{\mathrm{rec}}\) . Corresponding \(P\) - \(E\) loops are shown in Supplementary Fig. S13 for clarity. Owing to the improved breakdown strength, the BHO12 exhibits much higher energy densities in high- temperature and charging/discharging cycling measurements. As shown in Fig. 4b, the amorphous BHO12 holds a similar temperature stability with that of the crystalline BHO0 and BHO50 but exhibits a more than 2 times higher \(U_{\mathrm{rec}}\) of \(\sim 80\mathrm{J / cm}^3\) ( \(\eta = 84\%\) ) at \(400\mathrm{K}\) . In Fig. 4c, the BHO12 exhibits optimized energy storage properties up to \(5\times 10^6\) charging/discharging cycles with a large \(U_{\mathrm{rec}}\) of \(\sim 56\) \(\mathrm{J / cm}^3\) and a \(\eta\) of \(\sim 90\%\) at \(7.2\mathrm{MV / cm}\) .  
+
+<|ref|>text<|/ref|><|det|>[[147, 479, 855, 891]]<|/det|>
+In summary, this study has provided a new playground for dielectric energy storage, which could be widely applicable by the additional experiments on Sr- Hf- O and Ca- Hf- O systems where very high \(E_{\mathrm{b}}\) and \(U_{\mathrm{rec}}\) are also observed (Supplementary Fig. S1). In addition, the dependence of structure evolution on the intrinsic material parameters of the \(\mathrm{HfO_2}\) and the series of alkaline- earth perovskites (Fig. 1b) suggests that the amorphization method could be highly controllable for material design. Besides, from a practical point of view, the amorphous hafnium- based oxide, which is high- \(\kappa\) but shows ultrahigh \(E_{\mathrm{b}}\) comparable to the \(\mathrm{SiO_2}\) (Supplementary Fig. 3), would be promising in a broad spectrum. Especially, it has great potential to be compatible with the current CMOS techniques for developing advanced electronic devices that require high breakdown strengths.[33- 35] More generally, the proposed structure- design strategy may also open a new perspective for exploring new functionalities in the boundary among different categories of materials.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[148, 85, 245, 101]]<|/det|>
+## References  
+
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+1. Yang, L. et al. Perovskite lead-free dielectrics for energy storage applications. Prog. Mater. Sci. 102, 72-108 (2019).  
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+3. Silva, J. P. B., Sekhar, K. C., Pan, H., MacManus-Driscoll, J. L. & Pereira, M. Advances in dielectric thin films for energy storage applications, revealing the promise of group IV binary oxides. ACS Energy Lett. 6, 2208-2217 (2021).  
+4. Ali, F. et al. Fluorite-structured ferroelectric and antiferroelectric materials: a gateway of miniaturized electronic devices. Adv. Func. Mater. 32, 2201737 (2022).  
+5. He, Y. et al. Superhigh energy storage density on-chip capacitors with ferroelectric \(\mathrm{Hf_0.5Zr_0.5O_2}\) antiferroelectric \(\mathrm{Hf_{0.25}Zr_{0.75}O_2}\) bilayer nanofilms fabricated by plasma-enhanced atomic layer deposition. Nanoscale Adv. 4, 4648-4657 (2022).  
+6. McPherson, J. W., Kim, J., Shanware, A., Mogul, H., & Rodriguez, J. Trends in ultimate breakdown strength of high dielectric-constant materials. IEEE Tran. Electr. Dev. 50, 1771-1778 (2003).  
+7. McPherson, J., Kim, J., Shanware, A., Mogul, H., & Rodriguez, J. Proposed universal relationship between dielectric breakdown and dielectric constant. IEDM Technical Digest 633 (2002).  
+8. Prateek, Thakur, V. K. & Gupta, R. K. Recent progress on ferroelectric polymer-based nanocomposites for high energy density capacitors: synthesis, dielectric properties, and future aspects. Chem. Rev. 116, 4260-4317 (2016).  
+9. Barshaw, E. J. et al. High energy density (HED) biaxially-oriented poly-propylene (BOPP) capacitors for pulse power applications. IEEE Trans. Magnet. 43, 223-225
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+(2007).  
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+12. Kim, J. et al. Ultrahigh capacitive energy density in ion-bombarded relaxor ferroelectric films. Science 369, 81-84 (2020).  
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+13. Pan, H. et al. Ultrahigh energy storage in superparaelectric relaxor ferroelectrics. Science 374, 100-104 (2021).  
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+14. Zhu, H. et al. Achieving a record-high capacitive energy density on Si with columnar nanograined ferroelectric films. ACS Appl. Mater. Interfaces 14, 7805-7813 (2022).  
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+15. Yang, B. et al. High-entropy enhanced capacitive energy storage. Nat. Mater. 21, 1074-1080 (2022).  
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+16. Sun, Z. et al. Ultrahigh energy storage performance of lead-free oxide multilayer film capacitors via interface engineering. Adv. Mater. 29, 1604427 (2017).  
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+17. Nguyen, M. D., Birkhölzer, Y. A., Houwman, E. P., Koster, G. & Rijnders, G. Enhancing the energy-storage density and breakdown strength in PbZrO₃/Pb₀.₉La₀.₁Zr₀.₅₂Ti₀.₄₈O₃-derived antiferroelectric/relaxor-ferroelectric multilayers. Adv. Energy. Mater. 12, 2200517 (2022).  
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+18. Hu, T.-Y. et al. Realizing high energy density and efficiency simultaneously via sub-grain modification in lead-free dielectric films. Nano Energy 98, 107313 (2022).  
+
+<|ref|>text<|/ref|><|det|>[[147, 805, 850, 888]]<|/det|>
+19. Xie, J. et al. Achieving ultrahigh energy storage performance in bismuth magnesium titanate film capacitors via amorphous-structure engineering. J. Mater. Chem. C 7, 13632 (2019).
+
+<--- Page Split --->
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+20. Reklaitis, I. et al. A comparative study on atomic layer deposited oxide film morphology and their electrical breakdown. Surf. Coat. Tech. 399, 126123 (2020).  
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+21. Schroeder, U. et al. Lanthanum-doped hafnium oxide: a robust ferroelectric material. Inorg. Chem. 57, 2752-2765 (2018).  
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+<|ref|>text<|/ref|><|det|>[[147, 215, 850, 267]]<|/det|>
+22. Schroeder, U., Park, M. H., Mikolajick, T. & Hwang, C. S. The fundamentals and applications of ferroelectric HfO₂. Nat. Rev. Mater. 7, 653-669 (2022).  
+
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+23. Gallington, L. C. et al. The structure of liquid and amorphous hafnia. Materials 10, 1290 (2017).  
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+24. Kaneta, C., Yamasaki, T. Oxygen-related defects in amorphous HfO₂ gate dielectrics. Microelectron. Eng. 84, 2370-2373 (2007).  
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+<|ref|>text<|/ref|><|det|>[[147, 411, 850, 497]]<|/det|>
+25. Lysaght, P. S. et al. Incipient amorphous-to-crystalline transition in HfO₂ as a function of thickness scaling and anneal temperature. J. Non-Crystal. Solids. 354, 399-403 (2008).  
+
+<|ref|>text<|/ref|><|det|>[[147, 509, 850, 593]]<|/det|>
+26. Cho, D.-Y., Park, T. J., Na, K. D., Kim, J. H. & Hwang, C. S. Structural disorders in an amorphous HfO₂ film probed by X-ray absorption fine structure analysis. Phys. Rev. B 78, 132102 (2008).  
+
+<|ref|>text<|/ref|><|det|>[[147, 607, 850, 659]]<|/det|>
+27. Viennet, R. et al. XAFS atomistic insight of the oxygen gettering in Ti/HfO₂ based OxRRAM. Phys. Rev. Mater. 2, 055002 (2018).  
+
+<|ref|>text<|/ref|><|det|>[[147, 672, 850, 757]]<|/det|>
+28. Sahiner, M. A. et al. Identification of structural phases in ferroelectric hafnium zirconium oxide by density-functional-theory-assisted EXAFS analysis. Appl. Phys. Lett. 118, 092903 (2021).  
+
+<|ref|>text<|/ref|><|det|>[[147, 771, 850, 824]]<|/det|>
+29. Zhang, L. et al. ALD preparation of high-\(k\) HfO₂ thin films with enhanced energy density and efficient electrostatic energy storage. RSC Adv. 7, 8388-8393 (2017).  
+
+<|ref|>text<|/ref|><|det|>[[147, 837, 850, 889]]<|/det|>
+30. Yim, K. et al. Novel high-\(k\) dielectrics for next-generation electronic devices screened by automated ab initio calculations. NPG Asia Mater. 7, e190 (2015).
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[145, 83, 852, 135]]<|/det|>
+31. Perevalov, T. V. et al. Atomic and electronic structure of amorphous and crystalline hafnium oxide: X-ray photoelectron spectroscopy and density functional calculations.  
+
+<|ref|>text<|/ref|><|det|>[[147, 150, 432, 168]]<|/det|>
+J. Appl. Phys. 101, 053704 (2007).  
+
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+32. Zhao, L. & Liu, C. L. Review and mechanism of the thickness effect of solid dielectrics. Nanomaterials 10, 2473 (2020).  
+
+<|ref|>text<|/ref|><|det|>[[147, 248, 850, 299]]<|/det|>
+33. Palumbo, F. et al. A review on dielectric breakdown in thin dielectrics: silicon dioxide, high-\(k\), and layered dielectrics. Adv. Func. Mater. 30, 1900657 (2020).  
+
+<|ref|>text<|/ref|><|det|>[[147, 313, 850, 364]]<|/det|>
+34. Ceresoli, D. & Vanderbilt, D. Structural and dielectric properties of amorphous \(\mathrm{ZrO_2}\) and \(\mathrm{HfO_2}\) . Phys. Rev. B 74, 125108 (2006).  
+
+<|ref|>text<|/ref|><|det|>[[147, 379, 850, 430]]<|/det|>
+35. Luo, X. & Demkov, A. A. Structure, thermodynamics, and crystallization of amorphous hafnia. J. Appl. Phys. 118, 124105 (2015).
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[148, 85, 226, 101]]<|/det|>
+## Methods  
+
+<|ref|>text<|/ref|><|det|>[[147, 115, 853, 430]]<|/det|>
+Device preparation. The \(A\) - Hf- O thin films and LSMO electrodes were grown on (001) single- crystalline STO substrates by pulsed laser deposition using a KrF excimer laser (Coherent COMPexPro 201). The LSMO thin films were deposited at a laser energy density of \(\sim 3.0 \mathrm{J / cm^2}\) with a repetition rate of \(2 \mathrm{Hz}\) , keeping the substrate at \(973 \mathrm{K}\) and the oxygen pressure at \(0.2 \mathrm{mbar}\) . The \(A\) - Hf- O thin films were deposited with \(2.6 \mathrm{J / cm^2}\) laser energy density at \(4 \mathrm{Hz}\) repetition, keeping the substrate temperature at \(873 \mathrm{K}\) and the \(\mathrm{O_2}\) pressure at \(0.1 \mathrm{mbar}\) . After the deposition, the \(A\) - Hf- O heterostructures were annealed at \(973 \mathrm{K}\) for 1 hour in flowing \(\mathrm{O_2}\) . Pt top electrodes of \(\sim 30 \mu \mathrm{m}\) in diameter and \(\sim 50 \mathrm{nm}\) in thickness were deposited on the surface of \(A\) - Hf- O heterostructures by sputtering with a shadow mask to form the thin- film capacitors.  
+
+<|ref|>text<|/ref|><|det|>[[147, 443, 853, 725]]<|/det|>
+First- principles calculation. Density- functional theory (DFT) calculations are performed using Quantum ESPRESSO. The exchange and correlation effects are treated within the generalized gradient approximation (GGA) of Perdew- Burke- Ernzerhof (PBE). The Brillouin zone is sampled with \(6 \times 6 \times 6\) Monkhorst- Pack k- point meshes for the conventional unit cell of \(\mathrm{HfO_2}\) which is reduced reciprocally for larger supercells. The electronic wave functions are expanded in a plane- wave basis set limited by a cut- off energy of \(900 \mathrm{eV}\) . The atomic positions and lattice parameters are optimized until the force on each atom is converges to less than \(1 \mathrm{meV / \AA}\) in all supercells.  
+
+<|ref|>text<|/ref|><|det|>[[147, 738, 852, 891]]<|/det|>
+As shown in the table below, the lattice parameters of the three phases of \(\mathrm{HfO_2}\) are calculated which agree well with the experimental results. In order to study the effects of alkaline- earth metal \(\mathrm{Ba^{2 + }}\) (or \(\mathrm{Sr^{2 + }}\) , \(\mathrm{Ca^{2 + }}\) ) doping on the structural stability of \(\mathrm{HfO_2}\) , we construct several supercells: \(1 \times 1 \times 1\) , \(\sqrt{2} \times \sqrt{2} \times 1\) , \(\sqrt{2} \times \sqrt{2} \approx 2\) , and \(2 \times 2 \times 2\) unit cells which include 4, 8, 16 and \(32 \mathrm{Hf^{4 + }}\) ions respectively. With one \(\mathrm{Hf^{4 + }}\)
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[147, 83, 850, 135]]<|/det|>
+substituted by one alkaline-earth metal ion, we could simulate different doping concentrations of 1/4, 1/8, 1/16 and 1/32.  
+
+<|ref|>text<|/ref|><|det|>[[146, 149, 852, 309]]<|/det|>
+The oxygen vacancy formation energy is defined by \(E^{f}(V_{O}) = E_{\mathrm{defect}} - E_{\mathrm{pure}} + \mu_{0}\) . In our calculation, \(E_{\mathrm{defect}}\) is the total energy of a supercell containing a \(\mathrm{Ba}^{2 + }\) (or \(\mathrm{Sr}^{2 + }\) , \(\mathrm{Ca}^{2 + }\) ) ion and an oxygen vacancy; \(E_{\mathrm{pure}}\) is the total energy for the equivalent supercell substituted with a \(\mathrm{Ba}^{2 + }\) (or \(\mathrm{Sr}^{2 + }\) , \(\mathrm{Ca}^{2 + }\) ) ion, and \(\mu_{0}\) is the chemical potential of oxygen atom \((\mu_{0} = \mu_{O_{2}} / 2)\) .  
+
+<|ref|>text<|/ref|><|det|>[[147, 323, 833, 343]]<|/det|>
+The structural parameters of the monoclinic, orthorhombic and cubic phase of \(\mathrm{HfO_2}\) .  
+
+<|ref|>table<|/ref|><|det|>[[186, 354, 808, 576]]<|/det|>
+
+<table><tr><td></td><td>Calculation</td><td>Experiment [36-39]</td></tr><tr><td>Monoclinic</td><td></td><td></td></tr><tr><td>a</td><td>5.11Å</td><td>5.12Å</td></tr><tr><td>b</td><td>5.15Å</td><td>5.17Å</td></tr><tr><td>c</td><td>5.29Å</td><td>5.30Å</td></tr><tr><td>β</td><td>99.65°</td><td>99.20°</td></tr><tr><td>Orthorhombic</td><td></td><td></td></tr><tr><td>a</td><td>5.24Å</td><td>5.23Å</td></tr><tr><td>b</td><td>5.01Å</td><td>5.00Å</td></tr><tr><td>c</td><td>5.05Å</td><td>5.05Å</td></tr><tr><td>Cubic</td><td></td><td></td></tr><tr><td>a</td><td>5.04Å</td><td>5.08Å</td></tr></table>  
+
+<|ref|>text<|/ref|><|det|>[[146, 585, 852, 901]]<|/det|>
+Characterizations. XRD was performed on a Rigaku SmartLab diffractometer. The cross- sectional TEM specimens were prepared by focused ion beam (FIB, FEI Versa workstation) with a Ga ion source. The HAADF- STEM images were carried out at 200 kV by a JEOL ARM200CF microscope equipped with a cold field emission electron gun, an ASCOR probe corrector and a Gatan Quantum ER spectrometer. The Hf \(L_{\mathrm{III}}\) - edge x- ray adsorptions were measured on 150 nm- thick BHO films in fluorescence yield mode at room temperature at the BL14W1 beamline in the Shanghai Synchrotron Radiation Facility (SSRF). The EXAFS spectra were analyzed using FEFF6 code by Athena and Artemis packages.[40] XPS was performed on a Thermo ESCALAB 250 Xi, and the binding energy was calibrated by setting the C 1s at 284.6 eV. P- E hysteresis
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[147, 83, 851, 167]]<|/det|>
+loops were measured by a Radiant Premier II ferroelectric tester. Capacitances were recorded using an Agilent 4294A impedance analyzer. The testing pulses were applied to the Pt electrodes and the LSMO were always grounded.  
+
+<|ref|>sub_title<|/ref|><|det|>[[148, 182, 293, 199]]<|/det|>
+## Data availability  
+
+<|ref|>text<|/ref|><|det|>[[148, 215, 850, 265]]<|/det|>
+The data supporting the findings of this study are available within the article and its Supplementary Information.  
+
+<|ref|>sub_title<|/ref|><|det|>[[148, 281, 246, 298]]<|/det|>
+## References  
+
+<|ref|>text<|/ref|><|det|>[[147, 313, 850, 362]]<|/det|>
+36. J. Wang, H. P. Li, R. Stevens, Hafnia and hafnia-toughened ceramics. J. Mater. Sci. 27, 5397-5430 (1992).  
+
+<|ref|>text<|/ref|><|det|>[[147, 377, 851, 464]]<|/det|>
+37. D. M. Adams, S. Leonard, D. R. Russell, R. J. Cernik, X-ray diffraction study of Hafnia under high pressure using synchrotron radiation. J. Phys. Chem. Solids 52, 1181-1186 (1991).  
+
+<|ref|>text<|/ref|><|det|>[[147, 477, 849, 528]]<|/det|>
+38. D. W. Stacy, J. K. Johnstone, D. R. Wilder, Axial thermal expansion of HfO₂. J. Am. Ceram. Soc. 55, 482-483 (1972).  
+
+<|ref|>text<|/ref|><|det|>[[147, 542, 850, 593]]<|/det|>
+39. X. H. Sang, E. D. Grimley, T. Schenk, U. Schroeder, J. M. LeBeau, On the structural origins of ferroelectricity in HfO₂ thin films. Appl. Phys. Lett. 106, 162905 (2015).  
+
+<|ref|>text<|/ref|><|det|>[[147, 607, 850, 658]]<|/det|>
+40. B. Ravel, M. Newville, ATHENA, ARTEMIS, HEPHAESTUS: data analysis for X-ray absorption spectroscopy using IFEFFIT. J. Synchrotron Rad. 12, 537-541 (2005).  
+
+<|ref|>sub_title<|/ref|><|det|>[[148, 673, 318, 690]]<|/det|>
+## Acknowledgements  
+
+<|ref|>text<|/ref|><|det|>[[147, 705, 851, 824]]<|/det|>
+This work was jointly sponsored by Natural Science Foundation of China (51872148 and 11974211), Natural Science Foundation of Shandong Province (ZR2020JQ03), the Taishan Scholar Program of Shandong Province (tsqn201812045), and Qilu Young Scholar Program of Shandong University.  
+
+<|ref|>sub_title<|/ref|><|det|>[[148, 838, 334, 855]]<|/det|>
+## Author contributions  
+
+<|ref|>text<|/ref|><|det|>[[186, 870, 848, 888]]<|/det|>
+Z.W. and X.L. conceived this work and designed the experiments and calculations.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[147, 83, 852, 300]]<|/det|>
+Q.Z. carried out the first-principles calculations. Y.Y., Z.Y.X., and W.Z. deposited the heterostructures, fabricated the capacitors, and measured the energy storage properties. Y.Y., Z.N.X., and J.X. collected the XRD data. C.D. measured the capacitances. L.Z. and Y.C. performed the XPS measurements. Z.W. performed the STEM and EXAFS analyses. Z.W., X.L., Y.Q., S.L., A.L., D.W. and K.M.R analyzed the experimental data and the first-principles calculation. Z.W., X.L., Y.Y., Q.Z. and K.M.R. wrote the manuscript. All authors discussed the data and contributed to the manuscript.  
+
+<|ref|>sub_title<|/ref|><|det|>[[149, 315, 323, 332]]<|/det|>
+## Competing interests  
+
+<|ref|>text<|/ref|><|det|>[[188, 347, 544, 365]]<|/det|>
+The authors declare no competing interests.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[44, 42, 311, 70]]<|/det|>
+## Supplementary Files  
+
+<|ref|>text<|/ref|><|det|>[[44, 93, 765, 113]]<|/det|>
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+<|ref|>text<|/ref|><|det|>[[61, 130, 333, 150]]<|/det|>
+SupplementaryMaterials.pdf
+
+<--- Page Split --->

preprint/preprint__c9fb907249bb69095e1ff9d6815adb18ea1a79c2ccd7872dc27f4f5d49e40f92/images_list.json

@@ -0,0 +1,62 @@
+[
+  {
+    "type": "image",
+    "img_path": "images/Figure_1.jpg",
+    "caption": "Figure 1. Experimental Design and Behavior. a. Participants learned 36 scene-object associations. The 36 scenes comprised 18 scene pairmats which consisted of highly similar image pairs (e.g., 'barn 1' and 'barn 2'). Scene pairmats were also associated with similar objects (e.g., 'guitar 1' and 'guitar 2'). b. Participants completed 6 rounds of study, test, and exposure phases. During study, participants viewed scenes and associated objects. During test, participants were presented with scenes and had to select the associated object from a set of two choices, followed by a confidence rating (high or low confidence; not shown). During exposure, scenes (rounds 1-6) or objects (round 1 and 6) were presented and participants made an old/new judgment. fMRI data were only collected during the scene and object exposure phases. c. Mean percentage of high confidence correct responses for each test round. d. Data from a representative participant showing the 'inflection point' in learning, for each pairmate. The inflection point was defined as the point at which participants transitioned to high-confidence correct retrieval for both scenes within a pairmate—a transition from 'pre-learned' to 'learned.' e. The number of pairs that transitioned to a learned state at each round, aggregated across all participants and pairmates. N.L. indicates pairmates that were never learned. Notes: error bars reflect S.E.M.",
+    "footnote": [],
+    "bbox": [
+      [
+        297,
+        90,
+        697,
+        560
+      ]
+    ],
+    "page_idx": 5
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_2.jpg",
+    "caption": "Figure 2. Pairmate similarity scores change at the behavioral inflection point. a. Regions of interest included CA23DG and CA1 in the hippocampus, the parahippocampal place area (PPA), and early visual cortex (EVC). b. Correlation matrix illustrating how pairmate similarity scores were computed for the behavioral inflection point. c. Pairmate similarity scores at the behavioral inflection point (IP) and just prior to the inflection point (pre-IP) across different regions of interest (ROIs). Pairmate similarity scores significantly varied by ROI \\((p = 0.009)\\) and there was a significant interaction between ROIs and behavioral state \\((p = 0.011)\\) . d. A permutation test (1,000 iterations) was performed by shuffling, within participants, the mapping between the behavioral inflection point and scene pairmates. In CA23DG the actual mean group-level pairmate similarity score at the IP was lower than \\(98.70\\%\\) of the permuted mean similarity scores. e. Pairmate similarity scores calculated by correlating the learned round (LR) with each of the three preceding rounds (- distance to LR) and each of the three succeeding rounds (+ distance to LR). In CA23DG, pairmate similarity scores were significantly lower when the LR was correlated with preceding round compared to succeeding rounds \\((p = 0.006)\\) . The difference was not significant for any other ROIs \\((p > 0.435)\\) . f. Conceptual illustration of a decrease in pairmate similarity scores from pre-IP to IP. In the pre-IP state (top panel), A1 and A2 are nearby in representational space. In the IP state (bottom panel), the representational distance between A1 and A2 has been exaggerated. When pairmates (e.g., A1 and A2) are farther apart in representational space than non-pairmates (e.g., A1 and B2) the pairmate similarity score will be negative (i.e., pairmate similarity < non-pairmate similarity), consistent with a repulsion of competing representations. Notes: \\(^{*}p < .05\\) , \\(^{**}p < .01\\) , error bars reflect S.E.M.",
+    "footnote": [],
+    "bbox": [
+      [
+        131,
+        90,
+        860,
+        494
+      ]
+    ],
+    "page_idx": 8
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_3.jpg",
+    "caption": "Figure 3. Representational structure across timepoints. a. Schematic illustration showing the rank order of scene pairmates based on pairmate similarity scores at various time points (N, \\(\\mathsf{N} + 1\\) , \\(\\mathsf{N} + 2\\) ). If scene pairmates with relatively high pairmate similarity scores at a given timepoint are systematically associated with relatively low pairmate similarity scores at a succeeding time point (red arrows), this will produce a negative rank correlation. b. Mean rank order correlations of pairmate similarity scores across timepoints for CA23DG and CA1. Lag 1 correlations reflect correlations between a given timepoint and an immediate succeeding timepoint (e.g., timepoints 2 and 3). Lag 2 correlations reflect correlations between a given timepoint and a timepoint two steps away (e.g., timepoints 2 and 4). At lag 1, there was a negative correlation in CA23DG \\((p = 0.004)\\) , but a positive correlation in CA1 \\((p = 0.045)\\) . At lag2, correlations were not significant in either CA23DG or CA1 indicating that correlations in representational structure were specific to temporally adjacent rounds. c. Pairmate similarity scores at the inflection point (IP) as a function of relative pairmate similarity scores in the pre-IP state ( \\(1^{\\text{st}}\\) quartile = lowest similarity, \\(4^{\\text{th}}\\) quartile = highest similarity). Pairmate similarity scores in CA23DG were significantly lower than CA1 \\((p = 0.017)\\) and significantly below 0 \\((p = 0.008)\\) for pairmates with the highest pre-IP similarity (4th quartile). Notes: \\* \\(p < .05\\) , \\*\\* \\(p < .01\\) , error bars reflect S.E.M.",
+    "footnote": [],
+    "bbox": [
+      [
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+      ]
+    ],
+    "page_idx": 10
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_4.jpg",
+    "caption": "Figure 4. Scene-object similarity as a function of behavioral state. a. Example associations between scene pairmates and objects. Scene-object similarity was calculated by correlating activity patterns evoked during the scene exposure phases (at different behavioral states) and the object exposure phases. Target similarity refers to correlations between a given scene and the object with which it was studied. Competitor similarity refers to correlations between a given scene and the object with which its pairmate was studied. b. Scene-object similarity as a function of object relevance (target, competitor), ROI (CA23DG, CA1), and behavioral state (pre-learned, learned). Correlations between unrelated scenes and objects (across pairmate similarity; not shown) was subtracted from target and competitor similarity values. For CA23DG, there was a significant interaction between behavioral state and object relevance \\((p = 0.002)\\) . Notes: \\(^{**}p< .01\\) , error bars reflect S.E.M.",
+    "footnote": [],
+    "bbox": [
+      [
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+    "page_idx": 11
+  }
+]

preprint/preprint__c9fb907249bb69095e1ff9d6815adb18ea1a79c2ccd7872dc27f4f5d49e40f92/preprint__c9fb907249bb69095e1ff9d6815adb18ea1a79c2ccd7872dc27f4f5d49e40f92.mmd

@@ -0,0 +1,378 @@
+
+# Abrupt remapping in human CA3/dentate gyrus signals resolution of memory interference  
+
+Wanjia Guo (wanjiag@uoregon.edu) University of Oregon https://orcid.org/0000- 0002- 5893- 6894  
+
+Serra Favila Columbia University https://orcid.org/0000- 0003- 1528- 2875  
+
+Ghootae Kim Korea Brain Research Institute  
+
+Robert Molitor University of Oregon  
+
+Brice Kuhl University of Oregon https://orcid.org/0000- 0001- 5229- 5400  
+
+Article  
+
+Keywords:  
+
+Posted Date: February 12th, 2021  
+
+DOI: https://doi.org/10.21203/rs.3.rs- 148842/v1  
+
+License: © © This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License  
+
+Version of Record: A version of this preprint was published at Nature Communications on August 10th, 2021. See the published version at https://doi.org/10.1038/s41467- 021- 25126- 0.
+
+<--- Page Split --->
+
+# Abrupt remapping in human CA3/dentate gyrus signals resolution of memory interference  
+
+Wanjia Guo \(^{1}\) , Serra E. Favila \(^{2}\) , Ghootae Kim \(^{3}\) , Robert J. Molitor \(^{1}\) , Brice A. Kuhl \(^{1}\)  
+
+4 Word Counts  5 Abstract: 150  6 Introduction, Results, Discussion: 4703  7 Methods: 3009  
+
+8 # of Figures: 4  
+
+9 1 Supplementary Table  
+
+10 Keywords: hippocampus, episodic memory, pattern separation, repulsion, competition  
+
+11 Acknowledgments: This work was supported by NIH- NINDS R01 NS089729 awarded to B.A.K.  
+
+12 Author Contributions: W.G., G.K., and B.A.K. designed the experiment. W.G. and B.A.K. analyzed the 13 data. S.E.F. consulted on data analyses. All authors wrote and edited the manuscript.
+
+<--- Page Split --->
+
+## ABSTRACT:  
+
+Remapping refers to a decorrelation of hippocampal representations of similar spatial environments. While it has been speculated that remapping may contribute to the resolution of episodic memory interference in humans, direct evidence is surprisingly limited. Here, we tested this idea using high- resolution, pattern- based fMRI analyses. We show that activity patterns in human CA3/dentate gyrus exhibit an abrupt, temporally- specific decorrelation of highly similar memory representations that is precisely coupled with behavioral expressions of successful learning. Strikingly, the magnitude of this learning- related decorrelation was predicted by the amount of pattern overlap during initial stages of learning, with greater initial overlap leading to stronger decorrelation. Finally, we show that remapped activity patterns carry relatively more information about learned episodic associations compared to competing associations, further validating the learning- related significance of remapping. Collectively, these findings establish a critical link between hippocampal remapping and episodic memory interference and provide novel insight into why remapping occurs.
+
+<--- Page Split --->
+
+The hippocampus is critical for forming long- term, episodic memories \(^{1 - 3}\) . However, one of the fundamental challenges that the hippocampus faces is that many experiences are similar, creating the potential for memory interference \(^{4,5}\) . In rodents, it is well established that minor alterations to the environment can trigger sudden changes in hippocampal activity patterns—a phenomenon termed remapping \(^{6,7}\) . An appealing possibility is that hippocampal remapping also occurs in human episodic memory, allowing for similar memories to be encoded in distinct activity patterns that prevent interference \(^{8}\) . At present, however, there remains an important gap between evidence of place cell remapping in the rodent hippocampus and episodic memory interference in humans. To bridge this gap, it is informative to consider how properties of place cell remapping, as demonstrated in the rodent hippocampus, might translate to episodic memory interference in humans.  
+
+One of the most important properties of remapping in the rodent hippocampus is that it is characterized by abrupt transitions between representations \(^{9 - 12}\) . These abrupt transitions, evidenced by decorrelations in patterns of neural activity, have most typically been observed as a function of the degree of environmental change \(^{9,11}\) . However, abrupt remapping can also occur as a function of experience with a new environment \(^{10,12}\) . Evidence of experience- dependent remapping \(^{6,13}\) suggests an important point: that remapping fundamentally reflects changes in internal representations, as opposed to changes in environmental states \(^{14,15}\) . An emphasis on internal representations lends itself well to human episodic memory in that it suggests that hippocampal remapping should occur as memories change. More specifically, this perspective makes the critical prediction that when two events are highly similar, hippocampal remapping will occur if, and when, corresponding memories become distinct. Testing this prediction requires repeatedly probing internal representations (memories) as well as hippocampal representations. However, standard approaches of averaging neuroimaging data across memories and participants can easily obscure or wash out abrupt changes in hippocampal representations if the timing of those changes varies across memories or participants.  
+
+Evidence of place cell remapping in rodents also motivates specific predictions regarding the relative contributions of hippocampal subfields, with a major distinction being between CA3/dentate gyrus and CA1 \(^{8,16,17}\) . In general, CA3 and dentate gyrus are thought to be more important than CA1 for discriminating between similar stimuli \(^{15,17 - 20}\) and remapping has been shown to occur more abruptly in CA3 than in CA1 \(^{10,12,21}\) . Human fMRI studies also support this general distinction, with several studies specifically implicating CA3 and dentate gyrus in discriminating similar memories \(^{22 - 27}\) . However, these studies have not directly established a link between temporally abrupt changes in CA3/dentate gyrus activity and changes in episodic memory states.  
+
+Here, we tested whether the resolution of interference between highly similar episodic memories is associated with an abrupt remapping of activity patterns in human CA3/dentate gyrus. We used an associative memory paradigm in which participants learned and were repeatedly tested on associations between scene images and object images \(^{28}\) . The critical design feature was that the set of scene images included pairs of extremely similar scenes (Fig. 1a). These scene pairmats were intended to elicit associative memory interference. Across six rounds of learning, we tracked improvement in associative memory for each set of pairmates while also continuously tracking representational changes indexed by fMRI. Specifically, after each associative memory test round, participants were shown each scene image one at a time (exposure phase) which allowed us to measure the activity pattern evoked by each scene and, critically, the representational distance between scene pairmates. To preview, we find that behavioral
+
+<--- Page Split --->
+
+expressions of memory interference resolution are temporally- coupled to abrupt, stimulus- specific remapping of human CA3/dentate gyrus activity patterns. This remapping specifically exaggerated the representational distance between similar memories. In additional analyses, we show that the magnitude of remapping that individual memories experienced was predicted by the degree of initial pattern overlap among CA3/dentate gyrus representations and that remapped CA3/dentate gyrus representations carried increased and highly specific information about learned episodic associations.  
+
+## RESULTS:  
+
+Participants completed six rounds of the experimental paradigm while inside an fMRI scanner. Each round included a study phase, an associative memory test phase, and a scene exposure phase (Fig. 1b). fMRI scanning was only conducted during the exposure phases. During the study phases, participants viewed scene- object associations one at a time. During the associative memory test phases, participants were shown scenes, one at a time, along with two very similar object choices (e.g., two guitars); one object was the target (i.e., the object that had been paired with the current scene) and the other object was the competitor (i.e., the object that had been paired with the scene pairmate). After selecting an object, participants indicated their confidence (high or low). During exposure phases, participants were shown each scene, along with novel scenes, and made a simple old/new judgment (mean \(\pm 95\%\) CI: \(d' = 5.40 \pm 0.88\) ; one- sample \(t\) - test vs. 0: \(t_{30} = 12.58\) , \(p < 0.001\) , Cohen's \(d = 2.26\) ).  
+
+## Behavior.  
+
+During the associative memory test phases, participants chose the correct object with above- chance accuracy in each of the 6 rounds ( \(t_{30}\) 's \(\geq 2.65\) , \(p\) 's \(\leq 0.013\) , \(d\) 's \(\geq 0.48\) ; chance accuracy \(= 50\%\) ). Accuracy markedly improved across rounds, from a mean of \(56.45\%\) \(\pm 4.98\%\) in round 1 to a mean of \(94.71\% \pm 2.21\%\) in round 6 (main effect of round: \(F_{1,30} = 318.86\) , \(p < 0.001\) , \(\eta^2 = 0.91\) ). The rate of choosing the correct object with high- confidence also robustly increased across rounds, from a mean of \(27.15\% \pm 4.71\%\) in round 1 to \(92.83\% \pm 3.58\%\) in round 6 (main effect of round: \(F_{1,30} = 574.44\) , \(p < 0.001\) , \(\eta^2 = 0.95\) ; Fig. 1c).  
+
+To test whether hippocampal remapping was temporally coupled with the resolution of memory interference, we identified, for each participant and for each set of pairmates, the learning round in which scene- object associations were recalled with high confidence (for both scenes in a pairmate). We refer to this timepoint as the 'learned round' (LR; see Methods). Of critical interest for our remapping analyses was the correlation of activity patterns evoked by scene images during the learned round (LR) with activity patterns evoked immediately prior to the learned round (LR- 1). We refer to this transition (from pre- learned to learned) as the 'inflection point' (IP) in learning (Fig. 1d). For example, if the LR for a particular set of pairmates was round 4, then the IP was the transition from round 3 to 4. Our rationale for correlating activity patterns from LR- 1 with LR was that this correlation would capture the critical change in hippocampal representations (remapping) that putatively supports learning.
+
+<--- Page Split --->
+![](images/Figure_1.jpg)
+
+<center>Figure 1. Experimental Design and Behavior. a. Participants learned 36 scene-object associations. The 36 scenes comprised 18 scene pairmats which consisted of highly similar image pairs (e.g., 'barn 1' and 'barn 2'). Scene pairmats were also associated with similar objects (e.g., 'guitar 1' and 'guitar 2'). b. Participants completed 6 rounds of study, test, and exposure phases. During study, participants viewed scenes and associated objects. During test, participants were presented with scenes and had to select the associated object from a set of two choices, followed by a confidence rating (high or low confidence; not shown). During exposure, scenes (rounds 1-6) or objects (round 1 and 6) were presented and participants made an old/new judgment. fMRI data were only collected during the scene and object exposure phases. c. Mean percentage of high confidence correct responses for each test round. d. Data from a representative participant showing the 'inflection point' in learning, for each pairmate. The inflection point was defined as the point at which participants transitioned to high-confidence correct retrieval for both scenes within a pairmate—a transition from 'pre-learned' to 'learned.' e. The number of pairs that transitioned to a learned state at each round, aggregated across all participants and pairmates. N.L. indicates pairmates that were never learned. Notes: error bars reflect S.E.M. </center>  
+
+Remapping in CA3/dentate gyrus is time- locked to the inflection point in learning.  
+
+For our fMRI analyses, our primary focus was on pattern similarity between scene pairmates. Pattern similarity was measured by correlating patterns of fMRI activity evoked by each scene during the scene exposure phases. Pairmate similarity was defined as the correlation between activity patterns evoked by scene pairmates (e.g., 'barn 1' and 'barn 2'; Fig. 2b). Correlations between scenes that were not pairmates
+
+<--- Page Split --->
+
+(e.g., 'barn 1' and 'airplane 2'; Fig. 2b) provided an important baseline measure of non- pairmate similarity. We refer to the difference between these two measures (pairmate – non- pairmate similarity) as the pairmate similarity score<sup>28</sup>. A positive pairmate similarity score would indicate that visually similar scenes (e.g., two barns) are associated with more similar neural representations than two unrelated scenes. Critically, because pairmate similarity scores are a relative measure, they can be directly compared across different brain regions<sup>29</sup> – something that would be inadvisable with raw correlation values. For all pattern similarity analyses, correlations were always performed across learning rounds (e.g., correlating 'barn 1' at LR- 1 with 'barn 2' at LR). This ensured independence of fMRI data<sup>30</sup>, but was also intended to capture transitions in hippocampal representations (remapping).  
+
+Following a prior study that used similar stimuli and analyses<sup>28</sup>, fMRI analyses targeted the following regions of interest (ROIs): hippocampus, parahippocampal place area (PPA), and early visual cortex (EVC). PPA and EVC served as important control regions indexing high- level (PPA) and low- level (EVC) visual representations. We did not anticipate that these regions would demonstrate learning- related remapping. Within the hippocampus, we leveraged our high- resolution fMRI protocol to segment the hippocampus body into subfields comprising CA1 and CA2/CA3/dentate gyrus (CA23DG). Motivated by past empirical findings<sup>23,31</sup> and theoretical models<sup>8</sup>, we predicted that remapping would occur in CA23DG. More specifically, we predicted that CA23DG remapping would occur at the inflection point (IP) in learning. To test this prediction, we compared pairmate similarity scores at the IP to pairmate similarity scores at a timepoint just prior to the IP (pre- IP). Whereas pairmate similarity scores at the IP were based on correlations between activity patterns from the Learned Round (LR) and the preceding round (LR- 1), pairmate similarity scores at the pre- IP were based on correlations shifted back one step in time: i.e., between LR- 1 and LR- 2. Thus, whereas the IP captured the transition from pre- learned to learned, the pre- IP was an important reference point that corresponded to a 'non- transition' (pre- learned to pre- learned).  
+
+An ANOVA with factors of behavioral state (pre- IP, IP) and ROI (CA1, CA23DG, PPA, EVC) revealed a significant main effect of ROI \((F_{3,90} = 4.08, p = 0.009, \eta^2 = 0.04)\) , reflecting overall differences in pairmate similarity scores across ROIs. Scores were numerically lowest in CA23DG and numerically highest in EVC. There was no main effect of behavioral state \((F_{1,30} = 2.71, p = 0.110, \eta^2 = 0.01)\) , indicating that learning did not have a global effect on representational structure across ROIs. Critically, however, the interaction between behavioral state and ROI was significant \((F_{3,90} = 2.95, p = 0.037, \eta^2 = 0.04)\) , indicating that learning differentially influenced pairmate similarity scores across ROIs.  
+
+Within CA23DG, pairmate similarity scores were significantly lower at the IP than the pre- IP \((t_{30} = - 2.24, p = 0.033, d = 0.40, CI = [- 0.012 \pm 0.011])\) , consistent with our prediction that remapping would specifically occur at the behavioral inflection point. Importantly, we also confirmed via permutation test (see Methods) that CA23DG pairmate similarity scores at the IP were lower than would be expected if the mapping between pairmates and IP's was shuffled within participants \((p = 0.013, \text{one- tailed}; \text{Fig. 2d})\) .  
+
+Strikingly, CA23DG pairmate similarity scores not only decreased at the IP, but they were significantly below 0 at the IP \((t_{30} = - 2.36, p = 0.025, d = 0.19, CI = [- 0.008 \pm 0.007])\) . In other words, pairs of scenes with extremely high visual similarity were represented as less similar than completely unrelated scenes in CA23DG. While seemingly counterintuitive, several recent fMRI studies have also found that, in certain situations, hippocampal pattern similarity is lower for similar than dissimilar events<sup>23,28,32</sup>. This has led to the proposal that similarity triggers a repulsion of hippocampal representations. That is, just as physical proximity triggers repulsion of like magnetic poles, representational proximity triggers repulsion of similar
+
+<--- Page Split --->
+
+memories (Fig. 2f). The present results, however, provide critical new evidence that this repulsion is time-locked to—and may, in fact, underlie—the resolution of interference between competing memories.  
+
+In CA1, pairmate similarity scores did not significantly differ by learning state \((t_{30} = - 0.72, p = 0.474, d = 0.13, \text{CI} = [0.004 \pm 0.01])\) or differ from 0 either at the pre- IP \((t_{30} = - 0.63, p = 0.531, d = 0.11, \text{CI} = [0.003 \pm 0.009])\) or IP \((t_{30} = - 0.34, p = 0.735, d = 0.06, \text{CI} = [- 0.001 \pm 0.006])\) . In PPA, pairmate similarity scores decreased from pre- IP to IP \((t_{30} = - 2.28, p = 0.030, d = 0.41, \text{CI} = [0.008 \pm 0.007])\) , with scores significantly greater than 0 in the pre- IP \((t_{30} = 3.14, p = 0.004, d = 0.56, \text{CI} = [0.007 \pm 0.005])\) but not different from 0 at the IP \((t_{30} = - 0.26, p = 0.798, d = 0.05, \text{CI} = [- 0.0006 \pm 0.005])\) . In EVC, pairmate similarity scores did not significantly vary by learning state \((t_{30} = - 1.39, p = 0.175, d = 0.25, \text{CI} = [- 0.007 \pm 0.01])\) ; but there was a numerical increase from pre- IP to IP, with scores significantly above 0 at IP \((t_{30} = 3.13, p = 0.004, d = 0.56, \text{CI} = [0.01 \pm 0.007])\) but not at pre- IP \((t_{30} = 0.92, p = 0.366, d = 0.16, \text{CI} = [0.004 \pm 0.008])\) .  
+
+The qualitative difference between CA23DG and EVC is striking in that, at the inflection point, these regions exhibited fully opposite representational structures: scene pairmates were more similar than non- pairmates in EVC, but less similar than non- pairmates in CA23DG. This finding parallels prior evidence of opposite representational structures in hippocampus and EVC<sup>28,32</sup> and argues against the possibility that CA23DG 'inherited' representational structure from early visual regions. More generally, it is striking that differences in pairmate similarity scores markedly varied across the four ROIs at the IP \((F_{3,90} = 8.73, p < 0.001, \eta^2 = 0.14)\) , but not at the pre- IP \((F_{3,90} = 0.33, p = 0.804, \eta^2 = 0.008)\) , underscoring the influence of learning on representational structure.  
+
+For the preceding fMRI analyses, the IP was defined as the correlation between the learned round (LR) and the immediately preceding round (LR- 1). To more fully characterize how the representational state at the LR compared to other rounds, we additionally correlated representations at LR to representations at LR- 2 and LR- 3 (i.e., other rounds that preceded the LR) and also correlated LR with LR+1, LR+2, and LR+3 (rounds that followed the LR) (Fig. 2e). Within CA23DG, pairmate similarity scores were significantly lower when correlating the LR with rounds that preceded learning compared to rounds that followed learning \((t_{30} = - 2.98, p = 0.006, d = 0.54, \text{CI} = [- 0.009 \pm 0.006])\) . This striking asymmetry indicates that CA23DG representations expressed at the LR were systematically biased away from the initial representational position of competing memories. More generally, these data support the idea of an abrupt representational change (remapping) in CA23DG that was time- locked to the specific round at which learning occurred for individual pairmates. For CA1, PPA, and EVC, there were no significant differences in pairmate similarity scores when correlating the LR to rounds that preceded learning vs. followed learning \((t_{30} \leq 0.79, p \leq 0.435, d \leq 0.14; \text{Fig. 2e})\) .
+
+<--- Page Split --->
+![](images/Figure_2.jpg)
+
+<center>Figure 2. Pairmate similarity scores change at the behavioral inflection point. a. Regions of interest included CA23DG and CA1 in the hippocampus, the parahippocampal place area (PPA), and early visual cortex (EVC). b. Correlation matrix illustrating how pairmate similarity scores were computed for the behavioral inflection point. c. Pairmate similarity scores at the behavioral inflection point (IP) and just prior to the inflection point (pre-IP) across different regions of interest (ROIs). Pairmate similarity scores significantly varied by ROI \((p = 0.009)\) and there was a significant interaction between ROIs and behavioral state \((p = 0.011)\) . d. A permutation test (1,000 iterations) was performed by shuffling, within participants, the mapping between the behavioral inflection point and scene pairmates. In CA23DG the actual mean group-level pairmate similarity score at the IP was lower than \(98.70\%\) of the permuted mean similarity scores. e. Pairmate similarity scores calculated by correlating the learned round (LR) with each of the three preceding rounds (- distance to LR) and each of the three succeeding rounds (+ distance to LR). In CA23DG, pairmate similarity scores were significantly lower when the LR was correlated with preceding round compared to succeeding rounds \((p = 0.006)\) . The difference was not significant for any other ROIs \((p > 0.435)\) . f. Conceptual illustration of a decrease in pairmate similarity scores from pre-IP to IP. In the pre-IP state (top panel), A1 and A2 are nearby in representational space. In the IP state (bottom panel), the representational distance between A1 and A2 has been exaggerated. When pairmates (e.g., A1 and A2) are farther apart in representational space than non-pairmates (e.g., A1 and B2) the pairmate similarity score will be negative (i.e., pairmate similarity < non-pairmate similarity), consistent with a repulsion of competing representations. Notes: \(^{*}p < .05\) , \(^{**}p < .01\) , error bars reflect S.E.M. </center>  
+
+## Overlap of CA23DG representations triggers remapping.  
+
+The fact that pairmate similarity scores in CA23DG were negative at the IP (Fig. 2c) suggests that learning- related remapping involved an active repulsion of competing hippocampal representations (Fig. 2f). Conceptually, the key feature of a repulsion account is that separation of hippocampal representations is a reaction to initial overlap among memories<sup>33</sup>. Here, because we measured representational states throughout the course of learning, we were able to test this hypothesis directly. Specifically, we tested the
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+prediction that relatively greater pairmate similarity scores (i.e., higher overlap between memories) at a given timepoint is associated with relatively lower pairmate similarity scores (i.e., lower overlap between memories) at a successive timepoint.  
+
+To test this hypothesis, we first translated the 6 learning rounds into 5 'timepoints' (see Methods). Each timepoint corresponded to the set of scene pair similarity scores obtained by correlating activity patterns across consecutive learning rounds [e.g., timepoint 1 = r(round 1, round 2)]. These scores reflected the representational structure at each timepoint (i.e., which pairmates were relatively similar, which pairmates were relatively dissimilar). We then rank correlated the pairmate similarity scores across successive timepoints [r(timepoint 1, timepoint 2)]. Whereas a positive rank correlation would indicate that representational structure is preserved across time points, a negative rank correlation would indicate that representational structure is inverted across time points. Critically, an inversion of representational structure is precisely what would be predicted if initial overlap among activity patterns (i.e., high pairmate similarity scores) triggers a repulsion of activity patterns (i.e., low pairmate similarity scores).  
+
+Strikingly, the rank correlation in CA23DG was significantly negative ( \(t_{30} = - 2.99\) , \(p = 0.006\) , \(d = 0.54\) , CI = [- 0.06 ± 0.04]). In contrast, the rank correlation in CA1 was significantly positive ( \(t_{30} = 2.11\) , \(p = 0.043\) , \(d = 0.38\) , CI = [0.06 ± 0.05]). The difference between CA23DG and CA1 was also significant ( \(t_{30} = 3.73\) , \(p < 0.001\) , \(d = 0.67\) , CI = [0.12 ± 0.06]). Importantly, the negative correlation in CA23DG cannot be explained by regression to the mean (see Methods). Moreover, when we tested correlations at a lag of 2 [r(timepoint N, timepoint N+2)], correlations did not significantly differ from 0 for either CA23DG ( \(t_{30} = - 0.71\) , \(p = 0.485\) , \(d = 0.13\) , CI = [- 0.02 ± 0.05]) or CA1( \(t_{30} = - 1.60\) , \(p = 0.120\) , \(d = 0.29\) , CI = [- 0.04 ± 0.05]). Further, the interaction between lag (1, 2) and ROI (CA23DG, CA1) was also significant ( \(F_{1,30} = 7.09\) , \(p = 0.012\) , \(\eta^2 = 0.06\) ), indicating that the dissociation between CA23DG and CA1 was relatively stronger at lag 1 (consecutive timepoints) than lag 2 (non-consecutive timepoints). Thus, representational structure at a given time point specifically predicted representational structure at a successive timepoint. Rank correlations did not differ from 0 in either PPA or EVC, either for lag 1 or lag 2 ( \(t_{30}\) 's ≤ 1.12, \(p\) 's ≥ 0.272, \(d\) 's ≤ 0.20).  
+
+While the negative correlation in CA23DG was fully consistent with our prediction—and with the idea that high pattern overlap triggers repulsion—the negative correlation could alternatively be explained by pairmates with relatively low pairmate similarity at timepoint N tending to have relatively high similarity at timepoint N+1. Additionally, because our analysis was entirely agnostic to behavioral data, it does not specifically establish that the negative pairmate similarity scores that we observed at the behavioral IP (Fig. 2c and 2e) were triggered by pattern overlap at IP- 1. Thus, as a complementary analysis, we binned all pairmates, by quartiles, according to pairmate similarity scores at IP- 1, with the 4<sup>th</sup> quartile representing pairmates with the highest pairmate similarity scores. We then computed the mean pairmate similarity scores for those bins at the IP. Again, this analysis was separately performed for CA23DG and CA1. An ANOVA with factors of ROI (CA23DG, CA1) and pairmate similarity scores at IP- 1 (4 quartiles) revealed a significant interaction ( \(F_{3,90} = 3.19\) , \(p = 0.027\) , \(\eta^2 = 0.03\)). Critically, this interaction was driven by a marked difference between CA23DG and CA1 when considering the bin with the highest overlap at IP- 1 (i.e., 4th quartile: \(t_{30} = - 2.87\) , \(p = 0.008\) , \(d = 0.51\) , CI = [- 0.03 ± 0.02], Fig. 3c). For CA23DG, pairmate similarity scores at the IP were significantly below 0 and numerically lowest for pairmates whose similarity scores at IP- 1 were in the 4<sup>th</sup> quartile (comparison to 0: \(t_{30} = - 2.54\) , \(p = 0.017\) , \(d = 0.46\) , CI = [- 0.023 ± 0.019]); the pattern in CA1 was qualitatively opposite. Collectively, these results provide novel, theory- consistent evidence that remapping of competing representations is actively triggered by initial representational overlap.
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+
+<center>Figure 3. Representational structure across timepoints. a. Schematic illustration showing the rank order of scene pairmates based on pairmate similarity scores at various time points (N, \(\mathsf{N} + 1\) , \(\mathsf{N} + 2\) ). If scene pairmates with relatively high pairmate similarity scores at a given timepoint are systematically associated with relatively low pairmate similarity scores at a succeeding time point (red arrows), this will produce a negative rank correlation. b. Mean rank order correlations of pairmate similarity scores across timepoints for CA23DG and CA1. Lag 1 correlations reflect correlations between a given timepoint and an immediate succeeding timepoint (e.g., timepoints 2 and 3). Lag 2 correlations reflect correlations between a given timepoint and a timepoint two steps away (e.g., timepoints 2 and 4). At lag 1, there was a negative correlation in CA23DG \((p = 0.004)\) , but a positive correlation in CA1 \((p = 0.045)\) . At lag2, correlations were not significant in either CA23DG or CA1 indicating that correlations in representational structure were specific to temporally adjacent rounds. c. Pairmate similarity scores at the inflection point (IP) as a function of relative pairmate similarity scores in the pre-IP state ( \(1^{\text{st}}\) quartile = lowest similarity, \(4^{\text{th}}\) quartile = highest similarity). Pairmate similarity scores in CA23DG were significantly lower than CA1 \((p = 0.017)\) and significantly below 0 \((p = 0.008)\) for pairmates with the highest pre-IP similarity (4th quartile). Notes: \* \(p < .05\) , \*\* \(p < .01\) , error bars reflect S.E.M. </center>  
+
+## CA23DG scene representations differentiate between competing object associations.  
+
+Thus far, we have focused on similarity among neural representations evoked while viewing the scene images (scene exposure phase). However, our paradigm also included two fMRI runs during which participants viewed each of the objects associated with the scene images (object exposure phase; see Methods). This allowed us to test whether hippocampal activity patterns evoked while viewing the scenes resembled—or came to resemble—activity patterns evoked while viewing corresponding object images.  
+
+Whereas, pairmate similarity scores were computed by correlating activity patterns across rounds of the scene exposure phase (e.g., LR- 1 and LR), here we computed correlations between a single round of the scene exposure phase (e.g., LR) and the average of the two object rounds (see Methods). For this analysis, there were three important factors that we considered. First, we considered whether scene representations were in a 'pre- learned' state (LR- 1) or 'learned' state (LR). Second, we separately tested correlations between each scene and (a) the target object (e.g., 'guitar 1') vs. (b) the competing object (e.g., 'guitar 2') (Fig. 4a). Third, we again compared results in CA23DG vs. CA1.  
+
+A repeated measures ANOVA with factors of ROI (CA23DG, CA1), behavioral state (pre- learned, learned), and object relevance (target, competitor) revealed a significant interaction between behavioral state and object relevance \((F_{1,30} = 12.42\) , \(p = 0.001\) , \(\eta^2 = 0.02\) ). Qualitatively, this interaction reflected a learning- related change wherein hippocampal representations of scene images became relatively more similar to
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+275 target objects and less similar to competitor objects. However, this 2- way interaction between behavioral 276 state and object relevance was qualified by a trend toward a 3- way interaction between behavioral state, 277 object relevance, and ROI \((F_{1,30} = 4.07\) \(p = 0.053\) \(\eta^2 = 0.01\) ). Specifically, the interaction between 278 behavioral state (pre- learned, learned) and object relevance (target, competitor) was significant in CA23DG 279 \((F_{1,30} = 11.98\) \(p = 0.002\) \(\eta^2 = 0.06\) ) but not in CA1 \((F_{1,30} = 0.44\) \(p = 0.510\) \(\eta^2 = 0.002\) ) (Fig. 4b). For 280 CA23DG, there was a qualitative increase, from the pre- learned to learned state, in similarity between 281 scenes and target objects and a qualitative decrease, from the pre- learned to learned state, in similarity 282 between scenes and competing objects. In other words, the remapping of CA23DG scene representations 283 that occurred at the learned round yielded a relative strengthening of information related to target object 284 associations and a relative weakening of information related to competing object associations. This 285 dissociation in CA23DG is striking when considering that target and competitor objects were extremely 286 similar (see Fig.1a, Fig. 4a) and even more so when considering that during the scene and object exposure 287 phases participants were not instructed or required in any way to recall the corresponding images. The 2- 288 way interaction between behavioral state and object relevance was not significant for PPA or EVC \([F_{1,30}\) 's 289 \(\leq 3.23\) \(p^{\prime}s\geq 0.082\) \(\eta^2 s\leq 0.02]\)  
+
+![](images/Figure_4.jpg)
+
+<center>Figure 4. Scene-object similarity as a function of behavioral state. a. Example associations between scene pairmates and objects. Scene-object similarity was calculated by correlating activity patterns evoked during the scene exposure phases (at different behavioral states) and the object exposure phases. Target similarity refers to correlations between a given scene and the object with which it was studied. Competitor similarity refers to correlations between a given scene and the object with which its pairmate was studied. b. Scene-object similarity as a function of object relevance (target, competitor), ROI (CA23DG, CA1), and behavioral state (pre-learned, learned). Correlations between unrelated scenes and objects (across pairmate similarity; not shown) was subtracted from target and competitor similarity values. For CA23DG, there was a significant interaction between behavioral state and object relevance \((p = 0.002)\) . Notes: \(^{**}p< .01\) , error bars reflect S.E.M. </center>
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+## DISCUSSION:  
+
+Here, we show that learning to discriminate competing episodic memories is associated with an abrupt remapping of activity patterns in CA3/dentate gyrus. Specifically, fMRI pattern similarity in CA3/dentate gyrus decreased precisely when behavioral expressions of learning emerged. Additionally, the degree to which remapping occurred in CA3/dentate gyrus was predicted by the degree of initial pattern overlap among competing memories. Finally, remapped CA3/dentate gyrus representations contained relatively stronger information about relevant episodic associations and relatively weaker information about competing episodic associations, confirming the learning- related significance of the remapping effect.  
+
+Our findings complement recent demonstrations of remapping- like phenomena in the human hippocampus \(^{34,35}\) as well as evidence of abrupt remapping in the rodent hippocampus \(^{9 - 12}\) . However, our findings provide unique and direct support for the proposal that hippocampal remapping is associated with the resolution of human episodic memory interference \(^{8}\) . Specifically, we demonstrate an abrupt transition in hippocampal representations that occurred at an important inflection point in learning—the point at which participants were able to correctly discriminate similar memories and retrieve associations with high confidence. Notably, this finding was only possible because (a) we repeatedly probed episodic memory and hippocampal representations over the course of learning and (b) we identified inflection points in a participant- and pairmate- specific manner. Indeed, inflection points varied considerably across and within participants (Fig. 1d and Sup. table 1) and the observed hippocampal remapping effect was significantly weaker when the specific mapping between behavior and fMRI data was shuffled within participants (Fig. 2d).  
+
+The fact that CA23DG remapping occurred precisely at the inflection point in learning strongly suggests that remapping was related to learning. This argument is also reinforced by our independent finding that remapped CA23DG activity patterns, evoked while participants viewed individual scene images, carried more information (compared to the pre- learning state) about target versus competing object associations. In other words, the inflection point defined from behavioral expressions of associative memory also captured a critical change in associative representations encoded in CA23DG activity patterns. The fact that CA23DG exaggerated the representational distance between competing scenes (remapping) while simultaneously reflecting learned associations (scene- object similarity) is consistent with the idea that CA3 balances both pattern separation and pattern completion mechanisms \(^{4,17,36,37}\) . The fact that remapped activity patterns contained information about learned associations is also consistent with the argument that hippocampal remapping does not simply reflect changes in the external environment—which did not change over the course of the experiment—but instead fundamentally reflects changes in internal models of the environment \(^{14,15}\) .  
+
+One aspect of our findings which does not, to our knowledge, have a direct analog in rodent studies of remapping is the negative pairmate similarity score we observed at the inflection point in CA23DG. The negative score indicates that scene pairmates—which were extremely similar images—were associated with less overlapping CA23DG representations than completely unrelated scenes. In rodents, the most extreme version of remapping occurs when two similar environments are associated with fully independent place codes \(^{8}\) . In our study, however, if each scene was associated with an independent representation, then the similarity between pairmates would be equal to, but not lower than, the similarity between non- pairmates. Instead, the negative pairmate similarity score requires a dependence between competing hippocampal representations wherein a given memory representation systematically moves away from the representational position of a competing memory (Fig. 2f). We refer to this dependence as ‘repulsion’ in
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+order to emphasize the oppositional influence that competing memories exerted. Several recent human fMRI studies have reported conceptually similar effects in the hippocampus<sup>28,32,38</sup>—and in CA3/dentate gyrus, specifically<sup>22-26</sup>. However, the current findings are the first to directly establish that the repulsion of competing hippocampal representations is temporally coupled to the resolution of memory interference.  
+
+Based on computational models<sup>33,39,40</sup>, our prediction was that the repulsion effect in CA23DG was a direct consequence of initial overlap among activity patterns. Indeed, a recent study found that hippocampal repulsion was more likely to occur for behaviorally- confusable memories<sup>32</sup>, potentially because confusable memories are associated with greater pattern overlap during initial learning. In the current study, we tested—and confirmed—this account directly. Specifically, we found that the representational structure (relative pairmate similarity) in CA23DG at a given timepoint was negatively correlated with representational structure at an immediately following timepoint. This negative relationship is highly consistent with the idea that overlap, itself, triggers plasticity that ‘punishes’ those features which are shared across memories<sup>24,33,39,40</sup>. While our study does not afford inferences about the causal relationship between repulsion and learning, the idea that repulsion (or remapping more generally) is triggered by representational overlap, combined with the fact that remapping was associated with learning, is consistent with the possibility that repulsion of CA3/dentate gyrus representations is a causal factor in learning.  
+
+Across multiple analyses, we observed dissociations between CA3/dentate gyrus and CA1. The fact that the remapping effects were selective to CA3/dentate gyrus is consistent with evidence from rodent studies of remapping and pattern separation<sup>8,16,36</sup> and with several human fMRI studies<sup>22- 25,36</sup>. Perhaps the most striking dissociation between CA23DG and CA1 comes from our analysis of representational structure across time points. Whereas CA23DG exhibited a negative rank correlation across successive timepoints, CA1 exhibited a positive rank correlation (Fig. 3b). Thus, in contrast to CA23DG, CA1 was characterized by stability (though only modest stability) of representational structure across timepoints<sup>4</sup>. This dissociation between CA23DG and CA1 is consistent with the idea that CA3, in particular, supports rapid plasticity that allows for changes in memory representations on short time scales<sup>41</sup> and is also consistent with evidence of faster remapping in CA3/dentate gyrus than in CA1<sup>10,12,21</sup>. It is also notable that the remapping effect we observed in CA23DG at the inflection point in learning strongly contrasted with the pattern of data in early visual cortex. Whereas CA23DG exhibited a negative pairmate similarity score at the inflection point, EVC exhibited a significant, positive pairmate similarity score at the inflection point. This finding makes the important point that CA23DG was not inheriting representational structure from early sensory regions (e.g., due to visual attention)—rather, CA23DG fully inverted the representational structure that was expressed in early visual cortex<sup>28</sup>.  
+
+Taken together, our findings constitute novel evidence for a remapping of human CA3/dentate gyrus representations that is temporally- coupled to the resolution of episodic memory interference. These findings were motivated by—and complement—existing evidence of remapping in the rodent hippocampus. Yet, our findings also go beyond existing rodent or human studies by establishing a direct link between remapping and changes in internal memory states<sup>14,15</sup>. Additionally, our conclusion that overlap among CA3/dentate gyrus representations actively triggers a repulsion of memory representations has important implications for theoretical accounts of how the hippocampus resolves memory interference<sup>5,8,36,39</sup> and will hopefully inspire targeted new analyses that test for similar mechanisms in rodent models.
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+
+## METHODS:  
+
+## Participants.  
+
+Participants.Thirty- six participants (21 female; mean age = 23.69 yrs, range = 18 - 34 yrs) were enrolled in the experiment following procedures approved by the University of Oregon Institutional Review Board. All participants were right- handed native- English speakers with normal or corrected- to- normal vision, with no self- reported psychiatric or neurological disease. One participant was excluded due to excess motion in the scanner (max FD > 3.5 mm); another 4 participants were excluded due to low behavioral performance (see Results for more details). The final analysis included 31 participants. All participants received monetary compensation for participating.  
+
+## Stimuli.  
+
+Stimuli.Thirty- six images of scenes and 36 images of everyday objects were used in the experiment. The set of 36 scenes and the set of 36 objects were each comprised of 18 'pairmates' of visually and semantically similar images (Fig. 1a). An additional 36 scenes and 12 objects were used as lures for the scene and object exposure phases of the study, respectively. Separately for each participant, scene pairmates were randomly assigned to object pairmates (Fig. 1a). For example, if 'barn 1' was assigned to 'guitar 1', then 'barn 2' would be assigned to 'guitar 2.'  
+
+## Experimental procedure.  
+
+Experimental procedure.After providing consent and reviewing the instructions, participants entered the MRI scanner. Inside the scanner, participants completed 6 rounds of the experimental paradigm (Fig. 1b). The first round and the last round included 4 phases: study, test, scene exposure (scanned), and object exposure (scanned). Rounds 2- 5 were the same, except they did not include the object exposure phase. Across all phases, stimuli were displayed on a grey background, projected from the back of the scanner. After exiting the scanner, participants completed a separate memory task that involved learning new scene- object associations (not reported here). The experiment was implemented in PsychoPy<sup>1</sup> and lasted approximately 3 hrs, with about 2 hrs 15 min inside the scanner.  
+
+Study Phase. During the study phases, participants learned 36 scene- object associations, one association at a time. Each trial began with the presentation of a scene image (1000 ms), followed by a white fixation cross (200 ms), the associated object image (1000 ms) and then another white fixation cross (1200 ms) until the start of the next trial. The order in which the 36 scene- object associations were studied was randomized for each round and for each participant.  
+
+Test Phase. During the test phases, participants attempted to retrieve the object associated with each of the 36 scenes. Each trial began with the presentation of a scene (1000 ms), followed by a white fixation cross (200 ms), and then the presentation of two object pairmates (e.g., 'Guitar 1' and 'Guitar 2'). One of the object images was the 'target' (i.e., the object associated with the cued scene) and the other object image was the 'competitor' (i.e., the object associated with the cued scene's pairmate). Participants had a maximum of 4000 ms to select the correct object image (target) via a button box in their right hand. If no response was made, the next trial began after a white fixation cross was displayed for 1200 ms. If a response was made, a confidence rating then appeared beneath the objects and participants had a maximum of 3000 ms to indicate whether their response was a "Guess" or "Sure." After indicating their confidence (or after time ran out), a white fixation cross appeared (1200 ms) until the start of the next trial. The location of the correct object (left or right) and the order in which each of the 36 scene- object associations were tested were randomized for each round and for each participant.
+
+<--- Page Split --->
+
+Scene Exposure Phase. During the scene exposure phases, which were conducted during fMRI scanning, participants saw 39 scene images in each of two blocks (78 scenes per round). Each block included the 36 studied scenes and 3 novel lure scenes. Participants made an old/new judgment for each scene. Each trial began with the presentation of a scene image (500 ms), followed by a red fixation cross (1500 ms) which represented the response window. Participants again responded using the button box. After the red fixation cross, a white fixation cross (2000 ms) was presented until the start of the next trial. The order of the 39 scene trials within each block was randomized for each block, round, and participant. Between the two blocks of 39 trials, participants performed a short odd/even judgment task (4 trials). Each odd/even trial consisted of a single-digit number displayed on the screen (500 ms), followed by a red fixation cross (1000 ms) which represented the response window, and then a white fixation cross (1000 ms) until the start of the next trial.  
+
+Object Exposure Phase. The object exposure phase (conducted during fMRI scanning) was only included in the first and sixth rounds and followed an identical structure and procedure as the scene exposure phase. The only difference was that the 39 trials in each block corresponded to the 36 studied objects and 3 novel lure objects.  
+
+## MRI acquisition.  
+
+All images were acquired on a Siemens 3T Skyra MRI system in the Lewis Center for Neuroimaging at the University of Oregon. Functional data were acquired with a T2\\*- weighted echo- planar imaging sequence with partial- brain coverage that prioritized full coverage of the hippocampus and early visual cortex (repetition time \(= 2000\) ms, echo time \(= 36\) ms, flip angle \(= 90^{\circ}\) , 72 slices, \(1.7\times 1.7\times 1.7\) mm voxels). A total of 8 functional scans were acquired. Each functional scan comprised 177 volumes and included 10 s of lead- in time and 10 s of lead- out time at the beginning and end of each scan, respectively. The 8 functional scans corresponded to 6 rounds of the scene exposure phase (scans 1 and 3- 7) and 2 rounds of the object exposure phase (scans 2 and 8). Anatomical scans included a whole- brain high- resolution T1- weighted magnetization prepared rapid acquisition gradient echo anatomical volume (1x1x1mm voxels) and a high- resolution (coronal direction) T2- weighted scan (0.43x0.43x2mm voxels) to facilitate segmentation of hippocampal subfields.  
+
+## Anatomical data preprocessing.  
+
+Preprocessing was performed using fMRIPrep 1.5.0 \(^{2,3}\) (RRID:SCR_016216), which is based on Nipype 1.2. \(^{2,4,5}\) (RRID:SCR_002502). The T1- weighted (T1w) image was corrected for intensity non- uniformity (INU) with N4BiasFieldCorrection \(^{6}\) (ANTS 2.2.0 \(^{7}\) , RRID:SCR_004757), and used as the T1w- reference throughout the workflow. The T1w- reference was skull- stripped with the antsBrainExtraction.sh workflow (ANTS) in Nipype, using OASIS30ANTS as target template. Brain tissue segmentation of cerebrospinal fluid (CSF), white- matter (WM) and gray- matter (GM) was performed on the brain- extracted T1w using fast \(^{8}\) (FSL 5.0.9, RRID:SCR_002823). Volume- based spatial normalization to one standard space (MNI152NLin2009cAsym) was performed through nonlinear registration with antsRegistration (ANTS 2.2.0), using brain- extracted versions of both T1w reference and the T1w template. ICBM 152 Nonlinear Asymmetrical template version 2009c \(^{9}\) (RRID:SCR_008796; TemplateFlow ID: MNI152NLin2009cAsym) was used for spatial normalization.  
+
+## Functional data preprocessing.  
+
+For each of the 8 BOLD scans per participant, the following preprocessing was performed. First, a reference volume and its skull- stripped version were generated using fMRIPrep. A deformation field to correct for
+
+<--- Page Split --->
+
+susceptibility distortions was estimated based on two echo- planar imaging (EPI) references with opposing phase- encoding directions, using 3dQuwarp, AFN10. Based on the estimated susceptibility distortion, an unwarped BOLD reference was calculated for a more accurate co- registration with the anatomical reference. The BOLD reference was then co- registered to the T1w reference using bbregister (FreeSurfer) which implements boundary- based registration11. Co- registration was configured with six degrees of freedom. Head- motion parameters with respect to the BOLD reference (transformation matrices, and six corresponding rotation and translation parameters) were estimated before any spatiotemporal filtering using mcfilt FSL \(5.0.9^{12}\) . BOLD scans were slice- time corrected using 3dTshift AFN10(RRID:SCR_005927). The BOLD time- series (including slice- timing correction when applied) were resampled onto their original, native space by applying a single, composite transform to correct for head- motion and susceptibility distortions. Framewise displacement (FD) confounding time- series were calculated based on the resampled BOLD time- series for each functional scan13.  
+
+## fMRI first-level general linear model (GLM) analyses.  
+
+After fMRIPrep preprocessing, the first 5 volumes (10 s) of each functional scan were discarded. Then, the brain mask generated by fMRIPrep from the T1 anatomical image was used to perform brain extraction for each of the 8 functional scans. Each functional scan was then median centered. For the 6 scans of the scene exposure phase and 2 scans of the object exposure phase, all first level GLMs were performed in participants' native space with FSL using a Double- Gamma HRF with temporal derivatives, implemented with Nipype. GLMs were calculated using a variation of the Least Squares – Separate method14: a separate GLM was calculated for each of the 36 scenes (for scene exposure phases) or objects (for object exposure phases) across both repeats within a scan. For each GLM, there was one regressor of interest (representing a single scene or object image across its two repetitions per scan). All other trials (including lure images), framewise displacement, xyz translation and xyz rotation were represented with nuisance regressors. Additionally, a high pass filter (128 Hz) was applied for each GLM. This model resulted in 36 beta- maps per scan (one map per scene/object) which were converted to t- maps that represented the pattern of activity elicited by each scene/object for each scan.  
+
+## Regions of interest.  
+
+A region of interest (ROI) for early visual cortex (EVC) was created from the probabilistic maps of Visual Topography15 in the MNI space with a 0.5 threshold. This ROI was transformed into each participant's native space using inverse T1w- to- MNI non- linear transformation. For each participant, the top 300 EVC voxels were then selected by averaging the t- maps of all scenes and objects and then choosing the voxels with the highest t- statistics (i.e., the voxels most responsive to visual stimuli). An ROI for the parahippocampal place area (PPA) was created by first using an automated meta- analysis in Neurosynth with the key term "place". Then, clusters were created using voxels with a z- score \(>2\) based on the Neurosynth associative tests. Since these clusters were generated through an automated meta- analysis and were not anatomically exclusive to PPA, we visually inspected the results and manually selected the two largest clusters that were spatially consistent with PPA. One cluster was in the right hemisphere (voxel size \(= 247\) ) and one cluster was in the left hemisphere (voxel size \(= 163\) ). These clusters were combined into a single PPA mask. This mask was then transformed into each participant's native space using the inverse T1w- to- MNI transformation. For each participant, a final PPA ROI was generated by averaging the t- maps of all scene exposure phase scans and then selecting the 300 voxels with the highest average t- statistics (i.e., the most scene- responsive voxels). To create hippocampal ROIs, we used the Automatic Segmentation of Hippocampal Subfields (ASHS)16 toolbox with the upenn2017 atlas to generate subfield ROIs in each participant's hippocampal body, including CA23DG—the combination of CA2, CA3 and dentate gyrus—and CA1. The most anterior and posterior slices of the hippocampal body were manually
+
+<--- Page Split --->
+
+determined for each participant based on the T2- weighted anatomical structure. Each participant's subfield segmentations were also manually inspected to ensure accuracy of the segmentation protocol. Then, each subfield ROI was transformed into each participant's native space using the T2- to- T1w transformation, calculated with FLIRT (fsl) with 6 degrees of freedom, implemented with Nipype. All ROIs were again visually inspected following the transformation to native space to ensure the ROIs were anatomically correct.  
+
+## fMRI pattern similarity analyses.  
+
+Pairmate Similarity Scores. Pattern similarity was calculated as the Fisher z- transformed Pearson correlation between \(t\) - maps within each ROI. All pattern similarity analyses were performed by correlating the \(t\) - maps for stimuli across scans (i.e., correlations were never performed within the same scan). For our primary analyses related to pattern similarity between scene images, of critical interest was mean similarity between pairmate scenes (pairmate similarity) relative to mean similarity between non- pairmate scenes (non- pairmate similarity). For example, the correlation between the \(t\) - maps for 'barn 1' from scan 3 and 'barn 2' from scan 4 would reflect pairmate similarity, whereas the correlation between the \(t\) - maps for 'barn 1' from scan 3 and 'airplane 2' from scan 4 would reflect non- pairmate similarity. We then calculated the mean difference between pairmate similarity and non- pairmate similarity, which we refer to as the pairmate similarity score.  
+
+Learned Round. To relate pairmate similarity scores to behavioral measures of learning, we identified the Learned Round (LR) for each pairmate, separately for each participant. The LR was based on performance in the associative memory test. Specifically, the LR was defined as the first round in which the target object was selected with high confidence for both scenes in a pairmate, with the additional requirement that performance remained stable in all subsequent rounds. It was therefore possible that both scenes in a pairmate were associated with high confidence correct responses in round N, not in round N+1, and then (again) in round N+2 and thereafter; in this case, the LR would be round N+2.  
+
+Inflection Point. The inflection point (IP) was defined as the transition from LR - 1 to LR (i.e., the transition from 'pre- learned' to 'learned'). Thus, pattern similarity analyses of the IP refer to the correlation of \(t\) - maps from LR- 1 to \(t\) - maps from LR. We hypothesized that the behavioral state change from LR- 1 to LR would correspond to a reduction in pattern similarity between pairmates. Pattern similarity analyses at the IP were contrasted against the 'pre- IP' state, which was based on the correlation of \(t\) - maps from LR- 2 and LR- 1 (i.e., a non- transition from 'not learned' to 'not learned') (Fig. 2c). Pairmates for which participants never reached and sustained high- confidence correct responses (mean \(\pm \mathrm{s.d.}\) , \(1.81 \pm 2.27\) per participant) and pairmates that were learned in the \(1^{\text{st}}\) round (LR = 1; mean \(\pm \mathrm{s.d.}\) , \(1.00 \pm 1.26\) ) were excluded from the IP analysis because neither the pre- IP nor IP states could be measured. For pairmates that were learned in the \(2^{\text{nd}}\) round (LR = 2; mean \(\pm \mathrm{s.d.}\) , \(3.23 \pm 2.80\) ), pattern similarity at the IP was calculated and included in the analyses, but pattern similarity at the pre- IP state could not be calculated because an LR - 2 did not exist. For rest of the pairmates (LR = 3, 4, 5, or 6), we calculated pattern similarity for both pre- IP and IP (Fig. 1e). Similar restrictions applied to correlations between LR and LR- 3, LR + 1, LR + 2, and LR + 3 (Fig. 2e). The number of pairmates included in each comparison and for each participant are reported in Supplementary Table 1.  
+
+Representational Structure Across Time Points. To test whether representational overlap triggered remapping (related to Fig. 3), the 6 learning rounds were translated into 5 timepoints. Each timepoint corresponded to a pair of consecutive learning rounds ([1,2], [2,3], [3,4], [4,5], [5,6]). For each timepoint, pairmate similarity scores were calculated, as described above, by correlating activity patterns from consecutive learning rounds (e.g., pairmate similarity scores at timepoint 1 were based on correlations
+
+<--- Page Split --->
+
+between round 1 and round 2). This yielded a set of pairmate similarity scores at each of the 5 timepoints. These sets of similarity scores reflected the representational structure at each timepoint (i.e., which pairmates were relatively similar and which pairmates were relatively dissimilar). Pairmate similarity scores were then correlated across timepoints using Spearman's rank correlation (Fisher \(z\) transformed). Lag 1 correlations refer to rank correlations between successive timepoints whereas lag 2 correlations refer to correlations between timepoints two steps apart. To facilitate a direct comparison between lag 1 vs. lag 2 correlations, correlations were computed for the following timepoints: Lag \(1 = r\) (timepoint 1, 2), \(r\) (timepoint 2, 3), \(r\) (timepoint 3, 4); Lag \(2 = r\) (timepoint 1, 3), \(r\) (timepoint 2, 4), \(r\) (timepoint 3, 5). It is important to emphasize that we did not correlate initial pairmate similarity scores with the change in pairmate similarity as this would produce an artifactual correlation (via regression to the mean). In contrast, a negative rank correlation (as we observed in CA23DG) cannot be explained by regression to the mean. Mathematically, if all values at timepoint N partially regressed toward the mean at timepoint \(\mathsf{N} + 1\) , this would yield a positive rank correlation (i.e., representational structure would be partially preserved). If all values fully regressed toward the mean (i.e., variance at timepoint \(\mathsf{N} + 1 = 0\) ), this would yield a null correlation ( \(r = 0\) ; representational structure fully abolished).  
+
+Scene- Object Similarity. To calculate pattern similarity between scenes and objects (related to Fig. 4), activation patterns for objects were first generated by averaging \(t\) - maps across the two object exposure phases, resulting in a single, mean activity pattern for each object. These object- specific activity patterns were then correlated with activity patterns from the scene exposure phases at LR - 1 (i.e., the pre- learned state) and LR (i.e., the learned state). Correlations were separated into three groups: (1) target correlations refer to the correlation between a scene and the object it was associated with during the study phase (e.g., 'barn 1' and 'guitar 1'), (2) competitor correlations refer to the correlation between a scene and the object that was associated with that scene's pairmate during the study phase (e.g., 'barn 1' and 'guitar 2'), and (3) across pairmate correlations refer to correlations between a scene and an object that was not associated with that scene or its pairmate during the study phase (e.g., 'barn 1' and 'scissors 1'). Target and competitor correlations were expressed relative to across pairmate correlations.  
+
+## Statistics.  
+
+To compare pairmate similarity scores and other measures across ROIs and learning states, repeated measures ANOVAs and paired- samples \(t\) - tests were used. To test whether pairmate similarity scores and other measures were significantly positive or negative (i.e., above/below 0), one- sample \(t\) - tests were used. To test whether the negative pairmate similarity score observed in CA23DG at the inflection point depended on the specific mapping between behavioral and fMRI measures, we randomly shuffled the mapping between the behavioral inflection point and scene pairmate, within each participant (see Fig. 1d), and then computed the group- level mean pairmate similarity score at the permuted inflection point. This was repeated 1,000 times, producing a distribution of 1,000 permuted means. The observed pairmate similarity score at the inflection point was then compared against this distribution of permuted means.  
+
+## Data Availability.  
+
+The data that support the findings of this study are available from the corresponding author upon reasonable request.
+
+<--- Page Split --->
+
+## METHODS REFERENCES:  
+
+1. Peirce, J. et al. PsychoPy2: Experiments in behavior made easy. Behav. Res. Methods 51, 195-203 (2019).  
+
+2. Esteban, O. et al. fMRIPrep: a robust preprocessing pipeline for functional MRI. Nat. Methods 16, 111-116 (2019).  
+
+3. Esteban, Oscar, Ross Blair, Christopher J. Markiewicz, Shoshana L. Berleant, Craig Moodie, Feilong Ma, Ayse Ilkay Isik, et al. 2018. "FMRIPrep." Software.  
+
+Zenodo. https://doi.org/10.5281/zenodo.852659.  
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+4. Gorgolewski, K. et al. Nipype: A Flexible, Lightweight and Extensible Neuroimaging Data Processing Framework in Python. Front. Neuroinformatics 5, (2011).  
+
+5. Gorgolewski, Krzysztof J., Oscar Esteban, Christopher J. Markiewicz, Erik Ziegler, David Gage Ellis, Michael Philipp Notter, Dorota Jarecka, et al. 2018. "Nipype." Software.  
+
+Zenodo. https://doi.org/10.5281/zenodo.596855.  
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+6. Tustison, N. J. et al. N4ITK: Improved N3 Bias Correction. IEEE Trans. Med. Imaging 29, 1310-1320 (2010).  
+
+7. Avants, B. B., Epstein, C. L., Grossman, M. & Gee, J. C. Symmetric diffeomorphic image registration with cross-correlation: Evaluating automated labeling of elderly and neurodegenerative brain. Med. Image Anal. 12, 26-41 (2008).  
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+8. Zhang, Y., Brady, M. & Smith, S. Segmentation of brain MR images through a hidden Markov random field model and the expectation-maximization algorithm. IEEE Trans. Med. Imaging 20, 45-57 (2001).  
+
+9. Fonov, V., Evans, A., McKinstry, R., Almli, C. & Collins, D. Unbiased nonlinear average age-appropriate brain templates from birth to adulthood. NeuroImage 47, S102 (2009).  
+
+10. Cox, R. W. & Hyde, J. S. Software tools for analysis and visualization of fMRI data. NMR Biomed. 10, 171-178 (1997).  
+
+11. Greve, D. N. & Fischl, B. Accurate and robust brain image alignment using boundary-based registration. NeuroImage 48, 63-72 (2009).
+
+<--- Page Split --->
+
+12. Jenkinson, M., Bannister, P., Brady, M. & Smith, S. Improved Optimization for the Robust and Accurate Linear Registration and Motion Correction of Brain Images. \*Neurolmage\* 17, 825–841 (2002).  
+13. Power, J. D. \*et al.\* Methods to detect, characterize, and remove motion artifact in resting state fMRI. \*Neurolmage\* 84, 320–341 (2014).  
+14. Mumford, J. A., Turner, B. O., Ashby, F. G. & Poldrack, R. A. Deconvolving BOLD activation in event-related designs for multivoxel pattern classification analyses. \*Neurolmage\* 59, 2636–2643 (2012).  
+15. Wang, L., Mruczek, R. E. B., Arcaro, M. J. & Kastner, S. Probabilistic Maps of Visual Topography in Human Cortex. \*Cereb. Cortex N. Y. N\* 1991 25, 3911–3931 (2015).  
+16. Yushkevich, P. A. \*et al.\* Automated volumetry and regional thickness analysis of hippocampal subfields and medial temporal cortical structures in mild cognitive impairment. \*Hum. Brain Mapp.\* 36, 258–287 (2015).
+
+<--- Page Split --->
+
+
+Supplementary information   
+
+<table><tr><td>Round Participant #</td><td>1</td><td>2</td><td>3</td><td>4</td><td>5</td><td>6</td><td>Never Learned</td></tr><tr><td>1</td><td>1</td><td>7</td><td>6</td><td>4</td><td>0</td><td>0</td><td>0</td></tr><tr><td>2</td><td>1</td><td>1</td><td>4</td><td>4</td><td>6</td><td>2</td><td>0</td></tr><tr><td>3</td><td>1</td><td>7</td><td>5</td><td>5</td><td>0</td><td>0</td><td>0</td></tr><tr><td>4</td><td>0</td><td>3</td><td>0</td><td>5</td><td>4</td><td>3</td><td>3</td></tr><tr><td>5</td><td>0</td><td>2</td><td>3</td><td>6</td><td>4</td><td>2</td><td>1</td></tr><tr><td>6</td><td>3</td><td>6</td><td>2</td><td>6</td><td>0</td><td>1</td><td>0</td></tr><tr><td>7</td><td>0</td><td>6</td><td>4</td><td>3</td><td>3</td><td>1</td><td>1</td></tr><tr><td>8</td><td>0</td><td>2</td><td>5</td><td>4</td><td>5</td><td>1</td><td>1</td></tr><tr><td>9</td><td>0</td><td>1</td><td>1</td><td>2</td><td>2</td><td>2</td><td>10</td></tr><tr><td>10</td><td>0</td><td>0</td><td>8</td><td>2</td><td>5</td><td>2</td><td>1</td></tr><tr><td>11</td><td>3</td><td>3</td><td>4</td><td>3</td><td>2</td><td>2</td><td>1</td></tr><tr><td>12</td><td>0</td><td>1</td><td>2</td><td>5</td><td>2</td><td>5</td><td>3</td></tr><tr><td>13</td><td>1</td><td>1</td><td>2</td><td>4</td><td>7</td><td>2</td><td>1</td></tr><tr><td>14</td><td>0</td><td>0</td><td>3</td><td>4</td><td>4</td><td>5</td><td>2</td></tr><tr><td>15</td><td>1</td><td>6</td><td>7</td><td>2</td><td>1</td><td>1</td><td>0</td></tr><tr><td>16</td><td>1</td><td>2</td><td>6</td><td>1</td><td>2</td><td>4</td><td>2</td></tr><tr><td>17</td><td>2</td><td>3</td><td>3</td><td>5</td><td>3</td><td>2</td><td>0</td></tr><tr><td>18</td><td>5</td><td>3</td><td>2</td><td>3</td><td>4</td><td>0</td><td>1</td></tr><tr><td>19</td><td>0</td><td>0</td><td>2</td><td>7</td><td>6</td><td>2</td><td>1</td></tr><tr><td>20</td><td>0</td><td>1</td><td>6</td><td>2</td><td>1</td><td>4</td><td>4</td></tr><tr><td>21</td><td>0</td><td>1</td><td>3</td><td>3</td><td>4</td><td>7</td><td>0</td></tr><tr><td>22</td><td>1</td><td>3</td><td>4</td><td>2</td><td>3</td><td>1</td><td>4</td></tr><tr><td>23</td><td>0</td><td>6</td><td>5</td><td>4</td><td>1</td><td>2</td><td>0</td></tr><tr><td>24</td><td>3</td><td>4</td><td>7</td><td>1</td><td>2</td><td>1</td><td>0</td></tr><tr><td>25</td><td>1</td><td>10</td><td>4</td><td>3</td><td>0</td><td>0</td><td>0</td></tr><tr><td>26</td><td>0</td><td>0</td><td>2</td><td>9</td><td>2</td><td>1</td><td>4</td></tr><tr><td>27</td><td>3</td><td>0</td><td>4</td><td>2</td><td>2</td><td>1</td><td>6</td></tr><tr><td>28</td><td>1</td><td>8</td><td>4</td><td>3</td><td>0</td><td>0</td><td>2</td></tr><tr><td>29</td><td>0</td><td>6</td><td>2</td><td>1</td><td>1</td><td>2</td><td>6</td></tr><tr><td>30</td><td>2</td><td>6</td><td>6</td><td>1</td><td>0</td><td>2</td><td>1</td></tr><tr><td>31</td><td>1</td><td>1</td><td>3</td><td>6</td><td>3</td><td>3</td><td>1</td></tr></table>
+
+Table1. Number of pairmates that transitioned to learned round (LR') status, for each participant and each round. Note: pairmates that were learned in the first round or never learned were excluded from fMRI analyses.
+
+<--- Page Split --->

preprint/preprint__c9fb907249bb69095e1ff9d6815adb18ea1a79c2ccd7872dc27f4f5d49e40f92/preprint__c9fb907249bb69095e1ff9d6815adb18ea1a79c2ccd7872dc27f4f5d49e40f92_det.mmd

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+<|ref|>title<|/ref|><|det|>[[44, 108, 872, 177]]<|/det|>
+# Abrupt remapping in human CA3/dentate gyrus signals resolution of memory interference  
+
+<|ref|>text<|/ref|><|det|>[[44, 196, 592, 238]]<|/det|>
+Wanjia Guo (wanjiag@uoregon.edu) University of Oregon https://orcid.org/0000- 0002- 5893- 6894  
+
+<|ref|>text<|/ref|><|det|>[[44, 243, 590, 285]]<|/det|>
+Serra Favila Columbia University https://orcid.org/0000- 0003- 1528- 2875  
+
+<|ref|>text<|/ref|><|det|>[[44, 290, 320, 331]]<|/det|>
+Ghootae Kim Korea Brain Research Institute  
+
+<|ref|>text<|/ref|><|det|>[[44, 337, 234, 377]]<|/det|>
+Robert Molitor University of Oregon  
+
+<|ref|>text<|/ref|><|det|>[[44, 383, 592, 424]]<|/det|>
+Brice Kuhl University of Oregon https://orcid.org/0000- 0001- 5229- 5400  
+
+<|ref|>text<|/ref|><|det|>[[44, 464, 102, 481]]<|/det|>
+Article  
+
+<|ref|>text<|/ref|><|det|>[[44, 502, 137, 520]]<|/det|>
+Keywords:  
+
+<|ref|>text<|/ref|><|det|>[[44, 540, 333, 559]]<|/det|>
+Posted Date: February 12th, 2021  
+
+<|ref|>text<|/ref|><|det|>[[44, 578, 463, 597]]<|/det|>
+DOI: https://doi.org/10.21203/rs.3.rs- 148842/v1  
+
+<|ref|>text<|/ref|><|det|>[[42, 615, 910, 658]]<|/det|>
+License: © © This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License  
+
+<|ref|>text<|/ref|><|det|>[[42, 694, 930, 737]]<|/det|>
+Version of Record: A version of this preprint was published at Nature Communications on August 10th, 2021. See the published version at https://doi.org/10.1038/s41467- 021- 25126- 0.
+
+<--- Page Split --->
+<|ref|>title<|/ref|><|det|>[[75, 197, 633, 240]]<|/det|>
+# Abrupt remapping in human CA3/dentate gyrus signals resolution of memory interference  
+
+<|ref|>text<|/ref|><|det|>[[75, 267, 686, 286]]<|/det|>
+Wanjia Guo \(^{1}\) , Serra E. Favila \(^{2}\) , Ghootae Kim \(^{3}\) , Robert J. Molitor \(^{1}\) , Brice A. Kuhl \(^{1}\)  
+
+<|ref|>text<|/ref|><|det|>[[75, 330, 425, 390]]<|/det|>
+4 Word Counts  5 Abstract: 150  6 Introduction, Results, Discussion: 4703  7 Methods: 3009  
+
+<|ref|>text<|/ref|><|det|>[[75, 405, 231, 421]]<|/det|>
+8 # of Figures: 4  
+
+<|ref|>text<|/ref|><|det|>[[75, 437, 297, 453]]<|/det|>
+9 1 Supplementary Table  
+
+<|ref|>text<|/ref|><|det|>[[70, 481, 754, 498]]<|/det|>
+10 Keywords: hippocampus, episodic memory, pattern separation, repulsion, competition  
+
+<|ref|>text<|/ref|><|det|>[[70, 525, 816, 543]]<|/det|>
+11 Acknowledgments: This work was supported by NIH- NINDS R01 NS089729 awarded to B.A.K.  
+
+<|ref|>text<|/ref|><|det|>[[70, 571, 874, 603]]<|/det|>
+12 Author Contributions: W.G., G.K., and B.A.K. designed the experiment. W.G. and B.A.K. analyzed the 13 data. S.E.F. consulted on data analyses. All authors wrote and edited the manuscript.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[115, 90, 212, 105]]<|/det|>
+## ABSTRACT:  
+
+<|ref|>text<|/ref|><|det|>[[112, 123, 883, 333]]<|/det|>
+Remapping refers to a decorrelation of hippocampal representations of similar spatial environments. While it has been speculated that remapping may contribute to the resolution of episodic memory interference in humans, direct evidence is surprisingly limited. Here, we tested this idea using high- resolution, pattern- based fMRI analyses. We show that activity patterns in human CA3/dentate gyrus exhibit an abrupt, temporally- specific decorrelation of highly similar memory representations that is precisely coupled with behavioral expressions of successful learning. Strikingly, the magnitude of this learning- related decorrelation was predicted by the amount of pattern overlap during initial stages of learning, with greater initial overlap leading to stronger decorrelation. Finally, we show that remapped activity patterns carry relatively more information about learned episodic associations compared to competing associations, further validating the learning- related significance of remapping. Collectively, these findings establish a critical link between hippocampal remapping and episodic memory interference and provide novel insight into why remapping occurs.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 121, 883, 299]]<|/det|>
+The hippocampus is critical for forming long- term, episodic memories \(^{1 - 3}\) . However, one of the fundamental challenges that the hippocampus faces is that many experiences are similar, creating the potential for memory interference \(^{4,5}\) . In rodents, it is well established that minor alterations to the environment can trigger sudden changes in hippocampal activity patterns—a phenomenon termed remapping \(^{6,7}\) . An appealing possibility is that hippocampal remapping also occurs in human episodic memory, allowing for similar memories to be encoded in distinct activity patterns that prevent interference \(^{8}\) . At present, however, there remains an important gap between evidence of place cell remapping in the rodent hippocampus and episodic memory interference in humans. To bridge this gap, it is informative to consider how properties of place cell remapping, as demonstrated in the rodent hippocampus, might translate to episodic memory interference in humans.  
+
+<|ref|>text<|/ref|><|det|>[[112, 314, 883, 560]]<|/det|>
+One of the most important properties of remapping in the rodent hippocampus is that it is characterized by abrupt transitions between representations \(^{9 - 12}\) . These abrupt transitions, evidenced by decorrelations in patterns of neural activity, have most typically been observed as a function of the degree of environmental change \(^{9,11}\) . However, abrupt remapping can also occur as a function of experience with a new environment \(^{10,12}\) . Evidence of experience- dependent remapping \(^{6,13}\) suggests an important point: that remapping fundamentally reflects changes in internal representations, as opposed to changes in environmental states \(^{14,15}\) . An emphasis on internal representations lends itself well to human episodic memory in that it suggests that hippocampal remapping should occur as memories change. More specifically, this perspective makes the critical prediction that when two events are highly similar, hippocampal remapping will occur if, and when, corresponding memories become distinct. Testing this prediction requires repeatedly probing internal representations (memories) as well as hippocampal representations. However, standard approaches of averaging neuroimaging data across memories and participants can easily obscure or wash out abrupt changes in hippocampal representations if the timing of those changes varies across memories or participants.  
+
+<|ref|>text<|/ref|><|det|>[[112, 576, 883, 715]]<|/det|>
+Evidence of place cell remapping in rodents also motivates specific predictions regarding the relative contributions of hippocampal subfields, with a major distinction being between CA3/dentate gyrus and CA1 \(^{8,16,17}\) . In general, CA3 and dentate gyrus are thought to be more important than CA1 for discriminating between similar stimuli \(^{15,17 - 20}\) and remapping has been shown to occur more abruptly in CA3 than in CA1 \(^{10,12,21}\) . Human fMRI studies also support this general distinction, with several studies specifically implicating CA3 and dentate gyrus in discriminating similar memories \(^{22 - 27}\) . However, these studies have not directly established a link between temporally abrupt changes in CA3/dentate gyrus activity and changes in episodic memory states.  
+
+<|ref|>text<|/ref|><|det|>[[112, 732, 883, 908]]<|/det|>
+Here, we tested whether the resolution of interference between highly similar episodic memories is associated with an abrupt remapping of activity patterns in human CA3/dentate gyrus. We used an associative memory paradigm in which participants learned and were repeatedly tested on associations between scene images and object images \(^{28}\) . The critical design feature was that the set of scene images included pairs of extremely similar scenes (Fig. 1a). These scene pairmats were intended to elicit associative memory interference. Across six rounds of learning, we tracked improvement in associative memory for each set of pairmates while also continuously tracking representational changes indexed by fMRI. Specifically, after each associative memory test round, participants were shown each scene image one at a time (exposure phase) which allowed us to measure the activity pattern evoked by each scene and, critically, the representational distance between scene pairmates. To preview, we find that behavioral
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 88, 884, 194]]<|/det|>
+expressions of memory interference resolution are temporally- coupled to abrupt, stimulus- specific remapping of human CA3/dentate gyrus activity patterns. This remapping specifically exaggerated the representational distance between similar memories. In additional analyses, we show that the magnitude of remapping that individual memories experienced was predicted by the degree of initial pattern overlap among CA3/dentate gyrus representations and that remapped CA3/dentate gyrus representations carried increased and highly specific information about learned episodic associations.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 212, 199, 227]]<|/det|>
+## RESULTS:  
+
+<|ref|>text<|/ref|><|det|>[[113, 245, 884, 420]]<|/det|>
+Participants completed six rounds of the experimental paradigm while inside an fMRI scanner. Each round included a study phase, an associative memory test phase, and a scene exposure phase (Fig. 1b). fMRI scanning was only conducted during the exposure phases. During the study phases, participants viewed scene- object associations one at a time. During the associative memory test phases, participants were shown scenes, one at a time, along with two very similar object choices (e.g., two guitars); one object was the target (i.e., the object that had been paired with the current scene) and the other object was the competitor (i.e., the object that had been paired with the scene pairmate). After selecting an object, participants indicated their confidence (high or low). During exposure phases, participants were shown each scene, along with novel scenes, and made a simple old/new judgment (mean \(\pm 95\%\) CI: \(d' = 5.40 \pm 0.88\) ; one- sample \(t\) - test vs. 0: \(t_{30} = 12.58\) , \(p < 0.001\) , Cohen's \(d = 2.26\) ).  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 440, 191, 455]]<|/det|>
+## Behavior.  
+
+<|ref|>text<|/ref|><|det|>[[113, 473, 884, 578]]<|/det|>
+During the associative memory test phases, participants chose the correct object with above- chance accuracy in each of the 6 rounds ( \(t_{30}\) 's \(\geq 2.65\) , \(p\) 's \(\leq 0.013\) , \(d\) 's \(\geq 0.48\) ; chance accuracy \(= 50\%\) ). Accuracy markedly improved across rounds, from a mean of \(56.45\%\) \(\pm 4.98\%\) in round 1 to a mean of \(94.71\% \pm 2.21\%\) in round 6 (main effect of round: \(F_{1,30} = 318.86\) , \(p < 0.001\) , \(\eta^2 = 0.91\) ). The rate of choosing the correct object with high- confidence also robustly increased across rounds, from a mean of \(27.15\% \pm 4.71\%\) in round 1 to \(92.83\% \pm 3.58\%\) in round 6 (main effect of round: \(F_{1,30} = 574.44\) , \(p < 0.001\) , \(\eta^2 = 0.95\) ; Fig. 1c).  
+
+<|ref|>text<|/ref|><|det|>[[112, 594, 884, 769]]<|/det|>
+To test whether hippocampal remapping was temporally coupled with the resolution of memory interference, we identified, for each participant and for each set of pairmates, the learning round in which scene- object associations were recalled with high confidence (for both scenes in a pairmate). We refer to this timepoint as the 'learned round' (LR; see Methods). Of critical interest for our remapping analyses was the correlation of activity patterns evoked by scene images during the learned round (LR) with activity patterns evoked immediately prior to the learned round (LR- 1). We refer to this transition (from pre- learned to learned) as the 'inflection point' (IP) in learning (Fig. 1d). For example, if the LR for a particular set of pairmates was round 4, then the IP was the transition from round 3 to 4. Our rationale for correlating activity patterns from LR- 1 with LR was that this correlation would capture the critical change in hippocampal representations (remapping) that putatively supports learning.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[297, 90, 697, 560]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[114, 568, 883, 744]]<|/det|>
+<center>Figure 1. Experimental Design and Behavior. a. Participants learned 36 scene-object associations. The 36 scenes comprised 18 scene pairmats which consisted of highly similar image pairs (e.g., 'barn 1' and 'barn 2'). Scene pairmats were also associated with similar objects (e.g., 'guitar 1' and 'guitar 2'). b. Participants completed 6 rounds of study, test, and exposure phases. During study, participants viewed scenes and associated objects. During test, participants were presented with scenes and had to select the associated object from a set of two choices, followed by a confidence rating (high or low confidence; not shown). During exposure, scenes (rounds 1-6) or objects (round 1 and 6) were presented and participants made an old/new judgment. fMRI data were only collected during the scene and object exposure phases. c. Mean percentage of high confidence correct responses for each test round. d. Data from a representative participant showing the 'inflection point' in learning, for each pairmate. The inflection point was defined as the point at which participants transitioned to high-confidence correct retrieval for both scenes within a pairmate—a transition from 'pre-learned' to 'learned.' e. The number of pairs that transitioned to a learned state at each round, aggregated across all participants and pairmates. N.L. indicates pairmates that were never learned. Notes: error bars reflect S.E.M. </center>  
+
+<|ref|>text<|/ref|><|det|>[[115, 795, 750, 813]]<|/det|>
+Remapping in CA3/dentate gyrus is time- locked to the inflection point in learning.  
+
+<|ref|>text<|/ref|><|det|>[[115, 831, 883, 900]]<|/det|>
+For our fMRI analyses, our primary focus was on pattern similarity between scene pairmates. Pattern similarity was measured by correlating patterns of fMRI activity evoked by each scene during the scene exposure phases. Pairmate similarity was defined as the correlation between activity patterns evoked by scene pairmates (e.g., 'barn 1' and 'barn 2'; Fig. 2b). Correlations between scenes that were not pairmates
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 88, 884, 247]]<|/det|>
+(e.g., 'barn 1' and 'airplane 2'; Fig. 2b) provided an important baseline measure of non- pairmate similarity. We refer to the difference between these two measures (pairmate – non- pairmate similarity) as the pairmate similarity score<sup>28</sup>. A positive pairmate similarity score would indicate that visually similar scenes (e.g., two barns) are associated with more similar neural representations than two unrelated scenes. Critically, because pairmate similarity scores are a relative measure, they can be directly compared across different brain regions<sup>29</sup> – something that would be inadvisable with raw correlation values. For all pattern similarity analyses, correlations were always performed across learning rounds (e.g., correlating 'barn 1' at LR- 1 with 'barn 2' at LR). This ensured independence of fMRI data<sup>30</sup>, but was also intended to capture transitions in hippocampal representations (remapping).  
+
+<|ref|>text<|/ref|><|det|>[[113, 261, 884, 508]]<|/det|>
+Following a prior study that used similar stimuli and analyses<sup>28</sup>, fMRI analyses targeted the following regions of interest (ROIs): hippocampus, parahippocampal place area (PPA), and early visual cortex (EVC). PPA and EVC served as important control regions indexing high- level (PPA) and low- level (EVC) visual representations. We did not anticipate that these regions would demonstrate learning- related remapping. Within the hippocampus, we leveraged our high- resolution fMRI protocol to segment the hippocampus body into subfields comprising CA1 and CA2/CA3/dentate gyrus (CA23DG). Motivated by past empirical findings<sup>23,31</sup> and theoretical models<sup>8</sup>, we predicted that remapping would occur in CA23DG. More specifically, we predicted that CA23DG remapping would occur at the inflection point (IP) in learning. To test this prediction, we compared pairmate similarity scores at the IP to pairmate similarity scores at a timepoint just prior to the IP (pre- IP). Whereas pairmate similarity scores at the IP were based on correlations between activity patterns from the Learned Round (LR) and the preceding round (LR- 1), pairmate similarity scores at the pre- IP were based on correlations shifted back one step in time: i.e., between LR- 1 and LR- 2. Thus, whereas the IP captured the transition from pre- learned to learned, the pre- IP was an important reference point that corresponded to a 'non- transition' (pre- learned to pre- learned).  
+
+<|ref|>text<|/ref|><|det|>[[113, 523, 884, 646]]<|/det|>
+An ANOVA with factors of behavioral state (pre- IP, IP) and ROI (CA1, CA23DG, PPA, EVC) revealed a significant main effect of ROI \((F_{3,90} = 4.08, p = 0.009, \eta^2 = 0.04)\) , reflecting overall differences in pairmate similarity scores across ROIs. Scores were numerically lowest in CA23DG and numerically highest in EVC. There was no main effect of behavioral state \((F_{1,30} = 2.71, p = 0.110, \eta^2 = 0.01)\) , indicating that learning did not have a global effect on representational structure across ROIs. Critically, however, the interaction between behavioral state and ROI was significant \((F_{3,90} = 2.95, p = 0.037, \eta^2 = 0.04)\) , indicating that learning differentially influenced pairmate similarity scores across ROIs.  
+
+<|ref|>text<|/ref|><|det|>[[113, 664, 884, 752]]<|/det|>
+Within CA23DG, pairmate similarity scores were significantly lower at the IP than the pre- IP \((t_{30} = - 2.24, p = 0.033, d = 0.40, CI = [- 0.012 \pm 0.011])\) , consistent with our prediction that remapping would specifically occur at the behavioral inflection point. Importantly, we also confirmed via permutation test (see Methods) that CA23DG pairmate similarity scores at the IP were lower than would be expected if the mapping between pairmates and IP's was shuffled within participants \((p = 0.013, \text{one- tailed}; \text{Fig. 2d})\) .  
+
+<|ref|>text<|/ref|><|det|>[[113, 767, 884, 890]]<|/det|>
+Strikingly, CA23DG pairmate similarity scores not only decreased at the IP, but they were significantly below 0 at the IP \((t_{30} = - 2.36, p = 0.025, d = 0.19, CI = [- 0.008 \pm 0.007])\) . In other words, pairs of scenes with extremely high visual similarity were represented as less similar than completely unrelated scenes in CA23DG. While seemingly counterintuitive, several recent fMRI studies have also found that, in certain situations, hippocampal pattern similarity is lower for similar than dissimilar events<sup>23,28,32</sup>. This has led to the proposal that similarity triggers a repulsion of hippocampal representations. That is, just as physical proximity triggers repulsion of like magnetic poles, representational proximity triggers repulsion of similar
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 88, 883, 125]]<|/det|>
+memories (Fig. 2f). The present results, however, provide critical new evidence that this repulsion is time-locked to—and may, in fact, underlie—the resolution of interference between competing memories.  
+
+<|ref|>text<|/ref|><|det|>[[113, 140, 884, 300]]<|/det|>
+In CA1, pairmate similarity scores did not significantly differ by learning state \((t_{30} = - 0.72, p = 0.474, d = 0.13, \text{CI} = [0.004 \pm 0.01])\) or differ from 0 either at the pre- IP \((t_{30} = - 0.63, p = 0.531, d = 0.11, \text{CI} = [0.003 \pm 0.009])\) or IP \((t_{30} = - 0.34, p = 0.735, d = 0.06, \text{CI} = [- 0.001 \pm 0.006])\) . In PPA, pairmate similarity scores decreased from pre- IP to IP \((t_{30} = - 2.28, p = 0.030, d = 0.41, \text{CI} = [0.008 \pm 0.007])\) , with scores significantly greater than 0 in the pre- IP \((t_{30} = 3.14, p = 0.004, d = 0.56, \text{CI} = [0.007 \pm 0.005])\) but not different from 0 at the IP \((t_{30} = - 0.26, p = 0.798, d = 0.05, \text{CI} = [- 0.0006 \pm 0.005])\) . In EVC, pairmate similarity scores did not significantly vary by learning state \((t_{30} = - 1.39, p = 0.175, d = 0.25, \text{CI} = [- 0.007 \pm 0.01])\) ; but there was a numerical increase from pre- IP to IP, with scores significantly above 0 at IP \((t_{30} = 3.13, p = 0.004, d = 0.56, \text{CI} = [0.01 \pm 0.007])\) but not at pre- IP \((t_{30} = 0.92, p = 0.366, d = 0.16, \text{CI} = [0.004 \pm 0.008])\) .  
+
+<|ref|>text<|/ref|><|det|>[[113, 315, 884, 455]]<|/det|>
+The qualitative difference between CA23DG and EVC is striking in that, at the inflection point, these regions exhibited fully opposite representational structures: scene pairmates were more similar than non- pairmates in EVC, but less similar than non- pairmates in CA23DG. This finding parallels prior evidence of opposite representational structures in hippocampus and EVC<sup>28,32</sup> and argues against the possibility that CA23DG 'inherited' representational structure from early visual regions. More generally, it is striking that differences in pairmate similarity scores markedly varied across the four ROIs at the IP \((F_{3,90} = 8.73, p < 0.001, \eta^2 = 0.14)\) , but not at the pre- IP \((F_{3,90} = 0.33, p = 0.804, \eta^2 = 0.008)\) , underscoring the influence of learning on representational structure.  
+
+<|ref|>text<|/ref|><|det|>[[112, 470, 884, 700]]<|/det|>
+For the preceding fMRI analyses, the IP was defined as the correlation between the learned round (LR) and the immediately preceding round (LR- 1). To more fully characterize how the representational state at the LR compared to other rounds, we additionally correlated representations at LR to representations at LR- 2 and LR- 3 (i.e., other rounds that preceded the LR) and also correlated LR with LR+1, LR+2, and LR+3 (rounds that followed the LR) (Fig. 2e). Within CA23DG, pairmate similarity scores were significantly lower when correlating the LR with rounds that preceded learning compared to rounds that followed learning \((t_{30} = - 2.98, p = 0.006, d = 0.54, \text{CI} = [- 0.009 \pm 0.006])\) . This striking asymmetry indicates that CA23DG representations expressed at the LR were systematically biased away from the initial representational position of competing memories. More generally, these data support the idea of an abrupt representational change (remapping) in CA23DG that was time- locked to the specific round at which learning occurred for individual pairmates. For CA1, PPA, and EVC, there were no significant differences in pairmate similarity scores when correlating the LR to rounds that preceded learning vs. followed learning \((t_{30} \leq 0.79, p \leq 0.435, d \leq 0.14; \text{Fig. 2e})\) .
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[131, 90, 860, 494]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[114, 503, 883, 737]]<|/det|>
+<center>Figure 2. Pairmate similarity scores change at the behavioral inflection point. a. Regions of interest included CA23DG and CA1 in the hippocampus, the parahippocampal place area (PPA), and early visual cortex (EVC). b. Correlation matrix illustrating how pairmate similarity scores were computed for the behavioral inflection point. c. Pairmate similarity scores at the behavioral inflection point (IP) and just prior to the inflection point (pre-IP) across different regions of interest (ROIs). Pairmate similarity scores significantly varied by ROI \((p = 0.009)\) and there was a significant interaction between ROIs and behavioral state \((p = 0.011)\) . d. A permutation test (1,000 iterations) was performed by shuffling, within participants, the mapping between the behavioral inflection point and scene pairmates. In CA23DG the actual mean group-level pairmate similarity score at the IP was lower than \(98.70\%\) of the permuted mean similarity scores. e. Pairmate similarity scores calculated by correlating the learned round (LR) with each of the three preceding rounds (- distance to LR) and each of the three succeeding rounds (+ distance to LR). In CA23DG, pairmate similarity scores were significantly lower when the LR was correlated with preceding round compared to succeeding rounds \((p = 0.006)\) . The difference was not significant for any other ROIs \((p > 0.435)\) . f. Conceptual illustration of a decrease in pairmate similarity scores from pre-IP to IP. In the pre-IP state (top panel), A1 and A2 are nearby in representational space. In the IP state (bottom panel), the representational distance between A1 and A2 has been exaggerated. When pairmates (e.g., A1 and A2) are farther apart in representational space than non-pairmates (e.g., A1 and B2) the pairmate similarity score will be negative (i.e., pairmate similarity < non-pairmate similarity), consistent with a repulsion of competing representations. Notes: \(^{*}p < .05\) , \(^{**}p < .01\) , error bars reflect S.E.M. </center>  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 787, 553, 804]]<|/det|>
+## Overlap of CA23DG representations triggers remapping.  
+
+<|ref|>text<|/ref|><|det|>[[115, 821, 883, 908]]<|/det|>
+The fact that pairmate similarity scores in CA23DG were negative at the IP (Fig. 2c) suggests that learning- related remapping involved an active repulsion of competing hippocampal representations (Fig. 2f). Conceptually, the key feature of a repulsion account is that separation of hippocampal representations is a reaction to initial overlap among memories<sup>33</sup>. Here, because we measured representational states throughout the course of learning, we were able to test this hypothesis directly. Specifically, we tested the
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[115, 88, 883, 141]]<|/det|>
+prediction that relatively greater pairmate similarity scores (i.e., higher overlap between memories) at a given timepoint is associated with relatively lower pairmate similarity scores (i.e., lower overlap between memories) at a successive timepoint.  
+
+<|ref|>text<|/ref|><|det|>[[115, 158, 883, 333]]<|/det|>
+To test this hypothesis, we first translated the 6 learning rounds into 5 'timepoints' (see Methods). Each timepoint corresponded to the set of scene pair similarity scores obtained by correlating activity patterns across consecutive learning rounds [e.g., timepoint 1 = r(round 1, round 2)]. These scores reflected the representational structure at each timepoint (i.e., which pairmates were relatively similar, which pairmates were relatively dissimilar). We then rank correlated the pairmate similarity scores across successive timepoints [r(timepoint 1, timepoint 2)]. Whereas a positive rank correlation would indicate that representational structure is preserved across time points, a negative rank correlation would indicate that representational structure is inverted across time points. Critically, an inversion of representational structure is precisely what would be predicted if initial overlap among activity patterns (i.e., high pairmate similarity scores) triggers a repulsion of activity patterns (i.e., low pairmate similarity scores).  
+
+<|ref|>text<|/ref|><|det|>[[113, 350, 883, 577]]<|/det|>
+Strikingly, the rank correlation in CA23DG was significantly negative ( \(t_{30} = - 2.99\) , \(p = 0.006\) , \(d = 0.54\) , CI = [- 0.06 ± 0.04]). In contrast, the rank correlation in CA1 was significantly positive ( \(t_{30} = 2.11\) , \(p = 0.043\) , \(d = 0.38\) , CI = [0.06 ± 0.05]). The difference between CA23DG and CA1 was also significant ( \(t_{30} = 3.73\) , \(p < 0.001\) , \(d = 0.67\) , CI = [0.12 ± 0.06]). Importantly, the negative correlation in CA23DG cannot be explained by regression to the mean (see Methods). Moreover, when we tested correlations at a lag of 2 [r(timepoint N, timepoint N+2)], correlations did not significantly differ from 0 for either CA23DG ( \(t_{30} = - 0.71\) , \(p = 0.485\) , \(d = 0.13\) , CI = [- 0.02 ± 0.05]) or CA1( \(t_{30} = - 1.60\) , \(p = 0.120\) , \(d = 0.29\) , CI = [- 0.04 ± 0.05]). Further, the interaction between lag (1, 2) and ROI (CA23DG, CA1) was also significant ( \(F_{1,30} = 7.09\) , \(p = 0.012\) , \(\eta^2 = 0.06\) ), indicating that the dissociation between CA23DG and CA1 was relatively stronger at lag 1 (consecutive timepoints) than lag 2 (non-consecutive timepoints). Thus, representational structure at a given time point specifically predicted representational structure at a successive timepoint. Rank correlations did not differ from 0 in either PPA or EVC, either for lag 1 or lag 2 ( \(t_{30}\) 's ≤ 1.12, \(p\) 's ≥ 0.272, \(d\) 's ≤ 0.20).  
+
+<|ref|>text<|/ref|><|det|>[[113, 593, 883, 908]]<|/det|>
+While the negative correlation in CA23DG was fully consistent with our prediction—and with the idea that high pattern overlap triggers repulsion—the negative correlation could alternatively be explained by pairmates with relatively low pairmate similarity at timepoint N tending to have relatively high similarity at timepoint N+1. Additionally, because our analysis was entirely agnostic to behavioral data, it does not specifically establish that the negative pairmate similarity scores that we observed at the behavioral IP (Fig. 2c and 2e) were triggered by pattern overlap at IP- 1. Thus, as a complementary analysis, we binned all pairmates, by quartiles, according to pairmate similarity scores at IP- 1, with the 4<sup>th</sup> quartile representing pairmates with the highest pairmate similarity scores. We then computed the mean pairmate similarity scores for those bins at the IP. Again, this analysis was separately performed for CA23DG and CA1. An ANOVA with factors of ROI (CA23DG, CA1) and pairmate similarity scores at IP- 1 (4 quartiles) revealed a significant interaction ( \(F_{3,90} = 3.19\) , \(p = 0.027\) , \(\eta^2 = 0.03\)). Critically, this interaction was driven by a marked difference between CA23DG and CA1 when considering the bin with the highest overlap at IP- 1 (i.e., 4th quartile: \(t_{30} = - 2.87\) , \(p = 0.008\) , \(d = 0.51\) , CI = [- 0.03 ± 0.02], Fig. 3c). For CA23DG, pairmate similarity scores at the IP were significantly below 0 and numerically lowest for pairmates whose similarity scores at IP- 1 were in the 4<sup>th</sup> quartile (comparison to 0: \(t_{30} = - 2.54\) , \(p = 0.017\) , \(d = 0.46\) , CI = [- 0.023 ± 0.019]); the pattern in CA1 was qualitatively opposite. Collectively, these results provide novel, theory- consistent evidence that remapping of competing representations is actively triggered by initial representational overlap.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[123, 141, 877, 310]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[114, 316, 883, 496]]<|/det|>
+<center>Figure 3. Representational structure across timepoints. a. Schematic illustration showing the rank order of scene pairmates based on pairmate similarity scores at various time points (N, \(\mathsf{N} + 1\) , \(\mathsf{N} + 2\) ). If scene pairmates with relatively high pairmate similarity scores at a given timepoint are systematically associated with relatively low pairmate similarity scores at a succeeding time point (red arrows), this will produce a negative rank correlation. b. Mean rank order correlations of pairmate similarity scores across timepoints for CA23DG and CA1. Lag 1 correlations reflect correlations between a given timepoint and an immediate succeeding timepoint (e.g., timepoints 2 and 3). Lag 2 correlations reflect correlations between a given timepoint and a timepoint two steps away (e.g., timepoints 2 and 4). At lag 1, there was a negative correlation in CA23DG \((p = 0.004)\) , but a positive correlation in CA1 \((p = 0.045)\) . At lag2, correlations were not significant in either CA23DG or CA1 indicating that correlations in representational structure were specific to temporally adjacent rounds. c. Pairmate similarity scores at the inflection point (IP) as a function of relative pairmate similarity scores in the pre-IP state ( \(1^{\text{st}}\) quartile = lowest similarity, \(4^{\text{th}}\) quartile = highest similarity). Pairmate similarity scores in CA23DG were significantly lower than CA1 \((p = 0.017)\) and significantly below 0 \((p = 0.008)\) for pairmates with the highest pre-IP similarity (4th quartile). Notes: \* \(p < .05\) , \*\* \(p < .01\) , error bars reflect S.E.M. </center>  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 546, 776, 563]]<|/det|>
+## CA23DG scene representations differentiate between competing object associations.  
+
+<|ref|>text<|/ref|><|det|>[[115, 580, 882, 666]]<|/det|>
+Thus far, we have focused on similarity among neural representations evoked while viewing the scene images (scene exposure phase). However, our paradigm also included two fMRI runs during which participants viewed each of the objects associated with the scene images (object exposure phase; see Methods). This allowed us to test whether hippocampal activity patterns evoked while viewing the scenes resembled—or came to resemble—activity patterns evoked while viewing corresponding object images.  
+
+<|ref|>text<|/ref|><|det|>[[115, 684, 882, 807]]<|/det|>
+Whereas, pairmate similarity scores were computed by correlating activity patterns across rounds of the scene exposure phase (e.g., LR- 1 and LR), here we computed correlations between a single round of the scene exposure phase (e.g., LR) and the average of the two object rounds (see Methods). For this analysis, there were three important factors that we considered. First, we considered whether scene representations were in a 'pre- learned' state (LR- 1) or 'learned' state (LR). Second, we separately tested correlations between each scene and (a) the target object (e.g., 'guitar 1') vs. (b) the competing object (e.g., 'guitar 2') (Fig. 4a). Third, we again compared results in CA23DG vs. CA1.  
+
+<|ref|>text<|/ref|><|det|>[[115, 825, 882, 894]]<|/det|>
+A repeated measures ANOVA with factors of ROI (CA23DG, CA1), behavioral state (pre- learned, learned), and object relevance (target, competitor) revealed a significant interaction between behavioral state and object relevance \((F_{1,30} = 12.42\) , \(p = 0.001\) , \(\eta^2 = 0.02\) ). Qualitatively, this interaction reflected a learning- related change wherein hippocampal representations of scene images became relatively more similar to
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[112, 88, 884, 352]]<|/det|>
+275 target objects and less similar to competitor objects. However, this 2- way interaction between behavioral 276 state and object relevance was qualified by a trend toward a 3- way interaction between behavioral state, 277 object relevance, and ROI \((F_{1,30} = 4.07\) \(p = 0.053\) \(\eta^2 = 0.01\) ). Specifically, the interaction between 278 behavioral state (pre- learned, learned) and object relevance (target, competitor) was significant in CA23DG 279 \((F_{1,30} = 11.98\) \(p = 0.002\) \(\eta^2 = 0.06\) ) but not in CA1 \((F_{1,30} = 0.44\) \(p = 0.510\) \(\eta^2 = 0.002\) ) (Fig. 4b). For 280 CA23DG, there was a qualitative increase, from the pre- learned to learned state, in similarity between 281 scenes and target objects and a qualitative decrease, from the pre- learned to learned state, in similarity 282 between scenes and competing objects. In other words, the remapping of CA23DG scene representations 283 that occurred at the learned round yielded a relative strengthening of information related to target object 284 associations and a relative weakening of information related to competing object associations. This 285 dissociation in CA23DG is striking when considering that target and competitor objects were extremely 286 similar (see Fig.1a, Fig. 4a) and even more so when considering that during the scene and object exposure 287 phases participants were not instructed or required in any way to recall the corresponding images. The 2- 288 way interaction between behavioral state and object relevance was not significant for PPA or EVC \([F_{1,30}\) 's 289 \(\leq 3.23\) \(p^{\prime}s\geq 0.082\) \(\eta^2 s\leq 0.02]\)  
+
+<|ref|>image<|/ref|><|det|>[[310, 408, 670, 714]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[113, 725, 884, 867]]<|/det|>
+<center>Figure 4. Scene-object similarity as a function of behavioral state. a. Example associations between scene pairmates and objects. Scene-object similarity was calculated by correlating activity patterns evoked during the scene exposure phases (at different behavioral states) and the object exposure phases. Target similarity refers to correlations between a given scene and the object with which it was studied. Competitor similarity refers to correlations between a given scene and the object with which its pairmate was studied. b. Scene-object similarity as a function of object relevance (target, competitor), ROI (CA23DG, CA1), and behavioral state (pre-learned, learned). Correlations between unrelated scenes and objects (across pairmate similarity; not shown) was subtracted from target and competitor similarity values. For CA23DG, there was a significant interaction between behavioral state and object relevance \((p = 0.002)\) . Notes: \(^{**}p< .01\) , error bars reflect S.E.M. </center>
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[115, 88, 225, 104]]<|/det|>
+## DISCUSSION:  
+
+<|ref|>text<|/ref|><|det|>[[115, 123, 883, 245]]<|/det|>
+Here, we show that learning to discriminate competing episodic memories is associated with an abrupt remapping of activity patterns in CA3/dentate gyrus. Specifically, fMRI pattern similarity in CA3/dentate gyrus decreased precisely when behavioral expressions of learning emerged. Additionally, the degree to which remapping occurred in CA3/dentate gyrus was predicted by the degree of initial pattern overlap among competing memories. Finally, remapped CA3/dentate gyrus representations contained relatively stronger information about relevant episodic associations and relatively weaker information about competing episodic associations, confirming the learning- related significance of the remapping effect.  
+
+<|ref|>text<|/ref|><|det|>[[115, 263, 883, 473]]<|/det|>
+Our findings complement recent demonstrations of remapping- like phenomena in the human hippocampus \(^{34,35}\) as well as evidence of abrupt remapping in the rodent hippocampus \(^{9 - 12}\) . However, our findings provide unique and direct support for the proposal that hippocampal remapping is associated with the resolution of human episodic memory interference \(^{8}\) . Specifically, we demonstrate an abrupt transition in hippocampal representations that occurred at an important inflection point in learning—the point at which participants were able to correctly discriminate similar memories and retrieve associations with high confidence. Notably, this finding was only possible because (a) we repeatedly probed episodic memory and hippocampal representations over the course of learning and (b) we identified inflection points in a participant- and pairmate- specific manner. Indeed, inflection points varied considerably across and within participants (Fig. 1d and Sup. table 1) and the observed hippocampal remapping effect was significantly weaker when the specific mapping between behavior and fMRI data was shuffled within participants (Fig. 2d).  
+
+<|ref|>text<|/ref|><|det|>[[115, 489, 883, 715]]<|/det|>
+The fact that CA23DG remapping occurred precisely at the inflection point in learning strongly suggests that remapping was related to learning. This argument is also reinforced by our independent finding that remapped CA23DG activity patterns, evoked while participants viewed individual scene images, carried more information (compared to the pre- learning state) about target versus competing object associations. In other words, the inflection point defined from behavioral expressions of associative memory also captured a critical change in associative representations encoded in CA23DG activity patterns. The fact that CA23DG exaggerated the representational distance between competing scenes (remapping) while simultaneously reflecting learned associations (scene- object similarity) is consistent with the idea that CA3 balances both pattern separation and pattern completion mechanisms \(^{4,17,36,37}\) . The fact that remapped activity patterns contained information about learned associations is also consistent with the argument that hippocampal remapping does not simply reflect changes in the external environment—which did not change over the course of the experiment—but instead fundamentally reflects changes in internal models of the environment \(^{14,15}\) .  
+
+<|ref|>text<|/ref|><|det|>[[115, 733, 883, 907]]<|/det|>
+One aspect of our findings which does not, to our knowledge, have a direct analog in rodent studies of remapping is the negative pairmate similarity score we observed at the inflection point in CA23DG. The negative score indicates that scene pairmates—which were extremely similar images—were associated with less overlapping CA23DG representations than completely unrelated scenes. In rodents, the most extreme version of remapping occurs when two similar environments are associated with fully independent place codes \(^{8}\) . In our study, however, if each scene was associated with an independent representation, then the similarity between pairmates would be equal to, but not lower than, the similarity between non- pairmates. Instead, the negative pairmate similarity score requires a dependence between competing hippocampal representations wherein a given memory representation systematically moves away from the representational position of a competing memory (Fig. 2f). We refer to this dependence as ‘repulsion’ in
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 88, 883, 159]]<|/det|>
+order to emphasize the oppositional influence that competing memories exerted. Several recent human fMRI studies have reported conceptually similar effects in the hippocampus<sup>28,32,38</sup>—and in CA3/dentate gyrus, specifically<sup>22-26</sup>. However, the current findings are the first to directly establish that the repulsion of competing hippocampal representations is temporally coupled to the resolution of memory interference.  
+
+<|ref|>text<|/ref|><|det|>[[113, 174, 883, 386]]<|/det|>
+Based on computational models<sup>33,39,40</sup>, our prediction was that the repulsion effect in CA23DG was a direct consequence of initial overlap among activity patterns. Indeed, a recent study found that hippocampal repulsion was more likely to occur for behaviorally- confusable memories<sup>32</sup>, potentially because confusable memories are associated with greater pattern overlap during initial learning. In the current study, we tested—and confirmed—this account directly. Specifically, we found that the representational structure (relative pairmate similarity) in CA23DG at a given timepoint was negatively correlated with representational structure at an immediately following timepoint. This negative relationship is highly consistent with the idea that overlap, itself, triggers plasticity that ‘punishes’ those features which are shared across memories<sup>24,33,39,40</sup>. While our study does not afford inferences about the causal relationship between repulsion and learning, the idea that repulsion (or remapping more generally) is triggered by representational overlap, combined with the fact that remapping was associated with learning, is consistent with the possibility that repulsion of CA3/dentate gyrus representations is a causal factor in learning.  
+
+<|ref|>text<|/ref|><|det|>[[112, 401, 883, 681]]<|/det|>
+Across multiple analyses, we observed dissociations between CA3/dentate gyrus and CA1. The fact that the remapping effects were selective to CA3/dentate gyrus is consistent with evidence from rodent studies of remapping and pattern separation<sup>8,16,36</sup> and with several human fMRI studies<sup>22- 25,36</sup>. Perhaps the most striking dissociation between CA23DG and CA1 comes from our analysis of representational structure across time points. Whereas CA23DG exhibited a negative rank correlation across successive timepoints, CA1 exhibited a positive rank correlation (Fig. 3b). Thus, in contrast to CA23DG, CA1 was characterized by stability (though only modest stability) of representational structure across timepoints<sup>4</sup>. This dissociation between CA23DG and CA1 is consistent with the idea that CA3, in particular, supports rapid plasticity that allows for changes in memory representations on short time scales<sup>41</sup> and is also consistent with evidence of faster remapping in CA3/dentate gyrus than in CA1<sup>10,12,21</sup>. It is also notable that the remapping effect we observed in CA23DG at the inflection point in learning strongly contrasted with the pattern of data in early visual cortex. Whereas CA23DG exhibited a negative pairmate similarity score at the inflection point, EVC exhibited a significant, positive pairmate similarity score at the inflection point. This finding makes the important point that CA23DG was not inheriting representational structure from early sensory regions (e.g., due to visual attention)—rather, CA23DG fully inverted the representational structure that was expressed in early visual cortex<sup>28</sup>.  
+
+<|ref|>text<|/ref|><|det|>[[113, 697, 883, 838]]<|/det|>
+Taken together, our findings constitute novel evidence for a remapping of human CA3/dentate gyrus representations that is temporally- coupled to the resolution of episodic memory interference. These findings were motivated by—and complement—existing evidence of remapping in the rodent hippocampus. Yet, our findings also go beyond existing rodent or human studies by establishing a direct link between remapping and changes in internal memory states<sup>14,15</sup>. Additionally, our conclusion that overlap among CA3/dentate gyrus representations actively triggers a repulsion of memory representations has important implications for theoretical accounts of how the hippocampus resolves memory interference<sup>5,8,36,39</sup> and will hopefully inspire targeted new analyses that test for similar mechanisms in rodent models.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[115, 90, 235, 106]]<|/det|>
+## REFERENCES:  
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+23. Dimsdale-Zucker, H. R., Ritchey, M., Ekstrom, A. D., Yonelinas, A. P. & Ranganath, C. CA1 and CA3 differentially support spontaneous retrieval of episodic contexts within human hippocampal subfields. *Nat. Commun.* 9, 294 (2018). 
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+28. Favila, S. E., Chanales, A. J. H. & Kuhl, B. A. Experience-dependent hippocampal pattern differentiation prevents interference during subsequent learning. Nat. Commun. 7, 11066 (2016).  
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+29. Kriegeskorte, N. Representational similarity analysis – connecting the branches of systems neuroscience. Front. Syst. Neurosci. (2008) doi:10.3389/neuro.06.004.2008.  
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+32. Chanales, A. J. H., Oza, A., Favila, S. E. & Kuhl, B. A. Overlap among Spatial Memories Triggers Repulsion of Hippocampal Representations. Curr. Biol. 27, 2307-2317.e5 (2017).  
+
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+33. Hulbert, J. C. & Norman, K. A. Neural Differentiation Tracks Improved Recall of Competing Memories Following Interleaved Study and Retrieval Practice. Cereb. Cortex 25, 3994–4008 (2015).  
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+34. Kyle, C. T., Stokes, J. D., Lieberman, J. S., Hassan, A. S. & Ekstrom, A. D. Successful retrieval of competing spatial environments in humans involves hippocampal pattern separation mechanisms. eLife 4, e10499 (2015).  
+
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+35. Steemers, B. et al. Hippocampal Attractor Dynamics Predict Memory-Based Decision Making. Curr. Biol. 26, 1750–1757 (2016).  
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+36. Yassa, M. A. & Stark, C. E. L. Pattern separation in the hippocampus. Trends Neurosci. 34, 515–525 (2011).  
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+37. Hindy, N. C., Ng, F. Y. & Turk-Browne, N. B. Linking pattern completion in the hippocampus to predictive coding in visual cortex. Nat. Neurosci. 19, 665–667 (2016).
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[57, 88, 884, 370]]<|/det|>
+38. Jiang, J., Wang, S.-F., Guo, W., Fernandez, C. & Wagner, A. D. Prefrontal reinstatement of contextual task demand is predicted by separable hippocampal patterns. Nat. Commun. 11, 2053 (2020).39. Ritvo, V. J. H., Turk-Browne, N. B. & Norman, K. A. Nonmonotonic Plasticity: How Memory Retrieval Drives Learning. Trends Cogn. Sci. 23, 726–742 (2019).40. Norman, K. A., Newman, E. L. & Detre, G. A neural network model of retrieval-induced forgetting. Psychol. Rev. 114, 887–953 (2007).41. Rebola, N., Carta, M. & Mulle, C. Operation and plasticity of hippocampal CA3 circuits: implications for memory encoding. Nat. Rev. Neurosci. 18, 208–220 (2017).
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[115, 90, 205, 105]]<|/det|>
+## METHODS:  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 125, 215, 140]]<|/det|>
+## Participants.  
+
+<|ref|>text<|/ref|><|det|>[[115, 142, 883, 264]]<|/det|>
+Participants.Thirty- six participants (21 female; mean age = 23.69 yrs, range = 18 - 34 yrs) were enrolled in the experiment following procedures approved by the University of Oregon Institutional Review Board. All participants were right- handed native- English speakers with normal or corrected- to- normal vision, with no self- reported psychiatric or neurological disease. One participant was excluded due to excess motion in the scanner (max FD > 3.5 mm); another 4 participants were excluded due to low behavioral performance (see Results for more details). The final analysis included 31 participants. All participants received monetary compensation for participating.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 282, 177, 296]]<|/det|>
+## Stimuli.  
+
+<|ref|>text<|/ref|><|det|>[[115, 299, 883, 402]]<|/det|>
+Stimuli.Thirty- six images of scenes and 36 images of everyday objects were used in the experiment. The set of 36 scenes and the set of 36 objects were each comprised of 18 'pairmates' of visually and semantically similar images (Fig. 1a). An additional 36 scenes and 12 objects were used as lures for the scene and object exposure phases of the study, respectively. Separately for each participant, scene pairmates were randomly assigned to object pairmates (Fig. 1a). For example, if 'barn 1' was assigned to 'guitar 1', then 'barn 2' would be assigned to 'guitar 2.'  
+
+<|ref|>sub_title<|/ref|><|det|>[[116, 420, 308, 435]]<|/det|>
+## Experimental procedure.  
+
+<|ref|>text<|/ref|><|det|>[[115, 437, 883, 576]]<|/det|>
+Experimental procedure.After providing consent and reviewing the instructions, participants entered the MRI scanner. Inside the scanner, participants completed 6 rounds of the experimental paradigm (Fig. 1b). The first round and the last round included 4 phases: study, test, scene exposure (scanned), and object exposure (scanned). Rounds 2- 5 were the same, except they did not include the object exposure phase. Across all phases, stimuli were displayed on a grey background, projected from the back of the scanner. After exiting the scanner, participants completed a separate memory task that involved learning new scene- object associations (not reported here). The experiment was implemented in PsychoPy<sup>1</sup> and lasted approximately 3 hrs, with about 2 hrs 15 min inside the scanner.  
+
+<|ref|>text<|/ref|><|det|>[[115, 594, 883, 681]]<|/det|>
+Study Phase. During the study phases, participants learned 36 scene- object associations, one association at a time. Each trial began with the presentation of a scene image (1000 ms), followed by a white fixation cross (200 ms), the associated object image (1000 ms) and then another white fixation cross (1200 ms) until the start of the next trial. The order in which the 36 scene- object associations were studied was randomized for each round and for each participant.  
+
+<|ref|>text<|/ref|><|det|>[[115, 699, 883, 907]]<|/det|>
+Test Phase. During the test phases, participants attempted to retrieve the object associated with each of the 36 scenes. Each trial began with the presentation of a scene (1000 ms), followed by a white fixation cross (200 ms), and then the presentation of two object pairmates (e.g., 'Guitar 1' and 'Guitar 2'). One of the object images was the 'target' (i.e., the object associated with the cued scene) and the other object image was the 'competitor' (i.e., the object associated with the cued scene's pairmate). Participants had a maximum of 4000 ms to select the correct object image (target) via a button box in their right hand. If no response was made, the next trial began after a white fixation cross was displayed for 1200 ms. If a response was made, a confidence rating then appeared beneath the objects and participants had a maximum of 3000 ms to indicate whether their response was a "Guess" or "Sure." After indicating their confidence (or after time ran out), a white fixation cross appeared (1200 ms) until the start of the next trial. The location of the correct object (left or right) and the order in which each of the 36 scene- object associations were tested were randomized for each round and for each participant.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 106, 883, 298]]<|/det|>
+Scene Exposure Phase. During the scene exposure phases, which were conducted during fMRI scanning, participants saw 39 scene images in each of two blocks (78 scenes per round). Each block included the 36 studied scenes and 3 novel lure scenes. Participants made an old/new judgment for each scene. Each trial began with the presentation of a scene image (500 ms), followed by a red fixation cross (1500 ms) which represented the response window. Participants again responded using the button box. After the red fixation cross, a white fixation cross (2000 ms) was presented until the start of the next trial. The order of the 39 scene trials within each block was randomized for each block, round, and participant. Between the two blocks of 39 trials, participants performed a short odd/even judgment task (4 trials). Each odd/even trial consisted of a single-digit number displayed on the screen (500 ms), followed by a red fixation cross (1000 ms) which represented the response window, and then a white fixation cross (1000 ms) until the start of the next trial.  
+
+<|ref|>text<|/ref|><|det|>[[115, 315, 883, 384]]<|/det|>
+Object Exposure Phase. The object exposure phase (conducted during fMRI scanning) was only included in the first and sixth rounds and followed an identical structure and procedure as the scene exposure phase. The only difference was that the 39 trials in each block corresponded to the 36 studied objects and 3 novel lure objects.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 403, 243, 418]]<|/det|>
+## MRI acquisition.  
+
+<|ref|>text<|/ref|><|det|>[[113, 419, 883, 610]]<|/det|>
+All images were acquired on a Siemens 3T Skyra MRI system in the Lewis Center for Neuroimaging at the University of Oregon. Functional data were acquired with a T2\\*- weighted echo- planar imaging sequence with partial- brain coverage that prioritized full coverage of the hippocampus and early visual cortex (repetition time \(= 2000\) ms, echo time \(= 36\) ms, flip angle \(= 90^{\circ}\) , 72 slices, \(1.7\times 1.7\times 1.7\) mm voxels). A total of 8 functional scans were acquired. Each functional scan comprised 177 volumes and included 10 s of lead- in time and 10 s of lead- out time at the beginning and end of each scan, respectively. The 8 functional scans corresponded to 6 rounds of the scene exposure phase (scans 1 and 3- 7) and 2 rounds of the object exposure phase (scans 2 and 8). Anatomical scans included a whole- brain high- resolution T1- weighted magnetization prepared rapid acquisition gradient echo anatomical volume (1x1x1mm voxels) and a high- resolution (coronal direction) T2- weighted scan (0.43x0.43x2mm voxels) to facilitate segmentation of hippocampal subfields.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 630, 365, 645]]<|/det|>
+## Anatomical data preprocessing.  
+
+<|ref|>text<|/ref|><|det|>[[113, 646, 883, 837]]<|/det|>
+Preprocessing was performed using fMRIPrep 1.5.0 \(^{2,3}\) (RRID:SCR_016216), which is based on Nipype 1.2. \(^{2,4,5}\) (RRID:SCR_002502). The T1- weighted (T1w) image was corrected for intensity non- uniformity (INU) with N4BiasFieldCorrection \(^{6}\) (ANTS 2.2.0 \(^{7}\) , RRID:SCR_004757), and used as the T1w- reference throughout the workflow. The T1w- reference was skull- stripped with the antsBrainExtraction.sh workflow (ANTS) in Nipype, using OASIS30ANTS as target template. Brain tissue segmentation of cerebrospinal fluid (CSF), white- matter (WM) and gray- matter (GM) was performed on the brain- extracted T1w using fast \(^{8}\) (FSL 5.0.9, RRID:SCR_002823). Volume- based spatial normalization to one standard space (MNI152NLin2009cAsym) was performed through nonlinear registration with antsRegistration (ANTS 2.2.0), using brain- extracted versions of both T1w reference and the T1w template. ICBM 152 Nonlinear Asymmetrical template version 2009c \(^{9}\) (RRID:SCR_008796; TemplateFlow ID: MNI152NLin2009cAsym) was used for spatial normalization.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 856, 359, 871]]<|/det|>
+## Functional data preprocessing.  
+
+<|ref|>text<|/ref|><|det|>[[112, 873, 883, 907]]<|/det|>
+For each of the 8 BOLD scans per participant, the following preprocessing was performed. First, a reference volume and its skull- stripped version were generated using fMRIPrep. A deformation field to correct for
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[112, 88, 886, 299]]<|/det|>
+susceptibility distortions was estimated based on two echo- planar imaging (EPI) references with opposing phase- encoding directions, using 3dQuwarp, AFN10. Based on the estimated susceptibility distortion, an unwarped BOLD reference was calculated for a more accurate co- registration with the anatomical reference. The BOLD reference was then co- registered to the T1w reference using bbregister (FreeSurfer) which implements boundary- based registration11. Co- registration was configured with six degrees of freedom. Head- motion parameters with respect to the BOLD reference (transformation matrices, and six corresponding rotation and translation parameters) were estimated before any spatiotemporal filtering using mcfilt FSL \(5.0.9^{12}\) . BOLD scans were slice- time corrected using 3dTshift AFN10(RRID:SCR_005927). The BOLD time- series (including slice- timing correction when applied) were resampled onto their original, native space by applying a single, composite transform to correct for head- motion and susceptibility distortions. Framewise displacement (FD) confounding time- series were calculated based on the resampled BOLD time- series for each functional scan13.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 315, 523, 331]]<|/det|>
+## fMRI first-level general linear model (GLM) analyses.  
+
+<|ref|>text<|/ref|><|det|>[[113, 333, 884, 560]]<|/det|>
+After fMRIPrep preprocessing, the first 5 volumes (10 s) of each functional scan were discarded. Then, the brain mask generated by fMRIPrep from the T1 anatomical image was used to perform brain extraction for each of the 8 functional scans. Each functional scan was then median centered. For the 6 scans of the scene exposure phase and 2 scans of the object exposure phase, all first level GLMs were performed in participants' native space with FSL using a Double- Gamma HRF with temporal derivatives, implemented with Nipype. GLMs were calculated using a variation of the Least Squares – Separate method14: a separate GLM was calculated for each of the 36 scenes (for scene exposure phases) or objects (for object exposure phases) across both repeats within a scan. For each GLM, there was one regressor of interest (representing a single scene or object image across its two repetitions per scan). All other trials (including lure images), framewise displacement, xyz translation and xyz rotation were represented with nuisance regressors. Additionally, a high pass filter (128 Hz) was applied for each GLM. This model resulted in 36 beta- maps per scan (one map per scene/object) which were converted to t- maps that represented the pattern of activity elicited by each scene/object for each scan.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 578, 269, 593]]<|/det|>
+## Regions of interest.  
+
+<|ref|>text<|/ref|><|det|>[[112, 594, 884, 909]]<|/det|>
+A region of interest (ROI) for early visual cortex (EVC) was created from the probabilistic maps of Visual Topography15 in the MNI space with a 0.5 threshold. This ROI was transformed into each participant's native space using inverse T1w- to- MNI non- linear transformation. For each participant, the top 300 EVC voxels were then selected by averaging the t- maps of all scenes and objects and then choosing the voxels with the highest t- statistics (i.e., the voxels most responsive to visual stimuli). An ROI for the parahippocampal place area (PPA) was created by first using an automated meta- analysis in Neurosynth with the key term "place". Then, clusters were created using voxels with a z- score \(>2\) based on the Neurosynth associative tests. Since these clusters were generated through an automated meta- analysis and were not anatomically exclusive to PPA, we visually inspected the results and manually selected the two largest clusters that were spatially consistent with PPA. One cluster was in the right hemisphere (voxel size \(= 247\) ) and one cluster was in the left hemisphere (voxel size \(= 163\) ). These clusters were combined into a single PPA mask. This mask was then transformed into each participant's native space using the inverse T1w- to- MNI transformation. For each participant, a final PPA ROI was generated by averaging the t- maps of all scene exposure phase scans and then selecting the 300 voxels with the highest average t- statistics (i.e., the most scene- responsive voxels). To create hippocampal ROIs, we used the Automatic Segmentation of Hippocampal Subfields (ASHS)16 toolbox with the upenn2017 atlas to generate subfield ROIs in each participant's hippocampal body, including CA23DG—the combination of CA2, CA3 and dentate gyrus—and CA1. The most anterior and posterior slices of the hippocampal body were manually
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 88, 884, 177]]<|/det|>
+determined for each participant based on the T2- weighted anatomical structure. Each participant's subfield segmentations were also manually inspected to ensure accuracy of the segmentation protocol. Then, each subfield ROI was transformed into each participant's native space using the T2- to- T1w transformation, calculated with FLIRT (fsl) with 6 degrees of freedom, implemented with Nipype. All ROIs were again visually inspected following the transformation to native space to ensure the ROIs were anatomically correct.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 195, 366, 210]]<|/det|>
+## fMRI pattern similarity analyses.  
+
+<|ref|>text<|/ref|><|det|>[[113, 211, 884, 384]]<|/det|>
+Pairmate Similarity Scores. Pattern similarity was calculated as the Fisher z- transformed Pearson correlation between \(t\) - maps within each ROI. All pattern similarity analyses were performed by correlating the \(t\) - maps for stimuli across scans (i.e., correlations were never performed within the same scan). For our primary analyses related to pattern similarity between scene images, of critical interest was mean similarity between pairmate scenes (pairmate similarity) relative to mean similarity between non- pairmate scenes (non- pairmate similarity). For example, the correlation between the \(t\) - maps for 'barn 1' from scan 3 and 'barn 2' from scan 4 would reflect pairmate similarity, whereas the correlation between the \(t\) - maps for 'barn 1' from scan 3 and 'airplane 2' from scan 4 would reflect non- pairmate similarity. We then calculated the mean difference between pairmate similarity and non- pairmate similarity, which we refer to as the pairmate similarity score.  
+
+<|ref|>text<|/ref|><|det|>[[113, 402, 884, 524]]<|/det|>
+Learned Round. To relate pairmate similarity scores to behavioral measures of learning, we identified the Learned Round (LR) for each pairmate, separately for each participant. The LR was based on performance in the associative memory test. Specifically, the LR was defined as the first round in which the target object was selected with high confidence for both scenes in a pairmate, with the additional requirement that performance remained stable in all subsequent rounds. It was therefore possible that both scenes in a pairmate were associated with high confidence correct responses in round N, not in round N+1, and then (again) in round N+2 and thereafter; in this case, the LR would be round N+2.  
+
+<|ref|>text<|/ref|><|det|>[[112, 541, 884, 800]]<|/det|>
+Inflection Point. The inflection point (IP) was defined as the transition from LR - 1 to LR (i.e., the transition from 'pre- learned' to 'learned'). Thus, pattern similarity analyses of the IP refer to the correlation of \(t\) - maps from LR- 1 to \(t\) - maps from LR. We hypothesized that the behavioral state change from LR- 1 to LR would correspond to a reduction in pattern similarity between pairmates. Pattern similarity analyses at the IP were contrasted against the 'pre- IP' state, which was based on the correlation of \(t\) - maps from LR- 2 and LR- 1 (i.e., a non- transition from 'not learned' to 'not learned') (Fig. 2c). Pairmates for which participants never reached and sustained high- confidence correct responses (mean \(\pm \mathrm{s.d.}\) , \(1.81 \pm 2.27\) per participant) and pairmates that were learned in the \(1^{\text{st}}\) round (LR = 1; mean \(\pm \mathrm{s.d.}\) , \(1.00 \pm 1.26\) ) were excluded from the IP analysis because neither the pre- IP nor IP states could be measured. For pairmates that were learned in the \(2^{\text{nd}}\) round (LR = 2; mean \(\pm \mathrm{s.d.}\) , \(3.23 \pm 2.80\) ), pattern similarity at the IP was calculated and included in the analyses, but pattern similarity at the pre- IP state could not be calculated because an LR - 2 did not exist. For rest of the pairmates (LR = 3, 4, 5, or 6), we calculated pattern similarity for both pre- IP and IP (Fig. 1e). Similar restrictions applied to correlations between LR and LR- 3, LR + 1, LR + 2, and LR + 3 (Fig. 2e). The number of pairmates included in each comparison and for each participant are reported in Supplementary Table 1.  
+
+<|ref|>text<|/ref|><|det|>[[113, 821, 883, 907]]<|/det|>
+Representational Structure Across Time Points. To test whether representational overlap triggered remapping (related to Fig. 3), the 6 learning rounds were translated into 5 timepoints. Each timepoint corresponded to a pair of consecutive learning rounds ([1,2], [2,3], [3,4], [4,5], [5,6]). For each timepoint, pairmate similarity scores were calculated, as described above, by correlating activity patterns from consecutive learning rounds (e.g., pairmate similarity scores at timepoint 1 were based on correlations
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[112, 89, 884, 350]]<|/det|>
+between round 1 and round 2). This yielded a set of pairmate similarity scores at each of the 5 timepoints. These sets of similarity scores reflected the representational structure at each timepoint (i.e., which pairmates were relatively similar and which pairmates were relatively dissimilar). Pairmate similarity scores were then correlated across timepoints using Spearman's rank correlation (Fisher \(z\) transformed). Lag 1 correlations refer to rank correlations between successive timepoints whereas lag 2 correlations refer to correlations between timepoints two steps apart. To facilitate a direct comparison between lag 1 vs. lag 2 correlations, correlations were computed for the following timepoints: Lag \(1 = r\) (timepoint 1, 2), \(r\) (timepoint 2, 3), \(r\) (timepoint 3, 4); Lag \(2 = r\) (timepoint 1, 3), \(r\) (timepoint 2, 4), \(r\) (timepoint 3, 5). It is important to emphasize that we did not correlate initial pairmate similarity scores with the change in pairmate similarity as this would produce an artifactual correlation (via regression to the mean). In contrast, a negative rank correlation (as we observed in CA23DG) cannot be explained by regression to the mean. Mathematically, if all values at timepoint N partially regressed toward the mean at timepoint \(\mathsf{N} + 1\) , this would yield a positive rank correlation (i.e., representational structure would be partially preserved). If all values fully regressed toward the mean (i.e., variance at timepoint \(\mathsf{N} + 1 = 0\) ), this would yield a null correlation ( \(r = 0\) ; representational structure fully abolished).  
+
+<|ref|>text<|/ref|><|det|>[[113, 367, 884, 558]]<|/det|>
+Scene- Object Similarity. To calculate pattern similarity between scenes and objects (related to Fig. 4), activation patterns for objects were first generated by averaging \(t\) - maps across the two object exposure phases, resulting in a single, mean activity pattern for each object. These object- specific activity patterns were then correlated with activity patterns from the scene exposure phases at LR - 1 (i.e., the pre- learned state) and LR (i.e., the learned state). Correlations were separated into three groups: (1) target correlations refer to the correlation between a scene and the object it was associated with during the study phase (e.g., 'barn 1' and 'guitar 1'), (2) competitor correlations refer to the correlation between a scene and the object that was associated with that scene's pairmate during the study phase (e.g., 'barn 1' and 'guitar 2'), and (3) across pairmate correlations refer to correlations between a scene and an object that was not associated with that scene or its pairmate during the study phase (e.g., 'barn 1' and 'scissors 1'). Target and competitor correlations were expressed relative to across pairmate correlations.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 578, 197, 592]]<|/det|>
+## Statistics.  
+
+<|ref|>text<|/ref|><|det|>[[115, 594, 884, 750]]<|/det|>
+To compare pairmate similarity scores and other measures across ROIs and learning states, repeated measures ANOVAs and paired- samples \(t\) - tests were used. To test whether pairmate similarity scores and other measures were significantly positive or negative (i.e., above/below 0), one- sample \(t\) - tests were used. To test whether the negative pairmate similarity score observed in CA23DG at the inflection point depended on the specific mapping between behavioral and fMRI measures, we randomly shuffled the mapping between the behavioral inflection point and scene pairmate, within each participant (see Fig. 1d), and then computed the group- level mean pairmate similarity score at the permuted inflection point. This was repeated 1,000 times, producing a distribution of 1,000 permuted means. The observed pairmate similarity score at the inflection point was then compared against this distribution of permuted means.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 770, 247, 785]]<|/det|>
+## Data Availability.  
+
+<|ref|>text<|/ref|><|det|>[[115, 787, 884, 820]]<|/det|>
+The data that support the findings of this study are available from the corresponding author upon reasonable request.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[115, 88, 322, 106]]<|/det|>
+## METHODS REFERENCES:  
+
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+1. Peirce, J. et al. PsychoPy2: Experiments in behavior made easy. Behav. Res. Methods 51, 195-203 (2019).  
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+2. Esteban, O. et al. fMRIPrep: a robust preprocessing pipeline for functional MRI. Nat. Methods 16, 111-116 (2019).  
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+3. Esteban, Oscar, Ross Blair, Christopher J. Markiewicz, Shoshana L. Berleant, Craig Moodie, Feilong Ma, Ayse Ilkay Isik, et al. 2018. "FMRIPrep." Software.  
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+Zenodo. https://doi.org/10.5281/zenodo.852659.  
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+9. Fonov, V., Evans, A., McKinstry, R., Almli, C. & Collins, D. Unbiased nonlinear average age-appropriate brain templates from birth to adulthood. NeuroImage 47, S102 (2009).  
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+10. Cox, R. W. & Hyde, J. S. Software tools for analysis and visualization of fMRI data. NMR Biomed. 10, 171-178 (1997).  
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+11. Greve, D. N. & Fischl, B. Accurate and robust brain image alignment using boundary-based registration. NeuroImage 48, 63-72 (2009).
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[55, 87, 880, 450]]<|/det|>
+12. Jenkinson, M., Bannister, P., Brady, M. & Smith, S. Improved Optimization for the Robust and Accurate Linear Registration and Motion Correction of Brain Images. \*Neurolmage\* 17, 825–841 (2002).  
+13. Power, J. D. \*et al.\* Methods to detect, characterize, and remove motion artifact in resting state fMRI. \*Neurolmage\* 84, 320–341 (2014).  
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+15. Wang, L., Mruczek, R. E. B., Arcaro, M. J. & Kastner, S. Probabilistic Maps of Visual Topography in Human Cortex. \*Cereb. Cortex N. Y. N\* 1991 25, 3911–3931 (2015).  
+16. Yushkevich, P. A. \*et al.\* Automated volumetry and regional thickness analysis of hippocampal subfields and medial temporal cortical structures in mild cognitive impairment. \*Hum. Brain Mapp.\* 36, 258–287 (2015).
+
+<--- Page Split --->
+<|ref|>table<|/ref|><|det|>[[115, 115, 840, 790]]<|/det|>
+<|ref|>table_caption<|/ref|><|det|>[[115, 90, 330, 106]]<|/det|>
+Supplementary information   
+
+<table><tr><td>Round Participant #</td><td>1</td><td>2</td><td>3</td><td>4</td><td>5</td><td>6</td><td>Never Learned</td></tr><tr><td>1</td><td>1</td><td>7</td><td>6</td><td>4</td><td>0</td><td>0</td><td>0</td></tr><tr><td>2</td><td>1</td><td>1</td><td>4</td><td>4</td><td>6</td><td>2</td><td>0</td></tr><tr><td>3</td><td>1</td><td>7</td><td>5</td><td>5</td><td>0</td><td>0</td><td>0</td></tr><tr><td>4</td><td>0</td><td>3</td><td>0</td><td>5</td><td>4</td><td>3</td><td>3</td></tr><tr><td>5</td><td>0</td><td>2</td><td>3</td><td>6</td><td>4</td><td>2</td><td>1</td></tr><tr><td>6</td><td>3</td><td>6</td><td>2</td><td>6</td><td>0</td><td>1</td><td>0</td></tr><tr><td>7</td><td>0</td><td>6</td><td>4</td><td>3</td><td>3</td><td>1</td><td>1</td></tr><tr><td>8</td><td>0</td><td>2</td><td>5</td><td>4</td><td>5</td><td>1</td><td>1</td></tr><tr><td>9</td><td>0</td><td>1</td><td>1</td><td>2</td><td>2</td><td>2</td><td>10</td></tr><tr><td>10</td><td>0</td><td>0</td><td>8</td><td>2</td><td>5</td><td>2</td><td>1</td></tr><tr><td>11</td><td>3</td><td>3</td><td>4</td><td>3</td><td>2</td><td>2</td><td>1</td></tr><tr><td>12</td><td>0</td><td>1</td><td>2</td><td>5</td><td>2</td><td>5</td><td>3</td></tr><tr><td>13</td><td>1</td><td>1</td><td>2</td><td>4</td><td>7</td><td>2</td><td>1</td></tr><tr><td>14</td><td>0</td><td>0</td><td>3</td><td>4</td><td>4</td><td>5</td><td>2</td></tr><tr><td>15</td><td>1</td><td>6</td><td>7</td><td>2</td><td>1</td><td>1</td><td>0</td></tr><tr><td>16</td><td>1</td><td>2</td><td>6</td><td>1</td><td>2</td><td>4</td><td>2</td></tr><tr><td>17</td><td>2</td><td>3</td><td>3</td><td>5</td><td>3</td><td>2</td><td>0</td></tr><tr><td>18</td><td>5</td><td>3</td><td>2</td><td>3</td><td>4</td><td>0</td><td>1</td></tr><tr><td>19</td><td>0</td><td>0</td><td>2</td><td>7</td><td>6</td><td>2</td><td>1</td></tr><tr><td>20</td><td>0</td><td>1</td><td>6</td><td>2</td><td>1</td><td>4</td><td>4</td></tr><tr><td>21</td><td>0</td><td>1</td><td>3</td><td>3</td><td>4</td><td>7</td><td>0</td></tr><tr><td>22</td><td>1</td><td>3</td><td>4</td><td>2</td><td>3</td><td>1</td><td>4</td></tr><tr><td>23</td><td>0</td><td>6</td><td>5</td><td>4</td><td>1</td><td>2</td><td>0</td></tr><tr><td>24</td><td>3</td><td>4</td><td>7</td><td>1</td><td>2</td><td>1</td><td>0</td></tr><tr><td>25</td><td>1</td><td>10</td><td>4</td><td>3</td><td>0</td><td>0</td><td>0</td></tr><tr><td>26</td><td>0</td><td>0</td><td>2</td><td>9</td><td>2</td><td>1</td><td>4</td></tr><tr><td>27</td><td>3</td><td>0</td><td>4</td><td>2</td><td>2</td><td>1</td><td>6</td></tr><tr><td>28</td><td>1</td><td>8</td><td>4</td><td>3</td><td>0</td><td>0</td><td>2</td></tr><tr><td>29</td><td>0</td><td>6</td><td>2</td><td>1</td><td>1</td><td>2</td><td>6</td></tr><tr><td>30</td><td>2</td><td>6</td><td>6</td><td>1</td><td>0</td><td>2</td><td>1</td></tr><tr><td>31</td><td>1</td><td>1</td><td>3</td><td>6</td><td>3</td><td>3</td><td>1</td></tr></table>
+
+<|ref|>table_footnote<|/ref|><|det|>[[114, 802, 883, 850]]<|/det|>
+Table1. Number of pairmates that transitioned to learned round (LR') status, for each participant and each round. Note: pairmates that were learned in the first round or never learned were excluded from fMRI analyses.
+
+<--- Page Split --->

preprint/preprint__c9ff0cf38f21140158e1e895d08bf348ed7b4eac2e17e9d21e2f08be816d80ef/images_list.json

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+    "type": "image",
+    "img_path": "images/Figure_1.jpg",
+    "caption": "Fig. 1: (a) Schematic experimental setup for AXL characterization with X-ray mirror (VKB) used at Test Beamline B16 Diamond. Equal lateral shift of structure-A and structure-B in the opposite direction provides parabolic concave (b) and parabolic convex (c) shaped Alvarez lens that changes the effective focal length \\(\\Delta q_{ho}^{\\prime}\\) of two focusing optics up or down-stream to the focal plane of the second focusing element VKB (black dashed line).",
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+  {
+    "type": "image",
+    "img_path": "images/Figure_2.jpg",
+    "caption": "Fig. 2: Calibration curves of AXL1 and AXL2 for HKB. The parabolic coefficients were calculated from each measured wavefront as a function of the lateral shift of the structures over a range of \\(\\pm 24 \\mu \\mathrm{m}\\) . When the parabolic coefficient of the measured wavefront is zero the two sub-elements of AXL are aligned to each other.",
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+    "img_path": "images/Figure_3.jpg",
+    "caption": "Fig. 3: Change in the parabolic coefficient of the outgoing wavefield of HKB with and without Alvarez X-ray lens measured at different knife-edge positions around \\(1 \\text{mm}\\) of HKB's focal length. The role of the AXL is apparent in keeping defocus term of the mirror constant which is otherwise varying linearly in its focal plane.",
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+    "caption": "Fig. 4: HKB beam caustics after numerical propagation of the measured complex field to the intended focal positions of (a) HKB at 125 mm (b) HKB with AXL at 125 mm, (c) and (d) HKB with AXL at 125 mm \\(\\mp 1\\) mm, after lateral shifts of AXL sub-elements \\(\\Delta = \\mp 34\\mu m\\) and \\(\\Delta = \\pm 34\\mu m\\) respectively.",
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+    "img_path": "images/Figure_5.jpg",
+    "caption": "Figure 5: VKB beam caustics after numerical propagation of the measured complex field to the focal position at \\(235\\mathrm{mm}\\) (a), \\(232.4\\mathrm{mm}\\) (b), and focus beam profiles of VKB without AXL at two different focal distances and with AXL at \\(232.4\\mathrm{mm}\\) (c).",
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preprint/preprint__c9ff0cf38f21140158e1e895d08bf348ed7b4eac2e17e9d21e2f08be816d80ef/preprint__c9ff0cf38f21140158e1e895d08bf348ed7b4eac2e17e9d21e2f08be816d80ef.mmd

@@ -0,0 +1,245 @@
+
+# Alvarez varifocal X-ray lens  
+
+Vishal Dhamgaye ( \(\boxed{ \begin{array}{r l} \end{array} }\) vishal.dhamgaye@diamond.ac.uk) Diamond Light Source https://orcid.org/0000- 0002- 4919- 8957  
+
+David Laundy Diamond Light Source  
+
+Thomas Moxham Diamond Light Source  
+
+Sara Baldock Lancaster University https://orcid.org/0000- 0001- 9635- 7757  
+
+Hossein Khosroabadi Diamond Light Source  
+
+Oliver Fox Diamond Light Source  
+
+Kawal Sawhney Diamond Light Source  
+
+Article  
+
+Keywords:  
+
+Posted Date: July 19th, 2022  
+
+DOI: https://doi.org/10.21203/rs.3.rs- 1825147/v1  
+
+License: © This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License
+
+<--- Page Split --->
+
+## Alvarez varifocal X-ray lens  
+
+Vishal Dhamgaye \(^{1,2*}\) , David Laundy \(^{1}\) , Thomas Moxham \(^{1,3}\) , Sara Baldock \(^{4}\) , Hossein Khosroabadi \(^{1}\) , Oliver Fox \(^{1}\) & Kawal Sawhney \(^{1}\)  
+
+\(^{1}\) Diamond Light Source, Harwell Science and Innovation Campus, Didcot, Oxon. OX11 0DE, UK \(^{2}\) Synchrotron Utilisation Section, Raja Ramanna Centre for Advanced Technology, Indore, India \(^{3}\) Department of Engineering Science, University of Oxford, Parks Road, Oxford, Oxon. OX1 3PJ, UK \(^{4}\) Department of Chemistry, Lancaster University, Lancaster, LA1 4YB, UK  
+
+\*Corresponding Authors: vishal.dhamgaye@diamond.ac.uk  
+
+## Abstract  
+
+In the X- ray region, there exist optical elements analogous to lenses and mirrors for visible light. For visible light, a variable focusing power can be achieved by Alvarez lenses which consist of a pair of inline planar refractors with a cubic thickness profile, which when laterally displaced in opposite directions result in a parabolic component to the wavefront. This paper reports an implementation of this concept for X- rays using two planar microfabricated refractive elements which when used in conjunction with an elliptical mirror focusing system allowed the focal plane to be moved by up to 2 mm with high precision and within milli- seconds. The study presents the first working proof of an Alvarez lens for the adaptive correction of astigmatism and defocus aberrations of X- ray optics.
+
+<--- Page Split --->
+
+## Introduction  
+
+Major synchrotron facilities have done or are planning upgrades to reduce the source emittance and to thereby increase the X- ray's brightness and coherence to new levels [1]. X- ray optics is used to image the X- ray source onto a sample for a variety of experiments. Advances in the manufacturing of optical elements have pushed X- ray beam focusing to achieve diffraction- limited focus sizes at these facilities enabling a range of scientific applications [2, 3]. The key to exploiting this is the high stability of the optics, precise alignment of the optics, and then measurement and correction of the X- ray wavefront for errors caused by imperfections in the optics [4]. A major effort has been put into the correction of the X- ray wavefront using reflective or refractive corrective optics [5, 6, 7]. The corrective optics either requires measurement of the wavefront and then the design of a custom optical element or else the corrective optics is adaptable [8] in which case the correction can be varied in some way to best compensate for the wavefront error.  
+
+Astigmatism is an aberration that occurs when the optical system is not symmetrical about the optical axis and the focal plane position is different for focusing in two orthogonal planes. Defocus aberration occurs when the sample position is displaced longitudinally along the optical axis from the focal plane. Both prevent the optics from realizing the diffracted- limited spatial resolution. These aberrations in the X- ray focusing system can be caused by misalignment of the optics and by fabrication errors in the optics. In the case of Kirkpatrick- Baez (KB) mirror systems [9] which consist of two elliptical mirrors, independently focusing in horizontal and vertical directions, astigmatism can occur due to a mispositioning of either mirror along the optical axis or by an error in the setting of the pitch angle of either mirror. In the case of compound X- ray refractive lens (CRL), astigmatism may be introduced by the fabrication process causing error in the lens thickness, mispositioning of individual lenses from the axis, or angular misalignment of the stack of lenses [10]. Defocus aberration can be corrected by translating the sample to the correct focal plane but in practice, this may be difficult due to the constraints of complex sample environments. In addition, for CRLs, a change in the X- ray
+
+<--- Page Split --->
+
+energy results in a change to the lens focusing power which translates the focal plane along Z direction. To compensate for these effects, it would be advantageous to be able to have a simple method to be able to adjust the longitudinal position of the focal plane for beamline optics.  
+
+Control over the focal plane position has been shown using lens- based transfacators which work by translating individual lenses into a CRL lens stack to change the focal length in discrete steps [11, 12, 13] and zoom optics using multiple bendable elliptical mirrors [14, 15]. It is however challenging to achieve a precise continuous focal length variation of an optic. We propose a simple adaptive X- ray optics based on the Alvarez varifocal lens [16, 17] that could be used to independently change the focusing and focal distance in two orthogonal directions. The principle and design of the Alvarez X- ray lens (AXL) are described in the Methods section. It allows compensation of astigmatism and defocus aberrations present in any X- ray optical system. To demonstrate this, an AXL was fabricated and mounted in front of a KB mirror pair consisting of a vertically focusing elliptical mirror (VKB) of focal length 235 mm and a horizontally focusing elliptical mirror (HKB) of focal length 125 mm. Measurements show that the AXL gave fine control over the focal length of the HKB and the VKB with a range of \(\pm 1\mathrm{mm}\) . Two AXLs mounted at right angles, therefore, provided a variable focal length in two orthogonal directions allowing correction for astigmatism and defocus aberrations.  
+
+## Results  
+
+Nanoprobe based experiments are challenging to perform at the Synchrotron beamlines. The outcome of such an experiment is strongly dependent on the stability of the optics causing a broadening of the probe at the sample plane and it is difficult to achieve a diffraction- limited two- dimensional focused beam at a common focal plane due to astigmatism present in the optics. An X- ray Alvarez lens was used to dynamically correct the astigmatism and defocus aberrations of a KB mirror system. The optical sub- elements of the Alvarez X- ray lens were printed by two- photon polymerisation 3D printing technology. A hybrid optics consisting of an AXL (Structure- A and Structure- B) and a
+
+<--- Page Split --->
+
+KB mirror system was installed at the B16 Test beamline of Diamond Light Source and the experimental setup is shown in Fig. 1. The proof of the working principle of AXL was carried out using monochromatic X- rays from a Si (111) double crystal monochromator. The VKB and HKB were aligned using the knife- edge method [8] to optimise the mirror pitch angles \((\theta)\) and to locate the focal plane position (Z). In order to demonstrate AXL performance, the outgoing X- ray wavefronts of KB mirror were measured at a range of lateral positions of AXL's sub- elements and the change in the parabolic coefficient of the wavefront was evaluated.  
+
+![](images/Figure_1.jpg)
+
+<center>Fig. 1: (a) Schematic experimental setup for AXL characterization with X-ray mirror (VKB) used at Test Beamline B16 Diamond. Equal lateral shift of structure-A and structure-B in the opposite direction provides parabolic concave (b) and parabolic convex (c) shaped Alvarez lens that changes the effective focal length \(\Delta q_{ho}^{\prime}\) of two focusing optics up or down-stream to the focal plane of the second focusing element VKB (black dashed line). </center>
+
+<--- Page Split --->
+
+## Calibration of Alvarez X-ray lens  
+
+If there is no lateral shift between the sub- elements of the AXL, the AXL provides a constant phase shift across the mirror aperture and the focal length of the mirror remains unchanged. When structure- A is laterally moved by distance \(- \Delta\) and structure- B by an equal amount but in the opposite direction, \(+ \Delta\) , a concave phase profile is introduced which generates a parabolic contribution to the wavefront that reduces the mirror focal length (Fig. 1b). An increase in the focal length was observed in the case of opposite lateral shifting; \(+ \Delta\) shift for structure- A and \(- \Delta\) shift for structure- B (Fig. 1c). Figure 2 shows the calibration curves of AXL1 and AXL2 at 15 keV energy for the HKB when the AXL sub- elements were laterally shifted by a 4 \(\mu \mathrm{m}\) step and for a wavefront measured at the fixed focal plane 125 mm from the HKB. The resultant focal distance variation of 29.2 \(\mu \mathrm{m}\) and 55.5 \(\mu \mathrm{m}\) was obtained for a 1 \(\mu \mathrm{m}\) lateral shift in AXL1 and AXL2 respectively. In the present study, a minimum focal plane variation of \(\sim 0.29 \mu \mathrm{m}\) was achieved for a lateral shifting of 10 nm which is close to the movement resolution of the nano- positioning stage. Thus, the change in the focal plane was smaller than the focused beam FWHM 0.45 \(\mu \mathrm{m}\) (dominated by bending magnet source size) of the HKB which makes the Alvarez lens a promising optics for fine control of the focal plane position. Precision control of the focal length can therefore be engineered into the optics by appropriately choosing the AXL design parameters (equation 5). The calculated parabolic components shown in Fig. 2, agree well with the experimental values in case of the smaller lateral shifts and the difference between them increases linearly as shifting is increased. An error of \(\sim 6\%\) and \(\sim 12\%\) was observed between calculated and measured values for AXL1 and AXL2 respectively. This deviation may be due to the density difference of the deposited material and/or fabrication artifacts. The higher the structure thickness of optical elements (see Fig. S2), the higher the fabrication errors. Therefore, AXL1 performance was better compared to the AXL2 as more blocks were printed in the latter's optical elements. The fabrication error may be improved in the next fabrication cycle or using an alternate microfabrication technique such as X- ray lithography.
+
+<--- Page Split --->
+![](images/Figure_2.jpg)
+
+<center>Fig. 2: Calibration curves of AXL1 and AXL2 for HKB. The parabolic coefficients were calculated from each measured wavefront as a function of the lateral shift of the structures over a range of \(\pm 24 \mu \mathrm{m}\) . When the parabolic coefficient of the measured wavefront is zero the two sub-elements of AXL are aligned to each other. </center>  
+
+## Correction of astigmatism in the two elliptical mirrors  
+
+KB mirrors show astigmatism, presenting two different focal distances in the two orthogonal focusing directions. Astigmatism may be caused by mis- setting of the mirror pitch angles or an error in the relative positioning of the mirrors in the longitudinal (Z) direction. Despite better mirror alignment achieved through wavefront measurements in the present study, the focal plane of HKB was found \(\sim 700 \mu \mathrm{m}\) upstream compared to the VKB focal plane, which is probably caused by longitudinal mispositioning of the two mirrors in the mirror vessel. KB mirrors are sensitive to slow drifts, particularly changes in incidence angles at the \(\mu \mathrm{rad}\) level which change the focus position along the optical axis. In the previous section, we demonstrated that the focal plane of a mirror can be changed by an AXL. In order to demonstrate the role of AXL in achieving a change in the focal length of a mirror, X- ray wavefronts were measured at different planes with and without the AXL. The required lateral
+
+<--- Page Split --->
+
+movements of the AXL sub-elements were obtained from the calibration curves (Fig. 2). The AXL was adaptively tuned to bring the defocused beam to the focus at various focal planes that were a few hundred microns apart. Figure 3 shows the variation of the parabolic coefficients of the wavefronts measured at different knife- edge Z positions, around the focal plane of the HKB (125mm). The focal length of the HKB was adjusted by AXL1 and AXL2, on the fly, over a 2 mm distance. A focus plane variation using an AXL takes only a few milli- seconds as the speed of the nano positioning stage was about 4.5 mm/sec. Movement of the AXL1 elements from 0 \(\mu \mathrm{m}\) to 34 \(\mu \mathrm{m}\) took a time of 7.5 ms and gave a 1 mm focus distance variation and there was no settling time needed to achieve the stability. The numerical aperture of the AXL is small compared to the X- ray mirror, thus it does not significantly change the mirror numerical aperture. Figure 4 shows the beam caustics obtained by numerical propagation of the complex field obtained from the measured wavefronts at longitudinal position through the focus (Fig. 4 (a)). The wavefront error of the HKB has defocus aberration which is improved after the introduction of AXL (Fig. 4(b)). The wavefield intensities at focal lengths 124 mm (Fig. 4(c)) and 126 mm (Fig. 4(d)) show the good quantitative agreement with the focus variation made by AXL1. The Alvarez lenses were then mounted in the \(90^{\circ}\) rotated platform for their optical characterisation with the VKB. This study was performed at 13 keV X- ray energy. Again, the lateral translation of the AXL elements at 13 keV were determined from the calibration curve of AXL2. The focus plane of VKB could be moved by up to 3 mm upstream or downstream of its designed focal length (235 mm). The beam caustics calculated from the measured wavefronts are shown in Fig. 5 for the VKB without and with AXL2. AXL2 has improved the focus at 232.4 mm (Fig. 5(c)). Thus, independent focal plane movements of the VKB and HKB is possible to remove astigmatism in their dispersion planes.
+
+<--- Page Split --->
+![](images/Figure_3.jpg)
+
+<center>Fig. 3: Change in the parabolic coefficient of the outgoing wavefield of HKB with and without Alvarez X-ray lens measured at different knife-edge positions around \(1 \text{mm}\) of HKB's focal length. The role of the AXL is apparent in keeping defocus term of the mirror constant which is otherwise varying linearly in its focal plane. </center>  
+
+An AXL may be used to adjust the probe position for minimum beam size to give optimum real and reciprocal space sampling in ptychography experiments which otherwise requires movement of the object along the beam direction [18]. Scanning converging to diverging wavefronts by an AXL may also be able to solve the phase curvature problem in Coherent diffraction X- ray imaging by differentiating the phase signal from either sample or probe [19]. An Alvarez lens may be useful to employ in the wider X- ray energy range with achromatic KB mirrors, however, the AXL is chromatic as its focal length is an inverse function of \(\delta\) which changes with the X- ray energy. A recalibration of the AXL is therefore required after a change of the incident energy. The achievable focus variation is limited by X- ray absorption which increases with thicker AXL structures. It is planned to make 2- dimensional varifocal X- ray lenses based on Alvarez and Lohmann lenses [20].
+
+<--- Page Split --->
+![](images/Figure_4.jpg)
+
+<center>Fig. 4: HKB beam caustics after numerical propagation of the measured complex field to the intended focal positions of (a) HKB at 125 mm (b) HKB with AXL at 125 mm, (c) and (d) HKB with AXL at 125 mm \(\mp 1\) mm, after lateral shifts of AXL sub-elements \(\Delta = \mp 34\mu m\) and \(\Delta = \pm 34\mu m\) respectively. </center>
+
+<--- Page Split --->
+![](images/Figure_5.jpg)
+  
+
+![PLACEHOLDER_10_1]
+
+<center>Figure 5: VKB beam caustics after numerical propagation of the measured complex field to the focal position at \(235\mathrm{mm}\) (a), \(232.4\mathrm{mm}\) (b), and focus beam profiles of VKB without AXL at two different focal distances and with AXL at \(232.4\mathrm{mm}\) (c). </center>
+
+<--- Page Split --->
+
+## Discussion/Conclusion  
+
+We have successfully developed and demonstrated Alvarez X- ray lenses for fine control of the focal length of elliptical mirrors (KB mirror system) over a range of \(\pm 1 \text{mm}\) . The optics focal length was varied on the fly in less than one second. The AXL enabled an approximately constant focus beam size along with a variable image distance which means a large depth of field optics which is otherwise impossible to achieve in a highly de- magnified optical system. The AXL does have chromatic aberration, however, adaptive tuning allows chromatic aberrations to be removed, thus allowing its working over a wide energy range compared to the working energy range reported for an X- ray Achromat [21]. This study report for the first time the implementation of Alvarez lens in the X- ray region for an adaptive correction of the astigmatism aberration in a two- mirror system. The AXL can adaptively change the focal length in wider energy range of focusing optics based on reflective, refractive, and diffractive methods. The focal tuning by AXL can be increased or decreased by choosing appropriate design parameters. The AXL is expected to be beneficial for a range of experiments performed with X- rays, including but not limited to, in- situ nanoprobe experiments without disturbing the sample position, engineering wavefront curvatures for X- ray imaging, experiments requiring a large depth of field and removal of chromatic aberration. The AXL optics is small in footprint, easy to align, does not change optics axis and is quick in achieving precise axial focus variation that makes it a practical device on existing beamlines. Improvement in astigmatism of focusing elements will enable achieving a round nanobeam at the diffraction- limited storage rings. This new optics has the potential to profoundly change and improve the quality of nanoprobe or microprobe X- ray experiments at the Synchrotron radiation and XFEL facilities and aid novel scientific discoveries in a wide range of disciplines.
+
+<--- Page Split --->
+
+## Methods  
+
+## Design  
+
+AXL presented here consists of a pair of refractive optical elements named structure- A and structure- B each with a one- dimensional plano cubic thickness profile (see Fig. 1). The phase shift of the X- ray wavefront \((\phi)\) depends on the combined structure thickness \((z)\) , \(\phi = 2\pi \delta (E)z / \lambda\) where \(\delta (E)\) is the real part decrement of X- ray refractive index at X- ray energy \(E\) . The thickness profiles of structure- A and structure- B with lateral shift \((\Delta)\) are:  
+
+\[z_{1} = +A_{1}(y - \Delta)^{3} + A_{2}(y - \Delta) + A_{0} \quad (1a),\]  
+
+\[z_{2} = -A_{1}(y + \Delta)^{3} - A_{2}(y + \Delta) + A_{0} \quad (1b),\]  
+
+where \(A_0, A_1\) and \(A_2\) are constants that determines varifocal variation of AXL while minimizes the thickness of the AXL optical element. If there is no offset between the structures \((\Delta = 0)\) , it gives a constant thickness \((2A_0)\) and thus a constant phase shift to the X- ray wavefront. The resultant thickness profile when structure- A is translated by \(\Delta\) with its conjugate structure- B translated by \(- \Delta\) is:  
+
+\[\Delta z_{AXL} = z_{1} + z_{2} = -6A_{1}\Delta y^{2} - 2A_{1}\Delta^{3} - 2A_{2}\Delta +2A_{0} \quad (2).\]  
+
+The cubic thickness terms cancel out, and the quadratic, lateral shifts and the constants contribute to the overall thickness profile that produces phase modulation of the AXL. The resultant thickness has a parabolic term \(- 6A_{1}\Delta y^{2}\) and focal length of the AXL is given by [16]:  
+
+\[f_{\mathrm{AXL}} = 1 / (12A_{1}\delta \Delta) \quad (3).\]  
+
+The value of \(\delta\) for most of the materials in the X- ray region is of the order of \(\sim 10^{- 6}\) , thus the focal length of an AXL is in the range of a few tens of metres. Therefore, focusing from a single AXL is much weaker than can be achieved by compound refractive lenses [22]. We have therefore used a varifocal AXL in tandem with a KB mirror system to make adaptive variations in the latter's focal length. The focal length of the hybrid optics; two focusing elements, the AXL and the KB mirror pair
+
+<--- Page Split --->
+
+separated by a distance \(d\) , is given by the back focal length \((q_{ho}')\) and measured from the second focusing element is [23]:  
+
+\[q_{ho}^{\prime} = \frac{f_{KB}(d - f_{AXL})}{d - (f_{KB} + f_{AXL})} \quad (4),\]  
+
+where \(f_{KB}\) is focal length of a VKB or HKB elliptical mirror. Using equation (3) and equation (4), we obtained a relative change of focal length introduced due to the AXL:  
+
+\[\Delta q_{ho}^{\prime} = q_{ho}^{\prime} - f_{KB} = 12A_{1}\Delta \delta f_{KB}^{2} \quad (5).\]  
+
+The value of \(A_{1}\) was calculated to achieve approximately a \(1 \mathrm{mm}\) axial varifocal range on either side of the mirror focal plane. The coefficient \(A_{2}\) depends on the value of \(A_{1}\) and size of the optical elements. Thus, for \(\Delta = \sim 32 \mu \mathrm{m}\) , the values \(A_{1} = 141.5 \mathrm{mm}^{- 2}\) and \(A_{2} = - 4.25\) was determined for the two elements of first Alvarez lens; AXL1. The coefficients chosen for AXL2 and AXL3 were two and four times, respectively that of AXL1. The geometrical aperture of each structure was \(400 \mu \mathrm{m}\) , sufficient to cover the mirror aperture and to allow \(\pm 50 \mu \mathrm{m}\) lateral shifting of the structures. Fig. S1 shows the calculated back focal length tuning of the HKB using lateral shifting of optical elements of AXL1 and AXL2.  
+
+## Fabrication  
+
+The design layout of the AXL was prepared for fabrication by 3D printing. The design data of Structure- B of AXL in three- and two- dimensions is illustrated in Fig. S2. The AXLs were printed in photoresist on a glass plate substrate. A small amount of IP- S photoresist (Nanoscibe GmbH) was dropped on the glass plate. The commercially available 3D printer (Photonic Professional GT, Nanoscibe GmbH) was used in dip- in- lithography mode at laser wavelength \(800 \mathrm{nm}\) for two- photon polymerization. The photoresist was exposed in the bottom- to- top approach with the laser pulse focused into each voxel by a high- resolution objective. The photoresist after printing was developed in Propylene glycol methyl ether acetate, rinsed and dried following standard procedures.
+
+<--- Page Split --->
+
+## Optics characterization setup  
+
+Optics characterization setupExperiments were performed with a monochromatic beam on the B16 Test beamline of the Diamond Light Source [24]. The schematic arrangement of the AXL for varying the VKB focal length is shown in the experimental sketch (Fig. 1(a)). The KB mirror system consisted of two elliptical mirrors oriented orthogonally to each other providing focus to a common focal plane. Both elliptical mirrors had a 3 mrad grazing incidence angle and 90 mm active length. Two AXL optical elements were installed on two separate motion towers with five degrees of freedom and were placed upstream of the KB mirror system. The experimental setup for the investigation of HKB focal variation, was identical to VKB setup except the AXL was mounted on a \(90^{\circ}\) rotated platform. The minimum distance (d) between the centre of the AXL to VKB was \(\sim 354 \text{mm}\) and \(\sim 454 \text{mm}\) for the HKB limited by the KB mirror vacuum vessel and the AXL mounting platform. A scannable knife- edge in the vertical or horizontal direction was placed in the KB mirror's focal plane and the beam intensity variation due to scanning the knife- edge through the beam was recorded using a \(6.5 \mu \text{m}\) pixel area detector (Mini- FDS from Photonic Science). Each AXL and the knife- edge were mounted on nano- positioning stages (Attocube) that have a linear resolution better than 10 nm.  
+
+## Wavefront measurement and propagation  
+
+Wavefront measurement and propagationX- ray wavefront measurements are sensitive to errors in the optics surface [5, 25, 26, 27] and are used for the optics alignment [28, 29]. The residual wavefront error of Be CRLs had previously been measured using X- ray ptychography and a comparison of the wavefront error data with the data obtained using the knife- edge method showed good agreement [30]. The knife- edge method was used here to determine the wavefront error and obtain an estimate of the defocus component of the KB mirror, the details of the technique are given in reference [8]. The technique was used to achieve a good alignment of VKB, HKB, and the AXL sub- elements and then to measure the variation in the defocus component caused by the AXL. The X- ray LIGA fabricated Au knife- edge was scanned in the vertical or in the horizontal in the optic's focal plane. The wavefront error was extracted from the
+
+<--- Page Split --->
+
+recorded intensity variation during each knife- edge scan. Each measured wavefront was fitted with a polynomial to obtain the parabolic and cubic components. The parabolic component of the wave- front error is zero if the knife edge is scanned exactly at the focal plane and if the knife edge is displaced longitudinally, a parabolic component to the wavefront error appears that depends linearly on the displacement from the focal plane. This allows the Z- position of the focal plane of the focusing optic to be accurately determined. The measured intensity was numerically propagated using the Fresnel- Kirchhoff equation to investigate a change in the beam caustic and positions of the focal plane of KB mirrors when sub- elements of AXL are laterally shifted by equal amounts in the opposite direction.  
+
+## Contributors  
+
+Author Contributions V.D., D.L. and K.S. conceived the idea. V.D. prepared the designs. K.S. and V.D. coordinated sample preparation. S.B. fabricated the AXL optics and V.D. verified fabricated samples as per the design. V.D., D.L., T.M., H.K., and O.F. performed the synchrotron- based measurements. V.D., D.L., K.S. and T.M. analyzed the data. V.D., D.L., and K.S. wrote the paper. All authors participated in the interpretation of the data and read the manuscript.  
+
+## Acknowledgment:  
+
+The following funding is acknowledged: European Union's Horizon 2020 research and innovation program under the Marie Sklodowska- Curie Actions awarded to the Science and Technology Facilities Council, UK (grant No. 665593). Diamond Light Source (NT28044- 1). We thank Andrew Malandain for his technical support during experiments.  
+
+## Data availability:  
+
+Data supporting the findings of this study are available from the corresponding author on request.
+
+<--- Page Split --->
+
+## References  
+
+1. Eriksson, M., Van der Veen, J. F., & Quitmann, C. Diffraction-limited storage rings—a window to the science of tomorrow. J. of synchr. rad. 21(5), 837-842 (2014).  
+2. Ice, G. E., Budai, J. D., & Pang, J. W. The race to x-ray microbeam and nanobeam science. Science. 334(6060), 1234-1239 (2011).  
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+4. Cocco, D., Cutler, G., del Rio, M.S., Rebuffi, L., Shi, X. & Yamauchi, K. Wavefront preserving X-ray optics for Synchrotron and Free Electron Laser photon beam transport systems. Physics Reports 974, 1-40 (2022).  
+5. Matsuyama, S., Inoue, T., Yamada, J., Kim, J., Yumoto, H., Inubushi, Y., Osaka, T., Inoue, I., Koyama, T., Tono, K. & Ohashi, H. Nanofocusing of X-ray free-electron laser using wavefront-corrected multilayer focusing mirrors. Scientific Reports 8(1), 1-1 (2018).  
+6. Sawhney, K., Laundy, D., Dhamgaye, V. & Pape, I. Compensation of X-ray mirror shape-errors using refractive optics, Appl. Phys. Lett. 109, 051904 (2016).  
+7. Seiboth, F., Schropp, A., Scholz, M., Wittwer, F., Rödel, C., Wünsche, M., Ullsperger, T., Nolte, S., Rahomäki, J., Parfeniukas, K., Giakoumidis, S., Vogt, U., Wagner, U., Rau, C., Boesenberg, U., Garrevoet, J., Falkenberg, G., Galtier, E. C., Lee, H. Ja, Nagler, B., & Schroer, C. G. Perfect x-ray focusing via fitting corrective glasses to aberrated optics, Nature Comm. 8, 14623 (2017).  
+8. D Laundy, D., Dhamgaye, V., Moxham, T. & Sawhney, K. Adaptable refractive correctors for x-ray optics, Optica 6, 1484-1490 (2019).  
+9. Kirkpatrick, P. & Baez, A. V. Formation of optical images by X-rays. J. Opt. Soc. Am. 38, 766-774 (1948).  
+10. Dhamgaye, V., Laundy, D., Baldock, S., Moxham, T. & Sawhney, K. Correction of the X-ray wavefront from compound refractive lenses using 3D printed refractive structures. J. of Sync. Rad. 27(6), 1518-1527(2020).  
+11. Vaughan, G. B., Wright, J. P., Bytchkov, A., Rossat, M., Gleyzolle, H., Snigireva, I., & Snigirev, A. X-ray transfacators: focusing devices based on compound refractive lenses. J. of Sync. Rad. 18(2), 125-133 (2011).
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+<--- Page Split --->
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+12. Kornemann, E., Márkus, O., Opolka, A., Zhou, T., Greving, I., Storm, M., Krywka, C., Last, A. & Mohr, J. Miniaturized compound refractive X-ray zoom lens. Opt. express 25(19), 22455-22466 (2017).  
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+13. Heald, S. M., & Dufresne, E. M. Using refractive lenses to provide a variable spot size for Kirkpatrick-Baez mirrors. J. of Sync. Rad. 25(5), 1514-1516 (2018).  
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+14. Matsuyama, S., Nakamori, H., Goto, T., Kimura, T., Khakurel, K.P., Kohmura, Y., Sano, Y., Yabashi, M., Ishikawa, T., Nishino, Y. & Yamauchi, K. Nearly diffraction-limited X-ray focusing with variable-numerical-aperture focusing optical system based on four deformable mirrors. Scientific reports 6(1), pp.1-8 (2016).  
+
+15. Shi, X., Qiao, Z., Mashrafi, S., Harder, R., Shu, D., Wyman, M., Anton, J., Kearney, S., Rebuffi, L., Mooney, T. & Qian, J. Prototype design and experimental tests of a zoom mirror system for the APS upgrade. In Advances in X-Ray/EUV Optics and Components XV SPIE 11491, 66-73(2020).  
+
+16. Alvarez, L.W. & Humphrey, W.E. Variable Power Lens and System, Patent # 3,507,565 United States Patent Office (1970).  
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+17. Alvarez, L. W. Development of variable- focus lenses and a new refractor, J. Am. Optom. Assoc. 49(1), 24-29 (1978).  
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+18. da Silva, J. C., Guilloud, C., Hignette, O., Jarnias, C., Ponchut, C., Ruat, M., Labiche J. C., Pacureanu, A., Yang, Y., Salome, M., Bohic, S., & Cloetens, P. Overcoming the challenges of high-energy X-ray ptychography. J. of Sync. Rad. 26(5), 1751-1762 (2019).  
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+19. Robinson, I., & Harder, R. Coherent X-ray diffraction imaging of strain at the nanoscale. Nature materials 8(4), 291-298 (2009).  
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+20. Barbero, S. The Alvarez and Lohmann refractive lenses revisited. Opt. Express 17(11), 9376-9390 (2009).  
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+21. Kubec, A., Zdora, M.C., Sanli, U.T., Diaz, A., Vila-Comamala, J. & David, C. An achromatic X-ray lens.  
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+22. Snigirev, A., Kohn, V., Snigireva, I. & Lengeler, B. A compound refractive lens for focusing high-energy X-rays. Nature 384(6604), 49-51 (1996).  
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+23. Hecht, E. Optics (Addison-Wesley, 2001), 4<sup>th</sup> edition, page 168.  
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+25. Rutishauser, S., Zanette, I., Weitkamp, T., Donath, T. & David, C. At-wavelength characterization of refractive x-ray lenses using a two-dimensional grating interferometer. Appl. Phys. Lett. 99, 221104 (2011).
+
+<--- Page Split --->
+
+26. Wang, H., Kashyap, Y. & Sawhney, K. Speckle based X-ray wavefront sensing with nanoradian angular sensitivity. Opt. Express 23, 23310 (2015).  
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+27. Goto, T., Matsuyama, S., Nakamori, H., Sano, Y., Kohmura, Y., Yabashi, M., Ishikawa, T. & Yamauchi, K. Simulation and experimental study of wavefront measurement accuracy of the pencil-beam method. Synchrotron Radiat. News 29, 32–36 (2016).  
+
+28. Kewish, C.M., Guizar-Sicairos, M., Liu, C., Qian, J., Shi, B., Benson, C., Khounsary, A.M., Vila-Comamala, J., Bunk, O., Fienup, J.R. & Macrander, A.T. Reconstruction of an astigmatic hard x-ray beam and alignment of k-b mirrors from ptychographic coherent diffraction data, Opt. Express 18, 23420–23427 (2010).  
+
+29. Zhou, T., Wang, H., Fox, O. & Sawhney, K., Auto-alignment of X-ray focusing mirrors with speckle-based at-wavelength metrology. Opt. Express 26(21), 26961-26970 (2018).  
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+30. Moxham, T.E., Laundy, D., Dhamgaye, V., Fox, O.J., Sawhney, K. & Korsunsky, A.M. Aberration characterization of x-ray optics using multi-modal ptychography and a partially coherent source." App. Phys. Lett. 118(10), 104104 (2021).
+
+<--- Page Split --->
+
+## Supplementary Files  
+
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+SupplementaryInformationAlvarezvarifocalXraylens.docx
+
+<--- Page Split --->

preprint/preprint__c9ff0cf38f21140158e1e895d08bf348ed7b4eac2e17e9d21e2f08be816d80ef/preprint__c9ff0cf38f21140158e1e895d08bf348ed7b4eac2e17e9d21e2f08be816d80ef_det.mmd

@@ -0,0 +1,316 @@
+<|ref|>title<|/ref|><|det|>[[44, 108, 517, 141]]<|/det|>
+# Alvarez varifocal X-ray lens  
+
+<|ref|>text<|/ref|><|det|>[[44, 161, 609, 202]]<|/det|>
+Vishal Dhamgaye ( \(\boxed{ \begin{array}{r l} \end{array} }\) vishal.dhamgaye@diamond.ac.uk) Diamond Light Source https://orcid.org/0000- 0002- 4919- 8957  
+
+<|ref|>text<|/ref|><|det|>[[44, 208, 253, 245]]<|/det|>
+David Laundy Diamond Light Source  
+
+<|ref|>text<|/ref|><|det|>[[44, 254, 253, 291]]<|/det|>
+Thomas Moxham Diamond Light Source  
+
+<|ref|>text<|/ref|><|det|>[[44, 300, 590, 340]]<|/det|>
+Sara Baldock Lancaster University https://orcid.org/0000- 0001- 9635- 7757  
+
+<|ref|>text<|/ref|><|det|>[[44, 346, 253, 384]]<|/det|>
+Hossein Khosroabadi Diamond Light Source  
+
+<|ref|>text<|/ref|><|det|>[[44, 392, 253, 430]]<|/det|>
+Oliver Fox Diamond Light Source  
+
+<|ref|>text<|/ref|><|det|>[[44, 437, 253, 476]]<|/det|>
+Kawal Sawhney Diamond Light Source  
+
+<|ref|>text<|/ref|><|det|>[[44, 521, 102, 539]]<|/det|>
+Article  
+
+<|ref|>text<|/ref|><|det|>[[44, 559, 136, 577]]<|/det|>
+Keywords:  
+
+<|ref|>text<|/ref|><|det|>[[44, 596, 295, 616]]<|/det|>
+Posted Date: July 19th, 2022  
+
+<|ref|>text<|/ref|><|det|>[[44, 634, 473, 654]]<|/det|>
+DOI: https://doi.org/10.21203/rs.3.rs- 1825147/v1  
+
+<|ref|>text<|/ref|><|det|>[[44, 672, 909, 714]]<|/det|>
+License: © This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[118, 127, 422, 149]]<|/det|>
+## Alvarez varifocal X-ray lens  
+
+<|ref|>text<|/ref|><|det|>[[117, 180, 863, 230]]<|/det|>
+Vishal Dhamgaye \(^{1,2*}\) , David Laundy \(^{1}\) , Thomas Moxham \(^{1,3}\) , Sara Baldock \(^{4}\) , Hossein Khosroabadi \(^{1}\) , Oliver Fox \(^{1}\) & Kawal Sawhney \(^{1}\)  
+
+<|ref|>text<|/ref|><|det|>[[117, 254, 810, 333]]<|/det|>
+\(^{1}\) Diamond Light Source, Harwell Science and Innovation Campus, Didcot, Oxon. OX11 0DE, UK \(^{2}\) Synchrotron Utilisation Section, Raja Ramanna Centre for Advanced Technology, Indore, India \(^{3}\) Department of Engineering Science, University of Oxford, Parks Road, Oxford, Oxon. OX1 3PJ, UK \(^{4}\) Department of Chemistry, Lancaster University, Lancaster, LA1 4YB, UK  
+
+<|ref|>text<|/ref|><|det|>[[118, 358, 523, 373]]<|/det|>
+\*Corresponding Authors: vishal.dhamgaye@diamond.ac.uk  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 422, 186, 437]]<|/det|>
+## Abstract  
+
+<|ref|>text<|/ref|><|det|>[[116, 461, 874, 703]]<|/det|>
+In the X- ray region, there exist optical elements analogous to lenses and mirrors for visible light. For visible light, a variable focusing power can be achieved by Alvarez lenses which consist of a pair of inline planar refractors with a cubic thickness profile, which when laterally displaced in opposite directions result in a parabolic component to the wavefront. This paper reports an implementation of this concept for X- rays using two planar microfabricated refractive elements which when used in conjunction with an elliptical mirror focusing system allowed the focal plane to be moved by up to 2 mm with high precision and within milli- seconds. The study presents the first working proof of an Alvarez lens for the adaptive correction of astigmatism and defocus aberrations of X- ray optics.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[118, 85, 217, 100]]<|/det|>
+## Introduction  
+
+<|ref|>text<|/ref|><|det|>[[115, 124, 881, 463]]<|/det|>
+Major synchrotron facilities have done or are planning upgrades to reduce the source emittance and to thereby increase the X- ray's brightness and coherence to new levels [1]. X- ray optics is used to image the X- ray source onto a sample for a variety of experiments. Advances in the manufacturing of optical elements have pushed X- ray beam focusing to achieve diffraction- limited focus sizes at these facilities enabling a range of scientific applications [2, 3]. The key to exploiting this is the high stability of the optics, precise alignment of the optics, and then measurement and correction of the X- ray wavefront for errors caused by imperfections in the optics [4]. A major effort has been put into the correction of the X- ray wavefront using reflective or refractive corrective optics [5, 6, 7]. The corrective optics either requires measurement of the wavefront and then the design of a custom optical element or else the corrective optics is adaptable [8] in which case the correction can be varied in some way to best compensate for the wavefront error.  
+
+<|ref|>text<|/ref|><|det|>[[115, 485, 881, 888]]<|/det|>
+Astigmatism is an aberration that occurs when the optical system is not symmetrical about the optical axis and the focal plane position is different for focusing in two orthogonal planes. Defocus aberration occurs when the sample position is displaced longitudinally along the optical axis from the focal plane. Both prevent the optics from realizing the diffracted- limited spatial resolution. These aberrations in the X- ray focusing system can be caused by misalignment of the optics and by fabrication errors in the optics. In the case of Kirkpatrick- Baez (KB) mirror systems [9] which consist of two elliptical mirrors, independently focusing in horizontal and vertical directions, astigmatism can occur due to a mispositioning of either mirror along the optical axis or by an error in the setting of the pitch angle of either mirror. In the case of compound X- ray refractive lens (CRL), astigmatism may be introduced by the fabrication process causing error in the lens thickness, mispositioning of individual lenses from the axis, or angular misalignment of the stack of lenses [10]. Defocus aberration can be corrected by translating the sample to the correct focal plane but in practice, this may be difficult due to the constraints of complex sample environments. In addition, for CRLs, a change in the X- ray
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[117, 83, 876, 164]]<|/det|>
+energy results in a change to the lens focusing power which translates the focal plane along Z direction. To compensate for these effects, it would be advantageous to be able to have a simple method to be able to adjust the longitudinal position of the focal plane for beamline optics.  
+
+<|ref|>text<|/ref|><|det|>[[115, 188, 872, 590]]<|/det|>
+Control over the focal plane position has been shown using lens- based transfacators which work by translating individual lenses into a CRL lens stack to change the focal length in discrete steps [11, 12, 13] and zoom optics using multiple bendable elliptical mirrors [14, 15]. It is however challenging to achieve a precise continuous focal length variation of an optic. We propose a simple adaptive X- ray optics based on the Alvarez varifocal lens [16, 17] that could be used to independently change the focusing and focal distance in two orthogonal directions. The principle and design of the Alvarez X- ray lens (AXL) are described in the Methods section. It allows compensation of astigmatism and defocus aberrations present in any X- ray optical system. To demonstrate this, an AXL was fabricated and mounted in front of a KB mirror pair consisting of a vertically focusing elliptical mirror (VKB) of focal length 235 mm and a horizontally focusing elliptical mirror (HKB) of focal length 125 mm. Measurements show that the AXL gave fine control over the focal length of the HKB and the VKB with a range of \(\pm 1\mathrm{mm}\) . Two AXLs mounted at right angles, therefore, provided a variable focal length in two orthogonal directions allowing correction for astigmatism and defocus aberrations.  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 656, 177, 671]]<|/det|>
+## Results  
+
+<|ref|>text<|/ref|><|det|>[[115, 696, 872, 905]]<|/det|>
+Nanoprobe based experiments are challenging to perform at the Synchrotron beamlines. The outcome of such an experiment is strongly dependent on the stability of the optics causing a broadening of the probe at the sample plane and it is difficult to achieve a diffraction- limited two- dimensional focused beam at a common focal plane due to astigmatism present in the optics. An X- ray Alvarez lens was used to dynamically correct the astigmatism and defocus aberrations of a KB mirror system. The optical sub- elements of the Alvarez X- ray lens were printed by two- photon polymerisation 3D printing technology. A hybrid optics consisting of an AXL (Structure- A and Structure- B) and a
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[115, 83, 879, 293]]<|/det|>
+KB mirror system was installed at the B16 Test beamline of Diamond Light Source and the experimental setup is shown in Fig. 1. The proof of the working principle of AXL was carried out using monochromatic X- rays from a Si (111) double crystal monochromator. The VKB and HKB were aligned using the knife- edge method [8] to optimise the mirror pitch angles \((\theta)\) and to locate the focal plane position (Z). In order to demonstrate AXL performance, the outgoing X- ray wavefronts of KB mirror were measured at a range of lateral positions of AXL's sub- elements and the change in the parabolic coefficient of the wavefront was evaluated.  
+
+<|ref|>image<|/ref|><|det|>[[113, 315, 884, 656]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[115, 676, 880, 825]]<|/det|>
+<center>Fig. 1: (a) Schematic experimental setup for AXL characterization with X-ray mirror (VKB) used at Test Beamline B16 Diamond. Equal lateral shift of structure-A and structure-B in the opposite direction provides parabolic concave (b) and parabolic convex (c) shaped Alvarez lens that changes the effective focal length \(\Delta q_{ho}^{\prime}\) of two focusing optics up or down-stream to the focal plane of the second focusing element VKB (black dashed line). </center>
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[119, 85, 366, 100]]<|/det|>
+## Calibration of Alvarez X-ray lens  
+
+<|ref|>text<|/ref|><|det|>[[115, 120, 883, 880]]<|/det|>
+If there is no lateral shift between the sub- elements of the AXL, the AXL provides a constant phase shift across the mirror aperture and the focal length of the mirror remains unchanged. When structure- A is laterally moved by distance \(- \Delta\) and structure- B by an equal amount but in the opposite direction, \(+ \Delta\) , a concave phase profile is introduced which generates a parabolic contribution to the wavefront that reduces the mirror focal length (Fig. 1b). An increase in the focal length was observed in the case of opposite lateral shifting; \(+ \Delta\) shift for structure- A and \(- \Delta\) shift for structure- B (Fig. 1c). Figure 2 shows the calibration curves of AXL1 and AXL2 at 15 keV energy for the HKB when the AXL sub- elements were laterally shifted by a 4 \(\mu \mathrm{m}\) step and for a wavefront measured at the fixed focal plane 125 mm from the HKB. The resultant focal distance variation of 29.2 \(\mu \mathrm{m}\) and 55.5 \(\mu \mathrm{m}\) was obtained for a 1 \(\mu \mathrm{m}\) lateral shift in AXL1 and AXL2 respectively. In the present study, a minimum focal plane variation of \(\sim 0.29 \mu \mathrm{m}\) was achieved for a lateral shifting of 10 nm which is close to the movement resolution of the nano- positioning stage. Thus, the change in the focal plane was smaller than the focused beam FWHM 0.45 \(\mu \mathrm{m}\) (dominated by bending magnet source size) of the HKB which makes the Alvarez lens a promising optics for fine control of the focal plane position. Precision control of the focal length can therefore be engineered into the optics by appropriately choosing the AXL design parameters (equation 5). The calculated parabolic components shown in Fig. 2, agree well with the experimental values in case of the smaller lateral shifts and the difference between them increases linearly as shifting is increased. An error of \(\sim 6\%\) and \(\sim 12\%\) was observed between calculated and measured values for AXL1 and AXL2 respectively. This deviation may be due to the density difference of the deposited material and/or fabrication artifacts. The higher the structure thickness of optical elements (see Fig. S2), the higher the fabrication errors. Therefore, AXL1 performance was better compared to the AXL2 as more blocks were printed in the latter's optical elements. The fabrication error may be improved in the next fabrication cycle or using an alternate microfabrication technique such as X- ray lithography.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[137, 97, 572, 355]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[117, 388, 872, 501]]<|/det|>
+<center>Fig. 2: Calibration curves of AXL1 and AXL2 for HKB. The parabolic coefficients were calculated from each measured wavefront as a function of the lateral shift of the structures over a range of \(\pm 24 \mu \mathrm{m}\) . When the parabolic coefficient of the measured wavefront is zero the two sub-elements of AXL are aligned to each other. </center>  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 567, 533, 584]]<|/det|>
+## Correction of astigmatism in the two elliptical mirrors  
+
+<|ref|>text<|/ref|><|det|>[[115, 607, 881, 914]]<|/det|>
+KB mirrors show astigmatism, presenting two different focal distances in the two orthogonal focusing directions. Astigmatism may be caused by mis- setting of the mirror pitch angles or an error in the relative positioning of the mirrors in the longitudinal (Z) direction. Despite better mirror alignment achieved through wavefront measurements in the present study, the focal plane of HKB was found \(\sim 700 \mu \mathrm{m}\) upstream compared to the VKB focal plane, which is probably caused by longitudinal mispositioning of the two mirrors in the mirror vessel. KB mirrors are sensitive to slow drifts, particularly changes in incidence angles at the \(\mu \mathrm{rad}\) level which change the focus position along the optical axis. In the previous section, we demonstrated that the focal plane of a mirror can be changed by an AXL. In order to demonstrate the role of AXL in achieving a change in the focal length of a mirror, X- ray wavefronts were measured at different planes with and without the AXL. The required lateral
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[115, 78, 875, 775]]<|/det|>
+movements of the AXL sub-elements were obtained from the calibration curves (Fig. 2). The AXL was adaptively tuned to bring the defocused beam to the focus at various focal planes that were a few hundred microns apart. Figure 3 shows the variation of the parabolic coefficients of the wavefronts measured at different knife- edge Z positions, around the focal plane of the HKB (125mm). The focal length of the HKB was adjusted by AXL1 and AXL2, on the fly, over a 2 mm distance. A focus plane variation using an AXL takes only a few milli- seconds as the speed of the nano positioning stage was about 4.5 mm/sec. Movement of the AXL1 elements from 0 \(\mu \mathrm{m}\) to 34 \(\mu \mathrm{m}\) took a time of 7.5 ms and gave a 1 mm focus distance variation and there was no settling time needed to achieve the stability. The numerical aperture of the AXL is small compared to the X- ray mirror, thus it does not significantly change the mirror numerical aperture. Figure 4 shows the beam caustics obtained by numerical propagation of the complex field obtained from the measured wavefronts at longitudinal position through the focus (Fig. 4 (a)). The wavefront error of the HKB has defocus aberration which is improved after the introduction of AXL (Fig. 4(b)). The wavefield intensities at focal lengths 124 mm (Fig. 4(c)) and 126 mm (Fig. 4(d)) show the good quantitative agreement with the focus variation made by AXL1. The Alvarez lenses were then mounted in the \(90^{\circ}\) rotated platform for their optical characterisation with the VKB. This study was performed at 13 keV X- ray energy. Again, the lateral translation of the AXL elements at 13 keV were determined from the calibration curve of AXL2. The focus plane of VKB could be moved by up to 3 mm upstream or downstream of its designed focal length (235 mm). The beam caustics calculated from the measured wavefronts are shown in Fig. 5 for the VKB without and with AXL2. AXL2 has improved the focus at 232.4 mm (Fig. 5(c)). Thus, independent focal plane movements of the VKB and HKB is possible to remove astigmatism in their dispersion planes.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[119, 113, 560, 354]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[115, 385, 877, 500]]<|/det|>
+<center>Fig. 3: Change in the parabolic coefficient of the outgoing wavefield of HKB with and without Alvarez X-ray lens measured at different knife-edge positions around \(1 \text{mm}\) of HKB's focal length. The role of the AXL is apparent in keeping defocus term of the mirror constant which is otherwise varying linearly in its focal plane. </center>  
+
+<|ref|>text<|/ref|><|det|>[[115, 562, 880, 870]]<|/det|>
+An AXL may be used to adjust the probe position for minimum beam size to give optimum real and reciprocal space sampling in ptychography experiments which otherwise requires movement of the object along the beam direction [18]. Scanning converging to diverging wavefronts by an AXL may also be able to solve the phase curvature problem in Coherent diffraction X- ray imaging by differentiating the phase signal from either sample or probe [19]. An Alvarez lens may be useful to employ in the wider X- ray energy range with achromatic KB mirrors, however, the AXL is chromatic as its focal length is an inverse function of \(\delta\) which changes with the X- ray energy. A recalibration of the AXL is therefore required after a change of the incident energy. The achievable focus variation is limited by X- ray absorption which increases with thicker AXL structures. It is planned to make 2- dimensional varifocal X- ray lenses based on Alvarez and Lohmann lenses [20].
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[115, 81, 748, 520]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[115, 567, 880, 682]]<|/det|>
+<center>Fig. 4: HKB beam caustics after numerical propagation of the measured complex field to the intended focal positions of (a) HKB at 125 mm (b) HKB with AXL at 125 mm, (c) and (d) HKB with AXL at 125 mm \(\mp 1\) mm, after lateral shifts of AXL sub-elements \(\Delta = \mp 34\mu m\) and \(\Delta = \pm 34\mu m\) respectively. </center>
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[115, 83, 668, 465]]<|/det|>  
+
+<|ref|>image<|/ref|><|det|>[[155, 518, 592, 777]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[115, 808, 870, 889]]<|/det|>
+<center>Figure 5: VKB beam caustics after numerical propagation of the measured complex field to the focal position at \(235\mathrm{mm}\) (a), \(232.4\mathrm{mm}\) (b), and focus beam profiles of VKB without AXL at two different focal distances and with AXL at \(232.4\mathrm{mm}\) (c). </center>
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[118, 126, 293, 141]]<|/det|>
+## Discussion/Conclusion  
+
+<|ref|>text<|/ref|><|det|>[[115, 163, 881, 825]]<|/det|>
+We have successfully developed and demonstrated Alvarez X- ray lenses for fine control of the focal length of elliptical mirrors (KB mirror system) over a range of \(\pm 1 \text{mm}\) . The optics focal length was varied on the fly in less than one second. The AXL enabled an approximately constant focus beam size along with a variable image distance which means a large depth of field optics which is otherwise impossible to achieve in a highly de- magnified optical system. The AXL does have chromatic aberration, however, adaptive tuning allows chromatic aberrations to be removed, thus allowing its working over a wide energy range compared to the working energy range reported for an X- ray Achromat [21]. This study report for the first time the implementation of Alvarez lens in the X- ray region for an adaptive correction of the astigmatism aberration in a two- mirror system. The AXL can adaptively change the focal length in wider energy range of focusing optics based on reflective, refractive, and diffractive methods. The focal tuning by AXL can be increased or decreased by choosing appropriate design parameters. The AXL is expected to be beneficial for a range of experiments performed with X- rays, including but not limited to, in- situ nanoprobe experiments without disturbing the sample position, engineering wavefront curvatures for X- ray imaging, experiments requiring a large depth of field and removal of chromatic aberration. The AXL optics is small in footprint, easy to align, does not change optics axis and is quick in achieving precise axial focus variation that makes it a practical device on existing beamlines. Improvement in astigmatism of focusing elements will enable achieving a round nanobeam at the diffraction- limited storage rings. This new optics has the potential to profoundly change and improve the quality of nanoprobe or microprobe X- ray experiments at the Synchrotron radiation and XFEL facilities and aid novel scientific discoveries in a wide range of disciplines.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[118, 85, 191, 100]]<|/det|>
+## Methods  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 127, 173, 142]]<|/det|>
+## Design  
+
+<|ref|>text<|/ref|><|det|>[[115, 165, 880, 312]]<|/det|>
+AXL presented here consists of a pair of refractive optical elements named structure- A and structure- B each with a one- dimensional plano cubic thickness profile (see Fig. 1). The phase shift of the X- ray wavefront \((\phi)\) depends on the combined structure thickness \((z)\) , \(\phi = 2\pi \delta (E)z / \lambda\) where \(\delta (E)\) is the real part decrement of X- ray refractive index at X- ray energy \(E\) . The thickness profiles of structure- A and structure- B with lateral shift \((\Delta)\) are:  
+
+<|ref|>equation<|/ref|><|det|>[[236, 333, 700, 354]]<|/det|>
+\[z_{1} = +A_{1}(y - \Delta)^{3} + A_{2}(y - \Delta) + A_{0} \quad (1a),\]  
+
+<|ref|>equation<|/ref|><|det|>[[236, 375, 700, 396]]<|/det|>
+\[z_{2} = -A_{1}(y + \Delta)^{3} - A_{2}(y + \Delta) + A_{0} \quad (1b),\]  
+
+<|ref|>text<|/ref|><|det|>[[115, 417, 877, 533]]<|/det|>
+where \(A_0, A_1\) and \(A_2\) are constants that determines varifocal variation of AXL while minimizes the thickness of the AXL optical element. If there is no offset between the structures \((\Delta = 0)\) , it gives a constant thickness \((2A_0)\) and thus a constant phase shift to the X- ray wavefront. The resultant thickness profile when structure- A is translated by \(\Delta\) with its conjugate structure- B translated by \(- \Delta\) is:  
+
+<|ref|>equation<|/ref|><|det|>[[177, 555, 690, 575]]<|/det|>
+\[\Delta z_{AXL} = z_{1} + z_{2} = -6A_{1}\Delta y^{2} - 2A_{1}\Delta^{3} - 2A_{2}\Delta +2A_{0} \quad (2).\]  
+
+<|ref|>text<|/ref|><|det|>[[115, 596, 864, 680]]<|/det|>
+The cubic thickness terms cancel out, and the quadratic, lateral shifts and the constants contribute to the overall thickness profile that produces phase modulation of the AXL. The resultant thickness has a parabolic term \(- 6A_{1}\Delta y^{2}\) and focal length of the AXL is given by [16]:  
+
+<|ref|>equation<|/ref|><|det|>[[177, 701, 690, 721]]<|/det|>
+\[f_{\mathrm{AXL}} = 1 / (12A_{1}\delta \Delta) \quad (3).\]  
+
+<|ref|>text<|/ref|><|det|>[[115, 743, 866, 890]]<|/det|>
+The value of \(\delta\) for most of the materials in the X- ray region is of the order of \(\sim 10^{- 6}\) , thus the focal length of an AXL is in the range of a few tens of metres. Therefore, focusing from a single AXL is much weaker than can be achieved by compound refractive lenses [22]. We have therefore used a varifocal AXL in tandem with a KB mirror system to make adaptive variations in the latter's focal length. The focal length of the hybrid optics; two focusing elements, the AXL and the KB mirror pair
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[117, 84, 853, 135]]<|/det|>
+separated by a distance \(d\) , is given by the back focal length \((q_{ho}')\) and measured from the second focusing element is [23]:  
+
+<|ref|>equation<|/ref|><|det|>[[177, 157, 691, 190]]<|/det|>
+\[q_{ho}^{\prime} = \frac{f_{KB}(d - f_{AXL})}{d - (f_{KB} + f_{AXL})} \quad (4),\]  
+
+<|ref|>text<|/ref|><|det|>[[117, 213, 870, 267]]<|/det|>
+where \(f_{KB}\) is focal length of a VKB or HKB elliptical mirror. Using equation (3) and equation (4), we obtained a relative change of focal length introduced due to the AXL:  
+
+<|ref|>equation<|/ref|><|det|>[[177, 290, 692, 312]]<|/det|>
+\[\Delta q_{ho}^{\prime} = q_{ho}^{\prime} - f_{KB} = 12A_{1}\Delta \delta f_{KB}^{2} \quad (5).\]  
+
+<|ref|>text<|/ref|><|det|>[[115, 335, 874, 579]]<|/det|>
+The value of \(A_{1}\) was calculated to achieve approximately a \(1 \mathrm{mm}\) axial varifocal range on either side of the mirror focal plane. The coefficient \(A_{2}\) depends on the value of \(A_{1}\) and size of the optical elements. Thus, for \(\Delta = \sim 32 \mu \mathrm{m}\) , the values \(A_{1} = 141.5 \mathrm{mm}^{- 2}\) and \(A_{2} = - 4.25\) was determined for the two elements of first Alvarez lens; AXL1. The coefficients chosen for AXL2 and AXL3 were two and four times, respectively that of AXL1. The geometrical aperture of each structure was \(400 \mu \mathrm{m}\) , sufficient to cover the mirror aperture and to allow \(\pm 50 \mu \mathrm{m}\) lateral shifting of the structures. Fig. S1 shows the calculated back focal length tuning of the HKB using lateral shifting of optical elements of AXL1 and AXL2.  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 603, 207, 618]]<|/det|>
+## Fabrication  
+
+<|ref|>text<|/ref|><|det|>[[115, 642, 881, 885]]<|/det|>
+The design layout of the AXL was prepared for fabrication by 3D printing. The design data of Structure- B of AXL in three- and two- dimensions is illustrated in Fig. S2. The AXLs were printed in photoresist on a glass plate substrate. A small amount of IP- S photoresist (Nanoscibe GmbH) was dropped on the glass plate. The commercially available 3D printer (Photonic Professional GT, Nanoscibe GmbH) was used in dip- in- lithography mode at laser wavelength \(800 \mathrm{nm}\) for two- photon polymerization. The photoresist was exposed in the bottom- to- top approach with the laser pulse focused into each voxel by a high- resolution objective. The photoresist after printing was developed in Propylene glycol methyl ether acetate, rinsed and dried following standard procedures.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[119, 85, 345, 101]]<|/det|>
+## Optics characterization setup  
+
+<|ref|>text<|/ref|><|det|>[[115, 123, 880, 560]]<|/det|>
+Optics characterization setupExperiments were performed with a monochromatic beam on the B16 Test beamline of the Diamond Light Source [24]. The schematic arrangement of the AXL for varying the VKB focal length is shown in the experimental sketch (Fig. 1(a)). The KB mirror system consisted of two elliptical mirrors oriented orthogonally to each other providing focus to a common focal plane. Both elliptical mirrors had a 3 mrad grazing incidence angle and 90 mm active length. Two AXL optical elements were installed on two separate motion towers with five degrees of freedom and were placed upstream of the KB mirror system. The experimental setup for the investigation of HKB focal variation, was identical to VKB setup except the AXL was mounted on a \(90^{\circ}\) rotated platform. The minimum distance (d) between the centre of the AXL to VKB was \(\sim 354 \text{mm}\) and \(\sim 454 \text{mm}\) for the HKB limited by the KB mirror vacuum vessel and the AXL mounting platform. A scannable knife- edge in the vertical or horizontal direction was placed in the KB mirror's focal plane and the beam intensity variation due to scanning the knife- edge through the beam was recorded using a \(6.5 \mu \text{m}\) pixel area detector (Mini- FDS from Photonic Science). Each AXL and the knife- edge were mounted on nano- positioning stages (Attocube) that have a linear resolution better than 10 nm.  
+
+<|ref|>sub_title<|/ref|><|det|>[[119, 583, 446, 599]]<|/det|>
+## Wavefront measurement and propagation  
+
+<|ref|>text<|/ref|><|det|>[[115, 621, 879, 896]]<|/det|>
+Wavefront measurement and propagationX- ray wavefront measurements are sensitive to errors in the optics surface [5, 25, 26, 27] and are used for the optics alignment [28, 29]. The residual wavefront error of Be CRLs had previously been measured using X- ray ptychography and a comparison of the wavefront error data with the data obtained using the knife- edge method showed good agreement [30]. The knife- edge method was used here to determine the wavefront error and obtain an estimate of the defocus component of the KB mirror, the details of the technique are given in reference [8]. The technique was used to achieve a good alignment of VKB, HKB, and the AXL sub- elements and then to measure the variation in the defocus component caused by the AXL. The X- ray LIGA fabricated Au knife- edge was scanned in the vertical or in the horizontal in the optic's focal plane. The wavefront error was extracted from the
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[115, 83, 880, 357]]<|/det|>
+recorded intensity variation during each knife- edge scan. Each measured wavefront was fitted with a polynomial to obtain the parabolic and cubic components. The parabolic component of the wave- front error is zero if the knife edge is scanned exactly at the focal plane and if the knife edge is displaced longitudinally, a parabolic component to the wavefront error appears that depends linearly on the displacement from the focal plane. This allows the Z- position of the focal plane of the focusing optic to be accurately determined. The measured intensity was numerically propagated using the Fresnel- Kirchhoff equation to investigate a change in the beam caustic and positions of the focal plane of KB mirrors when sub- elements of AXL are laterally shifted by equal amounts in the opposite direction.  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 382, 218, 397]]<|/det|>
+## Contributors  
+
+<|ref|>text<|/ref|><|det|>[[115, 421, 871, 567]]<|/det|>
+Author Contributions V.D., D.L. and K.S. conceived the idea. V.D. prepared the designs. K.S. and V.D. coordinated sample preparation. S.B. fabricated the AXL optics and V.D. verified fabricated samples as per the design. V.D., D.L., T.M., H.K., and O.F. performed the synchrotron- based measurements. V.D., D.L., K.S. and T.M. analyzed the data. V.D., D.L., and K.S. wrote the paper. All authors participated in the interpretation of the data and read the manuscript.  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 592, 260, 607]]<|/det|>
+## Acknowledgment:  
+
+<|ref|>text<|/ref|><|det|>[[117, 631, 861, 745]]<|/det|>
+The following funding is acknowledged: European Union's Horizon 2020 research and innovation program under the Marie Sklodowska- Curie Actions awarded to the Science and Technology Facilities Council, UK (grant No. 665593). Diamond Light Source (NT28044- 1). We thank Andrew Malandain for his technical support during experiments.  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 770, 249, 785]]<|/det|>
+## Data availability:  
+
+<|ref|>text<|/ref|><|det|>[[115, 810, 857, 828]]<|/det|>
+Data supporting the findings of this study are available from the corresponding author on request.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[118, 152, 206, 167]]<|/det|>
+## References  
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+
+<|ref|>text<|/ref|><|det|>[[115, 309, 875, 343]]<|/det|>
+29. Zhou, T., Wang, H., Fox, O. & Sawhney, K., Auto-alignment of X-ray focusing mirrors with speckle-based at-wavelength metrology. Opt. Express 26(21), 26961-26970 (2018).  
+
+<|ref|>text<|/ref|><|det|>[[117, 353, 852, 404]]<|/det|>
+30. Moxham, T.E., Laundy, D., Dhamgaye, V., Fox, O.J., Sawhney, K. & Korsunsky, A.M. Aberration characterization of x-ray optics using multi-modal ptychography and a partially coherent source." App. Phys. Lett. 118(10), 104104 (2021).
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[44, 42, 312, 70]]<|/det|>
+## Supplementary Files  
+
+<|ref|>text<|/ref|><|det|>[[44, 93, 765, 113]]<|/det|>
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+<|ref|>text<|/ref|><|det|>[[59, 130, 580, 150]]<|/det|>
+SupplementaryInformationAlvarezvarifocalXraylens.docx
+
+<--- Page Split --->

preprint/preprint__ca09945ee4b008190f2b304d99b412af91f547544a1a61b8d6db409ecffa41d7/images_list.json

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+    "caption": "FIG. 2. (a) Calculated Hartree-Fock single-particle excitation spectrum of graphene coupled to a long-wavelength Coulomb potential, with \\(\\nu = 0\\) . (b) and (c) show by blue solid lines the Hartree-Fock band structures of \\(L_{s} = 50 \\mathrm{\\AA}\\) and \\(\\epsilon_{r} = 3.0\\) , with the filling factor \\(\\nu = 0\\) in (b) and \\(\\nu = -0.003\\) in (c). The red dashed lines represent the non-interacting Dirac cones. The insets zoom in energy close to the Dirac points. (d) The calculated gaps at CNP (filled stars) and the interaction-enhanced Fermi velocities at slight hole dopings \\(\\nu = -0.003\\) (hollow diamonds) as a function of the substrate's carrier density \\(n\\) . (e) The thermal activation gap \\(\\Delta\\) measured on the devices in [19] for different nominal dopings \\(n_{\\mathrm{tot}}\\) . (f) Distribution of Berry curvature of the highest valence subband of \\(K\\) valley for \\(r = 1.2\\) and \\(L_{s} = 50 \\mathrm{\\AA}\\) , which gives zero valley Chern number.",
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+    "caption": "FIG. 3. (a) and (b) shows the distribution of Berry curvature in the \\(r = 3\\) superlattice's BZ of the lowest valence and conduction band in valley \\(K\\) for \\(L_{s} = 50\\) and \\(600\\mathrm{\\AA}\\) , respectively. Their corresponding valley Chern number are also given on the top of each panel. (c) and (d) are the non-interacting band structure of the \\(r = 3\\) superlattice with \\(L_{s} = 50\\) and \\(600\\mathrm{\\AA}\\) . (e) Colormap of Fermi velocity in the \\(x\\) -direction \\(v_{x}\\) of the valence band for \\(\\epsilon_{r} = 3\\) . The color coding indicates \\(v_{x} / v_{F}\\) . Here we vary \\(L_{x}\\) from 50 to \\(600\\mathrm{\\AA}\\) and anisotropy parameter \\(r\\) from 1 to 6. The white dashed line, i.e., the \"magic lines\", mark the position in parameter space where \\(v_{x}\\) vanishes.",
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+    "caption": "FIG. 4. Left: charge density modulation after minimizing interlayer Coulomb interactions of gapped Dirac state in graphene (top) and EC state in substrate (bottom); Right: Condensation energies of the electronic crystal state \\(E_{\\mathrm{cond}}\\) vs. the carrier density \\(n\\) in the substrate.",
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+    "caption": "FIG. 5. Order of magnitudes of subband width (green) and intra- (red) and inter-layer (blue) Coulomb potential strength for different \\(L_{s}\\) . The dielectric constant is selected to be 4.",
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preprint/preprint__ca09945ee4b008190f2b304d99b412af91f547544a1a61b8d6db409ecffa41d7/preprint__ca09945ee4b008190f2b304d99b412af91f547544a1a61b8d6db409ecffa41d7.mmd

@@ -0,0 +1,267 @@
+
+# Synergistic correlated states and nontrivial topology in coupled graphene-insulator heterostructures  
+
+Xin Lu School of Physical Sciences and Technology, ShanghaiTech University, Shanghai 200031, China https://orcid.org/0000- 0002- 6228- 1480  
+
+Shihao Zhang School of Physics and Electronics, Hunan University https://orcid.org/0000- 0002- 5787- 5022  
+
+Xiang Gao Shanxi University  
+
+Kaining Yang Shanxi University  
+
+Yuchen Gao Peking University  
+
+Yu Ye Peking University https://orcid.org/0000- 0001- 6046- 063X  
+
+Zheng Han Shanxi University https://orcid.org/0000- 0001- 5721- 6206  
+
+Jianpeng Liu ( liujp@shanghaitech.edu.cn ) ShanghaiTech University https://orcid.org/0000- 0002- 8564- 0415  
+
+Article  
+
+Keywords:  
+
+Posted Date: March 7th, 2023  
+
+DOI: https://doi.org/10.21203/rs.3. rs- 2641075/v1  
+
+License: © This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License  
+
+Additional Declarations: There is NO Competing Interest.  
+
+Version of Record: A version of this preprint was published at Nature Communications on September 9th, 2023. See the published version at https://doi.org/10.1038/s41467- 023- 41293- 8.
+
+<--- Page Split --->
+
+# Synergistic correlated states and nontrivial topology in coupled graphene-insulator heterostructures  
+
+Xin Lu, \(^{1}\) Shihao Zhang, \(^{1}\) Xiang Gao, \(^{2,3}\) Kaining Yang, \(^{2,3}\) Yuchen Gao, \(^{4,5}\) Yu Ye, \(^{4,5}\) Zheng Vitto Han, \(^{2,3}\) and Jianpeng Liu \(^{1,6,*}\)  
+
+\(^{1}\) School of Physical Science and Technology, ShanghaiTech University, Shanghai 201210, China \(^{2}\) State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto- Electronics, Shanxi University, 030006 Taiyuan, China \(^{3}\) Collaborative Innovation Center of Extreme Optics, Shanxi University, 030006 Taiyuan, China \(^{4}\) Collaborative Innovation Center of Quantum Matter, Beijing 100871, China \(^{5}\) State Key Lab for Mesoscopic Physics and Frontiers Science Center for Nano- Optoelectronics, School of Physics, Peking University, Beijing 100871, China \(^{6}\) ShanghaiTech Laboratory for Topological Physics, ShanghaiTech University, Shanghai 201210, China  
+
+In this work, we study the synergistic correlated states in two distinct types of interacting electronic systems coupled by interlayer Coulomb interactions. We propose that this scenario can be realized in a new type of Coulomb- coupled graphene- insulator heterostructures with gate tunable band alignment. We find that, by virtue of the interlayer Coulomb coupling between the interacting electrons in the two layers, intriguing correlated physics that is not seen in either individual layer emerges in a cooperative and synergistic manner. Specifically, as a result of the band alignment, charge carriers can be transferred between graphene and the substrate under the control of gate voltages, which can yield a long- wavelength electronic crystal at the surface of the substrate. This electronic crystal exerts a superlattice Coulomb potential on the Dirac electrons in graphene, which generates subbands with reduced non- interacting Fermi velocity. As a result, \(e - e\) Coulomb interactions within graphene would play a more important role, giving rise to a gapped Dirac state at the charge neutrality point, accompanied by interaction- enhanced Fermi velocity. Moreover, the superlattice potential can give rise to topologically nontrivial subband structures which are tunable by superlattice's constant and anisotropy. Reciprocally, the electronic crystal formed in the substrate can be substantially stabilized in such coupled bilayer heterostructure by virtue of the cooperative interlayer Coulomb coupling. We further perform high- throughput first principles calculations to identify a number of promising insulating materials as candidate substrates for graphene to demonstrate these effects. Our findings provide new insights into the physics of correlated and topological electronic states in graphene- based heterostructures.  
+
+## INTRODUCTION  
+
+Graphene hosts two- dimensional (2D) massless Dirac electrons with linear dispersions and nontrivial Berry phases around two inequivalent \(K\) and \(K^{\prime}\) valleys in the Brillouin zone (BZ) [1, 2]. Such linear dispersions and topological properties of Dirac cones bestow various intriguing single- particle physical properties to graphene including the relativistic Landau levels, the Klein tunneling effects, and the nontrivial edge states, etc. [2]. Besides, low- energy Dirac fermions in graphene also exhibit distinct \(e - e\) interaction effects [3], such as the interaction- enhanced Fermi velocity [4, 5], the gap opening at the charge neutrality point [6- 8], and even chiral superconductivity when the Fermi level locates at the van Hove singularity [9].  
+
+Insulating transition metal oxides (TMOs) and transition metal chalcogenides (TMCs) have also stimulated significant research interests over the past few decades due to the diverse correlated phenomena discovered in these systems such as Mott insulator [10], excitonic insulator [11, 12], and various complex symmetry- breaking states [13, 14]. Under charge dopings, these insulating TMOs and/or TMCs may show more intriguing correlated states including unconventional superconductivity [15- 17] and long- wavelength charge density wave [18].  
+
+An open question is what would happen if two types of distinct interacting many- electron systems, i.e., the interacting Dirac fermions in graphene and the correlated electrons in (slightly) charge doped TMO and/or TMC insulators, are integrated into a single platform. Especially, how the mutual couplings would affect the interacting electronic states in both systems. Inspired by recent pioneering experiments in CrOCl- graphene [19], 1T- TaS \(_2\) - graphene [20], and CrI \(_3\) - graphene [21] heterostructures, here we propose that such a scenario (of interacting Dirac fermions coupled with the correlated electrons in charge doped TMO/TMC insulators) can be realized in graphene- insulator heterostructures with gate tunable band alignment. In this work, we show that, by virtue of the interlayer Coulomb coupling between the interacting electrons in the two layers, intriguing correlated physics that cannot be seen in either individual layer would emerge in a cooperative and synergistic manner in such band- aligned graphene- insulator heterostructures.
+
+<--- Page Split --->
+
+When Dirac points of graphene are energetically close to the band edge of the insulating substrate, charge carriers can be transferred between graphene and the substrate under the control of gate voltages due to quantum tunnelling effects. This may yield a long- wavelength electronic crystal (EC) at the surface of the substrate, given that the carrier density introduced to the substrate is below a threshold value, as schematically shown in Fig. 1(a,b). On the one hand, the long- wavelength EC at the surface of the substrate would impose an interlayer superlattice Coulomb potential to graphene, which would generate subbands with reduced non- interacting Fermi velocity of the Dirac cone, thus triggers gap opening at the Dirac points by \(e\) - \(e\) interactions in graphene. Meanwhile, concomitant with the gap opening, the Fermi velocities around the charge neutrality point (CNP) are dramatically enhanced due to \(e\) - \(e\) interactions effects. The subbands may also possess nontrivial topological properties with nonzero valley Chern numbers that can be controlled by superlattice constant and anisotropy. Especially, we find a number of "magic lines" in the parameter space of superlattice's constant and anisotropy, at which the Fermi velocity along one direction vanishes exactly. The subbands would acquire Chern numbers when passing through these magic lines. On the other hand, the gapped Dirac state at the CNP of graphene would further stabilize the long wavelength electronic- crystal state in the substrate by pinning the relative charge centers of the two layers in an anti- phase pattern, in order to optimize the interlayer Coulomb interactions.  
+
+![](images/Figure_1.jpg)
+
+<center>FIG. 1. (a) Cartoon illustration of a monolayer graphene supported by an insulating substrate with long-wavelength charge order (blue dots), with an interlayer distance \(d\) . (b) Schematic of charge transfer in a band-aligned graphene-insulator heterostructure and its effects on the Dirac dispersion. (c) shows the non-interacting band structure by blue solid lines with \(r = 1.2\) and \(L_{s} = 600 \text{Å}\) . The red dashed lines represent the non-interacting Dirac cones in free-standing graphene. The inset marks the high-symmetry points in the superlattice Brillouin zone. (d) shows the calculated effective fine structure constant \(\alpha (L_{s}, \epsilon_{r})\) , where the dashed line marks the critical value \(\alpha_{c} \approx 0.92\) . </center>  
+
+## COULOMB INTERACTIONS IN GRAPHENE  
+
+To describe the graphene- insulator heterostructure, we consider a model Hamiltonian consisted of a graphene part, an insulator substrate part, and the coupling between them (see Eqs. (4) and Sec. S6 of Supplementary Material [22]). As we are interested in the low- energy electronic properties, graphene's band structure is modelled by the low- energy Dirac cones around the \(K\) and \(K'\) valleys. The long- wavelength EC (charge ordered) state in the substrate is considered
+
+<--- Page Split --->
+
+56 as a charge insulator, with the electrons being frozen to form a superlattice [22]. Thus, long- wavelength charge order of the substrate is coupled to the graphene layer via interlayer Coulomb interactions to exert a superlattice potential on the Dirac electrons. Neglecting the intervalley coupling thanks to the large superlattice constant \(L_{s}\) ( \(\gtrsim 50 \mathrm{\AA}\) ) [23], we can construct an effective single- particle Hamiltonian for the continuum Dirac fermions in graphene that are coupled with a superlattice Coulomb potential [22]  
+
+\[H_{0}^{\mu}(\mathbf{r}) = \hbar v_{F}\mathbf{k}\cdot \pmb{\sigma}^{\mu} + U_{d}(\mathbf{r}) \quad (1)\]  
+
+61 where \(\sigma^{\mu}\) are the Pauli matrices \((\mu \sigma_{x},\sigma_{y})\) with the valley index \(\mu = \pm 1\) , \(v_{F}\) is the non- interacting Fermi velocity of graphene, and \(U_{d}(\mathbf{r})\) is the background superlattice potential with the period \(U_{d}(\mathbf{r}) = U_{d}(\mathbf{r} + \mathbf{L_{s}})\) . The superlattice of the EC is set to be rectangular, with anisotropy \(r = L_{y} / L_{x}\) and \(L_{x,y}\) being the superlattice constant in the \(x,y\) - direction, respectively. We denote \(L_{s} = L_{x}\) . As a result, the superlattice potential \(U_{d}(\mathbf{r})\) would fold Dirac cones into its small Brillouin zone (BZ), forming subbands and opening up a gap at the boundary of the supercell BZ, as shown in Fig. 1(c) for a rectangular superlattice with \(r = 1.2\) (same as that of CrOCl atomic lattice) in valley \(K\) ( \(\mu = 1\) ) with \(L_{s} = 600 \mathrm{\AA}\) . The energy degeneracies from folding are all lifted by \(U_{d}\) , whose Fourier component reads [22]  
+
+\[U_{d}(\mathbf{Q}) = \frac{e^{2}}{\epsilon_{0}\epsilon_{r}\Omega_{0}}\frac{e^{-|\mathbf{Q}|d}}{|\mathbf{Q}|}, \quad (2)\]  
+
+68 where \(\mathbf{Q} \neq \mathbf{0}\) is the reciprocal lattice vector associated with \(\mathbf{L}_{s}\) , \(\Omega_{0} = L_{x}L_{y}\) is the area of the primitive cell of the superlattice. The Coulomb potential \(U_{d}\) , screened by a dielectric constant \(\epsilon_{r}\) , decays exponentially in the reciprocal space \(\sim \exp (- Qd)\) , where \(d\) is the distance between the substrate surface and graphene monolayer. Furthermore, the Fermi velocities near the Dirac points of the subbands are suppressed by \(U_{d}\) [24] as clearly shown in Fig. 1(c).  
+
+While it is highly desirable to open a gap at the Dirac points in graphene for the purpose of field- effect device fabrication, the superlattice potential of Eq. (2) alone cannot gap out Dirac points in graphene as the system still preserves \(C_{2z} \mathcal{T}\) symmetry. However, the Dirac points can be unstable against \(e\) - \(e\) Coulomb interactions (with the spontaneous breaking of \(C_{2z} \mathcal{T}\) symmetry) once the Fermi velocity of the non- interacting band structure is suppressed below a threshold, which can be assisted by the superlattice potential from the long- wavelength charge order. One of the similar illustrations is twisted bilayer graphene (TBG) [25], where the Fermi velocity is strongly suppressed around the "magic angle", leading to moiré flat bands exhibiting diverse correlated and topological phases [26- 31]. Here we further calculate the Fermi velocity of the superlattice subbands around the Dirac point, denoted as \(v_{F}(L_{s}, \epsilon_{r})\) , which is dependent on both the superlattice constant \(L_{s}\) and the background dielectric constant \(\epsilon_{r}\) . Accordingly, the effective fine structure constant \(\alpha (L_{s}, \epsilon_{r}) = e^{2} / (4 \pi \epsilon_{0} \epsilon_{r} \hbar v_{F}(L_{s}, \epsilon_{r}))\) can also be tuned by \(L_{s}\) and \(\epsilon_{r}\) , as shown in Fig. 1(d). We see that there is a substantial region in the \((L_{s}, \epsilon_{r})\) phase space with \(\alpha (L_{s}, \epsilon_{r}) > \alpha_{c} \approx 0.92\) [32], which indicates that the Dirac- semimetal phase of graphene may no longer be stable against \(e\) - \(e\) interactions within this regime.  
+
+This motivates us to include \(e\) - \(e\) interactions in the graphene layer in our model. Despite several theoretical predictions of gapped Dirac states in graphene [3, 6- 8], to the best of our knowledge no gap at the CNP has been experimentally observed in suspended graphene yet [33, 34]. This can be attributed to interaction- enhanced Fermi velocity around the CNP, screening of \(e\) - \(e\) interactions due to ripple- induced charge puddles, disorder effects, etc. [3, 35- 38]. Nevertheless, analogous to TBG, the subbands in our system with reduced non- interacting Fermi velocity would quench the kinetic energy and further promote the \(e\) - \(e\) interaction effects in graphene.  
+
+Our unrestricted Hartree- Fock calculations [22] confirm precisely the argument above. As interaction effects are most prominent around the CNP, we project the Coulomb interactions onto only a low- energy subspace including three valence and three conduction subbands ( \(n_{\mathrm{cut}} = 3\) ) that are closest to CNP for each valley and spin. To incorporate the influences of Coulomb interactions from the high- energy remote bands, we rescale the Fermi velocity within the low- energy subspace using the formula derived from the renormalization group (RG) approach [2- 4, 39]  
+
+\[v_{F}^{*} = v_{F}\left(1 + \frac{\alpha_{0}}{4\epsilon_{r}}\log \frac{E_{c}}{E_{c}^{*}}\right) \quad (3)\]  
+
+where \(\alpha_{0} = e^{2} / (4 \pi \epsilon_{0} \hbar v_{F})\) is the ratio between the Coulomb interaction energy and kinetic energy, i.e., the effective fine- structure constant of free- standing graphene, \(E_{c}^{*}\) delimits the low- energy window within which the unrestricted Hartree- Fock calculations are to be performed, and \(E_{c}\) is an overall energy cut- off above which the Dirac- fermion description to graphene is no longer valid. Unlike TBG [40], other parameters of the effective Hamiltonian (Eq. (1)) such as \(U_{d}\) , are unchanged under the RG flow [22].  
+
+We first study the interaction effects of graphene coupled to a rectangular superlattice potential with \(r = 1.2\) and \(50 \mathrm{\AA} \leq L_{s} \leq 400 \mathrm{\AA}\) , corresponding to carrier density of the EC state at the surface of the substrate \(0.1 \times 10^{12} \mathrm{cm}^{- 2} \leq\)
+
+<--- Page Split --->
+![](images/Figure_2.jpg)
+
+<center>FIG. 2. (a) Calculated Hartree-Fock single-particle excitation spectrum of graphene coupled to a long-wavelength Coulomb potential, with \(\nu = 0\) . (b) and (c) show by blue solid lines the Hartree-Fock band structures of \(L_{s} = 50 \mathrm{\AA}\) and \(\epsilon_{r} = 3.0\) , with the filling factor \(\nu = 0\) in (b) and \(\nu = -0.003\) in (c). The red dashed lines represent the non-interacting Dirac cones. The insets zoom in energy close to the Dirac points. (d) The calculated gaps at CNP (filled stars) and the interaction-enhanced Fermi velocities at slight hole dopings \(\nu = -0.003\) (hollow diamonds) as a function of the substrate's carrier density \(n\) . (e) The thermal activation gap \(\Delta\) measured on the devices in [19] for different nominal dopings \(n_{\mathrm{tot}}\) . (f) Distribution of Berry curvature of the highest valence subband of \(K\) valley for \(r = 1.2\) and \(L_{s} = 50 \mathrm{\AA}\) , which gives zero valley Chern number. </center>  
+
+\(n \leq 6.58 \times 10^{12} \mathrm{~cm}^{- 2}\) (with \(n = 2 / (r L_{s}^{2})\) ), with \(\epsilon_{r} = 3,4\) , and \(d = 7 \mathrm{\AA}\) (obtained from first principles density functional theory calculations for a CrOCl- graphene heterostructure [22]). Here, we consider two different filling factors: exactly at the CNP \((\nu = 0)\) and a slight hole doping \((\nu \approx - 0.003)\) . When \(\nu = 0\) , a gap can be opened up due to interaction effects [see Fig. 2(a,b)], leading to two nearly degenerate insulating states, one is sublattice polarized and the other valley polarized. Then, intervalley Coulomb interactions would split such degeneracy, and the sublattice polarized insulator with zero Chern number becomes the unique ground state [22]. Notably, the gap decreases linearly with \(n\) as clearly shown in Fig. 2(d), and eventually vanishes as \(n \to 0\) . This is because the superlattice Coulomb potential exerted on graphene is proportional to the carrier density of the long- wavelength order from the substrate. Consequently, the Fermi velocity of the bare Dirac dispersion of graphene would be less suppressed at smaller carrier density \(n\) , which disfavors gap opening. Eventually in the limit of \(n \to 0\) , with a charge ordered state of infinite lattice constant, graphene would recover its non- interacting behavior as a gapless Dirac semimetal.  
+
+To verify our theory, we have also experimentally measured the gaps at CNP in graphene- CrOCl heterostructure at different nominal carrier densities [22]. The measured gaps also decrease linearly with \(n_{\mathrm{tot}}\) , from \(7.7 \mathrm{meV}\) with \(n_{\mathrm{tot}} = 3.4 \times 10^{12} \mathrm{~cm}^{- 2}\) , to \(5.8 \mathrm{meV}\) with \(n_{\mathrm{tot}} = 0.5 \times 10^{12} \mathrm{~cm}^{- 2}\) [22], consistent with the trend from theoretical calculations, as shown in Fig. 2(e). When \(n_{\mathrm{tot}} \to 0\) , such a linear dependence of the gap on \(n_{\mathrm{tot}}\) may no longer be valid [22], which is possibly due to the formation of an excitonic- like insulator in the graphene- substrate bilayer- type system, or due to some complex Coulomb screening effects.
+
+<--- Page Split --->
+![](images/Figure_3.jpg)
+
+<center>FIG. 3. (a) and (b) shows the distribution of Berry curvature in the \(r = 3\) superlattice's BZ of the lowest valence and conduction band in valley \(K\) for \(L_{s} = 50\) and \(600\mathrm{\AA}\) , respectively. Their corresponding valley Chern number are also given on the top of each panel. (c) and (d) are the non-interacting band structure of the \(r = 3\) superlattice with \(L_{s} = 50\) and \(600\mathrm{\AA}\) . (e) Colormap of Fermi velocity in the \(x\) -direction \(v_{x}\) of the valence band for \(\epsilon_{r} = 3\) . The color coding indicates \(v_{x} / v_{F}\) . Here we vary \(L_{x}\) from 50 to \(600\mathrm{\AA}\) and anisotropy parameter \(r\) from 1 to 6. The white dashed line, i.e., the "magic lines", mark the position in parameter space where \(v_{x}\) vanishes. </center>  
+
+We note that the electronic crystal at the surface of the substrate is expected to persist even if the carrier density exceeds the threshold value due to the extra energy gain from interlayer Coulomb coupling in such coupled system, which will be discussed in detail in Sec. . Strain is also inevitable in such graphene- insulator heterostructures, which would give rise to pseudo- magnetic fields coupled to the Dirac electrons [5, 41, 42], thus further enhances the \(e\) - \(e\) interaction effects in graphene.  
+
+The single- particle excitation spectrum is also significantly altered by Coulomb interactions within the low- energy window, as shown in Fig. 2(b) and (c) with fillings \(\nu = 0\) and \(\nu = - 0.003\) , respectively. We note that although the superlattice potential \(U_{d}\) suppresses Fermi velocity in graphene [see Fig. 1(c)], \(e\) - \(e\) interactions can compensate such effects. The Fermi velocity is not only enhanced by the Coulomb potentials from the remote energy bands [Eq. (3)], but also further boosted by \(e\) - \(e\) interactions within the low energy window \(E_{c}^{*} \sim n_{\mathrm{cut}} \hbar v_{F} 2 \pi / L_{s}\) . Eventually, the Fermi velocity can be magnified up to more than twice of the non- interacting value of free- standing graphene \((v_{F})\) at slight hole doping \(\nu = - 0.003\) , as shown in Fig. 2(d). This perfectly explains the recent experiment in gate- controlled graphene- CrOCl heterostructure, in which the Fermi velocity around CNP is significantly enhanced compared to non- interacting value at slight carrier doping, such that robust quantum Hall effect can be observed under tiny vertical magnetic fields \((\sim 0.1 \mathrm{T})\) and high temperatures [19]. We note that the EC state may be stabilized by vertical magnetic fields even when the carrier density in the substrate exceeds the zero- field threshold value [43, 44], which in turn boosts the low- field, high- temperature quantum Hall effect in the graphene layer due to the scenario discussed above.  
+
+The essential results discussed above, i.e., the gap opening at CNP and the concomitant drastic enhancement of Fermi velocity, remain valid for different types of the background superlattices. Specifically, we have also performed calculations for the case of triangular charge- ordered superlattices, which lead to qualitatively the same conclusions, as presented in Sec. S5 of Supplementary Material [22].  
+
+## TOPOLOGICAL PROPERTIES  
+
+Different from magic- angle TBG [45- 49], the low- energy subbands for graphene coupled to a rectangular superlattice potential \(U_{d}(\mathbf{r})\) with small anisotropy ( \(r \sim 1\) ) turn out to be topologically trivial with a compensating Berry- curvature distribution, leading to zero Chern number. This remains true even in the gapped Dirac state after including \(e\) - \(e\) interactions, as shown in Fig. 2(f). The trivial band topology is somehow anticipated because the superlattice potential is non- chiral in the sense that it is coupled equally to the two sublattice of graphene, which does not have any pseudo- gauge- field structure such as that in TBG [49, 50].  
+
+Hence, it is unexpected that changing the anisotropy \(r\) and the lattice size \(L_{s}\) of the superlattice potential \(U_{d}\) can make the subbands topological. For example, keeping \(L_{x} = 50\mathrm{\AA}\) but with \(r = 3.0\) , both the highest valence band and
+
+<--- Page Split --->
+
+the lowest conduction band acquire nonzero valley Chern numbers \(C = \pm 1\) (after adding an infinitesimal \(C_{2z}\) - breaking staggered sublattice potential). As shown in Fig. 3(a), besides the four high symmetry points, it appears another two "hot spots" (annotated by green circles) along the line connecting \(\Gamma_{s}\) and \(X_{s}\) . This new contribution breaks the balance between positive and negative contribution of Berry curvature to Chern number, leading to non- zero valley Chern number. Such contribution stems from a new crossing point between the low- energy valence and conduction bands along the \(k_{x}\) - direction through changing merely the anisotropy parameter \(r\) , as shown in Fig. 3(c) by red dot within green circle.  
+
+While increasing \(r\) from unity (with fixed \(L_{s}\) ), the Fermi velocity in the \(x\) - direction of the valence band around the Dirac point, \(v_{x}\) , is gradually reduced, as shown in Fig. 3(e). As the same origin of Klein tunneling effects, the spinor structure of graphene's wavefunction forces the Fermi velocity in the \(y\) - direction to be intact [24]. Further tuning \(r\) at some point would totally flatten \(v_{x}\) . In Fig. 3(e), we mark by white dashed lines "the magic lines" on which \(v_{x}\) of the valence band closest to Dirac points vanishes exactly. The magic lines always come in pair as an effect of chiral (particle- hole) symmetry breaking induced by the superlattice potential. As particle- hole symmetry is broken in the energy spectrum, when \(v_{x}\) vanishes in the valence band, the counterpart in the conduction band remains finite. The valence subband around the Dirac point has to curve upwards to create a band crossing point, after that \(v_{x}\) of the valence band becomes zero again. Therefore, a band crossing would be germinated at the Dirac point, and then move away along the \(k_{x}\) - direction with larger \(r\) . If the Dirac point is gapped, say, by a tiny staggered sublattice potential, the low- energy subbands become topological with nonzero valley Chern numbers. In particular, with the increase of \(r\) at fixed \(L_{s}\) , the absolute value of valley Chern number of the valence subband (closest to Dirac points) increases by 1 whenever one pair of the magic lines are passed through. The positions of these magic lines are also dependent on the background dielectric constant \(\epsilon_{r}\) since larger \(\epsilon_{r}\) corresponds to weaker Fermi- velocity renormalization effect, which would shift the magic lines to larger \(r\) values. Such topologically nontrivial subbands with extremely anisotropic Fermi velocities may provide a new platform to realize novel topological quantum matter.  
+
+We note that the anisotropic charge ordered superlattices may be realized in two ways. First, one can design a spatially modulated electrostatic potential, which has been realized in monolayer graphene by inserting a patterned dielectric superlattice between the gate and the sample [51]. Then, the anisotropy of the superlattice can be artificially tuned by the dielectric patterning in the substrate. Second, for some given carrier density, the Fermi surface of the conduction (or valence) band of the substrate may be (partially) nested, which may lead to a charge density wave (CDW) state with the nesting wavevector. For example, for CrOCl, the Fermi surfaces under different Fermi energies (above the conduction band minimum) are given in Fig. S14 (c) of Supplementary Material. Clearly, under some proper fillings, the Fermi surfaces are nested or partially nested, which may give rise to CDW states with anisotropic superlattices. We note that topologically nontrivial flat bands have also proposed to exist in Bernal bilayer graphene coupled with a background superlattice potential [52].  
+
+Furthermore, we find that changing \(L_{s}\) can also control the valley Chern number of the subbands. For example, with \(r = 3\) and \(L_{s} = 600 \mathrm{\AA}\) , as shown in Fig. 3(b), while the highest valence band remains topological with non- zero valley Chern number 1 for valley \(K\) with the two aforementioned crossing points (green circles) merely moving to \(X_{s}\) , the lowest conduction band turns out to be topologically trivial. This is due to two new band crossing points (orange circles) close to the \(Y_{s} - S_{s}\) line between the lowest and the second lowest conduction bands, as annotated by red dots in an orange circle in Fig. 3(d).  
+
+The nontrivial topology must arise from the intrinsic Berry phases of the Dirac cones. Such topologically nontrivial bands are particularly surprising for our system, since the Dirac fermions are subjected to a "trivial" superlattice potential, which couples identically with two sublattices of graphene. Nevertheless, the nontrivial subband topology is highly tunable by changing the superlattice's size and anisotropy [22].  
+
+## COOPERATIVE COUPLING BETWEEN GRAPHENE AND SUBSTRATE  
+
+In the previous calculations, a charge ordered superlattice in the substrate is presumed, which exerts a classical superlattice Coulomb potential to graphene. However, this assumption should be examined. We have to know to which extent that a presumed charge- ordered state underneath graphene is a viable starting point of our previous calculations. Even more importantly, in a coupled bilayer system, the coupling between graphene and the substrate has to be studied in a reciprocal way. Besides the effects from the substrate to graphene, the feedback effects from graphene to the substrate should be discussed as well. Therefore, here we study the coupled bilayer system as a whole, and treat the electrons in graphene layer and the substrate layer on equal footing. In particular, we model the carriers transferred to the substrate as 2D electron gas with long- range \(e - e\) Coulomb interactions. Electrons in the substrate and in graphene interact with each other via long- range Coulomb potential, whose Fourier component
+
+<--- Page Split --->
+
+of wavevector \(\mathbf{q}\) reads \(e^{2}\exp (- |\mathbf{q}| d) / (2\epsilon_{0}\epsilon_{r}|\mathbf{q}|)\) . Thus, the total Hamiltonian for the Coulomb- coupled graphene- insulator heterostructure system includes [22]:  
+
+\[\begin{array}{r l} & {H_{\mathrm{gr}}^{0} = \sum_{\mathbf{k},\mu ,\alpha ,\alpha^{\prime},\sigma}\left(\hbar v_{F}\mathbf{k}\cdot \pmb{\sigma}^{\mu}\right)_{\alpha ,\alpha^{\prime}}\hat{c}_{\sigma \mu \alpha}^{\dagger}(\mathbf{k})\hat{c}_{\sigma \mu \alpha^{\prime}}(\mathbf{k}),}\\ & {H_{\mathrm{sub}}^{0} = \sum_{\mathbf{k},\sigma}\left(\frac{\hbar^{2}\mathbf{k}^{2}}{2m^{*}} +E_{\mathrm{CBM}}\right)\hat{d}_{\sigma}^{\dagger}(\mathbf{k})\hat{d}_{\sigma}(\mathbf{k}),}\\ & {H_{\mathrm{gr}}^{\mathrm{intra}} = \frac{1}{2S}\sum_{\sigma ,\sigma^{\prime}}\sum_{\alpha ,\alpha^{\prime}}V_{\mathrm{int}}(\mathbf{q})\hat{c}_{\sigma \mu \alpha}^{\dagger}(\mathbf{k} + \mathbf{q})\hat{c}_{\sigma^{\prime}\mu^{\prime}\alpha^{\prime}}^{\dagger}(\mathbf{k}^{\prime} - \mathbf{q})\hat{c}_{\sigma^{\prime}\mu^{\prime}\alpha^{\prime}}(\mathbf{k}^{\prime})\hat{c}_{\sigma \mu \alpha}(\mathbf{k}),}\\ & {H_{\mathrm{sub}}^{\mathrm{intra}} = \frac{1}{2S}\sum_{\mathbf{k},\mathbf{k}^{\prime},\mathbf{q}}\sum_{\sigma ,\sigma^{\prime}}V_{\mathrm{int}}(\mathbf{q})\hat{d}_{\sigma}^{\dagger}(\mathbf{k} + \mathbf{q})\hat{d}_{\sigma^{\prime}}^{\dagger}(\mathbf{k}^{\prime} - \mathbf{q})\hat{d}_{\sigma^{\prime}}(\mathbf{k}^{\prime})\hat{d}_{\sigma}(\mathbf{k}),}\\ & {H_{\mathrm{gr - sub}} = \frac{1}{S}\sum_{\mu ,\alpha ,\sigma ,\sigma^{\prime}}\sum_{\mathbf{k},\mathbf{k}^{\prime},\mathbf{q}}\frac{e^{2}e^{-|\mathbf{q}|d}}{2\epsilon_{0}\epsilon_{r}|\mathbf{q}|}\hat{c}_{\sigma \mu \alpha}^{\dagger}(\mathbf{k})\hat{d}_{\sigma^{\prime}}^{\dagger}(\mathbf{k}^{\prime})\hat{d}_{\sigma^{\prime}}(\mathbf{k}^{\prime} - \mathbf{q})\hat{c}_{\sigma \mu \alpha}(\mathbf{k} + \mathbf{q}).} \end{array} \quad (4c)\]  
+
+On the graphene side, Eq. (4a) is the familiar Dirac Hamiltonian describing the non- interacting low- energy physics of graphene. The \(e\) - \(e\) Coulomb interactions within graphene are described by Eq. (4c), where the dominant intravalley long- range Coulomb interactions are considered and \(V_{\mathrm{int}}(\mathbf{q})\) is in the form of double- gate screened Coulomb potential (see Eq. (8). Here, \(\hat{c}_{\sigma \mu \alpha}(\mathbf{k})\) and \(\hat{c}_{\sigma \mu \alpha}^{\dagger}(\mathbf{k})\) denote annihilation and creation operators for the low- energy Dirac electrons with wavevector \(\mathbf{k}\) , valley \(\mu\) , spin \(\sigma\) , and sublattice \(\alpha\) . Note that \(S\) refers to the total surface area of the coupled system, and the atomic wavevectors \(\mathbf{k}, \mathbf{k}^{\prime}, \mathbf{q}\) are expanded around the Dirac points. On the substrate side, without loss of generality, we suppose that the chemical potential is close to the conduction band minimum (CBM) with its energy \(E_{\mathrm{CBM}}\) , and the energy dispersion of the low- energy electrons around CBM can be modelled by a parabolic band as for 2D free electron gas with effective mass \(m^{*}\) . Other electrons in the deep valence bands are supposed to be integrated into the static dielectric screening constant thanks to a large gap of the substrate. Therefore, the non- interacting Hamiltonian Eq. (4b) for electrons in the substrate can be written in the plane wave basis with creation and annihilation operators \(\{\hat{d}_{\sigma}^{\dagger}(\mathbf{k}), \hat{d}_{\sigma}(\mathbf{k})\}\) , where \(\mathbf{k}\) is the plane wave wavevector expanded around the CBM, and \(\sigma\) denotes spin. The \(e\) - \(e\) Coulomb interactions within substrate [Eq. (4d)] is taken to be the long- range Coulomb interaction with the same double- gate screened form of \(V_{\mathrm{int}}(\mathbf{q})\) . The coupling between graphene and substrate is only via the long- range Coulomb potential, which is captured by Eq. (4e). The prefactor \(e^{2}\exp (- |\mathbf{q}| d) / (2\epsilon_{0}\epsilon_{r}|\mathbf{q}|)\) in front of the field operators in Eq. (4e) is nothing but the 2D Fourier transform of 3D Coulomb potential. Interlayer hoppings can be neglected given that the interlayer distance \(d \gtrsim 5 \mathring{\mathrm{A}}\) in such heterostructures (e.g., \(d \approx 7 \mathring{\mathrm{A}}\) in graphene- CrOCl heterostructure from first principles calculations), thus the exponentially decaying interlayer hopping amplitude is much weaker than the power- law- decaying interlayer Coulomb interaction.  
+
+We use distinct letters to denote the ladder operators for electrons in graphene \((\hat{c}, \hat{c}^{\dagger})\) and substrate \((\hat{d}, \hat{d}^{\dagger})\) . This implies in a notational manner the approximation of distinguishable electrons. In other words, the many- body wavefunction of the coupled bilayer system (denoted as \(|\Psi \rangle\) ) can be written a separable fashion, namely a direct product of graphene's and substrate's part, i.e.,  
+
+\[|\Psi \rangle = |\Psi \rangle_{c}\otimes |\Psi \rangle_{d} \quad (5)\]  
+
+In a mean- field treatment, the corresponding many- body wavefunction would thus be a direct product of two Slater determinants, \(|\Psi \rangle_{c}\) and \(|\Psi \rangle_{d}\) for the graphene layer and the substrate layer, respectively. This is reminiscent of the Born- Oppenheimer approximation for electrons and ions. Technically, this means that order parameters \(\sim \langle \hat{c}^{\dagger} \hat{d} \rangle (\langle \hat{d}^{\dagger} \hat{c} \rangle)\) are not allowed in our treatment. A finite value of \(\langle \hat{c}^{\dagger} \hat{d} \rangle (\langle \hat{d}^{\dagger} \hat{c} \rangle)\) suggests the emergence of a new phase, an interlayer excitonic condensate in such coupled bilayer system. However, we note that such interlayer exciton has to be driven by intervalley Coulomb scattering between the \(K / K^{\prime}\) valley of graphene and (presumably) \(\Gamma\) valley of substrate's electrons, with the amplitude \(\sim e^{2}\exp (- |\mathbf{K}| d) / (2\epsilon_{0}\epsilon_{r}|\mathbf{K}|)\) being several orders of magnitudes smaller than the intravalley one in our problem. Thus, it is completely legitimate to neglect the interlayer particle- hole exchange in our problem, and the separable wavefunction hypothesis Eq. (5) is an excellent approximation. Then, we solve the full interacting Hamiltonian Eqs. (4) under the separable- wavefunction hypothesis Eq. (5), and the workflow is presented in Methods.
+
+<--- Page Split --->
+
+To explore how the interlayer Coulomb coupling would affect the electronic crystal state of the substrate, we first consider the situation as a reference that the substrate is decoupled from graphene, and treat the \(e - e\) interactions within the substrate by Hartree- Fock approximations [22]. We obtain the energy difference between the EC state and Fermi- liquid (FL) state (condensation energy) as a function of the carrier density \(n\) as shown by the green circles in the right panel of Fig. 4. The condensation energy reaches zero when \(n \approx 7 \times 10^{- 12} \mathrm{~cm}^{- 2}\) suggesting the transition from the EC to the FL state. We further include the interlayer Coulomb coupling between the substrate and graphene (setting the chemical potential at the CNP of graphene), which can be treated using perturbation theory given that the interlayer Coulomb energy is always much smaller than the sum of the intralayer Coulomb energy and kinetic energy within the relevant parameter regime (see Fig. 5 in Methods). More details about the perturbative treatment of interlayer Coulomb interactions are presented in Sec. S6 of Supplementary Material [22].  
+
+We find that the condensation energy of the EC is substantially enhanced after including the interlayer interactions, as shown by the orange diamonds in Fig. 4. As a result, the EC- FL transition is postponed to a higher density \(n \approx 8.6 \times 10^{- 12} \mathrm{~cm}^{- 2}\) (obtained from extrapolation). This is because the energy of the coupled bilayer can be further lowered by pinning the charge centers (marked as light blue stars in the left panel of Fig. 4) of the two layers in an anti- phase- like pattern, in order to optimize the repulsive interlayer Coulomb energy. The extra energy gain from such "charge corrugation" compensates the energy cost of the EC state when \(n \gtrsim 7 \times 10^{- 12} \mathrm{~cm}^{- 2}\) , thus substantially stabilizes the EC state.  
+
+Certainly the mean- field treatment overestimates the condensation energy, but the qualitative conclusion that the EC state gets stabilized by a cooperative interlayer Coulomb coupling should be valid even in a beyond- mean- field treatment. This is because under the separable- wavefunction hypothesis, the interlayer Coulomb energy in the EC state is always negative (compared to that of FL state) under an optimal choice of relative charge centers, which thus always stabilizes the EC state even if the intralayer interactions are treated using beyond- mean- field approaches.  
+
+![](images/Figure_4.jpg)
+
+<center>FIG. 4. Left: charge density modulation after minimizing interlayer Coulomb interactions of gapped Dirac state in graphene (top) and EC state in substrate (bottom); Right: Condensation energies of the electronic crystal state \(E_{\mathrm{cond}}\) vs. the carrier density \(n\) in the substrate. </center>  
+
+## MATERIALS REALIZATION  
+
+The scenario discussed above is not only closely related to CrOCl- graphene and \(\mathrm{CrI_3}\) - graphene heterostructures [19, 21], but can also be extended to various band- aligned graphene- insulator heterostructures. As along as the conduction band minimum (CBM) or valence band maximum (VBM) of the substrate is energetically close to the Dirac points of graphene, charges could be easily transferred between graphene and the substrate's surface by gate voltages. Furthermore, it is more likely to form long- wavelength ordered state at the surface of the substrate (with slight carrier doping) if the material has large effective masses at the CBM or VBM. Meanwhile, an insulator with relatively small dielectric constant would have weaker screening effects to \(e - e\) interactions, which also favours long- wavelength ordered state at small carrier doping.  
+
+Following these guiding principles, we have performed high- throughput first principles calculations based on density functional theory for various insulating van der Waals materials. Eventually we find twelve suitable candidate materials (including CrOCl and \(\mathrm{CrI_3}\) ), whose CBM and VBM energy positions, dielectric constants ( \(\epsilon_r\) ), effective masses at the band edges, and the corresponding Wigner- Seitz radii ( \(r_s\) ) are listed in Table I. Clearly, the Wigner- Seitz radii
+
+<--- Page Split --->
+
+TABLE I. Candidate substrate materials for the graphene-insulator heterostructure systems. The dielectric constants \(\epsilon_{r}\) [54- 56], conduction band minimum position \((E_{\mathrm{CBM}})\) , valence band maximum position \((E_{\mathrm{VBM}})\) , the corresponding effective mass \(m^{*}\) at the band edge that is closer to the Dirac point (set to zero) in energy, and the dimensionless Wigner-Seitz radius \(r_{s} = g_{v}m^{*} / \sqrt{\pi n}\epsilon_{r}m_{0}a_{\mathrm{B}}^{0}\) \((a_{\mathrm{B}}^{0}\) is the Bohr radius and \(m_{0}\) is the bare electron mass, \(g_{v}\) is the valley degeneracy) estimated under a small doping concentration \(n = 10^{12}\mathrm{cm}^{- 2}\) , are presented. Here "bi" and "tri" stand for bilayer and trilayer systems, respectively.  
+
+<table><tr><td>Materials</td><td>εr</td><td>ECBM</td><td>EVBM</td><td>m*/m0</td><td>gv</td><td>rs</td></tr><tr><td>AgScP2S6 (bi)</td><td>3.67</td><td>0.07 eV</td><td>-1.89 eV</td><td>3.94</td><td>6</td><td>683.4</td></tr><tr><td>AgScP2Se6 (bi)</td><td>4.06</td><td>0.15 eV</td><td>-1.37 eV</td><td>2.63</td><td>6</td><td>412.8</td></tr><tr><td>IrBr3 (bi)</td><td>6.53</td><td>0.23 eV</td><td>-1.43 eV</td><td>8.08</td><td>2</td><td>262.7</td></tr><tr><td>IrI3 (bi)</td><td>7.59</td><td>0.33 eV</td><td>-0.95 eV</td><td>1.76</td><td>2</td><td>49.1</td></tr><tr><td>YI3 (tri)</td><td>3.45</td><td>0.53 eV</td><td>-2.1 eV</td><td>2.12</td><td>1</td><td>65.3</td></tr><tr><td>YBr3 (tri)</td><td>6.78</td><td>0.68 eV</td><td>-3.15 eV</td><td>2.76</td><td>1</td><td>43.3</td></tr><tr><td>ReSe2 (bi)</td><td>6.38</td><td>0.32 eV</td><td>-0.83 eV</td><td>1.82</td><td>2</td><td>60.7</td></tr><tr><td>ScOCl (bi)</td><td>5.27</td><td>0.21 eV</td><td>-4.04 eV</td><td>3.29</td><td>1</td><td>66.2</td></tr><tr><td>PbO (bi)</td><td>8.47</td><td>2.02 eV</td><td>-0.03 eV</td><td>11.89</td><td>4</td><td>595.8</td></tr><tr><td>CrI3 (bi)</td><td>3.00</td><td>-0.32 eV</td><td>-1.58 eV</td><td>2.02</td><td>2</td><td>142.8</td></tr><tr><td>CrOCl (bi)</td><td>3~4</td><td>-0.13 eV</td><td>-3.26 eV</td><td>1.31</td><td>2</td><td>55.7-74.2</td></tr><tr><td>WS2 (tri,quad)</td><td>3.63</td><td>0~0.08 eV</td><td>-1.01~-0.97 eV</td><td>1.16</td><td>6</td><td>201~203</td></tr><tr><td>WSe2 (tri,quad)</td><td>4.07</td><td>0.27~0.47 eV</td><td>-0.65~-0.52 eV</td><td>0.53</td><td>6</td><td>87.4</td></tr><tr><td>MoSe2 (bi, tri, quad)</td><td>7.29</td><td>-0.01~-0.31 eV</td><td>-0.97~-0.86 eV</td><td>0.73~0.77</td><td>6</td><td>66~70</td></tr><tr><td>MoTe2 (bi, tri, quad)</td><td>6.75</td><td>0.31~-0.42 eV</td><td>-0.54~-0.47 eV</td><td>0.7~0.75</td><td>6</td><td>68~73</td></tr></table>  
+
+of these materials at the band edges (estimated under slight doping concentration \(n = 10^{12}\mathrm{cm}^{- 2}\) ) are all above the threshold of forming a Wigner- crystal state \((r_{s} \gtrsim 31)\) [53]. Additionally, the energy bands of these insulating substrate materials can be easily shifted using vertical displacement fields [22], such that charge transfer between graphene and the substrate can be controlled by non- disruptive gate voltages. We have also consider heterostructures consisted of graphene and TMDs. Besides trilayer (or thicker) \(\mathrm{WS}_2\) as already listed in Table I, we further nominate \(\mathrm{WSe}_2\) (trilayer or thicker), \(\mathrm{MoSe}_2\) (bilayer or thicker), and \(\mathrm{MoTe}_2\) (bilayer or thicker) as possible candidate substrates to realize the effects discussed above. More details are given in Sec. S7 of Supplementary Material.  
+
+## CONCLUSIONS  
+
+In conclusion, we have studied the synergistic correlated electronic states emerging from coupled graphene- insulator heterostructures with gate tunable band alignment. Based on comprehensive theoretical studies, we have shown that the gate tunable carrier doping may yield a long- wavelength electronic crystal at the surface of the substrate driven by \(e - e\) interactions within the substrate, which in turn exerts a superlattice Coulomb potential to the Dirac electrons in graphene layer. This would substantially change the low- energy spectrum of graphene, where a gapped Dirac state concomitant with drastically enhanced Fermi velocity would emerge as \(e - e\) interaction effects. These theoretical results are quantitatively supported by our transport measurements in graphene- CrOCl heterostructure. Besides, the Dirac subbands in graphene can be endowed with nontrivial topological properties by virtue of the interlayer Coulomb coupling with the long- wavelength electronic crystal. Reciprocally, the electronic crystal in the substrate can be substantially stabilized by virtue of a cooperative interlayer Coulomb coupling with the gapped Dirac state of graphene. We have further performed high- throughput first principles calculations, and suggested a number of promising insulating materials as candidate substrates for graphene to realize such effects.  
+
+A plethora of rich physics may emerge in such coupled bilayer correlated electronic systems, and our work only unveils a tip of the ice berg. First, the long- wavelength electronic crystal cannot be the only possible candidate ground state. Other correlated states such as magnetic or even superconducting states may also occur in the charge doped insulating substrate, e.g., in the case of high- temperature cuprate superconductor [15, 16] and monolayer \(1\mathrm{T}^{\prime}\) - WTe2 [57]. This may give rise to diverse quantum states of matter in graphene due to interfacial proximity couplings with Dirac fermions. Moreover, so far we have only considered the ground state properties of such coupled bilayer correlated electronic systems. What is more intriguing is the collective excitations. The collective excitations of the electronic crystal can be considered as quantum "phonons", which can be coupled with the Dirac electrons, and may lead to unusual "quantum phonon- Dirac electron" coupling effects. Around the quantum melting point of the electronic crystal, strong quantum fluctuations would be coupled with Dirac fermions with graphene via interlayer Coulomb
+
+<--- Page Split --->
+
+interactions, which may give rise to unique quantum critical properties. Therefore, our work may stimulate further exploration of the intriguing physics in such a new platform for correlated and topological electrons.  
+
+## METHODS  
+
+## Hartree-Fock approximations assisted by renormalization group approach  
+
+When graphene is coupled to a superlattice potential, the Coulomb interactions are suitably expressed in the subband eigenfunction basis, in which we have performed the Hartree- Fock approximations. Since interaction effects are most prominent around the CNP, we project the Coulomb interactions onto only a low- energy window including three valence and three conduction subbands that are closest to the Dirac point per valley per spin. We use a mesh of \(18 \times 18 \mathbf{k}\) - points to sample the mini Brillouin zone of the superlattice.  
+
+To incorporate the influences of Coulomb interactions from the high- energy remote bands, we rescale the Fermi velocity within the low- energy window of the effective Hamiltonian using Eq. (3). The other parameters of the non- interacting effective Hamiltonian are unchanged under the RG treatment since their corrections are of higher order, thus can be neglected. In other words, we find the following RG equations for Fermi velocity \(v_{F}\) and leading superlattice potential \(U_{d}\) with respect to energy cutoff \(E_{c}\)  
+
+\[\begin{array}{l}{\frac{d v_{F}}{d\log E_{c}} = -\frac{e^{2}}{16\pi\epsilon_{0}\epsilon_{r}},}\\ {\frac{d U_{d}(\mathbf{Q})}{d\log E_{c}} = 0.} \end{array} \quad (7)\]  
+
+The detailed derivations of the RG equations are presented in Sec. S3 of Supplementary Material.  
+
+We also neglect on- site Hubbard interactions and intervalley coupling in \(e - e\) Coulomb interactions, which turn out to be one or two order(s) of magnitude weaker than the dominant intravalley long- range Coulomb interactions in such graphene- based superlattice systems [58]. To model the screening effects to the \(e - e\) Coulomb interactions from the dielectric environment, we introduce the double gate screening form of \(V_{int}\) , whose Fourier transform is expressed as  
+
+\[V_{\mathrm{int}}(\mathbf{q}) = \frac{e^{2}\tanh(qd_{s})}{2\Omega_{0}\epsilon_{r}\epsilon_{0}q}, \quad (8)\]  
+
+where \(\Omega_{0}\) is the area of the superlattice's primitive cell, \(\epsilon_{r}\) is a background dielectric constant and the thickness between two gates is \(d_{s} = 400 \mathrm{\AA}\) . Then, we initialize the Hartree- Fock loop with the initial conditions in the form of various different order parameters and obtain the converged ground state self- consistently (see Sec. S4 of Supplementary Material [22]).  
+
+When we consider electrons in graphene and substrate on equal footing in Eq. (4), the routine of Hartree- Fock calculations is exactly the same. However, we need to first consider solely the substrate side. After doing similar Hartree- Fock calculations, we use the charge modulation of the converged charge- ordered state in the substrate as input for constructing the superlattice potential. Explicitly, we need to replace Eq. (2) by  
+
+\[U_{d}(\mathbf{Q}) = \frac{e^{2}}{2\epsilon_{0}\epsilon_{r}\Omega_{0}}\frac{e^{-|\mathbf{Q}|d}\rho_{d}(\mathbf{Q})}{|\mathbf{Q}|}. \quad (9)\]  
+
+where \(\rho_{d}(\mathbf{Q})\) is the Fourier component of the charge density in the substrate. More details can be found in Sec. S6 of Supplementary Material [22].  
+
+## Workflow to solve the coupled bilayer Hamiltonian Eqs. (4)  
+
+We solve the Hamiltonian of the coupled bilayer system described by Eqs. (4) in the following workflow:  
+
+- First, we start our calculations by considering solely the substrate Hamiltonian Eqs. (4b) and (4d), and the interaction Hamiltonian of the substrate Eq. (4d) is treated using the Hartree-Fock (HF) approximations for a presumed rectangular supercell with different superlattice constants \(L_{s}\) and fixed anisotropy \(r = L_{y} / L_{x} \approx 1.2\) (same as the atomic lattice of CrOCl). We focus on the range of parameters where the charge-ordered state is energetically more favored than the non-interacting Fermi liquid state.
+
+<--- Page Split --->
+![](images/Figure_5.jpg)
+
+<center>FIG. 5. Order of magnitudes of subband width (green) and intra- (red) and inter-layer (blue) Coulomb potential strength for different \(L_{s}\) . The dielectric constant is selected to be 4. </center>  
+
+- Second, with the help of the separable wavefunction hypothesis Eq. (5), we can integrate out the degrees of freedom of the substrate as we have done before so that the charge density modulation, which is characterized by the Fourier components of the charge density \(\{\rho_{d}(\mathbf{Q})\}\) ( \(\mathbf{Q}\) denotes the reciprocal vector of the superlattice), can be used as an input for the superlattice potential \(\bar{U}_{d}(\mathbf{Q})\) , as shown in Eq. (9). Compared to Eq. (2), this superlattice potential is more realistic and self-contained in our model. Eq. (9) would be recovered to Eq. (2) by setting \(\rho_{d}(\mathbf{Q}) = 2\) for any reciprocal vector \(\mathbf{Q}\) , which is equivalent to say that two (spin degenerate) charges per primitive supercell are localized in real space in a Dirac-\(\delta\) -function form.  
+
+- Third, we do the same type of HF calculations for the interacting Dirac electrons in graphene as explained in Methods. If the chemical potential is at the CNP of graphene, a gap opening will be triggered by \(e\) -\(e\) interactions within the graphene layer as discussed previously.  
+
+- From the above procedures, we would separately obtain converged HF ground states, \(|\Psi \rangle_{d}\) for the substrate, and \(|\Psi \rangle_{c}\) for graphene, respectively. From the ground-state wavefunctions \(|\Psi \rangle_{d}\) and \(|\Psi \rangle_{c}\) , one can extract the corresponding ground-state charge density modulations \(\{\rho_{d}(\mathbf{Q})\}\) and \(\{\rho_{c}(\mathbf{Q})\}\) , based on which the interlayer Coulomb energy [the expectation value of Eq. (4e)] can be calculated.  
+
+However, the ground states are obtained by minimizing (mostly) the intralayer parts of the full Hamiltonian, the interlayer Coulomb interaction Eq. (4e) is not optimized yet. We note that the intralayer kinetic energy and intralayer Coulomb interaction energy for both graphene and the substrate are unchanged under constant lateral shifts of the charge centers, thus the ground state \(|\Psi \rangle_{d} \otimes |\Psi \rangle_{c}\) obtained so far is massively degenerate up to global and relative shifts of the bilayer charge centers. Such degeneracy would be partially lifted by the interlayer Coulomb energy \(\langle H_{\mathrm{gr-sub}}\rangle\) . Obviously, \(\langle H_{\mathrm{gr-sub}}\rangle\) is invariant under the global shift of the charge centers of the bilayer system, but it varies with respect to a relative charge-center shift. Therefore, by the virtue of perturbation theory, optimizing the interlayer Coulomb energy amounts to find the optimal relative shift vector between the charge centers of the two layers within the degenerate ground-state manifold obtained in the previous procedures. Such perturbative treatment of \(H_{\mathrm{gr-sub}}\) is justified given that the interlayer Coulomb energy is always weaker than the intralayer one within relevant parameter regime, as shown in Fig. 5. For example, the interlayer Coulomb energy \(\sim 20 \mathrm{meV}\) for typical parameters \(L_{s} = 50 \mathrm{\AA}\) and \(\epsilon_{r} = 4\) , while the intralayer Coulomb energy \(\sim 60 \mathrm{meV}\) . More details for the perturbative calculation of interlayer Coulomb energy can be found in Sec. S6 of Supplementary Material [22].  
+
+- Finally, we gather all the contributions from Eq. (4) to find out the total energy of the coupled bilayer system staying in a gapped Dirac state (at the CNP) for graphene and a long-wavelength charge-ordered state for the substrate. By comparing it with that of a non-interacting Dirac state for graphene and a 2D electron-gas state for the substrate, we can then find out if the gapped graphene interplays with the long-wavelength charge-ordered substrate in a cooperative or competitive manner. It turns out that the bilayer system tends to cooperate with each other such that both the gapped Dirac state (at the CNP) of graphene and the long-wavelength charge ordered state in the substrate are substantially stabilized by the interlayer Coulomb coupling. The results are presented in Fig. 2 and 4 of main text.
+
+<--- Page Split --->
+
+The first principles calculations are performed with the projector augmented- wave method within the density functional theory [59], as implemented in the Vienna ab initio simulation package software [60]. The crystal structure is fully optimized until the energy difference between two successive steps is smaller than \(10^{- 6}\mathrm{eV}\) and the Hellmann- Feynman force on each atom is less than \(0.01\mathrm{eV}\cdot \mathrm{\AA}\) . The generalized gradient approximation by Perdew, Burke, and Ernzerhof is taken as the exchange- correlation potential [61]. As Cr is a transition metal element with localized \(3d\) orbitals, we use the on- site Hubbard parameter \(U = 5.48\mathrm{eV}\) for the Cr \(3d\) orbitals in the CrOCl bilayer and \(U = 3\mathrm{eV}\) for Cr \(3d\) orbitals in the \(\mathrm{CrI_3}\) bilayer. The so- called fully localized limit of the spin- polarized GGA+U functional is adopted as suggested by Liechtenstein and coworkers [62], and the non- spherical contributions from the gradient corrections are taken into consideration. The "DFT+D2" type of vdW correction has been adopted for all multilayer calculations to properly describe the interlayer interactions [63].  
+
+Our high- throughput filtering of the proper insulating substrate materials for graphene starts from the 2D materials computational database [64]. We only focus at those with bulk van der Waals structures which have been previously synthesized in laboratory. This ensures that it is experimentally feasible to exfoliate few layers from their bulk sample and then stack them on graphene to form heterostructures.  
+
+## Experimental measurements of the gaps in graphene-CrOCl heterostructure  
+
+By designing a dual- gated structure, we used few- layered CrOCl as an bottom dielectric while few- layered hexagonal boron nitride (h- BN) was served as top gate dielectric. The top and bottom gate voltages can then be converted into doping and displacement fields for further data analysis. Graphene, h- BN, and CrOCl flakes are mechanically exfoliated from high quality bulk crystals. The vertical assembly of few- layered hBN, monolayer graphene and few- layered CrOCl were made using the polymer- assisted dry- transfer method. Electron beam lithography was done using a Zeiss Sigma 300 SEM with a Raith Elphy Quantum graphic writer. Top and bottom gates as well as contacting electrodes were fabricated with an e- beam evaporator, with typical thicknesses of \(\mathrm{Ti / Au} \sim 5 / 50\mathrm{nm}\) . Electrical transport measurements of the devices were performed using an Oxford TeslaTron 1.5 K system. Gate voltages on the as- prepared multi- terminal devices were fed by a Keithley 2400 source meter. Channel resistances were recorded in 4- probe configurations using low frequency (13.33 Hz) lock- in technique with Stanford SR830 amplifiers. The gate dependencies of channel resistances were measured at various temperatures for the extraction of thermal gaps.  
+
+## DATA AVAILABILITY  
+
+The data that support the findings of this study are available from the corresponding author upon reasonable request.  
+
+## ACKNOWLEDGEMENT  
+
+We would like to thank Jian Kang and Jinhai Mao for valuable discussions, and to thank Hanwen Wang and Zhongqing Guo for the help in making the plots. This work is supported by the National Natural Science Foundation of China (grant No. 12174257, No. 11974357, and No. U1932151), the National Key R & D program of China (grant No. 2020YFA0309601 and No. 2019YFA0307800), and the start- up grant of ShanghaiTech University.  
+
+## AUTHOR CONTRIBUTIONS  
+
+J. L. conceived the idea and supervised the project. X. L. and S. Z. performed calculations. X. G., K. Y., Y. Y., and Z. V. H. performed transport measurements. X. L., Z. V. H., and J. L. analysed the data. X. L. and J. L. wrote the manuscript with inputs from all authors.
+
+<--- Page Split --->
+
+The Authors declare no competing interests.
+
+<--- Page Split --->
+
+* liujp@shanghaitech.edu.cn
+
+<--- Page Split --->
+
+[37] R. Zan, U. Bangert, C. Muryn, P. Mattocks, B. Hamilton, and K. S. Novoselov, Journal of Physics: Conference Series 371, 012070 (2012).[38] T. Stauber, P. Parida, M. Trushin, M. V. Ulybyshev, D. L. Boyda, and J. Schliemann, Phys. Rev. Lett. 118, 266801 (2017).[39] J. Gonzalez, F. Guinea, and V. M. A. H., Nuclear Physics B 424, 595 (1994).[40] O. Vafek and J. Kang, Phys. Rev. Lett. 125, 257602 (2020).[41] M. Vozmediano, M. Katsnelson, and F. Guinea, Physics Reports 496, 109 (2010).[42] N. Levy, S. A. Burke, K. L. Meaker, M. Panlasigui, A. Zettl, F. Guinea, A. H. C. Neto, and M. F. Crommie, Science 329, 544 (2010).[43] H. Fukuyama, P. M. Platzman, and P. W. Anderson, Phys. Rev. B 19, 5211 (1979).[44] E. Y. Andrei, G. Deville, D. C. Glattli, F. I. B. Williams, E. Paris, and B. Etienne, Phys. Rev. Lett. 60, 2765 (1988).[45] Z. Song, Z. Wang, W. Shi, G. Li, C. Fang, and B. A. Bernevig, Phys. Rev. Lett. 123, 036401 (2019).[46] J. Ahn, S. Park, and B.-J. Yang, Phys. Rev. X 9, 021013 (2019).[47] G. Tarnopolsky, A. J. Kruchkov, and A. Vishwanath, Phys. Rev. Lett. 122, 106405 (2019).[48] H. C. Po, L. Zou, T. Senthil, and A. Vishwanath, Phys. Rev. B 99, 195455 (2019).[49] J. Liu, J. Liu, and X. Dai, Phys. Rev. B 99, 155415 (2019).[50] P. San-Jose, J. Gonzalez, and F. Guinea, Phys. Rev. Lett. 108, 216802 (2012).[51] C. Forsythe, X. Zhou, K. Watanabe, T. Taniguchi, A. Pasupathy, P. Moon, M. Koshino, P. Kim, and C. R. Dean, Nature Nanotechnology 13, 566 (2018).[52] S. A. A. Ghorashi, A. Dunbrack, J. Sun, X. Du, and J. Cano, Topological and stacked flat bands in bilayer graphene with a superlattice potential (2022).[53] N. D. Drummond and R. J. Needs, Phys. Rev. Lett. 102, 126402 (2009).[54] I. Petousis, W. Chen, G. Hautier, T. Graf, T. D. Schladt, K. A. Persson, and F. B. Prinz, Phys. Rev. B 93, 115151 (2016).[55] I. Petousis, D. Mrdjenovich, E. Ballouz, M. Liu, D. Winston, W. Chen, T. Graf, T. D. Schladt, K. A. Persson, and F. B. Prinz, Scientific Data 4, 160134 (2017).[56] K. Choudhary, K. F. Garrity, A. C. Reid, B. DeCost, A. J. Biacchi, A. R. H. Walker, Z. Trautt, J. Hattrick-Simpers, A. G. Kusne, A. Centrone, et al., npj Computational Materials 6, 1-13 (2020).[57] E. Sajadi, T. Palomaki, Z. Fei, W. Zhao, P. Bement, C. Olsen, S. Luescher, X. Xu, J. A. Folk, and D. H. Cobden, Science 362, 922 (2018), https://www.science.org/doi/pdf/10.1126/science.aar4426.[58] S. Zhang, X. Dai, and J. Liu, Phys. Rev. Lett. 128, 026403 (2022).[59] P. E. Blochl, Phys. Rev. B 50, 17953 (1994).[60] G. Kresse and J. Furthmuller, Phys. Rev. B 54, 11169 (1996).[61] J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996).[62] A. I. Liechtenstein, V. I. Anisimov, and J. Zaanen, Phys. Rev. B 52, R5467 (1995).[63] S. Grimme, Journal of Computational Chemistry 27, 1787 (2006).[64] S. Haastrup, M. Strange, M. Pandey, T. Deilmann, P. S. Schmidt, N. F. Hinsche, M. N. Gjerding, D. Torelli, P. M. Larsen, A. C. Riis-Jensen, J. Gath, K. W. Jacobsen, J. J. Mortensen, T. Olsen, and K. S. Thygesen, 2D Mater. 5, 042002 (2018).
+
+<--- Page Split --->
+
+## Supplementary Files  
+
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+suppv5.4. pdf
+
+<--- Page Split --->

preprint/preprint__ca09945ee4b008190f2b304d99b412af91f547544a1a61b8d6db409ecffa41d7/preprint__ca09945ee4b008190f2b304d99b412af91f547544a1a61b8d6db409ecffa41d7_det.mmd

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+<|ref|>title<|/ref|><|det|>[[44, 108, 951, 175]]<|/det|>
+# Synergistic correlated states and nontrivial topology in coupled graphene-insulator heterostructures  
+
+<|ref|>text<|/ref|><|det|>[[44, 196, 888, 260]]<|/det|>
+Xin Lu School of Physical Sciences and Technology, ShanghaiTech University, Shanghai 200031, China https://orcid.org/0000- 0002- 6228- 1480  
+
+<|ref|>text<|/ref|><|det|>[[44, 265, 867, 308]]<|/det|>
+Shihao Zhang School of Physics and Electronics, Hunan University https://orcid.org/0000- 0002- 5787- 5022  
+
+<|ref|>text<|/ref|><|det|>[[44, 313, 210, 352]]<|/det|>
+Xiang Gao Shanxi University  
+
+<|ref|>text<|/ref|><|det|>[[44, 358, 209, 397]]<|/det|>
+Kaining Yang Shanxi University  
+
+<|ref|>text<|/ref|><|det|>[[44, 404, 208, 443]]<|/det|>
+Yuchen Gao Peking University  
+
+<|ref|>text<|/ref|><|det|>[[44, 450, 566, 490]]<|/det|>
+Yu Ye Peking University https://orcid.org/0000- 0001- 6046- 063X  
+
+<|ref|>text<|/ref|><|det|>[[44, 496, 566, 537]]<|/det|>
+Zheng Han Shanxi University https://orcid.org/0000- 0001- 5721- 6206  
+
+<|ref|>text<|/ref|><|det|>[[44, 541, 631, 584]]<|/det|>
+Jianpeng Liu ( liujp@shanghaitech.edu.cn ) ShanghaiTech University https://orcid.org/0000- 0002- 8564- 0415  
+
+<|ref|>text<|/ref|><|det|>[[44, 625, 102, 642]]<|/det|>
+Article  
+
+<|ref|>text<|/ref|><|det|>[[44, 664, 135, 682]]<|/det|>
+Keywords:  
+
+<|ref|>text<|/ref|><|det|>[[44, 702, 303, 721]]<|/det|>
+Posted Date: March 7th, 2023  
+
+<|ref|>text<|/ref|><|det|>[[44, 740, 473, 758]]<|/det|>
+DOI: https://doi.org/10.21203/rs.3. rs- 2641075/v1  
+
+<|ref|>text<|/ref|><|det|>[[44, 777, 910, 819]]<|/det|>
+License: © This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License  
+
+<|ref|>text<|/ref|><|det|>[[44, 838, 530, 857]]<|/det|>
+Additional Declarations: There is NO Competing Interest.  
+
+<|ref|>text<|/ref|><|det|>[[42, 893, 950, 936]]<|/det|>
+Version of Record: A version of this preprint was published at Nature Communications on September 9th, 2023. See the published version at https://doi.org/10.1038/s41467- 023- 41293- 8.
+
+<--- Page Split --->
+<|ref|>title<|/ref|><|det|>[[100, 61, 901, 98]]<|/det|>
+# Synergistic correlated states and nontrivial topology in coupled graphene-insulator heterostructures  
+
+<|ref|>text<|/ref|><|det|>[[180, 111, 825, 145]]<|/det|>
+Xin Lu, \(^{1}\) Shihao Zhang, \(^{1}\) Xiang Gao, \(^{2,3}\) Kaining Yang, \(^{2,3}\) Yuchen Gao, \(^{4,5}\) Yu Ye, \(^{4,5}\) Zheng Vitto Han, \(^{2,3}\) and Jianpeng Liu \(^{1,6,*}\)  
+
+<|ref|>text<|/ref|><|det|>[[179, 148, 825, 272]]<|/det|>
+\(^{1}\) School of Physical Science and Technology, ShanghaiTech University, Shanghai 201210, China \(^{2}\) State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto- Electronics, Shanxi University, 030006 Taiyuan, China \(^{3}\) Collaborative Innovation Center of Extreme Optics, Shanxi University, 030006 Taiyuan, China \(^{4}\) Collaborative Innovation Center of Quantum Matter, Beijing 100871, China \(^{5}\) State Key Lab for Mesoscopic Physics and Frontiers Science Center for Nano- Optoelectronics, School of Physics, Peking University, Beijing 100871, China \(^{6}\) ShanghaiTech Laboratory for Topological Physics, ShanghaiTech University, Shanghai 201210, China  
+
+<|ref|>text<|/ref|><|det|>[[175, 279, 830, 532]]<|/det|>
+In this work, we study the synergistic correlated states in two distinct types of interacting electronic systems coupled by interlayer Coulomb interactions. We propose that this scenario can be realized in a new type of Coulomb- coupled graphene- insulator heterostructures with gate tunable band alignment. We find that, by virtue of the interlayer Coulomb coupling between the interacting electrons in the two layers, intriguing correlated physics that is not seen in either individual layer emerges in a cooperative and synergistic manner. Specifically, as a result of the band alignment, charge carriers can be transferred between graphene and the substrate under the control of gate voltages, which can yield a long- wavelength electronic crystal at the surface of the substrate. This electronic crystal exerts a superlattice Coulomb potential on the Dirac electrons in graphene, which generates subbands with reduced non- interacting Fermi velocity. As a result, \(e - e\) Coulomb interactions within graphene would play a more important role, giving rise to a gapped Dirac state at the charge neutrality point, accompanied by interaction- enhanced Fermi velocity. Moreover, the superlattice potential can give rise to topologically nontrivial subband structures which are tunable by superlattice's constant and anisotropy. Reciprocally, the electronic crystal formed in the substrate can be substantially stabilized in such coupled bilayer heterostructure by virtue of the cooperative interlayer Coulomb coupling. We further perform high- throughput first principles calculations to identify a number of promising insulating materials as candidate substrates for graphene to demonstrate these effects. Our findings provide new insights into the physics of correlated and topological electronic states in graphene- based heterostructures.  
+
+<|ref|>sub_title<|/ref|><|det|>[[429, 560, 572, 575]]<|/det|>
+## INTRODUCTION  
+
+<|ref|>text<|/ref|><|det|>[[72, 592, 919, 700]]<|/det|>
+Graphene hosts two- dimensional (2D) massless Dirac electrons with linear dispersions and nontrivial Berry phases around two inequivalent \(K\) and \(K^{\prime}\) valleys in the Brillouin zone (BZ) [1, 2]. Such linear dispersions and topological properties of Dirac cones bestow various intriguing single- particle physical properties to graphene including the relativistic Landau levels, the Klein tunneling effects, and the nontrivial edge states, etc. [2]. Besides, low- energy Dirac fermions in graphene also exhibit distinct \(e - e\) interaction effects [3], such as the interaction- enhanced Fermi velocity [4, 5], the gap opening at the charge neutrality point [6- 8], and even chiral superconductivity when the Fermi level locates at the van Hove singularity [9].  
+
+<|ref|>text<|/ref|><|det|>[[72, 700, 919, 777]]<|/det|>
+Insulating transition metal oxides (TMOs) and transition metal chalcogenides (TMCs) have also stimulated significant research interests over the past few decades due to the diverse correlated phenomena discovered in these systems such as Mott insulator [10], excitonic insulator [11, 12], and various complex symmetry- breaking states [13, 14]. Under charge dopings, these insulating TMOs and/or TMCs may show more intriguing correlated states including unconventional superconductivity [15- 17] and long- wavelength charge density wave [18].  
+
+<|ref|>text<|/ref|><|det|>[[72, 777, 919, 913]]<|/det|>
+An open question is what would happen if two types of distinct interacting many- electron systems, i.e., the interacting Dirac fermions in graphene and the correlated electrons in (slightly) charge doped TMO and/or TMC insulators, are integrated into a single platform. Especially, how the mutual couplings would affect the interacting electronic states in both systems. Inspired by recent pioneering experiments in CrOCl- graphene [19], 1T- TaS \(_2\) - graphene [20], and CrI \(_3\) - graphene [21] heterostructures, here we propose that such a scenario (of interacting Dirac fermions coupled with the correlated electrons in charge doped TMO/TMC insulators) can be realized in graphene- insulator heterostructures with gate tunable band alignment. In this work, we show that, by virtue of the interlayer Coulomb coupling between the interacting electrons in the two layers, intriguing correlated physics that cannot be seen in either individual layer would emerge in a cooperative and synergistic manner in such band- aligned graphene- insulator heterostructures.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[66, 63, 920, 293]]<|/det|>
+When Dirac points of graphene are energetically close to the band edge of the insulating substrate, charge carriers can be transferred between graphene and the substrate under the control of gate voltages due to quantum tunnelling effects. This may yield a long- wavelength electronic crystal (EC) at the surface of the substrate, given that the carrier density introduced to the substrate is below a threshold value, as schematically shown in Fig. 1(a,b). On the one hand, the long- wavelength EC at the surface of the substrate would impose an interlayer superlattice Coulomb potential to graphene, which would generate subbands with reduced non- interacting Fermi velocity of the Dirac cone, thus triggers gap opening at the Dirac points by \(e\) - \(e\) interactions in graphene. Meanwhile, concomitant with the gap opening, the Fermi velocities around the charge neutrality point (CNP) are dramatically enhanced due to \(e\) - \(e\) interactions effects. The subbands may also possess nontrivial topological properties with nonzero valley Chern numbers that can be controlled by superlattice constant and anisotropy. Especially, we find a number of "magic lines" in the parameter space of superlattice's constant and anisotropy, at which the Fermi velocity along one direction vanishes exactly. The subbands would acquire Chern numbers when passing through these magic lines. On the other hand, the gapped Dirac state at the CNP of graphene would further stabilize the long wavelength electronic- crystal state in the substrate by pinning the relative charge centers of the two layers in an anti- phase pattern, in order to optimize the interlayer Coulomb interactions.  
+
+<|ref|>image<|/ref|><|det|>[[222, 304, 810, 676]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[84, 693, 920, 775]]<|/det|>
+<center>FIG. 1. (a) Cartoon illustration of a monolayer graphene supported by an insulating substrate with long-wavelength charge order (blue dots), with an interlayer distance \(d\) . (b) Schematic of charge transfer in a band-aligned graphene-insulator heterostructure and its effects on the Dirac dispersion. (c) shows the non-interacting band structure by blue solid lines with \(r = 1.2\) and \(L_{s} = 600 \text{Å}\) . The red dashed lines represent the non-interacting Dirac cones in free-standing graphene. The inset marks the high-symmetry points in the superlattice Brillouin zone. (d) shows the calculated effective fine structure constant \(\alpha (L_{s}, \epsilon_{r})\) , where the dashed line marks the critical value \(\alpha_{c} \approx 0.92\) . </center>  
+
+<|ref|>sub_title<|/ref|><|det|>[[316, 820, 686, 835]]<|/det|>
+## COULOMB INTERACTIONS IN GRAPHENE  
+
+<|ref|>text<|/ref|><|det|>[[63, 852, 919, 914]]<|/det|>
+To describe the graphene- insulator heterostructure, we consider a model Hamiltonian consisted of a graphene part, an insulator substrate part, and the coupling between them (see Eqs. (4) and Sec. S6 of Supplementary Material [22]). As we are interested in the low- energy electronic properties, graphene's band structure is modelled by the low- energy Dirac cones around the \(K\) and \(K'\) valleys. The long- wavelength EC (charge ordered) state in the substrate is considered
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[60, 64, 920, 141]]<|/det|>
+56 as a charge insulator, with the electrons being frozen to form a superlattice [22]. Thus, long- wavelength charge order of the substrate is coupled to the graphene layer via interlayer Coulomb interactions to exert a superlattice potential on the Dirac electrons. Neglecting the intervalley coupling thanks to the large superlattice constant \(L_{s}\) ( \(\gtrsim 50 \mathrm{\AA}\) ) [23], we can construct an effective single- particle Hamiltonian for the continuum Dirac fermions in graphene that are coupled with a superlattice Coulomb potential [22]  
+
+<|ref|>equation<|/ref|><|det|>[[402, 150, 916, 169]]<|/det|>
+\[H_{0}^{\mu}(\mathbf{r}) = \hbar v_{F}\mathbf{k}\cdot \pmb{\sigma}^{\mu} + U_{d}(\mathbf{r}) \quad (1)\]  
+
+<|ref|>text<|/ref|><|det|>[[60, 179, 920, 289]]<|/det|>
+61 where \(\sigma^{\mu}\) are the Pauli matrices \((\mu \sigma_{x},\sigma_{y})\) with the valley index \(\mu = \pm 1\) , \(v_{F}\) is the non- interacting Fermi velocity of graphene, and \(U_{d}(\mathbf{r})\) is the background superlattice potential with the period \(U_{d}(\mathbf{r}) = U_{d}(\mathbf{r} + \mathbf{L_{s}})\) . The superlattice of the EC is set to be rectangular, with anisotropy \(r = L_{y} / L_{x}\) and \(L_{x,y}\) being the superlattice constant in the \(x,y\) - direction, respectively. We denote \(L_{s} = L_{x}\) . As a result, the superlattice potential \(U_{d}(\mathbf{r})\) would fold Dirac cones into its small Brillouin zone (BZ), forming subbands and opening up a gap at the boundary of the supercell BZ, as shown in Fig. 1(c) for a rectangular superlattice with \(r = 1.2\) (same as that of CrOCl atomic lattice) in valley \(K\) ( \(\mu = 1\) ) with \(L_{s} = 600 \mathrm{\AA}\) . The energy degeneracies from folding are all lifted by \(U_{d}\) , whose Fourier component reads [22]  
+
+<|ref|>equation<|/ref|><|det|>[[411, 297, 916, 333]]<|/det|>
+\[U_{d}(\mathbf{Q}) = \frac{e^{2}}{\epsilon_{0}\epsilon_{r}\Omega_{0}}\frac{e^{-|\mathbf{Q}|d}}{|\mathbf{Q}|}, \quad (2)\]  
+
+<|ref|>text<|/ref|><|det|>[[60, 341, 920, 404]]<|/det|>
+68 where \(\mathbf{Q} \neq \mathbf{0}\) is the reciprocal lattice vector associated with \(\mathbf{L}_{s}\) , \(\Omega_{0} = L_{x}L_{y}\) is the area of the primitive cell of the superlattice. The Coulomb potential \(U_{d}\) , screened by a dielectric constant \(\epsilon_{r}\) , decays exponentially in the reciprocal space \(\sim \exp (- Qd)\) , where \(d\) is the distance between the substrate surface and graphene monolayer. Furthermore, the Fermi velocities near the Dirac points of the subbands are suppressed by \(U_{d}\) [24] as clearly shown in Fig. 1(c).  
+
+<|ref|>text<|/ref|><|det|>[[60, 403, 920, 585]]<|/det|>
+While it is highly desirable to open a gap at the Dirac points in graphene for the purpose of field- effect device fabrication, the superlattice potential of Eq. (2) alone cannot gap out Dirac points in graphene as the system still preserves \(C_{2z} \mathcal{T}\) symmetry. However, the Dirac points can be unstable against \(e\) - \(e\) Coulomb interactions (with the spontaneous breaking of \(C_{2z} \mathcal{T}\) symmetry) once the Fermi velocity of the non- interacting band structure is suppressed below a threshold, which can be assisted by the superlattice potential from the long- wavelength charge order. One of the similar illustrations is twisted bilayer graphene (TBG) [25], where the Fermi velocity is strongly suppressed around the "magic angle", leading to moiré flat bands exhibiting diverse correlated and topological phases [26- 31]. Here we further calculate the Fermi velocity of the superlattice subbands around the Dirac point, denoted as \(v_{F}(L_{s}, \epsilon_{r})\) , which is dependent on both the superlattice constant \(L_{s}\) and the background dielectric constant \(\epsilon_{r}\) . Accordingly, the effective fine structure constant \(\alpha (L_{s}, \epsilon_{r}) = e^{2} / (4 \pi \epsilon_{0} \epsilon_{r} \hbar v_{F}(L_{s}, \epsilon_{r}))\) can also be tuned by \(L_{s}\) and \(\epsilon_{r}\) , as shown in Fig. 1(d). We see that there is a substantial region in the \((L_{s}, \epsilon_{r})\) phase space with \(\alpha (L_{s}, \epsilon_{r}) > \alpha_{c} \approx 0.92\) [32], which indicates that the Dirac- semimetal phase of graphene may no longer be stable against \(e\) - \(e\) interactions within this regime.  
+
+<|ref|>text<|/ref|><|det|>[[60, 584, 920, 675]]<|/det|>
+This motivates us to include \(e\) - \(e\) interactions in the graphene layer in our model. Despite several theoretical predictions of gapped Dirac states in graphene [3, 6- 8], to the best of our knowledge no gap at the CNP has been experimentally observed in suspended graphene yet [33, 34]. This can be attributed to interaction- enhanced Fermi velocity around the CNP, screening of \(e\) - \(e\) interactions due to ripple- induced charge puddles, disorder effects, etc. [3, 35- 38]. Nevertheless, analogous to TBG, the subbands in our system with reduced non- interacting Fermi velocity would quench the kinetic energy and further promote the \(e\) - \(e\) interaction effects in graphene.  
+
+<|ref|>text<|/ref|><|det|>[[60, 675, 920, 752]]<|/det|>
+Our unrestricted Hartree- Fock calculations [22] confirm precisely the argument above. As interaction effects are most prominent around the CNP, we project the Coulomb interactions onto only a low- energy subspace including three valence and three conduction subbands ( \(n_{\mathrm{cut}} = 3\) ) that are closest to CNP for each valley and spin. To incorporate the influences of Coulomb interactions from the high- energy remote bands, we rescale the Fermi velocity within the low- energy subspace using the formula derived from the renormalization group (RG) approach [2- 4, 39]  
+
+<|ref|>equation<|/ref|><|det|>[[404, 760, 916, 796]]<|/det|>
+\[v_{F}^{*} = v_{F}\left(1 + \frac{\alpha_{0}}{4\epsilon_{r}}\log \frac{E_{c}}{E_{c}^{*}}\right) \quad (3)\]  
+
+<|ref|>text<|/ref|><|det|>[[60, 805, 920, 883]]<|/det|>
+where \(\alpha_{0} = e^{2} / (4 \pi \epsilon_{0} \hbar v_{F})\) is the ratio between the Coulomb interaction energy and kinetic energy, i.e., the effective fine- structure constant of free- standing graphene, \(E_{c}^{*}\) delimits the low- energy window within which the unrestricted Hartree- Fock calculations are to be performed, and \(E_{c}\) is an overall energy cut- off above which the Dirac- fermion description to graphene is no longer valid. Unlike TBG [40], other parameters of the effective Hamiltonian (Eq. (1)) such as \(U_{d}\) , are unchanged under the RG flow [22].  
+
+<|ref|>text<|/ref|><|det|>[[60, 883, 920, 914]]<|/det|>
+We first study the interaction effects of graphene coupled to a rectangular superlattice potential with \(r = 1.2\) and \(50 \mathrm{\AA} \leq L_{s} \leq 400 \mathrm{\AA}\) , corresponding to carrier density of the EC state at the surface of the substrate \(0.1 \times 10^{12} \mathrm{cm}^{- 2} \leq\)
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[144, 60, 852, 518]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[84, 530, 919, 624]]<|/det|>
+<center>FIG. 2. (a) Calculated Hartree-Fock single-particle excitation spectrum of graphene coupled to a long-wavelength Coulomb potential, with \(\nu = 0\) . (b) and (c) show by blue solid lines the Hartree-Fock band structures of \(L_{s} = 50 \mathrm{\AA}\) and \(\epsilon_{r} = 3.0\) , with the filling factor \(\nu = 0\) in (b) and \(\nu = -0.003\) in (c). The red dashed lines represent the non-interacting Dirac cones. The insets zoom in energy close to the Dirac points. (d) The calculated gaps at CNP (filled stars) and the interaction-enhanced Fermi velocities at slight hole dopings \(\nu = -0.003\) (hollow diamonds) as a function of the substrate's carrier density \(n\) . (e) The thermal activation gap \(\Delta\) measured on the devices in [19] for different nominal dopings \(n_{\mathrm{tot}}\) . (f) Distribution of Berry curvature of the highest valence subband of \(K\) valley for \(r = 1.2\) and \(L_{s} = 50 \mathrm{\AA}\) , which gives zero valley Chern number. </center>  
+
+<|ref|>text<|/ref|><|det|>[[55, 653, 919, 821]]<|/det|>
+\(n \leq 6.58 \times 10^{12} \mathrm{~cm}^{- 2}\) (with \(n = 2 / (r L_{s}^{2})\) ), with \(\epsilon_{r} = 3,4\) , and \(d = 7 \mathrm{\AA}\) (obtained from first principles density functional theory calculations for a CrOCl- graphene heterostructure [22]). Here, we consider two different filling factors: exactly at the CNP \((\nu = 0)\) and a slight hole doping \((\nu \approx - 0.003)\) . When \(\nu = 0\) , a gap can be opened up due to interaction effects [see Fig. 2(a,b)], leading to two nearly degenerate insulating states, one is sublattice polarized and the other valley polarized. Then, intervalley Coulomb interactions would split such degeneracy, and the sublattice polarized insulator with zero Chern number becomes the unique ground state [22]. Notably, the gap decreases linearly with \(n\) as clearly shown in Fig. 2(d), and eventually vanishes as \(n \to 0\) . This is because the superlattice Coulomb potential exerted on graphene is proportional to the carrier density of the long- wavelength order from the substrate. Consequently, the Fermi velocity of the bare Dirac dispersion of graphene would be less suppressed at smaller carrier density \(n\) , which disfavors gap opening. Eventually in the limit of \(n \to 0\) , with a charge ordered state of infinite lattice constant, graphene would recover its non- interacting behavior as a gapless Dirac semimetal.  
+
+<|ref|>text<|/ref|><|det|>[[84, 822, 919, 914]]<|/det|>
+To verify our theory, we have also experimentally measured the gaps at CNP in graphene- CrOCl heterostructure at different nominal carrier densities [22]. The measured gaps also decrease linearly with \(n_{\mathrm{tot}}\) , from \(7.7 \mathrm{meV}\) with \(n_{\mathrm{tot}} = 3.4 \times 10^{12} \mathrm{~cm}^{- 2}\) , to \(5.8 \mathrm{meV}\) with \(n_{\mathrm{tot}} = 0.5 \times 10^{12} \mathrm{~cm}^{- 2}\) [22], consistent with the trend from theoretical calculations, as shown in Fig. 2(e). When \(n_{\mathrm{tot}} \to 0\) , such a linear dependence of the gap on \(n_{\mathrm{tot}}\) may no longer be valid [22], which is possibly due to the formation of an excitonic- like insulator in the graphene- substrate bilayer- type system, or due to some complex Coulomb screening effects.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[135, 66, 879, 280]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[84, 292, 920, 374]]<|/det|>
+<center>FIG. 3. (a) and (b) shows the distribution of Berry curvature in the \(r = 3\) superlattice's BZ of the lowest valence and conduction band in valley \(K\) for \(L_{s} = 50\) and \(600\mathrm{\AA}\) , respectively. Their corresponding valley Chern number are also given on the top of each panel. (c) and (d) are the non-interacting band structure of the \(r = 3\) superlattice with \(L_{s} = 50\) and \(600\mathrm{\AA}\) . (e) Colormap of Fermi velocity in the \(x\) -direction \(v_{x}\) of the valence band for \(\epsilon_{r} = 3\) . The color coding indicates \(v_{x} / v_{F}\) . Here we vary \(L_{x}\) from 50 to \(600\mathrm{\AA}\) and anisotropy parameter \(r\) from 1 to 6. The white dashed line, i.e., the "magic lines", mark the position in parameter space where \(v_{x}\) vanishes. </center>  
+
+<|ref|>text<|/ref|><|det|>[[85, 400, 919, 476]]<|/det|>
+We note that the electronic crystal at the surface of the substrate is expected to persist even if the carrier density exceeds the threshold value due to the extra energy gain from interlayer Coulomb coupling in such coupled system, which will be discussed in detail in Sec. . Strain is also inevitable in such graphene- insulator heterostructures, which would give rise to pseudo- magnetic fields coupled to the Dirac electrons [5, 41, 42], thus further enhances the \(e\) - \(e\) interaction effects in graphene.  
+
+<|ref|>text<|/ref|><|det|>[[84, 476, 919, 670]]<|/det|>
+The single- particle excitation spectrum is also significantly altered by Coulomb interactions within the low- energy window, as shown in Fig. 2(b) and (c) with fillings \(\nu = 0\) and \(\nu = - 0.003\) , respectively. We note that although the superlattice potential \(U_{d}\) suppresses Fermi velocity in graphene [see Fig. 1(c)], \(e\) - \(e\) interactions can compensate such effects. The Fermi velocity is not only enhanced by the Coulomb potentials from the remote energy bands [Eq. (3)], but also further boosted by \(e\) - \(e\) interactions within the low energy window \(E_{c}^{*} \sim n_{\mathrm{cut}} \hbar v_{F} 2 \pi / L_{s}\) . Eventually, the Fermi velocity can be magnified up to more than twice of the non- interacting value of free- standing graphene \((v_{F})\) at slight hole doping \(\nu = - 0.003\) , as shown in Fig. 2(d). This perfectly explains the recent experiment in gate- controlled graphene- CrOCl heterostructure, in which the Fermi velocity around CNP is significantly enhanced compared to non- interacting value at slight carrier doping, such that robust quantum Hall effect can be observed under tiny vertical magnetic fields \((\sim 0.1 \mathrm{T})\) and high temperatures [19]. We note that the EC state may be stabilized by vertical magnetic fields even when the carrier density in the substrate exceeds the zero- field threshold value [43, 44], which in turn boosts the low- field, high- temperature quantum Hall effect in the graphene layer due to the scenario discussed above.  
+
+<|ref|>text<|/ref|><|det|>[[85, 670, 919, 732]]<|/det|>
+The essential results discussed above, i.e., the gap opening at CNP and the concomitant drastic enhancement of Fermi velocity, remain valid for different types of the background superlattices. Specifically, we have also performed calculations for the case of triangular charge- ordered superlattices, which lead to qualitatively the same conclusions, as presented in Sec. S5 of Supplementary Material [22].  
+
+<|ref|>sub_title<|/ref|><|det|>[[378, 757, 625, 772]]<|/det|>
+## TOPOLOGICAL PROPERTIES  
+
+<|ref|>text<|/ref|><|det|>[[85, 790, 919, 882]]<|/det|>
+Different from magic- angle TBG [45- 49], the low- energy subbands for graphene coupled to a rectangular superlattice potential \(U_{d}(\mathbf{r})\) with small anisotropy ( \(r \sim 1\) ) turn out to be topologically trivial with a compensating Berry- curvature distribution, leading to zero Chern number. This remains true even in the gapped Dirac state after including \(e\) - \(e\) interactions, as shown in Fig. 2(f). The trivial band topology is somehow anticipated because the superlattice potential is non- chiral in the sense that it is coupled equally to the two sublattice of graphene, which does not have any pseudo- gauge- field structure such as that in TBG [49, 50].  
+
+<|ref|>text<|/ref|><|det|>[[85, 882, 919, 913]]<|/det|>
+Hence, it is unexpected that changing the anisotropy \(r\) and the lattice size \(L_{s}\) of the superlattice potential \(U_{d}\) can make the subbands topological. For example, keeping \(L_{x} = 50\mathrm{\AA}\) but with \(r = 3.0\) , both the highest valence band and
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[77, 64, 919, 171]]<|/det|>
+the lowest conduction band acquire nonzero valley Chern numbers \(C = \pm 1\) (after adding an infinitesimal \(C_{2z}\) - breaking staggered sublattice potential). As shown in Fig. 3(a), besides the four high symmetry points, it appears another two "hot spots" (annotated by green circles) along the line connecting \(\Gamma_{s}\) and \(X_{s}\) . This new contribution breaks the balance between positive and negative contribution of Berry curvature to Chern number, leading to non- zero valley Chern number. Such contribution stems from a new crossing point between the low- energy valence and conduction bands along the \(k_{x}\) - direction through changing merely the anisotropy parameter \(r\) , as shown in Fig. 3(c) by red dot within green circle.  
+
+<|ref|>text<|/ref|><|det|>[[77, 172, 919, 412]]<|/det|>
+While increasing \(r\) from unity (with fixed \(L_{s}\) ), the Fermi velocity in the \(x\) - direction of the valence band around the Dirac point, \(v_{x}\) , is gradually reduced, as shown in Fig. 3(e). As the same origin of Klein tunneling effects, the spinor structure of graphene's wavefunction forces the Fermi velocity in the \(y\) - direction to be intact [24]. Further tuning \(r\) at some point would totally flatten \(v_{x}\) . In Fig. 3(e), we mark by white dashed lines "the magic lines" on which \(v_{x}\) of the valence band closest to Dirac points vanishes exactly. The magic lines always come in pair as an effect of chiral (particle- hole) symmetry breaking induced by the superlattice potential. As particle- hole symmetry is broken in the energy spectrum, when \(v_{x}\) vanishes in the valence band, the counterpart in the conduction band remains finite. The valence subband around the Dirac point has to curve upwards to create a band crossing point, after that \(v_{x}\) of the valence band becomes zero again. Therefore, a band crossing would be germinated at the Dirac point, and then move away along the \(k_{x}\) - direction with larger \(r\) . If the Dirac point is gapped, say, by a tiny staggered sublattice potential, the low- energy subbands become topological with nonzero valley Chern numbers. In particular, with the increase of \(r\) at fixed \(L_{s}\) , the absolute value of valley Chern number of the valence subband (closest to Dirac points) increases by 1 whenever one pair of the magic lines are passed through. The positions of these magic lines are also dependent on the background dielectric constant \(\epsilon_{r}\) since larger \(\epsilon_{r}\) corresponds to weaker Fermi- velocity renormalization effect, which would shift the magic lines to larger \(r\) values. Such topologically nontrivial subbands with extremely anisotropic Fermi velocities may provide a new platform to realize novel topological quantum matter.  
+
+<|ref|>text<|/ref|><|det|>[[77, 413, 919, 563]]<|/det|>
+We note that the anisotropic charge ordered superlattices may be realized in two ways. First, one can design a spatially modulated electrostatic potential, which has been realized in monolayer graphene by inserting a patterned dielectric superlattice between the gate and the sample [51]. Then, the anisotropy of the superlattice can be artificially tuned by the dielectric patterning in the substrate. Second, for some given carrier density, the Fermi surface of the conduction (or valence) band of the substrate may be (partially) nested, which may lead to a charge density wave (CDW) state with the nesting wavevector. For example, for CrOCl, the Fermi surfaces under different Fermi energies (above the conduction band minimum) are given in Fig. S14 (c) of Supplementary Material. Clearly, under some proper fillings, the Fermi surfaces are nested or partially nested, which may give rise to CDW states with anisotropic superlattices. We note that topologically nontrivial flat bands have also proposed to exist in Bernal bilayer graphene coupled with a background superlattice potential [52].  
+
+<|ref|>text<|/ref|><|det|>[[77, 564, 919, 654]]<|/det|>
+Furthermore, we find that changing \(L_{s}\) can also control the valley Chern number of the subbands. For example, with \(r = 3\) and \(L_{s} = 600 \mathrm{\AA}\) , as shown in Fig. 3(b), while the highest valence band remains topological with non- zero valley Chern number 1 for valley \(K\) with the two aforementioned crossing points (green circles) merely moving to \(X_{s}\) , the lowest conduction band turns out to be topologically trivial. This is due to two new band crossing points (orange circles) close to the \(Y_{s} - S_{s}\) line between the lowest and the second lowest conduction bands, as annotated by red dots in an orange circle in Fig. 3(d).  
+
+<|ref|>text<|/ref|><|det|>[[77, 655, 919, 715]]<|/det|>
+The nontrivial topology must arise from the intrinsic Berry phases of the Dirac cones. Such topologically nontrivial bands are particularly surprising for our system, since the Dirac fermions are subjected to a "trivial" superlattice potential, which couples identically with two sublattices of graphene. Nevertheless, the nontrivial subband topology is highly tunable by changing the superlattice's size and anisotropy [22].  
+
+<|ref|>sub_title<|/ref|><|det|>[[204, 743, 797, 758]]<|/det|>
+## COOPERATIVE COUPLING BETWEEN GRAPHENE AND SUBSTRATE  
+
+<|ref|>text<|/ref|><|det|>[[77, 777, 919, 913]]<|/det|>
+In the previous calculations, a charge ordered superlattice in the substrate is presumed, which exerts a classical superlattice Coulomb potential to graphene. However, this assumption should be examined. We have to know to which extent that a presumed charge- ordered state underneath graphene is a viable starting point of our previous calculations. Even more importantly, in a coupled bilayer system, the coupling between graphene and the substrate has to be studied in a reciprocal way. Besides the effects from the substrate to graphene, the feedback effects from graphene to the substrate should be discussed as well. Therefore, here we study the coupled bilayer system as a whole, and treat the electrons in graphene layer and the substrate layer on equal footing. In particular, we model the carriers transferred to the substrate as 2D electron gas with long- range \(e - e\) Coulomb interactions. Electrons in the substrate and in graphene interact with each other via long- range Coulomb potential, whose Fourier component
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[55, 64, 919, 98]]<|/det|>
+of wavevector \(\mathbf{q}\) reads \(e^{2}\exp (- |\mathbf{q}| d) / (2\epsilon_{0}\epsilon_{r}|\mathbf{q}|)\) . Thus, the total Hamiltonian for the Coulomb- coupled graphene- insulator heterostructure system includes [22]:  
+
+<|ref|>equation<|/ref|><|det|>[[235, 121, 916, 339]]<|/det|>
+\[\begin{array}{r l} & {H_{\mathrm{gr}}^{0} = \sum_{\mathbf{k},\mu ,\alpha ,\alpha^{\prime},\sigma}\left(\hbar v_{F}\mathbf{k}\cdot \pmb{\sigma}^{\mu}\right)_{\alpha ,\alpha^{\prime}}\hat{c}_{\sigma \mu \alpha}^{\dagger}(\mathbf{k})\hat{c}_{\sigma \mu \alpha^{\prime}}(\mathbf{k}),}\\ & {H_{\mathrm{sub}}^{0} = \sum_{\mathbf{k},\sigma}\left(\frac{\hbar^{2}\mathbf{k}^{2}}{2m^{*}} +E_{\mathrm{CBM}}\right)\hat{d}_{\sigma}^{\dagger}(\mathbf{k})\hat{d}_{\sigma}(\mathbf{k}),}\\ & {H_{\mathrm{gr}}^{\mathrm{intra}} = \frac{1}{2S}\sum_{\sigma ,\sigma^{\prime}}\sum_{\alpha ,\alpha^{\prime}}V_{\mathrm{int}}(\mathbf{q})\hat{c}_{\sigma \mu \alpha}^{\dagger}(\mathbf{k} + \mathbf{q})\hat{c}_{\sigma^{\prime}\mu^{\prime}\alpha^{\prime}}^{\dagger}(\mathbf{k}^{\prime} - \mathbf{q})\hat{c}_{\sigma^{\prime}\mu^{\prime}\alpha^{\prime}}(\mathbf{k}^{\prime})\hat{c}_{\sigma \mu \alpha}(\mathbf{k}),}\\ & {H_{\mathrm{sub}}^{\mathrm{intra}} = \frac{1}{2S}\sum_{\mathbf{k},\mathbf{k}^{\prime},\mathbf{q}}\sum_{\sigma ,\sigma^{\prime}}V_{\mathrm{int}}(\mathbf{q})\hat{d}_{\sigma}^{\dagger}(\mathbf{k} + \mathbf{q})\hat{d}_{\sigma^{\prime}}^{\dagger}(\mathbf{k}^{\prime} - \mathbf{q})\hat{d}_{\sigma^{\prime}}(\mathbf{k}^{\prime})\hat{d}_{\sigma}(\mathbf{k}),}\\ & {H_{\mathrm{gr - sub}} = \frac{1}{S}\sum_{\mu ,\alpha ,\sigma ,\sigma^{\prime}}\sum_{\mathbf{k},\mathbf{k}^{\prime},\mathbf{q}}\frac{e^{2}e^{-|\mathbf{q}|d}}{2\epsilon_{0}\epsilon_{r}|\mathbf{q}|}\hat{c}_{\sigma \mu \alpha}^{\dagger}(\mathbf{k})\hat{d}_{\sigma^{\prime}}^{\dagger}(\mathbf{k}^{\prime})\hat{d}_{\sigma^{\prime}}(\mathbf{k}^{\prime} - \mathbf{q})\hat{c}_{\sigma \mu \alpha}(\mathbf{k} + \mathbf{q}).} \end{array} \quad (4c)\]  
+
+<|ref|>text<|/ref|><|det|>[[81, 352, 919, 641]]<|/det|>
+On the graphene side, Eq. (4a) is the familiar Dirac Hamiltonian describing the non- interacting low- energy physics of graphene. The \(e\) - \(e\) Coulomb interactions within graphene are described by Eq. (4c), where the dominant intravalley long- range Coulomb interactions are considered and \(V_{\mathrm{int}}(\mathbf{q})\) is in the form of double- gate screened Coulomb potential (see Eq. (8). Here, \(\hat{c}_{\sigma \mu \alpha}(\mathbf{k})\) and \(\hat{c}_{\sigma \mu \alpha}^{\dagger}(\mathbf{k})\) denote annihilation and creation operators for the low- energy Dirac electrons with wavevector \(\mathbf{k}\) , valley \(\mu\) , spin \(\sigma\) , and sublattice \(\alpha\) . Note that \(S\) refers to the total surface area of the coupled system, and the atomic wavevectors \(\mathbf{k}, \mathbf{k}^{\prime}, \mathbf{q}\) are expanded around the Dirac points. On the substrate side, without loss of generality, we suppose that the chemical potential is close to the conduction band minimum (CBM) with its energy \(E_{\mathrm{CBM}}\) , and the energy dispersion of the low- energy electrons around CBM can be modelled by a parabolic band as for 2D free electron gas with effective mass \(m^{*}\) . Other electrons in the deep valence bands are supposed to be integrated into the static dielectric screening constant thanks to a large gap of the substrate. Therefore, the non- interacting Hamiltonian Eq. (4b) for electrons in the substrate can be written in the plane wave basis with creation and annihilation operators \(\{\hat{d}_{\sigma}^{\dagger}(\mathbf{k}), \hat{d}_{\sigma}(\mathbf{k})\}\) , where \(\mathbf{k}\) is the plane wave wavevector expanded around the CBM, and \(\sigma\) denotes spin. The \(e\) - \(e\) Coulomb interactions within substrate [Eq. (4d)] is taken to be the long- range Coulomb interaction with the same double- gate screened form of \(V_{\mathrm{int}}(\mathbf{q})\) . The coupling between graphene and substrate is only via the long- range Coulomb potential, which is captured by Eq. (4e). The prefactor \(e^{2}\exp (- |\mathbf{q}| d) / (2\epsilon_{0}\epsilon_{r}|\mathbf{q}|)\) in front of the field operators in Eq. (4e) is nothing but the 2D Fourier transform of 3D Coulomb potential. Interlayer hoppings can be neglected given that the interlayer distance \(d \gtrsim 5 \mathring{\mathrm{A}}\) in such heterostructures (e.g., \(d \approx 7 \mathring{\mathrm{A}}\) in graphene- CrOCl heterostructure from first principles calculations), thus the exponentially decaying interlayer hopping amplitude is much weaker than the power- law- decaying interlayer Coulomb interaction.  
+
+<|ref|>text<|/ref|><|det|>[[85, 640, 918, 703]]<|/det|>
+We use distinct letters to denote the ladder operators for electrons in graphene \((\hat{c}, \hat{c}^{\dagger})\) and substrate \((\hat{d}, \hat{d}^{\dagger})\) . This implies in a notational manner the approximation of distinguishable electrons. In other words, the many- body wavefunction of the coupled bilayer system (denoted as \(|\Psi \rangle\) ) can be written a separable fashion, namely a direct product of graphene's and substrate's part, i.e.,  
+
+<|ref|>equation<|/ref|><|det|>[[437, 714, 916, 732]]<|/det|>
+\[|\Psi \rangle = |\Psi \rangle_{c}\otimes |\Psi \rangle_{d} \quad (5)\]  
+
+<|ref|>text<|/ref|><|det|>[[84, 742, 919, 915]]<|/det|>
+In a mean- field treatment, the corresponding many- body wavefunction would thus be a direct product of two Slater determinants, \(|\Psi \rangle_{c}\) and \(|\Psi \rangle_{d}\) for the graphene layer and the substrate layer, respectively. This is reminiscent of the Born- Oppenheimer approximation for electrons and ions. Technically, this means that order parameters \(\sim \langle \hat{c}^{\dagger} \hat{d} \rangle (\langle \hat{d}^{\dagger} \hat{c} \rangle)\) are not allowed in our treatment. A finite value of \(\langle \hat{c}^{\dagger} \hat{d} \rangle (\langle \hat{d}^{\dagger} \hat{c} \rangle)\) suggests the emergence of a new phase, an interlayer excitonic condensate in such coupled bilayer system. However, we note that such interlayer exciton has to be driven by intervalley Coulomb scattering between the \(K / K^{\prime}\) valley of graphene and (presumably) \(\Gamma\) valley of substrate's electrons, with the amplitude \(\sim e^{2}\exp (- |\mathbf{K}| d) / (2\epsilon_{0}\epsilon_{r}|\mathbf{K}|)\) being several orders of magnitudes smaller than the intravalley one in our problem. Thus, it is completely legitimate to neglect the interlayer particle- hole exchange in our problem, and the separable wavefunction hypothesis Eq. (5) is an excellent approximation. Then, we solve the full interacting Hamiltonian Eqs. (4) under the separable- wavefunction hypothesis Eq. (5), and the workflow is presented in Methods.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[84, 64, 919, 217]]<|/det|>
+To explore how the interlayer Coulomb coupling would affect the electronic crystal state of the substrate, we first consider the situation as a reference that the substrate is decoupled from graphene, and treat the \(e - e\) interactions within the substrate by Hartree- Fock approximations [22]. We obtain the energy difference between the EC state and Fermi- liquid (FL) state (condensation energy) as a function of the carrier density \(n\) as shown by the green circles in the right panel of Fig. 4. The condensation energy reaches zero when \(n \approx 7 \times 10^{- 12} \mathrm{~cm}^{- 2}\) suggesting the transition from the EC to the FL state. We further include the interlayer Coulomb coupling between the substrate and graphene (setting the chemical potential at the CNP of graphene), which can be treated using perturbation theory given that the interlayer Coulomb energy is always much smaller than the sum of the intralayer Coulomb energy and kinetic energy within the relevant parameter regime (see Fig. 5 in Methods). More details about the perturbative treatment of interlayer Coulomb interactions are presented in Sec. S6 of Supplementary Material [22].  
+
+<|ref|>text<|/ref|><|det|>[[85, 216, 919, 322]]<|/det|>
+We find that the condensation energy of the EC is substantially enhanced after including the interlayer interactions, as shown by the orange diamonds in Fig. 4. As a result, the EC- FL transition is postponed to a higher density \(n \approx 8.6 \times 10^{- 12} \mathrm{~cm}^{- 2}\) (obtained from extrapolation). This is because the energy of the coupled bilayer can be further lowered by pinning the charge centers (marked as light blue stars in the left panel of Fig. 4) of the two layers in an anti- phase- like pattern, in order to optimize the repulsive interlayer Coulomb energy. The extra energy gain from such "charge corrugation" compensates the energy cost of the EC state when \(n \gtrsim 7 \times 10^{- 12} \mathrm{~cm}^{- 2}\) , thus substantially stabilizes the EC state.  
+
+<|ref|>text<|/ref|><|det|>[[85, 322, 919, 399]]<|/det|>
+Certainly the mean- field treatment overestimates the condensation energy, but the qualitative conclusion that the EC state gets stabilized by a cooperative interlayer Coulomb coupling should be valid even in a beyond- mean- field treatment. This is because under the separable- wavefunction hypothesis, the interlayer Coulomb energy in the EC state is always negative (compared to that of FL state) under an optimal choice of relative charge centers, which thus always stabilizes the EC state even if the intralayer interactions are treated using beyond- mean- field approaches.  
+
+<|ref|>image<|/ref|><|det|>[[293, 414, 705, 595]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[85, 611, 919, 653]]<|/det|>
+<center>FIG. 4. Left: charge density modulation after minimizing interlayer Coulomb interactions of gapped Dirac state in graphene (top) and EC state in substrate (bottom); Right: Condensation energies of the electronic crystal state \(E_{\mathrm{cond}}\) vs. the carrier density \(n\) in the substrate. </center>  
+
+<|ref|>sub_title<|/ref|><|det|>[[385, 699, 617, 713]]<|/det|>
+## MATERIALS REALIZATION  
+
+<|ref|>text<|/ref|><|det|>[[85, 731, 919, 853]]<|/det|>
+The scenario discussed above is not only closely related to CrOCl- graphene and \(\mathrm{CrI_3}\) - graphene heterostructures [19, 21], but can also be extended to various band- aligned graphene- insulator heterostructures. As along as the conduction band minimum (CBM) or valence band maximum (VBM) of the substrate is energetically close to the Dirac points of graphene, charges could be easily transferred between graphene and the substrate's surface by gate voltages. Furthermore, it is more likely to form long- wavelength ordered state at the surface of the substrate (with slight carrier doping) if the material has large effective masses at the CBM or VBM. Meanwhile, an insulator with relatively small dielectric constant would have weaker screening effects to \(e - e\) interactions, which also favours long- wavelength ordered state at small carrier doping.  
+
+<|ref|>text<|/ref|><|det|>[[85, 853, 919, 915]]<|/det|>
+Following these guiding principles, we have performed high- throughput first principles calculations based on density functional theory for various insulating van der Waals materials. Eventually we find twelve suitable candidate materials (including CrOCl and \(\mathrm{CrI_3}\) ), whose CBM and VBM energy positions, dielectric constants ( \(\epsilon_r\) ), effective masses at the band edges, and the corresponding Wigner- Seitz radii ( \(r_s\) ) are listed in Table I. Clearly, the Wigner- Seitz radii
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[85, 74, 919, 153]]<|/det|>
+TABLE I. Candidate substrate materials for the graphene-insulator heterostructure systems. The dielectric constants \(\epsilon_{r}\) [54- 56], conduction band minimum position \((E_{\mathrm{CBM}})\) , valence band maximum position \((E_{\mathrm{VBM}})\) , the corresponding effective mass \(m^{*}\) at the band edge that is closer to the Dirac point (set to zero) in energy, and the dimensionless Wigner-Seitz radius \(r_{s} = g_{v}m^{*} / \sqrt{\pi n}\epsilon_{r}m_{0}a_{\mathrm{B}}^{0}\) \((a_{\mathrm{B}}^{0}\) is the Bohr radius and \(m_{0}\) is the bare electron mass, \(g_{v}\) is the valley degeneracy) estimated under a small doping concentration \(n = 10^{12}\mathrm{cm}^{- 2}\) , are presented. Here "bi" and "tri" stand for bilayer and trilayer systems, respectively.  
+
+<|ref|>table<|/ref|><|det|>[[225, 155, 778, 370]]<|/det|>
+
+<table><tr><td>Materials</td><td>εr</td><td>ECBM</td><td>EVBM</td><td>m*/m0</td><td>gv</td><td>rs</td></tr><tr><td>AgScP2S6 (bi)</td><td>3.67</td><td>0.07 eV</td><td>-1.89 eV</td><td>3.94</td><td>6</td><td>683.4</td></tr><tr><td>AgScP2Se6 (bi)</td><td>4.06</td><td>0.15 eV</td><td>-1.37 eV</td><td>2.63</td><td>6</td><td>412.8</td></tr><tr><td>IrBr3 (bi)</td><td>6.53</td><td>0.23 eV</td><td>-1.43 eV</td><td>8.08</td><td>2</td><td>262.7</td></tr><tr><td>IrI3 (bi)</td><td>7.59</td><td>0.33 eV</td><td>-0.95 eV</td><td>1.76</td><td>2</td><td>49.1</td></tr><tr><td>YI3 (tri)</td><td>3.45</td><td>0.53 eV</td><td>-2.1 eV</td><td>2.12</td><td>1</td><td>65.3</td></tr><tr><td>YBr3 (tri)</td><td>6.78</td><td>0.68 eV</td><td>-3.15 eV</td><td>2.76</td><td>1</td><td>43.3</td></tr><tr><td>ReSe2 (bi)</td><td>6.38</td><td>0.32 eV</td><td>-0.83 eV</td><td>1.82</td><td>2</td><td>60.7</td></tr><tr><td>ScOCl (bi)</td><td>5.27</td><td>0.21 eV</td><td>-4.04 eV</td><td>3.29</td><td>1</td><td>66.2</td></tr><tr><td>PbO (bi)</td><td>8.47</td><td>2.02 eV</td><td>-0.03 eV</td><td>11.89</td><td>4</td><td>595.8</td></tr><tr><td>CrI3 (bi)</td><td>3.00</td><td>-0.32 eV</td><td>-1.58 eV</td><td>2.02</td><td>2</td><td>142.8</td></tr><tr><td>CrOCl (bi)</td><td>3~4</td><td>-0.13 eV</td><td>-3.26 eV</td><td>1.31</td><td>2</td><td>55.7-74.2</td></tr><tr><td>WS2 (tri,quad)</td><td>3.63</td><td>0~0.08 eV</td><td>-1.01~-0.97 eV</td><td>1.16</td><td>6</td><td>201~203</td></tr><tr><td>WSe2 (tri,quad)</td><td>4.07</td><td>0.27~0.47 eV</td><td>-0.65~-0.52 eV</td><td>0.53</td><td>6</td><td>87.4</td></tr><tr><td>MoSe2 (bi, tri, quad)</td><td>7.29</td><td>-0.01~-0.31 eV</td><td>-0.97~-0.86 eV</td><td>0.73~0.77</td><td>6</td><td>66~70</td></tr><tr><td>MoTe2 (bi, tri, quad)</td><td>6.75</td><td>0.31~-0.42 eV</td><td>-0.54~-0.47 eV</td><td>0.7~0.75</td><td>6</td><td>68~73</td></tr></table>  
+
+<|ref|>text<|/ref|><|det|>[[55, 408, 919, 516]]<|/det|>
+of these materials at the band edges (estimated under slight doping concentration \(n = 10^{12}\mathrm{cm}^{- 2}\) ) are all above the threshold of forming a Wigner- crystal state \((r_{s} \gtrsim 31)\) [53]. Additionally, the energy bands of these insulating substrate materials can be easily shifted using vertical displacement fields [22], such that charge transfer between graphene and the substrate can be controlled by non- disruptive gate voltages. We have also consider heterostructures consisted of graphene and TMDs. Besides trilayer (or thicker) \(\mathrm{WS}_2\) as already listed in Table I, we further nominate \(\mathrm{WSe}_2\) (trilayer or thicker), \(\mathrm{MoSe}_2\) (bilayer or thicker), and \(\mathrm{MoTe}_2\) (bilayer or thicker) as possible candidate substrates to realize the effects discussed above. More details are given in Sec. S7 of Supplementary Material.  
+
+<|ref|>sub_title<|/ref|><|det|>[[437, 546, 566, 560]]<|/det|>
+## CONCLUSIONS  
+
+<|ref|>text<|/ref|><|det|>[[85, 579, 919, 760]]<|/det|>
+In conclusion, we have studied the synergistic correlated electronic states emerging from coupled graphene- insulator heterostructures with gate tunable band alignment. Based on comprehensive theoretical studies, we have shown that the gate tunable carrier doping may yield a long- wavelength electronic crystal at the surface of the substrate driven by \(e - e\) interactions within the substrate, which in turn exerts a superlattice Coulomb potential to the Dirac electrons in graphene layer. This would substantially change the low- energy spectrum of graphene, where a gapped Dirac state concomitant with drastically enhanced Fermi velocity would emerge as \(e - e\) interaction effects. These theoretical results are quantitatively supported by our transport measurements in graphene- CrOCl heterostructure. Besides, the Dirac subbands in graphene can be endowed with nontrivial topological properties by virtue of the interlayer Coulomb coupling with the long- wavelength electronic crystal. Reciprocally, the electronic crystal in the substrate can be substantially stabilized by virtue of a cooperative interlayer Coulomb coupling with the gapped Dirac state of graphene. We have further performed high- throughput first principles calculations, and suggested a number of promising insulating materials as candidate substrates for graphene to realize such effects.  
+
+<|ref|>text<|/ref|><|det|>[[85, 761, 919, 913]]<|/det|>
+A plethora of rich physics may emerge in such coupled bilayer correlated electronic systems, and our work only unveils a tip of the ice berg. First, the long- wavelength electronic crystal cannot be the only possible candidate ground state. Other correlated states such as magnetic or even superconducting states may also occur in the charge doped insulating substrate, e.g., in the case of high- temperature cuprate superconductor [15, 16] and monolayer \(1\mathrm{T}^{\prime}\) - WTe2 [57]. This may give rise to diverse quantum states of matter in graphene due to interfacial proximity couplings with Dirac fermions. Moreover, so far we have only considered the ground state properties of such coupled bilayer correlated electronic systems. What is more intriguing is the collective excitations. The collective excitations of the electronic crystal can be considered as quantum "phonons", which can be coupled with the Dirac electrons, and may lead to unusual "quantum phonon- Dirac electron" coupling effects. Around the quantum melting point of the electronic crystal, strong quantum fluctuations would be coupled with Dirac fermions with graphene via interlayer Coulomb
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[57, 65, 919, 96]]<|/det|>
+interactions, which may give rise to unique quantum critical properties. Therefore, our work may stimulate further exploration of the intriguing physics in such a new platform for correlated and topological electrons.  
+
+<|ref|>sub_title<|/ref|><|det|>[[455, 121, 547, 136]]<|/det|>
+## METHODS  
+
+<|ref|>sub_title<|/ref|><|det|>[[220, 152, 782, 168]]<|/det|>
+## Hartree-Fock approximations assisted by renormalization group approach  
+
+<|ref|>text<|/ref|><|det|>[[85, 184, 919, 261]]<|/det|>
+When graphene is coupled to a superlattice potential, the Coulomb interactions are suitably expressed in the subband eigenfunction basis, in which we have performed the Hartree- Fock approximations. Since interaction effects are most prominent around the CNP, we project the Coulomb interactions onto only a low- energy window including three valence and three conduction subbands that are closest to the Dirac point per valley per spin. We use a mesh of \(18 \times 18 \mathbf{k}\) - points to sample the mini Brillouin zone of the superlattice.  
+
+<|ref|>text<|/ref|><|det|>[[85, 261, 919, 337]]<|/det|>
+To incorporate the influences of Coulomb interactions from the high- energy remote bands, we rescale the Fermi velocity within the low- energy window of the effective Hamiltonian using Eq. (3). The other parameters of the non- interacting effective Hamiltonian are unchanged under the RG treatment since their corrections are of higher order, thus can be neglected. In other words, we find the following RG equations for Fermi velocity \(v_{F}\) and leading superlattice potential \(U_{d}\) with respect to energy cutoff \(E_{c}\)  
+
+<|ref|>equation<|/ref|><|det|>[[420, 344, 915, 414]]<|/det|>
+\[\begin{array}{l}{\frac{d v_{F}}{d\log E_{c}} = -\frac{e^{2}}{16\pi\epsilon_{0}\epsilon_{r}},}\\ {\frac{d U_{d}(\mathbf{Q})}{d\log E_{c}} = 0.} \end{array} \quad (7)\]  
+
+<|ref|>text<|/ref|><|det|>[[84, 420, 784, 437]]<|/det|>
+The detailed derivations of the RG equations are presented in Sec. S3 of Supplementary Material.  
+
+<|ref|>text<|/ref|><|det|>[[85, 435, 919, 498]]<|/det|>
+We also neglect on- site Hubbard interactions and intervalley coupling in \(e - e\) Coulomb interactions, which turn out to be one or two order(s) of magnitude weaker than the dominant intravalley long- range Coulomb interactions in such graphene- based superlattice systems [58]. To model the screening effects to the \(e - e\) Coulomb interactions from the dielectric environment, we introduce the double gate screening form of \(V_{int}\) , whose Fourier transform is expressed as  
+
+<|ref|>equation<|/ref|><|det|>[[415, 505, 915, 540]]<|/det|>
+\[V_{\mathrm{int}}(\mathbf{q}) = \frac{e^{2}\tanh(qd_{s})}{2\Omega_{0}\epsilon_{r}\epsilon_{0}q}, \quad (8)\]  
+
+<|ref|>text<|/ref|><|det|>[[85, 547, 919, 609]]<|/det|>
+where \(\Omega_{0}\) is the area of the superlattice's primitive cell, \(\epsilon_{r}\) is a background dielectric constant and the thickness between two gates is \(d_{s} = 400 \mathrm{\AA}\) . Then, we initialize the Hartree- Fock loop with the initial conditions in the form of various different order parameters and obtain the converged ground state self- consistently (see Sec. S4 of Supplementary Material [22]).  
+
+<|ref|>text<|/ref|><|det|>[[85, 608, 919, 670]]<|/det|>
+When we consider electrons in graphene and substrate on equal footing in Eq. (4), the routine of Hartree- Fock calculations is exactly the same. However, we need to first consider solely the substrate side. After doing similar Hartree- Fock calculations, we use the charge modulation of the converged charge- ordered state in the substrate as input for constructing the superlattice potential. Explicitly, we need to replace Eq. (2) by  
+
+<|ref|>equation<|/ref|><|det|>[[381, 678, 915, 714]]<|/det|>
+\[U_{d}(\mathbf{Q}) = \frac{e^{2}}{2\epsilon_{0}\epsilon_{r}\Omega_{0}}\frac{e^{-|\mathbf{Q}|d}\rho_{d}(\mathbf{Q})}{|\mathbf{Q}|}. \quad (9)\]  
+
+<|ref|>text<|/ref|><|det|>[[85, 722, 919, 753]]<|/det|>
+where \(\rho_{d}(\mathbf{Q})\) is the Fourier component of the charge density in the substrate. More details can be found in Sec. S6 of Supplementary Material [22].  
+
+<|ref|>sub_title<|/ref|><|det|>[[275, 779, 728, 794]]<|/det|>
+## Workflow to solve the coupled bilayer Hamiltonian Eqs. (4)  
+
+<|ref|>text<|/ref|><|det|>[[100, 811, 848, 828]]<|/det|>
+We solve the Hamiltonian of the coupled bilayer system described by Eqs. (4) in the following workflow:  
+
+<|ref|>text<|/ref|><|det|>[[110, 835, 919, 911]]<|/det|>
+- First, we start our calculations by considering solely the substrate Hamiltonian Eqs. (4b) and (4d), and the interaction Hamiltonian of the substrate Eq. (4d) is treated using the Hartree-Fock (HF) approximations for a presumed rectangular supercell with different superlattice constants \(L_{s}\) and fixed anisotropy \(r = L_{y} / L_{x} \approx 1.2\) (same as the atomic lattice of CrOCl). We focus on the range of parameters where the charge-ordered state is energetically more favored than the non-interacting Fermi liquid state.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[330, 72, 656, 234]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[85, 248, 919, 277]]<|/det|>
+<center>FIG. 5. Order of magnitudes of subband width (green) and intra- (red) and inter-layer (blue) Coulomb potential strength for different \(L_{s}\) . The dielectric constant is selected to be 4. </center>  
+
+<|ref|>text<|/ref|><|det|>[[112, 305, 919, 415]]<|/det|>
+- Second, with the help of the separable wavefunction hypothesis Eq. (5), we can integrate out the degrees of freedom of the substrate as we have done before so that the charge density modulation, which is characterized by the Fourier components of the charge density \(\{\rho_{d}(\mathbf{Q})\}\) ( \(\mathbf{Q}\) denotes the reciprocal vector of the superlattice), can be used as an input for the superlattice potential \(\bar{U}_{d}(\mathbf{Q})\) , as shown in Eq. (9). Compared to Eq. (2), this superlattice potential is more realistic and self-contained in our model. Eq. (9) would be recovered to Eq. (2) by setting \(\rho_{d}(\mathbf{Q}) = 2\) for any reciprocal vector \(\mathbf{Q}\) , which is equivalent to say that two (spin degenerate) charges per primitive supercell are localized in real space in a Dirac-\(\delta\) -function form.  
+
+<|ref|>text<|/ref|><|det|>[[112, 429, 919, 476]]<|/det|>
+- Third, we do the same type of HF calculations for the interacting Dirac electrons in graphene as explained in Methods. If the chemical potential is at the CNP of graphene, a gap opening will be triggered by \(e\) -\(e\) interactions within the graphene layer as discussed previously.  
+
+<|ref|>text<|/ref|><|det|>[[112, 493, 919, 555]]<|/det|>
+- From the above procedures, we would separately obtain converged HF ground states, \(|\Psi \rangle_{d}\) for the substrate, and \(|\Psi \rangle_{c}\) for graphene, respectively. From the ground-state wavefunctions \(|\Psi \rangle_{d}\) and \(|\Psi \rangle_{c}\) , one can extract the corresponding ground-state charge density modulations \(\{\rho_{d}(\mathbf{Q})\}\) and \(\{\rho_{c}(\mathbf{Q})\}\) , based on which the interlayer Coulomb energy [the expectation value of Eq. (4e)] can be calculated.  
+
+<|ref|>text<|/ref|><|det|>[[112, 562, 919, 775]]<|/det|>
+However, the ground states are obtained by minimizing (mostly) the intralayer parts of the full Hamiltonian, the interlayer Coulomb interaction Eq. (4e) is not optimized yet. We note that the intralayer kinetic energy and intralayer Coulomb interaction energy for both graphene and the substrate are unchanged under constant lateral shifts of the charge centers, thus the ground state \(|\Psi \rangle_{d} \otimes |\Psi \rangle_{c}\) obtained so far is massively degenerate up to global and relative shifts of the bilayer charge centers. Such degeneracy would be partially lifted by the interlayer Coulomb energy \(\langle H_{\mathrm{gr-sub}}\rangle\) . Obviously, \(\langle H_{\mathrm{gr-sub}}\rangle\) is invariant under the global shift of the charge centers of the bilayer system, but it varies with respect to a relative charge-center shift. Therefore, by the virtue of perturbation theory, optimizing the interlayer Coulomb energy amounts to find the optimal relative shift vector between the charge centers of the two layers within the degenerate ground-state manifold obtained in the previous procedures. Such perturbative treatment of \(H_{\mathrm{gr-sub}}\) is justified given that the interlayer Coulomb energy is always weaker than the intralayer one within relevant parameter regime, as shown in Fig. 5. For example, the interlayer Coulomb energy \(\sim 20 \mathrm{meV}\) for typical parameters \(L_{s} = 50 \mathrm{\AA}\) and \(\epsilon_{r} = 4\) , while the intralayer Coulomb energy \(\sim 60 \mathrm{meV}\) . More details for the perturbative calculation of interlayer Coulomb energy can be found in Sec. S6 of Supplementary Material [22].  
+
+<|ref|>text<|/ref|><|det|>[[112, 791, 919, 913]]<|/det|>
+- Finally, we gather all the contributions from Eq. (4) to find out the total energy of the coupled bilayer system staying in a gapped Dirac state (at the CNP) for graphene and a long-wavelength charge-ordered state for the substrate. By comparing it with that of a non-interacting Dirac state for graphene and a 2D electron-gas state for the substrate, we can then find out if the gapped graphene interplays with the long-wavelength charge-ordered substrate in a cooperative or competitive manner. It turns out that the bilayer system tends to cooperate with each other such that both the gapped Dirac state (at the CNP) of graphene and the long-wavelength charge ordered state in the substrate are substantially stabilized by the interlayer Coulomb coupling. The results are presented in Fig. 2 and 4 of main text.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[84, 100, 919, 252]]<|/det|>
+The first principles calculations are performed with the projector augmented- wave method within the density functional theory [59], as implemented in the Vienna ab initio simulation package software [60]. The crystal structure is fully optimized until the energy difference between two successive steps is smaller than \(10^{- 6}\mathrm{eV}\) and the Hellmann- Feynman force on each atom is less than \(0.01\mathrm{eV}\cdot \mathrm{\AA}\) . The generalized gradient approximation by Perdew, Burke, and Ernzerhof is taken as the exchange- correlation potential [61]. As Cr is a transition metal element with localized \(3d\) orbitals, we use the on- site Hubbard parameter \(U = 5.48\mathrm{eV}\) for the Cr \(3d\) orbitals in the CrOCl bilayer and \(U = 3\mathrm{eV}\) for Cr \(3d\) orbitals in the \(\mathrm{CrI_3}\) bilayer. The so- called fully localized limit of the spin- polarized GGA+U functional is adopted as suggested by Liechtenstein and coworkers [62], and the non- spherical contributions from the gradient corrections are taken into consideration. The "DFT+D2" type of vdW correction has been adopted for all multilayer calculations to properly describe the interlayer interactions [63].  
+
+<|ref|>text<|/ref|><|det|>[[85, 254, 919, 314]]<|/det|>
+Our high- throughput filtering of the proper insulating substrate materials for graphene starts from the 2D materials computational database [64]. We only focus at those with bulk van der Waals structures which have been previously synthesized in laboratory. This ensures that it is experimentally feasible to exfoliate few layers from their bulk sample and then stack them on graphene to form heterostructures.  
+
+<|ref|>sub_title<|/ref|><|det|>[[210, 352, 792, 368]]<|/det|>
+## Experimental measurements of the gaps in graphene-CrOCl heterostructure  
+
+<|ref|>text<|/ref|><|det|>[[84, 387, 919, 555]]<|/det|>
+By designing a dual- gated structure, we used few- layered CrOCl as an bottom dielectric while few- layered hexagonal boron nitride (h- BN) was served as top gate dielectric. The top and bottom gate voltages can then be converted into doping and displacement fields for further data analysis. Graphene, h- BN, and CrOCl flakes are mechanically exfoliated from high quality bulk crystals. The vertical assembly of few- layered hBN, monolayer graphene and few- layered CrOCl were made using the polymer- assisted dry- transfer method. Electron beam lithography was done using a Zeiss Sigma 300 SEM with a Raith Elphy Quantum graphic writer. Top and bottom gates as well as contacting electrodes were fabricated with an e- beam evaporator, with typical thicknesses of \(\mathrm{Ti / Au} \sim 5 / 50\mathrm{nm}\) . Electrical transport measurements of the devices were performed using an Oxford TeslaTron 1.5 K system. Gate voltages on the as- prepared multi- terminal devices were fed by a Keithley 2400 source meter. Channel resistances were recorded in 4- probe configurations using low frequency (13.33 Hz) lock- in technique with Stanford SR830 amplifiers. The gate dependencies of channel resistances were measured at various temperatures for the extraction of thermal gaps.  
+
+<|ref|>sub_title<|/ref|><|det|>[[410, 593, 591, 608]]<|/det|>
+## DATA AVAILABILITY  
+
+<|ref|>text<|/ref|><|det|>[[84, 629, 919, 660]]<|/det|>
+The data that support the findings of this study are available from the corresponding author upon reasonable request.  
+
+<|ref|>sub_title<|/ref|><|det|>[[403, 697, 600, 712]]<|/det|>
+## ACKNOWLEDGEMENT  
+
+<|ref|>text<|/ref|><|det|>[[84, 732, 919, 794]]<|/det|>
+We would like to thank Jian Kang and Jinhai Mao for valuable discussions, and to thank Hanwen Wang and Zhongqing Guo for the help in making the plots. This work is supported by the National Natural Science Foundation of China (grant No. 12174257, No. 11974357, and No. U1932151), the National Key R & D program of China (grant No. 2020YFA0309601 and No. 2019YFA0307800), and the start- up grant of ShanghaiTech University.  
+
+<|ref|>sub_title<|/ref|><|det|>[[384, 832, 620, 847]]<|/det|>
+## AUTHOR CONTRIBUTIONS  
+
+<|ref|>text<|/ref|><|det|>[[84, 867, 919, 913]]<|/det|>
+J. L. conceived the idea and supervised the project. X. L. and S. Z. performed calculations. X. G., K. Y., Y. Y., and Z. V. H. performed transport measurements. X. L., Z. V. H., and J. L. analysed the data. X. L. and J. L. wrote the manuscript with inputs from all authors.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[101, 99, 421, 114]]<|/det|>
+The Authors declare no competing interests.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[84, 100, 291, 115]]<|/det|>
+* liujp@shanghaitech.edu.cn
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[50, 65, 920, 560]]<|/det|>
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+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[44, 42, 312, 70]]<|/det|>
+## Supplementary Files  
+
+<|ref|>text<|/ref|><|det|>[[44, 93, 765, 113]]<|/det|>
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+<|ref|>text<|/ref|><|det|>[[61, 130, 200, 150]]<|/det|>
+suppv5.4. pdf
+
+<--- Page Split --->

preprint/preprint__ca1b65642baef2758aeb4d86f3f31275365c6f1ab3f82f42128c419c8a3ef4e1/images_list.json

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