Pith. sign in

REVIEW 3 major objections 4 minor 1 cited by

Universal Magnetic Phases in Twisted Bilayer MoTe$_2$

T0 review · 3 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Twisted MoTe2 shows the same magnetic phases from 2.1° to 3.7°.

desk verdict Systematic twist-angle map of tMoTe2 ferromagnetism; ν=-1/-3 phases are robust across 2.1-3.7°, but the universality claim needs an independent density check at ν=-3. read the letter →

arxiv 2507.22354 v1 pith:SPU6PZKH submitted 2025-07-30 cond-mat.mes-hall cond-mat.str-el

Weijie Li , Evgeny Redekop , Christiano Wang Beach , Canxun Zhang , Xiaowei Zhang , Xiaoyu Liu , Will Holtzmann , Chaowei Hu
show 10 more authors
Eric Anderson Heonjoon Park Takashi Taniguchi Kenji Watanabe Jiun-haw Chu Liang Fu Ting Cao Di Xiao Andrea F. Young Xiaodong Xu
This is my paper
classification cond-mat.mes-hallcond-mat.str-el
keywords twistedbilayerMoTe2moiréferromagnetismChernbandstwistangledependencenanoSQUID-on-tipmagnetometryreflectivemagneticcirculardichroismCurietemperaturefractionalinsulator
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper reports that twisted bilayer MoTe$_2$ hosts spontaneous ferromagnetism at moiré filling factors $\nu = -1$ and $\nu = -3$ across a wide range of twist angles, from 2.1° to 3.7°, and that the magnetic phase diagram of the two lowest Chern bands is essentially unchanged as the twist angle varies. At the smallest angle, 2.1°, a third ferromagnetic phase appears at $\nu = -5$, which the authors take as evidence that higher moiré bands flatten at small twist angles. The Curie temperature of the $\nu = -1$ phase rises steeply with twist angle while that of $\nu = -3$ stays roughly constant, pointing to different competition between bandwidth and exchange in the two bands. If correct, the result means the magnetic ground states of the lowest two moiré bands do not require fine-tuned twist angles, simplifying the search for correlated topological phases in this material.

What carries the argument

The central objects are the moiré Chern bands of twisted bilayer MoTe$_2$ — the flat, valley-polarized bands that form in the moiré superlattice — and the competition between their bandwidth and the exchange interaction as twist angle is varied. The experimental workhorse is local magnetometry: scanning nanoSQUID-on-tip (nSOT) images the fringe magnetic field of the spontaneous magnetization at about 100 nm resolution, and reflective magnetic circular dichroism (RMCD) measures the valley/spin polarization and its hysteresis. Photoluminescence spectroscopy tracks correlated gaps through optical fan diagrams. The filling-factor axis is anchored by the well-defined $\nu = -1$ Chern-insulator gap, with $\nu$ defined as $-n_e/n_e(\nu=-1)$, and the twist angle is read off from that same density. Hartree–Fock calculations on a 12-orbital Wannier model provide the exchange gaps that the Curie temperatures are compared against.

What would settle it

Measure the nSOT phase diagram at a location with local twist angle outside 2.1°–3.7° on the same device, or on a device with a continuous twist-angle gradient spanning, say, 1.8° to 4.0°; if the $\nu = -3$ ferromagnetic pocket does not persist with the same sharp onset at exactly $\nu = -3$ throughout that range, the claimed universality is bounded. Alternatively, a clean transport measurement at 2.1° resolving a zero-field topological gap at $\nu = -3$ would contradict the paper's conclusion that the state there is gapless, altering the interpretation of the magnetic phase.

Watch

Extended reading notes

Core claim

Spontaneous zero-field ferromagnetism appears in the first and second moiré Chern bands of twisted bilayer MoTe$_2$ at fillings $\nu = -1$ and $\nu = -3$ for every twist angle studied, 2.1° through 3.7°, and the shape of the magnetic phase diagram as a function of filling and electric field is nearly identical across that entire range. The $\nu = -1$ phase shows a sharp feature at the integer filling characteristic of a Chern insulator with edge states, while the $\nu = -3$ phase onsets abruptly at $\nu = -3$ and has no internal structure. At 2.1° a clear ferromagnetic phase also appears at $\nu = -5$, absent at larger twist angles, consistent with the flattening of the third moiré band. Curie temperatures reveal a contrasting angle dependence: $T_c$ at $\nu = -1$ rises from about 6 K at 2.1° to 14 K at the largest angles, while $T_c$ at $\nu = -3$ remains between 4 and 6 K throughout, mirroring Hartree–Fock exchange-gap calculations. At $\nu = -3$, despite the broken time-reversal symmetry, no topological gap is observed, and the authors attribute the absence of a gap to the intrinsic state or to device disorder that transport and local probes can sample inhomogeneously.

Load-bearing premise

The load-bearing premise is that the filling factor $\nu$ at every location and twist angle is known from the parallel-plate capacitor model with $\nu = -n_e/n_e(\nu=-1)$ as the only anchor; if local strain, hBN-thickness variation, or density offsets shift the apparent density, then the exact $\nu$ positions of the $-3$ and $-5$ phases, and hence the universality claim, could be off.

Editorial extensions

If this is right

  • The lowest two Chern bands of tMoTe$_2$ have an intrinsic magnetic phase diagram that is essentially twist-angle independent, so device fabrication does not need sub-0.1° twist-angle control to access the same ferromagnetic states.
  • The $\nu = -5$ ferromagnetic phase only at 2.1° implies that the third moiré band becomes flat and exchange-dominated at small twist angles, making small-angle devices the place to look for correlated topological states in higher bands.
  • The different Curie-temperature trends for $\nu = -1$ and $\nu = -3$ provide a direct experimental handle on the bandwidth-to-exchange ratio of each band, which can be compared with first-principles models.
  • The absence of a topological gap at $\nu = -3$ over the entire angle range suggests that the zero-field ground state there is gapless or incipient, meaning that stronger magnetic field rather than twist-angle tuning is the route to stabilize a Chern insulator at this filling.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The paper's universality claim is made over the range 2.1°–3.7°; a natural extension would be to push the same local probes to twist angles outside this window, where the flattening of higher bands and the widening of lower bands could make the phase diagram non-universal at $\nu = -3$ or introduce new phases at $\nu = -5$ and beyond.
  • The filling-factor calibration at $\nu = -3$ relies on a capacitor model with $\nu = -n_e/n_e(\nu=-1)$ extrapolated to higher densities; if the local twist angle in the nSOT sample varies by more than 0.1°, the apparent 'universality' at $\nu = -3$ could partly reflect the calibration procedure, since the $\nu = -1$ anchor and the $\nu = -3$ position would shift together across locations.
  • If the $\nu = -5$ ferromagnetism is truly the signature of a flattened third band, then at even smaller twist angles (near 2.0° or below) one might expect the $\nu = -5$ phase to strengthen and possibly develop its own fractional descendants; this is a testable prediction from the paper's logic.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. This manuscript reports a combined nanoSQUID-on-tip (nSOT) magnetometry, reflective magnetic circular dichroism (RMCD), and photoluminescence study of twisted bilayer MoTe2 devices with twist angles between 2.1° and 3.7°. The authors observe spontaneous ferromagnetism at moiré fillings ν = −1 and ν = −3 in all devices, and at ν = −5 in the 2.1° device. They measure Curie temperatures that increase with twist angle at ν = −1 but remain roughly constant at ν = −3, and compare these trends with DFT/Wannier-based Hartree-Fock exchange-gap calculations. They conclude that the ferromagnetic phases are universal across this angle range, that higher bands flatten at small twist angles, and that no topological gap is resolved at ν = −3.

Significance. If the phase diagram is correct, the paper provides a systematic map of magnetism in the lowest two Chern bands and evidence for higher-band ferromagnetism at small twist angles, which is valuable for fractional Chern insulator and fractional quantum spin Hall research. Strengths include complementary local and optical probes, hysteresis measurements, multiple 2.1° devices, spatially resolved measurements, and explicit methods for density calibration. The main limitation is the absolute filling calibration, which is anchored only at ν = −1 and linearly extrapolated to higher fillings; this directly affects the central universality and no-gap claims.

major comments (3)
  1. [Methods: Determination of doping density and electric field; Determination of local filling factor from nSOT…] The absolute filling-factor axis is defined by ν = −n_e/n_e(ν = −1), with n_e from a parallel-plate capacitor model and n_offset fixed by the top-gate Landau fan kink. There is no independent anchor at the second or third moiré bands. A nonlinear gate-to-density conversion (quantum capacitance, local hBN thickness variation, or strain) would therefore shift the apparent positions of the ν = −3 and ν = −5 phases, and the reported 'absence of a gap at ν = −3' would be evaluated at a possibly misassigned filling. The stated ±0.05° twist-angle uncertainty only covers the uncertainty in n_e(ν = −1) and does not bound this nonlinearity. This concern directly affects Fig. 1e, where the coincidence of the ferromagnetic edge with ν = −3 across locations is the central evidence for universality. I request an independent calibration of the density axis at higher filling—for example, chemical-potential jumps at ν = −2 or ν = −3, a Landau fan anchored at a higher integer filling, or comparison with a known higher-band gap—before the universality claim can be fully supported.
  2. [Conclusions; Fig. 2a] The conclusion that the ν = −3 state is trivial because no topological gap is seen in RMCD/PL is stronger than the data support. The paper itself documents disorder-induced spatial inhomogeneity in Fig. 1f and notes that the base temperature (1.6 K) may obscure fragile phases. RMCD and PL are bulk/optical probes and cannot set a tight upper bound on a small charge gap, particularly in a spatially inhomogeneous sample. The statement 'which implies the trivial nature of the state at ν = −3' should be softened to 'no evidence of a gap within the sensitivity of these probes.'
  3. [Fig. 3b] The twist-angle dependence of the Curie temperature is based on a single device per angle for most points, with only two devices at 2.1°. Given that the nSOT sample itself shows substantial local twist-angle spread (2.2°–2.8°), device-to-device variations in strain and disorder could influence the reported Tc trends. Reporting the number of devices per angle and, where possible, an additional device at an intermediate angle would strengthen the empirical basis for the contrasting Tc behavior at ν = −1 versus ν = −3.
minor comments (4)
  1. [Fig. 1f caption and main text] The density value 'ne = −4.5 × 10−12cm−2' appears to be a typographical error; it should read '−4.5 × 10^12 cm^−2' with the exponent correctly formatted.
  2. [Main text, 'Robust Magnetic Phases in tMoTe2'] The text describing Fig. 2a gives the middle and right twist angles as 2.7° and 3.5°, while Extended Data Fig. 4 lists 2.8° and 3.7° devices; these labels should be reconciled.
  3. [Intro and Methods: nSOT sensor calibration] The introduction quotes a magnetic sensitivity 'as good as 0.3 nT/√Hz', whereas the Methods section gives 'approximately 1−10 nT/√Hz'; these numbers should be made consistent.
  4. [Methods: Numerical methods] The Hartree-Fock exchange gaps in Fig. 3d use a screening dielectric constant ε = 40 chosen to temper overestimation, with no sensitivity analysis. The comparison with the measured Tc trends should therefore be described as qualitative.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the phase diagram is measured, the filling axis is calibrated at ν = −1 rather than fitted to the ν = −3 feature, and the HF comparison is qualitative, not a fitted prediction.

full rationale

The paper's central claims are experimental observations: spontaneous ferromagnetism at ν = −1 and −3, its absence at ν = −2 and −4, the angle dependence of Tc, and the higher-band phase at ν = −5 for 2.1°. These are not derived from the theory in the paper. The only candidate circular step is the filling-factor calibration. The Methods state: "The filling factor is subsequently defined by -n_e/n_e(ν = −1) and this assignment is extended to higher fillings." This defines the coordinate axis; it does not determine where magnetic signal appears. Observing the second-band ferromagnetic pocket at the coordinate ν = −3 (three times the anchor density) is an unconstrained measurement on that axis, and it could have appeared at a different coordinate. The nSOT calibration additionally uses an independent top-gate Landau-fan kink for the density offset, and the paper validates the capacitor model against optical Landau fans. Possible nonlinearity in the gate-to-density conversion is a systematic uncertainty in the absolute ν assignment, not a circular reduction of the claim. The Hartree-Fock exchange gaps are computed from DFT/Wannier models with an explicitly stated screening constant ε = 40; they are not fitted to the measured Tc values, and the comparison is qualitative. Self-citations to Refs. 24 and 30 provide published methodology (MLFF relaxation and Wannier/Hartree-Fock construction) rather than the experimental conclusion, so they are not load-bearing. The paper also explicitly hedges the ν = −3 topology claim with "we find no evidence of a topological gap" and notes that fragile correlated topological phases could be obscured by disorder. No equation or fitted parameter reduces the central claims to their inputs.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

No new entities are postulated. The two free parameters are a hand-chosen screening constant in the theory and the experimental density offset calibration. The axioms are standard experimental and modeling assumptions.

free parameters (2)
  • screening dielectric constant ε = 40
    Used in Hartree-Fock exchange gap calculations to temper overestimation (Methods, Numerical methods). Chosen by hand; affects the computed Tc trends compared to experiment.
  • carrier density offset n_offset = derived from PL spectra
    Determined by fitting to integer and fractional states in PL spectra (Methods, Determination of doping density). Sets the absolute filling factor axis for all measurements.
assumptions (5)
  • domain assumption Parallel-plate capacitor model with fixed hBN dielectric constant 3.0 maps gate voltages to density and displacement field.
    Used throughout to convert gate voltages to n_e and D/ε0 (Methods, Determination of doping density). Spatial or sample-dependent variation in hBN thickness would propagate into ν.
  • domain assumption The relation ν = -n_e/n_e(ν = -1) holds linearly to ν = -5.
    Extends the filling factor axis calibrated at ν = -1 to higher fillings (Methods; used in all phase diagrams).
  • domain assumption DFT-PBE with MLFF-relaxed structures and the 12-orbital Wannier model describe the relevant moiré bands.
    Bandwidth and exchange gap calculations rely on these models (Methods, Numerical methods; details in Refs. 24 and 30).
  • domain assumption RMCD signal below trion resonance is proportional to the out-of-plane magnetization without significant optical perturbation.
    Authors verify excitation energy dependence and choose below-resonance excitation (main text, Fig. 2c), but the proportionality is assumed.
  • domain assumption Spontaneous hysteresis in RMCD implies time-reversal symmetry breaking bulk ferromagnetism.
    Standard interpretation used to identify ferromagnetic phases (Fig. 2b).

how reviews work

0 comments
Cite this review

Pith. "Pith review of Universal Magnetic Phases in Twisted Bilayer MoTe$_2$." pith.science (2026). https://pith.science/paper/SPU6PZKH

@misc{pith2026250722354,
  author       = {Pith},
  title        = {Pith review of: Universal Magnetic Phases in Twisted Bilayer MoTe$_2$},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SPU6PZKH}},
  note         = {Machine review of arXiv:2507.22354}
}
abstract

Twisted bilayer MoTe$_2$ (tMoTe$_2$) has emerged as a robust platform for exploring correlated topological phases, notably supporting fractional Chern insulator (FCI) states at zero magnetic field across a wide range of twist angles. The evolution of magnetism and topology with twist angle remains an open question. Here, we systematically map the magnetic phase diagram of tMoTe$_2$ using local optical spectroscopy and scanning nanoSQUID-on-tip (nSOT) magnetometry. We identify spontaneous ferromagnetism at moir\'e filling factors $\nu = -1$ and $-3$ over a twist angle range from 2.1$^\circ$ to 3.7$^\circ$, revealing a universal, twist-angle-insensitive ferromagnetic phase. At 2.1$^\circ$, we further observe robust ferromagnetism at $\nu = -5$, absent in the devices with larger twist angle -- a signature of the flattening of higher bands in this twist angle range. Temperature-dependent measurements reveal a contrasting twist-angle dependence of the Curie temperatures between $\nu = -1$ and $\nu = -3$, indicating distinct interplay between exchange interaction and bandwidth for the two Chern bands. Despite spontaneous time-reversal symmetry breaking, we find no evidence of a topological gap at $\nu = -3$; however, fragile correlated topological phases could be obscured by the device disorder evident in our spatially resolved measurements. Our results establish a global framework for understanding and controlling magnetic order in tMoTe$_2$ and highlight its potential for accessing correlated topological phases in higher energy Chern band.

Figures

Figures reproduced from arXiv: 2507.22354 by the authors.

Figure 1
Figure 1. FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

Discussion (0). Sign in to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Valley Order in Moir\'e Topological Insulators

    cond-mat.mes-hall 2025-09 conditional novelty 5.0 of 10

    At filling ν=1, intervalley-coherent states in opposite-Chern Landau level models are ground states only for reduced intravalley interactions, and their gapless spin mode rules them out as the sole explanation of the ...

Reference graph

Works this paper leans on

40 extracted references · 34 canonical work pages · cited by 1 Pith paper

  1. [1]

    Cao, Y. et al. Correlated insulator behaviour at half- filling in magic-angle graphene superlattices. Nature 556, 80–84 (2018)

    work page 2018

  2. [2]

    M., Watanabe, K., Taniguchi, T

    Cao, Y., Park, J. M., Watanabe, K., Taniguchi, T. & Jarillo-Herrero, P. Pauli-limit violation and re-entrant superconductivity in moir´ e graphene.Nature 595, 526– 531 (2021)

    work page 2021

  3. [3]

    M., Cao, Y., Watanabe, K., Taniguchi, T

    Park, J. M., Cao, Y., Watanabe, K., Taniguchi, T. & Jarillo-Herrero, P. Tunable strongly coupled supercon- ductivity in magic-angle twisted trilayer graphene. Na- ture 590, 249–255 (2021)

    2021

  4. [4]

    Xie, Y. et al. Fractional chern insulators in magic-angle twisted bilayer graphene. Nature 600, 439–443 (2021)

    work page 2021

  5. [5]

    Sharpe, A. L. et al. Emergent ferromagnetism near three- quarters filling in twisted bilayer graphene. Science 365, 605–608 (2019)

    work page 2019

  6. [6]

    Serlin, M. et al. Intrinsic quantized anomalous Hall effect in a moir´ e heterostructure.Science 367, 900–903 (2020)

    work page 2020

  7. [7]

    Tschirhart, C. L. et al. Imaging orbital ferromagnetism in a moir´ e Chern insulator.Science (2021)

    work page 2021

  8. [8]

    & Lin, S.-Z

    Li, H., Kumar, U., Sun, K. & Lin, S.-Z. Spontaneous fractional Chern insulators in transition metal dichalco- genide moir´ e superlattices.Physical Review Research 3, L032070 (2021)

    work page 2021

Show all 40 references
  1. [9]

    & MacDon- ald, A

    Wu, F., Lovorn, T., Tutuc, E., Martin, I. & MacDon- ald, A. Topological insulators in twisted transition metal dichalcogenide homobilayers. Physical Review Letters 122, 086402 (2019)

    2019

  2. [10]

    & Senthil, T

    Zhang, Y.-H., Mao, D., Cao, Y., Jarillo-Herrero, P. & Senthil, T. Nearly flat Chern bands in moir´ e superlat- tices. Physical Review B 99, 075127 (2019)

    2019

  3. [11]

    Devakul, T., Cr´ epel, V., Zhang, Y. & Fu, L. Magic in twisted transition metal dichalcogenide bilayers. Nature Communications 12, 6730 (2021)

    2021

  4. [12]

    & Yao, W

    Yu, H., Chen, M. & Yao, W. Giant magnetic field from moir´ e induced Berry phase in homobilayer semiconduc- tors. National Science Review 7, 12–20 (2020)

    2020

  5. [13]

    Spanton, E. M. et al. Observation of fractional chern insulators in a van der waals heterostructure. Science 360, 62–66 (2018)

    2018

  6. [14]

    Cai, J. et al. Signatures of fractional quantum anomalous Hall states in twisted MoTe2. Nature 622, 63–68 (2023)

    2023

  7. [15]

    Zeng, Y. et al. Thermodynamic evidence of fractional Chern insulator in moir´ e MoTe 2. Nature 622, 69–73 (2023)

    2023

  8. [16]

    Park, H. et al. Observation of fractionally quantized anomalous Hall effect. Nature 622, 74–79 (2023)

    2023

  9. [17]

    Xu, F. et al. Observation of integer and fractional quan- tum anomalous Hall effects in twisted bilayer MoTe 2. Physical Review X 13, 031037 (2023)

    2023

  10. [18]

    Ji, Z., Park, H., Barber, M. E. et al. Local probe of bulk and edge states in a fractional Chern insulator. Nature 635, 578–583 (2024)

    2024

  11. [19]

    Redekop, E., Zhang, C., Park, H. et al. Direct magnetic imaging of fractional Chern insulators in twisted MoTe 2. Nature 635, 584–589 (2024)

    2024

  12. [20]

    Park, H. et al. Observation of High-Temperature Dissi- pationless Fractional Chern Insulator (2025)

    2025

  13. [21]

    Xu, F. et al. Signatures of unconventional superconduc- tivity near reentrant and fractional quantum anomalous Hall insulators (2025)

    2025

  14. [22]

    Kang, K., Shen, B., Qiu, Y. et al. Evidence of the frac- tional quantum spin Hall effect in moir´ e MoTe2. Nature 628, 522–526 (2024)

    2024

  15. [23]

    Mao, N. et al. Transfer learning relaxation, elec- tronic structure and continuum model for twisted bilayer MoTe2. Communications Physics 7, 262 (2024)

    2024

  16. [24]

    W., Wang, C., Liu, X

    Zhang, X. W., Wang, C., Liu, X. et al. Polarization- driven band topology evolution in twisted MoTe 2 and WSe2. Nature Communications 15, 4223 (2024)

    2024

  17. [25]

    Qiu, W.-X., Li, B., Luo, X.-J. & Wu, F. Interaction- driven topological phase diagram of twisted bilayer mote

  18. [26]

    Physical Review X 13, 041026 (2023)

    2023

  19. [27]

    Chang, X. et al. Evidence of competing ground states be- tween fractional Chern insulator and antiferromagnetism in moir´ e MoTe2 (2025). URL http://arxiv.org/abs/ 2503.13213. ArXiv:2503.13213 [cond-mat]

    2025 arXiv

  20. [28]

    Chang, X. et al. Emergent charge-transfer ferromag- netism and fractional chern states in moir´ e mote2. arXiv e-prints arXiv–2503 (2025)

    2025

  21. [29]

    Park, H. et al. Ferromagnetism and topology of the higher flat band in a fractional Chern insulator. Nature Physics 21, 549–555 (2025)

    2025

  22. [30]

    Abouelkomsan, A. & Fu, L. Non-abelian spin Hall insu- lator (2024). 2406.14617

    2024 arXiv

  23. [31]

    Wang, C. et al. Higher Landau-level analogues and sig- natures of non-abelian states in twisted bilayer MoTe 2 (2024). 2404.05697

    2024 arXiv

  24. [32]

    Non-abelian and abelian descendants of a vortex spin liquid: Fractional quantum spin Hall effect in twisted MoTe2

    Zhang, Y.-H. Non-abelian and abelian descendants of a vortex spin liquid: Fractional quantum spin Hall effect in twisted MoTe2. Physical Review B 110, 155102 (2024)

    2024

  25. [33]

    Anderson, E. et al. Programming correlated magnetic states with gate-controlled moir´ e geometry.Science 381, 325–330 (2023)

    2023

  26. [34]

    Anderson, E., Cai, J., Reddy, A. P. et al. Trion sensing of a zero-field composite fermi liquid. Nature 635, 590–595 (2024)

    2024

  27. [35]

    Soler, J. M. et al. The siesta method for ab initio order- nmaterials simulation. Journal of Physics: Condensed Matter 14, 2745 (2002)

    2002

  28. [36]

    Optimized norm-conserving vanderbilt pseudopotentials

    Hamann, D. Optimized norm-conserving vanderbilt pseudopotentials. Physical Review B—Condensed Matter and Materials Physics 88, 085117 (2013)

    2013

  29. [37]

    P., Burke, K

    Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Physical review let- ters 77, 3865 (1996)

    1996

  30. [38]

    Zhang, L., Han, J., Wang, H., Car, R. & E, W. Deep potential molecular dynamics: a scalable model with the accuracy of quantum mechanics. Physical review letters 120, 143001 (2018)

    2018

  31. [39]

    Wang, H., Zhang, L., Han, J. et al. Deepmd-kit: A deep learning package for many-body potential energy repre- sentation and molecular dynamics. Computer Physics Communications 228, 178–184 (2018)

    2018

  32. [40]

    & Furthm¨ uller, J

    Kresse, G. & Furthm¨ uller, J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Computational materials science 6, 15–50 (1996). 8 METHODS Device fabrication The optical devices were fabricated using graphite, hBN, a...

    1996

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.