id string | question string | answer string | category string | type string | files list | rubrics list |
|---|---|---|---|---|---|---|
physci-001 | Regarding the Scanning Tunneling Microscopy (STM) experimental results for Ta and Cr doped CsV₃Sb₅ in Figure 1, which of the following statements are correct?
Options:
A. In the STM topography images at positive bias (Figs. c and e), the observed bright spots correspond to the substitutional Ta or Cr dopant atoms.
B. T... | A, E | atomic-answer | multimodal-qa | [
"file-001.png"
] | null |
physci-002 | Based on the analysis of the KV3Sb5 crystal structure and Scanning Tunneling Microscopy (STM) images (image_1 and image_2), determine which of the following two images corresponds to the antimony (Sb) surface and which to the potassium (K) surface, and analyze the reasons why. | Image_1 is the K surface, and Image_2 is the Sb surface. | atomic-answer | multimodal-qa | [
"file-002.png",
"file-003.png"
] | null |
physci-003 | Based on the given diffraction pattern, state the crystal system (e.g., cubic, hexagonal, tetragonal) and whether the sample is single-crystalline or polycrystalline | Hexagonal Symmetry and Single Crystallinity | atomic-anwser | multimodal-qa | [
"file-004.png"
] | null |
physci-004 | image_4_1 is the real-space MIM-Im mapping image of tBLG, and image_4_2 is its magnified view. Please estimate the moiré period length based on the images and then calculate the corresponding twist angle accurately. | The average real-space periodicity is (14.7 ± 0.4) nm, and the twist angle is (0.96 ± 0.03)°. | atomic-answer | multimodal-qa | [
"file-005.png",
"file-006.png"
] | null |
physci-005 | The image_5_1 is the experimentally obtained ARPES band map, and the following three(imag_5_2,imag_5_3,imag_5_4) are calculated band structures. Which of the latter three corresponds to the first image? Please explain. | image_5_4 | atomic-answer | multimodal-qa | [
"file-007.png",
"file-008.png",
"file-009.png",
"file-010.png"
] | null |
physci-006 | The provided image illustrates the atomic structures of a thin film grown on a substrate. A detailed analysis of the crystal structure for both the thin film and the substrate is requested. The analysis should include the determination of the following crystallographic parameters for each component:Crystal System，Brava... | 1.Substrate
Crystal System: Cubic
Bravais Lattice: Face-Centered Cubic (FCC)
Space Group: F-43m (No. 216)
Coordination Number: 4
Coordination Polyhedron: Tetrahedron
2.Thin Film
Crystal System: Cubic
Bravais Lattice: Simple Cubic
Space Group: Pm-3m (No. 221)
Coordination:
For the body-centered orange atom: Coordination... | long-form-answer | multimodal-qa | [
"file-011.jpg"
] | [
{
"criterion1": "Substrate Crystal System, Bravais Lattice, and Space Group",
"explanation": "Evaluates whether the response correctly identifies and clearly states the crystal system, Bravais lattice type, and space group for the substrate, in alignment with the reference answer. Full credit requires: (a) ... |
physci-007 | Answer the questions below based on the figure:
1.What special electronic-structure feature is observed near the K point? Approximately what is the binding energy (in eV) of its energy vertex?
2.Based on (1), what special electronic-structure feature is observed near the M′ point? In panels (f–e), what color arrow indi... | 1.A Dirac cone structure is observed near the K point. According to Fig. 1g, the binding energy of its energy vertex (the Dirac point) is about 0.06 eV (or 60 meV).
2.A saddle point, i.e., a van Hove singularity, is observed near the M′ point. In panels (f–e), this feature is indicated by cyan arrows. | long-form-answer | multimodal-qa | [
"file-012.png"
] | [
{
"criterion1": "Identification of K-point feature type",
"explanation": "Evaluates whether the response correctly identifies the special electronic-structure feature near the K point as a Dirac cone (or equivalent wording clearly describing a Dirac-like linear band crossing). Answers that name an incorrect... |
physci-008 | From the ARPES experimental data shown below, determine whether the sample is hole-doped or electron-doped. | n-type doped | atomic-answer | multimodal-qa | [
"file-013.png"
] | null |
physci-009 | Please accurately describe the differences between the surface electronic structures of Figure 1 and Figure 2 near the Γ-point. | Figure 1 displays the classic, single, linear Dirac cone surface state found in a topological insulator. In contrast, Figure 2 reveals an unconventional, unidirectional momentum-split surface electronic structure composed of two parabolic bands, which appears in a Kagome metal. The two are fundamentally different in te... | long-form-answer | multimodal-qa | [
"file-014.png",
"file-015.png"
] | [
{
"criterion1": "Description of Figure 1 Surface Electronic Structure",
"explanation": "Evaluates whether the response correctly and clearly describes the surface electronic structure in Figure 1 near the Γ-point. To score well, the student should identify that Figure 1 shows a *single*, *linear* Dirac-cone... |
physci-010 | Read the paper: https://doi.org/10.1038/s41598-017-04985-y
Figure 6 aims to investigate an effect known as “band bending,” i.e., an overall energy shift of the electronic bands at a material’s surface caused by molecules adsorbed on that surface. The authors performed a “heat–cool–reheat” thermal cycle on the sample in... | Ar gas (as well as N₂) induces a p-type (hole) doping effect in the sample. O₂ gas induces an n-type (electron) doping effect. | long-form-answer | multimodal-qa | [] | [
{
"criterion1": "Correct Doping Type for Ar Environment",
"explanation": "Evaluates whether the response correctly identifies the effect of Ar gas on the surface charge-carrier concentration. To earn full credit, the answer must explicitly state that Ar (in this experiment) leads to p-type doping (i.e., inc... |
physci-011 | Read the information in the figure and determine whether the following statement is correct: At 12 T, the phonon mean free path l_{\rm ph} in the low-temperature limit is approximately 15 μm. | Incorrect. | atomic-answer | multimodal-qa | [
"file-016.png"
] | null |
physci-012 | Read the article: Topological flat bands in a family of multilayer graphene moiré lattice. Please look at panel e (t1+2) and panel h (t2+4).
One is composed of three layers of graphene, and the other consists of six layers. Although the number of layers differs by a factor of two, the bright yellow high-resistance reg... | \nu = 0, \nu = -4, and \nu = +4 | atomic-answer | multimodal-qa | [] | null |
physci-013 | Read the article: https://doi.org/10.1038/s41586-022-04548-w .List all labeled material layers in the device stack (including electrodes) shown in Figure 1a | Si: The silicon substrate serving as the back-gate electrode.
SiO₂: An insulating layer.
hBN: Used to encapsulate the TDBG.
TDBG: The core active material of the device.
M: Metal electrodes located on both sides of the device.
Top hBN and monolayer graphene: The monolayer graphene acts as the top-gate electrode. | long-form-answer | multimodal-qa | [] | [
{
"criterion1": "Complete Identification of All Labeled Layers",
"explanation": "Evaluates whether the response lists all distinct labeled material layers and electrodes shown in Figure 1a as reflected in the reference answer: Si, SiO₂, hBN (encapsulating layer), TDBG, metal electrodes (M), and the top hBN ... |
physci-014 | The following figure shows the variation of the coherence length with doping concentration. Please read out the horizontal and vertical coordinates of the Present work data points, for example: (4.5 nm, 0.065) | 4.5 nm, 0.065), (4.4 nm, 0.070), (2.9 nm, 0.078), (2.5 nm, 0.090), (2.1 nm, 0.110), (2.0 nm, 0.150), (2.4 nm, 0.180), (2.7 nm, 0.202), (2.8 nm, 0.220), (3.0 nm, 0.221), (4.4 nm, 0.240). | atomic-answer | multimodal-qa | [
"file-017.png"
] | null |
physci-015 | The figure below shows how the ac magnetic susceptibility \chi_{\mathrm{ac}} varies with temperature T. What is the Curie temperature at a pressure of 0.52 GPa? | 2.1 K | atomic-answer | multimodal-qa | [
"file-018.png"
] | null |
physci-016 | One of the references in this paper investigates the growth of MgO thin films using IBAD technology. Please state the optimal values for deposition rate and ion beam flux mentioned in the article when the ion energy is fixed at 800 eV. | Deposition rate: 0.18 nm/s;ion beam flux: 60 mA | atomic-answer | long-context-qa | [
"file-019.pdf"
] | null |
physci-017 | Please search the literature and arrange the following four events in the chronological order of their scientific development:
A. Z2classification of three-dimensional topological insulators.
B. Realizing a topological phase transition in HgTe quantum wells by varying thickness.
C. The Quantum Spin Hall (QSH) state in ... | B、A、C、D | atomic-answer | long-context-qa | [] | null |
physci-018 | Based on this paper and the original articles it cites, which reference numbers in the paper report the band gap of 2H-WTe₂, and what indirect band-gap values do they provide? | References 5, 23, 29, 30: The result is approximately 0.7 eV；Reference 46: The result is 0.97 eV. | atomic-answer | long-context-qa | [
"file-020.pdf"
] | null |
physci-019 | Among the six core topics in this article:
* Stoichiometric analysis and kinetic extraction (including dwell-time fitting, HMM, Arrhenius analysis)
* Environmentally induced reactions (chemical / mechanical / light / plasmon)
* Electron-transfer reactions & electron catalysis
* Single-molecule redox reactions
*... | electrode–molecule coupling homogeneity
(i.e., the assumption of a single, uniform electrode-molecule coupling strength) | atomic-answer | long-context-qa | [
"file-021.pdf"
] | null |
physci-020 | In the main text and all Supplementary Notes (1–4) of this paper, the authors, in order to prove that the electron–hole asymmetry in graphene can only originate from electron–electron correlations, constructed a multi-layered exclusion framework based on experimental self-energy, band velocity, carrier density calibrat... | Consistency of the Luttinger surface density under charge carrier momentum conservation（Luttinger-consistency of the carrier density） | atomic-answer | long-context-qa | [
"file-022.pdf"
] | null |
physci-021 | Use only the following four papers (main text, figures, captions, Methods/Supplement):
- Roldán-Molina et al., "Topological spin waves in the atomic-scale magnetic skyrmion crystal" — triangular-lattice J + DMI + anisotropy + field → skyrmion crystal with magnon Chern bands & chiral edge modes.
- McClarty, "Topologic... | B>A>E>G>J>F>H>C>K>L>N | atomic-answer | long-context-qa | [
"file-023.pdf",
"file-024.pdf",
"file-025.pdf",
"file-026.pdf"
] | null |
physci-022 | (Four-paper integrated mega-sorting · 12-step “from micromagnetics to programmable DW in-memory computing” chain)
Use only the following four papers (main text + figures + captions + methods + SI) as ground truth:
Parkin 2008 – Magnetic Domain-Wall Racetrack Memory (PARKIN).
Gu 2022 – Three-dimensional racetrac... | B>E>A>D>C>F>G>H>I>J>K>L | atomic-answer | long-context-qa | [
"file-027.pdf",
"file-028.pdf",
"file-029.pdf",
"file-030.pdf"
] | null |
physci-023 |
You may only use the information contained in the following four papers (including main text, figures, captions, Methods and Supplementary where needed):
Cao et al., Nature 556, 43–50 (2018) – Unconventional superconductivity in magic-angle graphene superlattices (abbrev. SC-TBG paper).
Cao et al., Nature 556, 80... | N>A>B>C>J>K>D>E>F>G>H>I>M>L | atomic-answer | long-context-qa | [
"file-031.pdf",
"file-032.pdf",
"file-033.pdf",
"file-034.pdf"
] | null |
physci-024 | You may only use the following three papers (including their main text, figures, captions, and any brief descriptions of canonical materials in the references) as ground truth:
Q. Si & F. Steglich, Heavy fermions and quantum phase transitions, Science 329, 1161 (2010).
P. Gegenwart, Q. Si & F. Steglich, Quantum cr... | I: Q3-K3-F4-T1-S1
II: Q2-K1-F2-T2-S2
III: Q2-K4-F2-T3-S2
IV: Q4-K2-F3-T4-S3 | atomic-answer | long-context-qa | [
"file-035.pdf",
"file-036.pdf",
"file-037.pdf"
] | null |
physci-025 | Read the four provided papers [1]–[4] (full PDFs are available in the workspace).
Each paper discusses one or more *materials- and interface-level bottlenecks* that currently prevent 2D TMDs from being used in industrial-scale CMOS-like logic technology.
However, the bottlenecks addressed by these papers are **not ... | A → { [1] } ; not { [2], [3], [4] }
B → { [2] } ; not { [1], [3], [4] }
C → { [3] } ; not { [1], [2], [4] }
D → { [4] } ; not { [1], [2], [3] }
E → { [1], [2], [3] } ; not { [4] }
F → { [1], [2], [3], [4] } ; not { } | atomic-answer | long-context-qa | [
"file-038.pdf",
"file-039.pdf",
"file-040.pdf",
"file-041.pdf",
"file-042.pdf",
"file-043.pdf"
] | null |
physci-026 | ### Task: Classify Graphene Transport Regimes
You are presented with a set of experimental scenarios observed in high-mobility graphene devices. Each scenario is paired with a proposed transport regime (Diffusive / Ballistic / Viscous) and one or more supporting references.
Your task is to:
1. Carefully read all the... | C, D, G, H, J, L | atomic-answer | long-context-qa | [
"file-044.pdf",
"file-045.pdf",
"file-046.pdf",
"file-047.pdf",
"file-048.pdf",
"file-049.pdf",
"file-050.pdf",
"file-051.pdf",
"file-052.pdf"
] | null |
physci-027 | **Context**
You are provided with 8 reference documents related to semiclassical transport, Berry curvature, and condensed matter theory. These texts are excerpts from research articles and book chapters.
Your task is to determine the correct logical order in which some of these documents contribute to the derivati... | G → C → F → A → D | atomic-answer | long-context-qa | [
"file-053.pdf",
"file-054.pdf",
"file-055.pdf",
"file-056.pdf",
"file-057.pdf",
"file-058.pdf",
"file-059.pdf",
"file-060.pdf",
"file-061.pdf",
"file-062.pdf"
] | null |
physci-028 | You are given references A–G, covering multiple transport formalisms: relativistic hydrodynamics, thermo-electric response, plasmon damping, imbalance relaxation, phonon scattering, Boltzmann transport, etc. Some references may be directly relevant to the reasoning, some only indirectly; determine relevance yourself.
... | C | atomic-answer | long-context-qa | [
"file-063.pdf",
"file-064.pdf",
"file-065.pdf",
"file-066.pdf",
"file-067.pdf",
"file-068.pdf",
"file-069.pdf"
] | null |
physci-029 |
Read the provided literature on lattice strain and answer the following question:
CuAg bimetallic electrodes were synthesized through the following two methods:
(1) All CuAg bimetallic electrodes were prepared by melting physical mixtures of Cu (99.999%) and Ag (99.999%) in the desired atomic ratios under Ar in a... | indeterminate | atomic-answer | long-context-qa | [
"file-070.pdf",
"file-071.pdf",
"file-072.pdf",
"file-073.pdf",
"file-074.pdf",
"file-075.pdf"
] | null |
physci-030 |
A Mott insulator is a class of materials named in honor of the British physicist Sir Nevill F. Mott (recipient of the 1977 Nobel Prize in Physics). According to conventional band theory, such materials ought to be metallic, but due to strong electron–electron correlations they instead exhibit insulating behavior. In 1... | C | atomic-answer | long-context-qa | [
"file-076.pdf",
"file-077.pdf",
"file-078.pdf",
"file-079.pdf",
"file-080.pdf"
] | null |
physci-031 | Take \lambda = Z = 2, calculate the ground-state magnetic susceptibility of the helium atom.Check values for the Bohr radius a_0, electron charge e, electron mass m_e, Planck’s constant \hbar, and unit conversions,convert to eV/G² (using 1/T^2 = 10^{-8}/G^2)Using the variational hydrogenic wavefunction ψ₀(r) = (λ³/πa₀³... | \alpha_{B}=-1.23\times10^{-18}\ \text{eV}/(\text{G})^{2}. | atomic-answer | scientific-reasoning | [] | null |
physci-032 | Consider a nucleon moving in the \(-z\) direction, described in the Color Glass Condensate effective
theory by the colour current
\[
J_a^\mu \equiv \delta^{\mu -}\delta(x^+)\rho_a(x_\perp)
\]
(this form is valid in a frame where the nucleon is very fast). Recall from the solution in Lorenz gauge of the classical Yang–... | \[
\frac{d\sigma}{d^2p_\perp} = \frac{1}{(2\pi)^2}\int d^2X_\perp d^2r_\perp \, e^{-ip_\perp\cdot r_\perp}
\frac{1}{N}\,\text{tr}\Big((U(X_\perp+\tfrac{r_\perp}{2})-1)(U^\dagger(X_\perp-\tfrac{r_\perp}{2})-1)\Big).
\] | atomic-answer | scientific-reasoning | [
"file-081.pdf"
] | null |
physci-033 | A quantum mechanical system has eigenvalues and orthonormal eigenfunctions of the energy operator H_{0} given byE_{1} \longrightarrow \psi_{1}, \quad E_{2} \longrightarrow \psi_{2}, \psi_{3}.Suppose the system is subject to a perturbation. In the H_{0} representation, the perturbation operator has the matrix formH’= \b... | \[\begin{aligned}E &= E_{1} + \frac{c^{2} + b^{2}}{E_{1} - E_{2}} + \frac{a(c^{2} - b^{2})}{(E_{1} - E_{2})^{2}}, \\[6pt]E &= E_{2} + a + \frac{c^{2}}{E_{2} - E_{1}} + \frac{b^{2}c^{2}}{2a(E_{2} - E_{1})^{2}} - \frac{ac^{2}}{(E_{2} - E_{1})^{2}}, \\[6pt]E &= E_{2} - a + \frac{b^{2}}{E_{2} - E_{1}} + \frac{ab^{2}}{(E_{2... | atomic-answer | scientific-reasoning | [
"file-082.pdf"
] | null |
physci-034 | Hamiltonian of a forced harmonic oscillator system:
$$\n\hat H=\hat H_0+\hat U,\qquad
\hat H_0=\hbar\omega\left(\hat a^\dagger \hat a+ frac{1}{2}
ight),\qquad
\hat U=\hbar g(\hat a+\hat a^\dagger).
$$
The initial state of the system is the ground state $\lvert 0\rangle$ of $\hat H_0$. We can take $\hbar$ as 1 for ease ... | $\\langle p\\rangle = -\\frac{\\sqrt{2}g}{\\omega}\\sin(\\omega t)$ | atomic-answer | scientific-reasoning | [] | null |
physci-035 | Calculate the transmission probability for a particle (energy $E > 0$) through a delta potential barrier
\[
V(x) = V_{0}\,\delta(x)
\]
using the momentum representation.Please search and consult Zeng Jin-Yan, Quantum Mechanics, Vol. I (4th Edition), in the perturbation and scattering-related parts, for references on th... | \[
T=\frac{1}{\left|1+i\,\dfrac{mV_0}{\hbar^{2}k}\right|^{2}}
=\frac{1}{1+\left(\dfrac{mV_0}{\hbar^{2}k}\right)^{2}}
\] | atomic-answer | scientific-reasoning | [
"file-082.pdf"
] | null |
physci-036 | Using the tight-binding method to treat s-state electrons in a two-dimensional rectangular crystal with lattice constants a (x-direction) and b (y-direction), considering only nearest-neighbor hopping. Due to the spherical symmetry of the s-state wave function, let the hopping integrals be:
$$
J(\pm a, 0) = J_1^s, \qu... | Electron effective mass at band bottom (k = 0):
$$
m_e^* =
\begin{pmatrix}
-\dfrac{\hbar^2}{2J_1^s a^2} & 0 \\
0 & -\dfrac{\hbar^2}{2J_2^s b^2}
\end{pmatrix}
$$
Hole effective mass at band top (k = (π/a, π/b)):
$$
m_h^* = -m_e^{\prime *} =
\begin{pmatrix}
-\dfrac{\hbar^2}{2J_1^s a^2} & 0 \\
0 & -\dfrac{\hbar^2}{2J_2^s... | atomic-answer | scientific-reasoning | [] | null |
physci-037 | We consider QED with only photons (thus, it is a free theory). Given a closed contour $\gamma$ in spacetime, we define the following quantity,
\[
W_\gamma \equiv \langle 0 | T \exp \left( i e \int_\gamma dx^\mu \, A_\mu(x) \right) | 0 \rangle .
\]
Express it in terms of the photon propagator. Calculate the coordinate s... | \[
W_\gamma=\exp\!\left(-\frac{e^2}{8\pi^2}\int_\gamma \mathrm{d}u^\mu\,\mathrm{d}v^\nu\,
\frac{g_{\mu\nu}}{(u-v)^2-i0^+}\right).
\] | atomic-answer | scientific-reasoning | [
"file-081.pdf"
] | null |
physci-038 | Consider a real massless scalar field φ in D = 6 − 2ε dimensions with Lagrangian density: L = ½(∂μφ)² + (λ/3!)φ³ Using dimensional regularization and momentum-subtraction renormalization at the symmetric point p² = q² = (p+q)² = −M², calculate the one-loop β-function β = M ∂λ/∂M.For a detailed derivation of renormali... | \[
\beta = \lim_{\epsilon \to 0} M \frac{\partial}{\partial M}\!\left( \frac{\lambda^3}{8 (4\pi)^3 \epsilon}
\left[ 1 - 2\epsilon \ln\!\left(\frac{M}{\mu}\right) + O(\epsilon^2)\right]\right)
= -\frac{3 \lambda^3}{4 (4\pi)^3}.
\] | atomic-answer | scientific-reasoning | [
"file-081.pdf"
] | null |
physci-039 | Using a BCFW shift on the lines 3,4, derive an expression of the colour ordered amplitude
\(1^- 2^- 3^- 4^+ 5^+ 6^+\) that has only two terms.For a systematic treatment of on-shell recursion, spinor-helicity, and factorization used above, see the relevant scattering-amplitudes chapters in François Gelis, Quantum Fiel... | \[
\mathcal{A}_6(1^-2^-3^-4^+5^+6^+)
= -\frac{4ig^4}{[2|P_3+P_4|5\rangle}
\left\{
\frac{\langle 1|P_2+P_3|4]^3}{[23]\langle 34\rangle \langle 56\rangle \langle 61\rangle (p_2+p_3+p_4)^2}
+ \frac{\langle 3|P_4+P_5|6]^3}{[61][12]\langle 34\rangle \langle 45\rangle (p_3+p_4+p_5)^2}
\right\}.
\] | atomic-answer | scientific-reasoning | [
"file-081.pdf"
] | null |
physci-040 | Write down the Green’s formula for a classical scalar field whose initial condition is set on the time-like
surface t = z. A more systematic derivation of the characteristic initial value (Goursat) problem and Green’s formula on light-like hypersurfaces can be found in François Gelis’ Quantum Field Theory, in the chap... | The standard solution is the Green's formula for the Goursat problem on the light-front (t=z).
Standard Form (Double-sided derivative):
\[\Phi(x) = -i \int_{y^->0} d^4y \, G_R^0(x,y)\, U'(\Phi(y)) + i \int_{y^-=0} dy^+ d^2y_\perp \, G_R^0(x,y)\,\overleftrightarrow{\partial^-}\Phi(y)\]
ACCEPT the answer if it matches... | atomic-answer | scientific-reasoning | [
"file-081.pdf"
] | null |
physci-041 | Calculate the expression in coordinate space of the retarded propagator given below (for m = 0)：
\[
\tilde{G}^{0}_{R}(k)
=\frac{i}{\left(k_{0}+i0^{+}\right)^{2}-\left(\mathbf{k}^{2}+m^{2}\right)}\
\]See François Gelis, Quantum Field Theory, chapter on Green’s Functions and Causal Propagators for the coordinate-space d... | \[
G_{R}^{0}(x,y)
= \pm \frac{i}{2\pi}\theta(r^{0})\delta(r_{0}^{2}-\mathbf{r}^{2}) \, .
\] | atomic-answer | scientific-reasoning | [
"file-081.pdf"
] | null |
physci-042 | It is possible to write field theories with continuous symmetries linking fermions and bosons; such transformations are called supersymmetries.It is possible to write supersymmetric nonlinear field equations by adding cubic and higher-order terms to the Lagrangian. Show that the following rather general field theory, c... | \[
\mathcal{L} = \partial_\mu \phi^* \partial^\mu \phi
+ \chi^\dagger i \bar{\sigma}^\mu \partial_\mu \chi
- g^2 (\phi^* \phi)^2
+ i g (\phi \chi^T \sigma^2 \chi - \phi^* \chi^\dagger \sigma^2 \chi^*). \tag{3.50}
\] | atomic-answer | scientific-reasoning | [] | null |
physci-043 | Determine the limiting behavior of the surface tension coefficient $\alpha$ of liquid ammonia near absolute zero, as a function of temperature, and write down the explicit expression (Assume the low-temperature ripplon model of Atkins (1953), originally developed for liquid helium, can be formally applied to liquid am... | $$
\alpha
= \alpha_{0} - 0.13 \frac{T^{7/3}}{\hbar^{4/3}}
\frac{\rho^{2/3}}{\alpha_{0}^{2/3}}.
$$ | atomic-answer | scientific-reasoning | [] | null |
physci-044 | Let the BCS superconducting Hamiltonian under an external magnetic field h be:
$$
\hat{H} = \sum_k [(\xi_k + \mu_B h)\hat{C}_{k\uparrow}^{\dagger}\hat{C}_{k\uparrow} + (\xi_k - \mu_B h)\hat{C}_{k\downarrow}^{\dagger}\hat{C}_{k\downarrow}] - \Delta \sum_k (\hat{C}_{k\uparrow}^{\dagger}\hat{C}_{-k\downarrow}^{\dagger} +... | $$
1 = -g \int \frac{d\vec{k}}{(2\pi)^3} \frac{1}{2E_k} [n_F(\mu_B h + E_k) - n_F(\mu_B h - E_k)]
$$ | atomic-answer | scientific-reasoning | [] | null |
physci-045 | In the presence of an external magnetic field h, the BCS Hamiltonian is
\[\hat{H} = \sum_k [(\xi_k + \mu_B h)\hat{C}{k\uparrow}^{\dagger}\hat{C}{k\uparrow} + (\xi_k - \mu_B h)\hat{C}{k\downarrow}^{\dagger}\hat{C}{k\downarrow}] - \Delta \sum_k (\hat{C}{k\uparrow}^{\dagger}\hat{C}{-k\downarrow}^{\dagger} + \hat{C}{-k\do... | \[
\begin{aligned}
\langle \hat{C}_{k\uparrow}^{\dagger}\hat{C}_{k\uparrow} \rangle
&= V\frac{1}{\beta }\sum_{\omega_n} \int \frac{d\vec{k}}{(2\pi)^3}
G_{\uparrow\uparrow}(\vec{k}, i\omega_n) e^{i\omega_n \eta} \\
&= \sum_k \big[ u_k^2\, n_F(\mu_B h + E_k)+v_k^2\, n_F(\mu_B h - E_k) \big],
\end{aligned}
\],\[
\begin{al... | atomic-answer | scientific-reasoning | [] | null |
physci-046 | I'm reading the Nature paper "Ambient-pressure superconductivity onset above 40 K in (La,Pr)₃Ni₂O₇ films" (Vol. 640, 17 April 2025, pp. 641–646).
Please extract all reported superconducting parameters from the main text and figure captions.
The parameters to extract are:
- Sample chemical composition
- Substrate (typ... | {
"Sample chemical composition": "La2.85Pr0.15Ni2O7",
"Substrate": "SrLaAlO4 (001), ~2% in-plane compressive strain",
"Film thickness (nm)": 6.6,
"Tc_onset (K)": 45,
"Tc_zero (K)": "NA",
"TBKT (K)": 9,
"TM (K)": 8.5,
"Out-of-plane critical field Bc⊥ (T, 90%)": 68,
"In-plane critical field Bc∥ (T, 90%)... | long-form-answer | structured-information-extraction | [] | null |
physci-047 | I’ve been looking into McCrone et al.’s 2003 study on doped RuSr₂GdCu₂O₈ about magneto-transport properties, which you can find online from open-access sources(such as arxiv).
I’d like you to pull out a specific subset of the samples discussed there.
Please go through the whole paper carefully and focus only on sampl... | [
{
"composition": "Ru0.975Sn0.025Sr2GdCu2O8",
"dopant_element": "Sn",
"doping_level_percent": 2.5,
"datasets_reported": ["rho_T", "Hall_RH_T", "TEP_S_T"],
"superconductivity": "Yes",
"Tc_onset_K": 40.5
},
{
"composition": "Ru0.925Sn0.075Sr2GdCu2O8",
"dopant_element": "Sn",
"do... | long-form-answer | structured-information-extraction | [] | null |
physci-048 | I’m reading the PRX paper “Many-Body Electronic Structure of NdNiO₂ and CaCuO₂”. I’m mainly interested in what is described in the main text and figure captions. Does it include a summary table with the bandwidth (W) and hopping parameters (e.g., t, t′, t″, tz, and any Ni–Nd hybridization terms such as tNi–Nd³ᶻ²⁻ʳ² and... | NdNiO₂,3.01,−0.357,0.091,−0.043,−0.032,0.023,0.012
CaCuO₂,4.14,−0.469,0.100,−0.090,−0.054,null,null | long-form-answer | structured-information-extraction | [] | null |
physci-049 | I need your assistance with analyzing a Phys. Rev. B study on the two-dimensional nature of superconductivity in Li-intercalated nitride-chloride systems (LixZrNCl and LixHfNCl).
Please locate this study and extract the quantitative superconducting parameters reported for each sample composition listed in the main text... | [
{
"sample_name": "Li₀.₁₇ZrNCl",
"host_system": "ZrNCl",
"intercalant_type": "Li",
"c0_div3_Angstrom": "9.4",
"Tc_K": "14.2",
"lambda_ab_muSR_Angstrom": "3700",
"lambda_ab_M_Angstrom": "4700",
"kappa": "56",
"Hc2_parallel_c_T": "4.7",
"xi_ab_Angstrom": "83"
},
{
"sampl... | long-form-answer | structured-information-extraction | [] | null |
physci-050 | For a recent analysis on electron–phonon coupling effects, I’m compiling quantitative Raman-scattering data from the paper “Measurements of Raman scattering by electrons in metals: The effects of electron–phonon coupling.” Please go through the main text, figure captions, and tables, but do not need to refer to numeric... | [
{ "element_or_compound": "Al", "lambda_exp": "0.26", "Gamma_exp_cm-1": "375", "qualitative_coupling_category": "weak" },
{ "element_or_compound": "Mo", "lambda_exp": "0.33", "Gamma_exp_cm-1": "450", "qualitative_coupling_category": "weak" },
{ "element_or_compound": "Nb", "lambda_exp": "1.15", "Gamma_exp_c... | long-form-answer | structured-information-extraction | [] | null |
physci-051 | We are analyzing how structural vacancy ordering correlates with superconducting behavior in Fe-based layered compounds.
Around 2011, a research group from USTC reported that several alkali- and thallium-intercalated Fe–Se single crystals exhibited both superconductivity and high-temperature antiferromagnetic ordering.... | [
{
"sample_name": "K0.8Fe2−ySe2",
"Tc_onset_K": 31.5,
"Tc_zero_K": 30.5,
"Thump_K": 170,
"TN_K": 540,
"TS_K": 551
},
{
"sample_name": "Rb0.8Fe2−ySe2",
"Tc_onset_K": 32.0,
"Tc_zero_K": 31.5,
"Thump_K": 250,
"TN_K": 534,
"TS_K": 540
},
{
"sample_name": "Cs0.8... | long-form-answer | structured-information-extraction | [] | null |
physci-052 | A 2013 study on universal scaling relations in superconductors investigated whether organic and other exotic materials follow the same empirical relation among the superconducting penetration depth (λₛ), DC conductivity (σdc), and critical temperature (Tc).
The authors compared results obtained from different spectrosc... | [
{
"sample_name": "(BEDT-TTF)2Cu(NCS)2",
"sigma_dc_Ohm_inv_cm": 3800,
"lambda_s_micrometer": 0.8,
"Tc_K": 8.6,
"measurement_technique": "MW SI (35 GHz)",
"reference_ID": "[19]",
"consistent_measurement": "yes",
"on_scaling_line": "true"
},
{
"sample_name": "(BEDT-TTF)2Cu(NCS)2... | long-form-answer | structured-information-extraction | [] | null |
physci-053 | A 2008 study used high-field magnetization and μSR measurements to determine exchange parameters in quasi-two-dimensional Heisenberg magnets of the form [Cu(HF2)(pyz)2]X. For each compound, the paper reports the saturation field Bc, the in-plane exchange J, and the ordering temperature TN, and uses these values to esti... | [
{
"compound": "[Cu(HF2)(pyz)2]BF4",
"anion": "BF4−",
"Bc_T": 18.0,
"g_factor": 2.13,
"J_K": 6.3,
"TN_K": 1.54,
"Jperp_over_J": 9e-4,
"dimensionality_rank": "highest_2D"
},
{
"compound": "[Cu(HF2)(pyz)2]ClO4",
"anion": "ClO4−",
"Bc_T": 19.1,
"g_factor": 2.30,
"... | long-form-answer | structured-information-extraction | [] | null |
physci-054 | A 2009 optical study reconstructs the electron–boson "glue" function P̃(ω) from normal-state infrared conductivity for ten cuprates, and tabulates room-temperature strong-coupling parameters per sample (doping x, Tc, ħωp, ħω̃, λ, plus the split into peak ≤100 meV and continuum ≥100 meV, with corresponding Tc_pk and Tc_... | family,sample_label,doping_x,Tc_K,omega_p_eV,omega_tilde_meV,lambda_total,lambda_pk,lambda_cnt,Tc_pk_K,Tc_cnt_K,dominant_channel
Bi-2201,UD0,0.09,0,1.75,,,,,,,
Bi-2201,UD1,0.11,10,1.77,70,2.96,2.85,0.11,160,5,peak
Bi-2201,OpD,0.16,35,1.92,81,2.95,2.47,0.48,140,116,peak
Bi-2201,OD,0.22,0,1.93,103,1.42,0.95,0.47,64,113,c... | long-form-answer | structured-information-extraction | [] | null |
physci-055 | A 2010 crystallographic study determined effective atomic radii in the iron-arsenide family REFeAsO (RE = La, Ce, Pr, Nd, Sm, Gd, Tb) using a hard-sphere model.
The table lists r_RE, r_Fe, r_As, half_a, and r_O (in pm).
Based on those values, note that r_As and r_Fe remain nearly constant, while r_RE decreases with inc... | RE,r_RE_pm,r_Fe_pm,r_As_pm,half_a_pm,r_O_pm,trend_type
La,143.42,46.76,194.42,201.84,93.12,null
Ce,139.28,46.11,194.46,200.29,95.10,decreasing
Pr,137.62,45.72,194.66,199.45,95.15,decreasing
Nd,136.06,45.37,194.57,198.57,95.45,decreasing
Sm,133.17,44.81,194.86,197.35,95.97,decreasing
Gd,130.50,44.20,194.94,196.00,96.50,... | long-form-answer | structured-information-extraction | [] | null |
physci-056 | A 2004 experimental study investigated field-induced quantum fluctuations and competing orders in several hole- and electron-doped cuprate superconductors.
For each compound discussed (La-112, NCCO, PCCO, Y-123, Bi-2212, Hg-1234), the authors compared the irreversibility field H*, the upper critical field Hc2, and thei... | compound,Tc_K,Hc2_T,Hstar_T,hstar_ratio,proximity_to_QCP
Hg-1234,125,500,,,closest
La-112,43,,,,closest
Bi-2212,93,,,0.45,intermediate
PCCO,21,,,0.53,intermediate
NCCO,21,,,,intermediate
Y-123,93,,,,farther | long-form-answer | structured-information-extraction | [] | null |
physci-057 | Find the 2005 study that analyzed the universal scaling relation between the superfluid stiffness (1/λ²) and the normal-state conductivity σ₀ in molecular superconductors.
The work compared several families including quasi-one-dimensional (TMTSF) salts, quasi-two-dimensional BEDT/BETS-based charge-transfer salts, and t... | material,dimensionality,Tc_K,lambda_um,sigma0_1e3_S_cm,inv_lambda2_um_inv2,sigma0_S_cm,gamma_e_tilde
kappa-BETS2GaCl4,2D,0.16,2.3,250,0.189,250000,0.000
(TMTSF)2ClO4,q1D,1.1,1.27,39,0.620,39000,0.000
alpha-ET2NH4Hg(SCN)4,2D,1.1,1.1,36,0.826,36000,0.000
beta-ET2IBr2,2D,2.2,0.90,26,1.235,26000,0.000
lambda-BETS2GaCl4,2D,... | long-form-answer | structured-information-extraction | [] | null |
physci-058 | Identify the early high-field experimental study (circa 2008–2009) that analyzed Pauli-limited behaviour of the upper critical field in FeAs-based superconductors, comparing a clean LaO₀․₉₃F₀․₀₇FeAs sample with an As-deficient LaO₀․₉F₀․₁FeAs₁₋δ sample prepared using tantalum-foil wrapping during final annealing (which ... | {
"As_deficient_sample": {
"Tc_K": 28.5,
"(dBc2/dT)_Tc_T_per_K": -5.4,
"B*_c2(0)_T": 106,
"alpha_Maki": 1.31,
"Bp_c2(0)_T": 63,
"PLB_observed": true,
"H_orientation": "H∥ab"
},
"Clean_reference_sample": {
"Tc_K": 25.0,
"(dBc2/dT)_Tc_T_per_K": -2.9,
"B*_c2(0)_T": 45,
"al... | long-form-answer | structured-information-extraction | [] | null |
physci-059 | Identify the early high-field local-probe transport study on iron-pnictide superconductors that decomposes the critical current density into a field-independent collective pinning term and a low-field defect term, compares charge-doped 1111/122 compounds to isovalently substituted BaFe₂(As₁₋ₓPₓ)₂, and infers quasiparti... | {
"compounds": [
{
"name": "PrFeAsO1-y",
"doping_type": "charge_doped",
"collective_pinning_detected": true,
"beta_range_low": 0.5,
"beta_range_high": 0.63,
"sigma_tr_A2": 6.7,
"sigma_tr_A2_upper_bound": null,
"sin_delta0": 0.3,
"mean_free_path_l_nm": 10,
... | long-form-answer | structured-information-extraction | [] | null |
physci-060 | Identify the ultrafast pump-probe study that compared nonthermal destruction of superconductivity and melting of charge-density-wave (CDW) order under femtosecond laser excitation.
From that work, extract quantitative parameters for representative materials, distinguishing superconductors (SC) and CDW compounds.
Return... | {
"superconductors": [
{
"name": "La1.85Sr0.15CuO4",
"category": "SC",
"Tc_or_Tm_K": 38.5,
"FT_uJ_per_cm2": 5.8,
"lambda_op_nm": 150,
"Uv_K_per_atom": 2.6,
"Uc_K_per_atom": 0.3,
"Uv_to_Uc_ratio": 8.5,
"tau_ps": 0.9,
"dominant_destruction_mechanism": "pho... | long-form-answer | structured-information-extraction | [] | null |
physci-061 | Identify the ARPES study that systematically compared dopant-induced scattering and bandwidth control across multiple Fe-based superconductor families.
The paper analyzes (i) band-selective scattering strongest on the dxy-derived γ band, and (ii) universal bandwidth control governing superconductivity through a bandwid... | {
"series": [
{
"name": "LiFe1-xCoxAs",
"dopant_site": "Fe",
"doping_type": "electron",
"gamma_band_scattering": "strong",
"bandwidth_trend": "increase",
"bond_length_trend": "decrease",
"scattering_absent_statement": null,
"notes": "Co@Fe strongest",
"consist... | long-form-answer | structured-information-extraction | [] | null |
physci-062 | Identify the mid-2010s single-crystal study on the RPdBi half-Heusler family that combines
(i) non-centrosymmetric superconductivity at an extremely low carrier density (~10¹⁹ cm⁻³),
(ii) type-II antiferromagnetic order at Q = (½, ½, ½) for selected rare-earth members, and
(iii) a de Gennes scaling trend in which Tₙ in... | {
"samples": [
{
"sample": "YPdBi",
"Hc2_0_T": 2.7,
"alpha_WHH_equiv": 0.82,
"exceeds_orbital_limit": true,
"Hc2_linear_down_to_T_over_Tc": 0.20,
"Pauli_limit_relation": "comparable",
"AFM_Q": null,
"TN_K": null,
"topology_expected": "trivial"
},
{
... | long-form-answer | structured-information-extraction | [] | null |
physci-063 | Identify the early-2000s experimental study that investigated low-temperature thermal conductivity in magnetic superconductors of the RNi₂B₂C borocarbide family (R = Y, Lu, Tm, Er, Ho, Dy), focusing on how superconductivity coexists or competes with local-moment magnetism.
The work compared nonmagnetic and magnetic mem... | {
"samples": [
{
"sample": "YNi2B2C",
"Tc_K": 15.6,
"TN_K": null,
"kappa_peak_ratio": 0.60,
"phonon_suppression_below_TN": false,
"electronic_contribution_fraction": 0.35,
"scattering_dominant_mechanism": "electron-phonon",
"magnetism_effect_on_Tc": "none"
},
{
"sample": "ErNi2B2C",
"Tc_K": 11.0,
"TN_K":... | long-form-answer | structured-information-extraction | [] | null |
physci-064 | Identify the experimental–computational study on transition-metal diborides TMB₂ (TM = Ti, V, Ta, Nb, Y) that measured generalized phonon density-of-states (GDOS) by inelastic neutron scattering on polycrystalline ¹¹B-based samples, compared with ab-initio DFT calculations (mixed-basis pseudopotentials), and derived is... | compound,a_A,c_A,a_opt_A,c_opt_A,MB_A,BB_A,sigma_over_m_barn_per_amu,E2g_meV,B1g_meV,lambda,omega_log_meV,Tc_mu013_K,N0_states_per_cell_spin,superconductivity_comment
TaB2,3.08,3.27,3.08,3.27,2.42,1.80,0.033,100.6,68.8,0.79,25.8,10.6,0.452,modest_coupling_low_ωlog
VB2,2.998,3.056,2.979,2.995,2.30,1.77,0.098,114.9,69.6,... | long-form-answer | structured-information-extraction | [] | null |
physci-065 | Identify the early-2000s theoretical–experimental analysis that re-evaluated the temperature dependence of the upper critical field Hc₂(T) in high-Tc cuprate superconductors using a scaling of reversible magnetization M(H,T), while introducing a correction for a temperature-dependent Ginzburg–Landau parameter κ(T).
Th... | sample_id,compound,crystal_type,Tc_K,group_label,kappa_assumption_effect,hc2_norm_ref_tempK,hc2_slope_near_Tc,curve_shape,notable_features,reference_number
Bi#1,Bi2.12Sr1.9Ca1.2Cu1.96O8+x,single crystal,86.9,group2,minor,70,linear,downward_curvature,curves_identical_for_kappa_variants,7
Bi#2,Bi2.12Sr1.9Ca1.2Cu1.96O8+... | long-form-answer | structured-information-extraction | [] | null |
physci-066 | ### Question
Modeling the Motion of a Charged Particle in a Uniform Magnetic Field
# Problem Description
Model the motion of a charged particle (mass m = 9.1 × 10^(-31) kg, charge q = -1.6 × 10^(-19) C) in a uniform magnetic field by Python. The magnetic field is aligned along the z-axis with a strength B = 0.1 T. The... | import numpy as np
def particle_position_at_time(velocity, position, magnet_field, mass, charge, t):
"""
velocity: np.array shape (1,3)
position: np.array shape (1,3)
magnet_field: np.array shape (1,3)
mass: float
charge: float
t: time in seconds (float)
Returns: np.array shape (3,) pos... | long-form-answer | code-generation | [] | null |
physci-067 | ### Question
Calculating the Photonic Band Structure of a Two-Dimensional Photonic Crystal with Broken Inversion Symmetry
# Problem Description
Please write a Python script to design a two-dimensional photonic crystal with a triangular lattice of dielectric rods with a permittivity of ε = 12. Within the real-space uni... | import numpy as np
from numpy import pi, sqrt
import math
# Try to import efficient symmetric eigensolver
try:
from scipy.linalg import eigh
eigh_func = eigh
except Exception:
# fallback to numpy.linalg.eig (less optimal for hermitian matrices but acceptable)
eigh_func = np.linalg.eig
# --------------... | long-form-answer | code-generation | [] | null |
physci-068 | ### Question
Simulating Exciton Dynamics in a Quantum Dot with Phonon Assistance
# Problem Description
Please write a Python script to model the dynamics of an exciton (an electron-hole pair) in a quantum dot interacting with a phonon reservoir. The system's evolution is governed by a Lindblad master equation:
\frac{... | import numpy as np
import math
from scipy.linalg import expm
# Physical constants
hbar = 1.054571817e-34 # J*s
eV = 1.602176634e-19 # J
kB = 1.380649e-23 # J/K
# Given/problem parameters
Delta_meV = 0.1 # meV (interpreted as energy splitting Δ_E = ħΔ)
Delta_J = Delta_meV * 1e-3 * eV # convert ... | long-form-answer | code-generation | [] | null |
physci-069 | ### Question
Electronic Transport in Zigzag Graphene Nanoribbon
# Problem Description
Please write a Python script to simulate the electronic transport properties of a zigzag graphene nanoribbon (ZGNR) using the non-equilibrium Green's function (NEGF) method. The system consists of a central scattering region connecte... | import numpy as np
from scipy import linalg
# physical constants
e_charge = 1.602176634e-19 # C
h_planck = 6.62607015e-34 # J*s
# tight-binding parameters (eV)
t_ev = -2.7
t = t_ev
# geometry parameters
a_cc = 1.42e-10 # m (C-C bond length)
N = 2 # ribbon width (zigzag chains)
M = 10 # numbe... | long-form-answer | code-generation | [] | null |
physci-070 | ### Question
Spatiotemporal Chaos in Coupled Pendulum Array
# Problem Description
Please write a Python script to investigate spatiotemporal chaos in a one-dimensional array of N coupled pendulums. Each pendulum experiences gravitational potential and harmonic coupling with its nearest neighbors. The equations of moti... | import numpy as np
from scipy.integrate import solve_ivp
# Parameters
N = 10
alpha = 0.01
t_max = 500.0
dt = 0.1
t_eval = np.arange(0, t_max + dt, dt)
theta0 = np.linspace(0.01, 0.1, N)
omega0 = np.zeros(N)
y0 = np.concatenate([theta0, omega0])
def coupled_pendulum(t, y, k):
theta = y[:N]
omega = y[N:]
dt... | long-form-answer | code-generation | [] | null |
physci-071 | ### Question
Pattern Formation in Reaction-Diffusion System
# Problem Description
Write a Python script to study pattern formation in a one-dimensional Gray-Scott reaction-diffusion system. The system consists of two chemical species U and V with the following equations:
∂U_i/∂t = D_u(U_{i+1} - 2U_i + U_{i-1}) - U_iV_... | import numpy as np
# Parameters
N = 12
Du = 0.16
Dv = 0.08
F = 0.04
k = 0.06
dt = 0.1
t_max = 10.0
steps = int(t_max / dt)
# Initialize concentrations
U = np.ones(N)
V = 0.5 + 0.01 * np.arange(1, N + 1)
# Time evolution
for _ in range(steps):
U_new = U.copy()
V_new = V.copy()
for i in range(N):
l... | long-form-answer | code-generation | [] | null |
physci-072 | ### Question
Critical Temperature of Ferromagnetic Ising Chain
# Problem Description
Write a Python script to calculate the critical temperature of a one-dimensional ferromagnetic Ising chain with nearest-neighbor coupling. The Hamiltonian is: H = -J Σ⟨i,j⟩ S_i S_j, where S_i = ±1 are spin variables and J > 0 is the f... | import numpy as np
def critical_temperature_ising_1d(J, k_B=1.0):
"""
计算一维Ising链的临界温度
根据精确解，一维Ising链没有有限温度相变，临界温度为0
"""
return 0.0
# 计算不同耦合强度的临界温度
J_values = [1.0, 2.0]
results = []
for J in J_values:
T_c = critical_temperature_ising_1d(J)
results.append((J, T_c))
print(f"Coupling str... | long-form-answer | code-generation | [] | null |
physci-073 | ### Question
Quantum Wavefunction Evolution in Coupled Quantum Wells
# Problem Description
Write a Python script to investigate quantum wavefunction evolution in a one-dimensional array of N coupled quantum wells. Each well has a finite potential barrier, and the wavefunctions couple through quantum tunneling. The tim... | import numpy as np
# Parameters
N = 6
ħ = 1.0
m = 1.0
V_i = 0.5
k = 0.8
σ = 0.2
dt = 0.01
t_final = 10.0
def initialize_wavefunctions():
# 每个阱的位置
x_positions = np.arange(N)
# 均匀分布的相位
phases = np.linspace(0, np.pi/4, N)
# 初始化波函数
ψ = np.zeros(N, dtype=complex)
# 在每个阱中心放置高斯波包
fo... | long-form-answer | code-generation | [] | null |
physci-074 | ### Question
Quantum Tunneling Probability in Double Potential Well
# Problem Description
Write a Python script to calculate the quantum tunneling probability between two coupled potential wells. The system consists of two quantum wells separated by a potential barrier, described by the time-independent Schrödinger eq... |
import numpy as np
from scipy import sparse
from scipy.sparse.linalg import eigsh
def compute_tunneling_split(V0, a=1.0, N=1000):
x_min, x_max = -2.0 * a, 2.0 * a
x = np.linspace(x_min, x_max, N)
dx = x[1] - x[0]
V = V0 * ((x / a)**2 - 1.0)**2
# Kinetic finite-difference: main diag = 1/dx^2,... | long-form-answer | code-generation | [] | null |
physci-075 | ### Question
Superconducting Gap Parameter in BCS Theory
# Problem Description
Write a Python script to calculate the superconducting energy gap Δ at zero temperature using the BCS gap equation:
1 = V Σ_k 1/√(ξ_k² + Δ²)
where ξ_k is the electron energy measured from Fermi level, V is the pairing interaction strength, ... |
# Compute BCS gap Δ (T=0) with constant DOS N(0)
import math
# Given parameters
V = 0.5 # eV
N0 = 1.0 # eV^{-1}
omega_D = 0.1 # eV
# Analytical formula derived above:
Delta = omega_D / math.sinh(1.0 / (2.0 * V * N0))
print(f"Interaction strength V = {V:.1f} eV, Gap parameter Δ = {Del... | long-form-answer | code-generation | [] | null |
physci-076 | ### Question
Heat Conduction in a Metal Rod
# Problem Description
Please write a Python script to investigate heat conduction in a one-dimensional metal rod divided into N segments. The ends of the rod are perfectly insulated. Each segment has a specific temperature, and heat transfer occurs through conduction with ne... |
# Python simulation of 1D heat conduction (forward Euler, Neumann BC - insulated ends)
import numpy as np
def simulate_heat_1d(N, k, dt, dx, t_end, T0):
steps = int(round(t_end / dt))
T = T0.copy().astype(float)
for step in range(steps):
Tn = T.copy()
# Neumann (insulated) boundaries... | long-form-answer | code-generation | [] | null |
physci-077 | ### Question
Light Propagation in a Multilayer Medium
# Problem Description
Please write a Python script to simulate the propagation of light through a one-dimensional multilayer medium. Each layer has a specific refractive index, and the electric field amplitude is calculated using the transfer matrix method. The sys... |
import numpy as np
def transfer_matrix_layer(n, d, wavelength, theta_i):
"""Compute the characteristic matrix for one layer (TE polarization)."""
# Snell's law: n_i * sin(theta_i) = n_j * sin(theta_j)
theta_t = np.arcsin(np.sin(theta_i) / n)
k0 = 2 * np.pi / wavelength
delta = k0 * n * d * n... | long-form-answer | code-generation | [] | null |
physci-078 | ### Question
Magnetization Dynamics in a Ferromagnetic Chain
# Problem Description
Please write a Python script to investigate magnetization dynamics in a one-dimensional chain of N spins. Each spin experiences exchange coupling with its nearest neighbors and damping. The Landau-Lifshitz-Gilbert equation is:
dM_i/dt =... |
import numpy as np
def llg_step(M, H_eff, gamma, alpha):
"""Compute dM/dt using the Gilbert-form LLG rearranged:
dM/dt = -gamma/(1+alpha^2) * ( M x H + alpha * M x (M x H) )
where M and H are 3D vectors.
"""
cross_M_H = np.cross(M, H_eff)
cross_M_cross = np.cross(M, cross_M_H)
... | long-form-answer | code-generation | [] | null |
physci-079 | ### Question
Quantum Dot Energy Spectrum in Magnetic Field
# Problem Description
Please write a Python script to calculate the energy spectrum of a semiconductor quantum dot in the presence of both perpendicular magnetic field and spin-orbit coupling. The Hamiltonian includes:
Confinement potential: V(x,y) = ½m*ω₀²(x²... |
# Further reduced run for timely results: Nx=10, Ny=10 grid to allow execution within time limits.
import numpy as np
import scipy.sparse as sp
import scipy.sparse.linalg as spla
# Constants and parameters (same conversions)
hbar = 1.054571817e-34
e_charge = 1.602176634e-19
m_e = 9.1093837015e-31
mu_B = 9.27401... | long-form-answer | code-generation | [] | null |
physci-080 | ### Question
Nonlinear Optical Response in a Two-Level System
# Problem Description
Please write a Python script to simulate the nonlinear optical response of a two-level system under intense laser excitation. The system is described by the optical Bloch equations including dephasing:
dρ/dt = -i/ℏ[H,ρ] - Γ(ρ - ρ_equil... |
import numpy as np
# Parameters (units: time in ps, rates in ps^-1)
Gamma = 0.1 # ps^-1 decoherence rate
# Pulse parameters (ps units)
Omega0 = 2.0 # ps^-1 (peak Rabi frequency)
t0 = 2.5 # ps
tau = 0.5 # ps
# Time grid
t_start = 0.0
t_end = 5.0
dt = 1e-3 # ps
times = np.arange(t_start, t_end + dt, dt)
# ... | long-form-answer | code-generation | [] | null |
physci-081 | ### Question
Phase Transition in the Bose-Hubbard Model
# Problem Description
Please write a Python script to study the superfluid-to-Mott insulator transition in the 2D Bose-Hubbard model using mean-field theory. The Hamiltonian is:
H = -J∑_{⟨ij⟩}(b_i†b_j + h.c.) + (U/2)∑_in_i(n_i-1) - μ∑_in_i
Use the Gutzwiller ansa... |
import numpy as np
from scipy.linalg import eigh
U = 1.0 # energy unit
n_target = 1.0 # filling
z = 4 # coordination number for 2D square lattice
n_max = 6 # Fock truncation (0..n_max)
dim = n_max + 1
# Operators in Fock basis
a = np.zeros((dim, dim))
adag = np.zeros((dim, dim))
n_op = np.zeros((dim, dim)... | long-form-answer | code-generation | [] | null |
physci-082 | ### Question
Relativistic Electron Dynamics in Laser Field
# Problem Description
Please write a Python script to simulate the motion of a relativistic electron in an intense laser field. Use the Lorentz force equation including radiation reaction:
dp/dt = -e(E + v×B) + F_RR
where F_RR is the Landau-Lifshitz radiation ... |
# Relativistic electron in laser pulse with approximate Landau-Lifshitz radiation reaction
import numpy as np
# Physical constants (SI)
c = 299792458.0
epsilon0 = 8.8541878128e-12
mu0 = 1.0 / (epsilon0 * c**2)
e_charge = 1.602176634e-19
m_e = 9.1093837015e-31
pi = np.pi
# Laser parameters
wavelength = 800e-9 ... | long-form-answer | code-generation | [] | null |
physci-083 | ### Question
Quantum Transport in Disordered Nanowires
# Problem Description
Please write a Python script to study quantum transport in a disordered nanowire using the Landauer-Büttiker formalism and the recursive Green's function method. The system is described by a tight-binding Hamiltonian with Anderson disorder:
H... |
"""
Quantum transport in disordered nanowire using tight-binding + recursive Green's function.
Outputs average conductance (T=0 and finite T), fits localization length xi from scaling,
and estimates dG/dT at 300 K.
Usage:
python nanowire_transport.py --mode quick
python nanowire_transport.py --mode full
Quic... | long-form-answer | code-generation | [] | null |
physci-084 | ### Question
Topological Insulator Surface States
# Problem Description
Please write a Python script to calculate the surface states of a 3D topological insulator using the 4-band BHZ model. The Hamiltonian in momentum space is:
H(k) = ε(k) + ∑_i d_i(k)Γ_i
where Γ_i are Dirac matrices. Include the effect of magnetic i... |
import numpy as np
# Parameters (from problem)
M0 = -0.2 # eV (bulk, not used in effective surface model)
A = 3.0 # eV·Å
B = -20.0 # eV·Å^2 (not used explicitly)
C = 0.0
D = -10.0
J = 0.1 # eV (magnetic impurity strength)
lam = 100.0 # eV·Å^3 (hexagonal warping parameter)
# Assumption: effective su... | long-form-answer | code-generation | [] | null |
physci-085 | ### Question
Gravitational Lensing in Strong Field Limit
# Problem Description
Please write a Python script to simulate gravitational lensing by a Kerr black hole using the ray-tracing method in general relativity. Solve the geodesic equations for light rays:
d²x^μ/dλ² + Γ^μ_{αβ}(dx^α/dλ)(dx^β/dλ) = 0
where Γ^μ_{αβ} a... |
"""
Compute apparent Kerr black hole shadow radius using spherical photon orbits method.
Outputs shadow angular radius (microarcseconds) for an observer at r_obs (in units of M).
Requires: numpy, scipy
"""
import numpy as np
from math import sin, cos, sqrt
from scipy import optimize
# -------------------- Parameters ... | long-form-answer | code-generation | [] | null |
physci-086 | I will provide you with the experiment objective and alternative experimental steps. Each alternative experimental step is labeled with a letter, and their order is scrambled. Your task is to select 5 of the most effective and mutually coordinated steps from the alternative experimental steps based on the experiment ob... | ['B','E','D','F','C'] | atomic-answer | experimental-design | [] | null |
physci-087 | I will provide you with the experiment objective and alternative experimental steps. Each alternative experimental step is labeled with a letter, and their order is scrambled. Your task is to select 5 of the most effective and mutually coordinated steps from the alternative experimental steps based on the experiment ob... | ['C', 'G', 'F', 'A', 'D'] | atomic-answer | experimental-design | [] | null |
physci-088 | # Task Description
I will provide you with the experimental objective. Your task is to collect information related to it based on this objective. The collected information includes two aspects: the experimental support, and theoretical support.
## Experimental Objective
The experimental objective is to investigate the... | "experimental_support": {
"material_systems": [
"Few-layer graphene (FLG) films prepared by mechanical exfoliation of highly oriented pyrolytic graphite",
"Oxidized silicon substrate (SiO₂/Si) for gate voltage application",
"Water vapor or ammonia (NH₃) for intentional p-type or n-type doping studies"
],
"instruments":... | long-form-answer | experimental-design | [] | [
{
"criterion1": "Coverage and Correctness of Material Systems",
"explanation": "Evaluates whether the response provides an appropriate, clearly labeled **Material Systems** section that is specific to the stated experimental objective (electric field effect in few-layer graphene). A high-quality response: (... |
physci-089 | # Task Description
I will provide you with the experimental objective. Your task is to collect information related to it based on this objective. The collected information includes two aspects: the experimental support, and theoretical support.
## Experimental Objective
The objective of this experiment is to investiga... | "experimental_support": {
"material_systems": [
"MoS₂ flakes of varying thicknesses (monolayer, bilayer, quadrilayer, hexalayer, and bulk)",
"Quartz substrate",
"Si/SiO₂ wafer with thermal oxide layer"
],
"instruments": [
"Optical microscope",
"Atomic force microscope (AFM)",
"Confocal microscopy setup",
"Spectrometer ... | long-form-answer | experimental-design | [] | [
{
"criterion1": "Experimental Support – Material Systems",
"explanation": "Evaluates whether the response correctly identifies and lists appropriate material systems under a clearly labeled \"Material Systems\" section. A high-quality answer should (1) include MoS₂ flakes of different, explicitly mentioned ... |
physci-090 | I will provide you with an experimental objective and 3 experimental steps in sequence. In fact, this experimental objective corresponds to 5 experimental steps. You need to design the missing experimental step based on the experimental objective, and combine it with the 3 given experimental steps to form a complete ex... | {"step1":"Materials: Computational software (SIESTA and VASP codes) with density functional theory (DFT) using PBE and HSE06 functionals. Instruments: High-performance computing resources. Methods and Specific Steps: Perform ab initio DFT calculations with periodic boundary conditions. Optimize the geometry of black ph... | long-form-answer | experimental-design | [] | [
{
"criterion1": "Correct Identification and Positioning of the Missing Step",
"explanation": "Evaluates whether the student correctly infers that the missing step is an intermediate transport/electrical characterization step (anisotropic transport and Schottky barrier characterization) that should be placed... |
physci-091 | I will provide you with an experimental objective and 3 experimental steps in sequence. In fact, this experimental objective corresponds to 5 experimental steps. You need to design the two missing experimental steps based on the experimental objective, and combine it with the 3 given experimental steps to form a comple... | {"step1":"Preparation of pristine few-layer 2D-phosphane samples in an oxygen-free environment. Materials: Black phosphorus crystal (99.998%), polydimethylsiloxane (PDMS) stamps, SiO2/Si substrates (305 nm or 291 nm oxide). Instruments: Nitrogen-filled glove box, optical microscope with long-pass filter (λ > 580 nm), a... | long-form-answer | experimental-design | [] | [
{
"criterion1": "Conceptual Alignment with Experimental Objective",
"explanation": "Evaluates whether the two designed missing steps (and the reordered 5-step plan) are conceptually consistent with the given experimental objective and hypotheses. A high-quality response should: (1) clearly target the stated... |
physci-092 | I will provide you with an experimental objective and 3 experimental steps in sequence. In fact, this experimental objective corresponds to 5 experimental steps. You need to design the two missing experimental steps based on the experimental objective, and combine it with the 3 given experimental steps to form a comple... | {
"step1": "Prepare the printing system: Use a custom-built printer with two droplet generators capable of ejecting ~65 pL aqueous droplets into a bath of lipid-containing oil. The oil bath is mounted on a motorized micromanipulator. The goal is to form lipid monolayers around each droplet and enable bilayer formatio... | long-form-answer | experimental-design | [] | [
{
"criterion1": "Scientific Correctness and Conceptual Alignment",
"explanation": "Evaluates whether the two missing experimental steps are scientifically plausible and consistent with the experimental objective and theory described. The response should maintain the core concepts: picoliter aqueous droplets... |
physci-093 | I will provide you with 1 experimental objective and 5 experimental steps arranged in sequence. In fact, one of the 5 experimental steps contains two wrong steps. You need to identify the incorrect experimental step based on the experimental objective, correct it, and finally, only present the complete experimental pla... | {
"step1": "Prepare the multilayer film sample using DC magnetron sputtering. The stack structure is [Pt(3 nm)/Gd25Fe65.6Co9.4(5 nm)/MgO(1 nm)] with a repetition number n = 20. Use Ar gas at 1 mTorr for Pt and GdFeCo and 4 mTorr for MgO. Characterize the film using vibrating sample magnetometry (VSM) to estimate the ma... | long-form-answer | experimental-design | [] | [
{
"criterion1": "Identification and Correction of the Wrong Step",
"explanation": "Evaluates whether the response correctly identifies which original experimental step is (or contains) the error, pinpoints the specific erroneous sub-points within that step (e.g., wrong sputtering pressures and/or wrong puls... |
physci-094 | I will provide you with 1 experimental objective and 5 experimental steps arranged in sequence. In fact, two of the 5 experimental steps are wrong steps. You need to identify the incorrect experimental step based on the experimental objective, correct it, and finally present a complete experimental plan.
Experimental ... | {
"step1":"Synthesis of CsPbBr₃: Materials - CsBr and PbBr2 in equimolar amounts. Instruments - Sealed fused silica ampule, furnace. Methods - React at 600°C in a sealed ampule or by mixing in concentrated HBr solution. Goal - To prepare pure CsPbBr₃ compound for crystal growth.",
"step2":"Crystal Growth: Materials - C... | long-form-answer | experimental-design | [] | [
{
"criterion1": "Identification of Incorrect Steps",
"explanation": "Evaluates whether the response correctly identifies which of the original experimental steps are incorrect or partially incorrect, based on the experimental objective and in comparison to the reference answer. For this problem, the student... |
physci-095 | I will provide you with 1 experimental objective and 5 experimental steps arranged in sequence. In fact, two of the 5 experimental steps are wrong steps. You need to identify the incorrect experimental step based on the experimental objective, correct it, and finally present a complete experimental plan.
Experimental ... | {
"step1": "Synthesis of Cs₂Ni₃S₄: Materials include cesium carbonate (Cs₂CO₃), nickel powder (Ni), and sulfur powder (S). Instruments: mortar and pestle, alumina crucible, flow furnace with argon gas supply. Methods: Grind Cs₂CO₃, Ni, and S in a molar ratio of 6:1:12 (Cs:Ni:S). Press into a pellet and place in an al... | long-form-answer | experimental-design | [] | [
{
"criterion1": "Identification of Incorrect Steps and Conceptual Justification",
"explanation": "Evaluates whether the response correctly identifies exactly which of the original five experimental steps are wrong, and briefly explains why they are inappropriate given the experimental objective. The student... |
physci-096 | I will provide you with an experimental objective and 3 experimental steps in sequence. In fact, this experimental objective corresponds to 5 experimental steps. You need to design the two missing experimental steps based on the experimental objective, and combine it with the 3 given experimental steps to form a comple... | {"step1":"Perform structural optimization of the AMN₂ compounds using density functional theory (DFT) calculations in the Vienna ab initio simulation package (VASP). Use the Perdew-Burke-Ernzerhof (PBE) functional within the generalized gradient approximation (GGA). Fully relax the lattice structure and atomic position... | long-form-answer | experimental-design | [] | [
{
"criterion1": "Correct Experimental Step Identification and Positioning",
"explanation": "Evaluates whether the response clearly understands that there are 5 total experimental steps, that the user already provided a 6‑step framework (step1–step6), and that the task is to design TWO missing steps and then... |
physci-097 | I will provide you with an experimental objective and 3 experimental steps in sequence. In fact, this experimental objective corresponds to 5 experimental steps. You need to design the missing experimental step based on the experimental objective, and combine it with the 3 given experimental steps to form a complete ex... | {"step1":"Materials: Lignin (from Suzano Papel e Cellulose S.A. Corp.), methanol solvent (AR grade), ferrocene catalyst precursor (99%), thiophene additive (99%). Instruments: Vacuum oven, magnetic stirrer, ultrasonic bath. Methods: Dry lignin in a vacuum oven at 60°C for 12 hours. Dissolve the dried lignin in methanol... | long-form-answer | experimental-design | [] | [
{
"criterion1": "Correct Identification and Positioning of the Missing Step",
"explanation": "Evaluates whether the student correctly infers that the given 3 steps actually correspond to steps 1, 2, and 4 of a 5-step process, and that the missing step is an intermediate post-synthesis handling step between ... |
physci-098 | I will provide you with 1 experimental objective and 5 experimental steps arranged in sequence. In fact, two of the 5 experimental steps are wrong steps. You need to identify the incorrect experimental step based on the experimental objective, correct it, and finally present a complete experimental plan.
Experimental ... | { "step1": "Select a series of 3d perovskite oxide compounds (e.g., YTiO₃, LaVO₃, CaMnO₃, LaMnO₃, CaFeO₃, YNiO₃) for investigation. Use crystallographic databases to obtain initial structural parameters. The goal is to cover a range of electronic configurations and tolerance factors to analyze diverse gapping mechanism... | long-form-answer | experimental-design | [] | [
{
"criterion1": "Identification of Incorrect Steps",
"explanation": "Evaluates whether the student correctly identifies which of the original five experimental steps are wrong relative to the experimental objective and the reference answer. Full credit requires pinpointing both incorrect steps (here, step2 ... |
physci-099 | I will provide you with 1 experimental objective and 5 experimental steps arranged in sequence. In fact, two of the 5 experimental steps are wrong steps. You need to identify the incorrect experimental step based on the experimental objective, correct it, and finally present a complete experimental plan.
Experimental ... | {
"step1": "Synthesize polycrystalline or single-crystal RTiO₃ samples (e.g., R = La, Y) using solid-state reaction. Materials: high-purity La₂O₃, Y₂O₃, and TiO₂ powders. Instruments: ball mill, pellet press, high-temperature furnace. Methods: Weigh stoichiometric powders, mix via ball milling, press into pellets, and ... | long-form-answer | experimental-design | [] | [
{
"criterion1": "Identification and Correction of Incorrect Steps",
"explanation": "Evaluates whether the student correctly identifies that two of the five original experimental steps are incorrect (step3 field strength and step4 probe technique), clearly states what is wrong in each, and proposes appropria... |
physci-100 | I will provide you with 1 experimental objective and 5 experimental steps arranged in sequence. In fact, two of the 5 experimental steps are wrong steps. You need to identify the incorrect experimental step based on the experimental objective, correct it, and finally present a complete experimental plan.
Experimental ... | {"step1":"Materials: Mining dump samples from the abandoned Nagyborzsony Au deposit at Alsô-Rôzsa, Hungary. Instruments: Optical microscope, scanning electron microscope (SEM). Methods: Examine grain morphology and luster. Steps: Collect samples, observe under microscope to identify black metallic luster grains, check ... | long-form-answer | experimental-design | [] | [
{
"criterion1": "Identification and Correction of Wrong Experimental Steps",
"explanation": "Evaluates whether the response correctly identifies which of the original five steps are wrong (here: use of EDS instead of WDS in step 2, and omission of SOC in step 4) and provides appropriate corrections that ali... |
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