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REVIEW 4 major objections 6 minor 57 references

Spin-valley-layer coupling with dual control via stacking and electric field in antiferromagnetic bilayer Janus YIBr

T0 review · 4 major / 6 minor · reviewed 2026-08-01 · deepseek-v4-flash

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Pith's one-line read Stacking sets the magnetic easy-axis direction of bilayer YIBr; an out-of-plane easy axis turns on spin splitting, valley polarization, and a quantum valley Hall state tunable by electric field.

desk verdict Useful material-specific DFT data on six stackings of bilayer Janus YIBr, but the effective-model parameters contradict the reported splittings and the quantum valley Hall claim is not backed by a topological invariant. read the letter →

arxiv 2607.17199 v1 pith:CJCDEUFG submitted 2026-07-19 cond-mat.mes-hall cond-mat.mtrl-sci

Bo-Wen Yu This is my paper · ORCID
classification cond-mat.mes-hallcond-mat.mtrl-sci PACS 73.43.-f75.70.Tj71.70.Ej
keywords bilayerJanusYIBrantiferromagnetstackingcontroleasyaxisspin-valleycouplingquantumvalleyHalleffectBerrycurvatureelectric-field
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 argues that in a bilayer of the Janus material YIBr (I-Y-Br stacked on Y-I inverted), the way the two layers are stacked controls the direction of the magnetic easy axis. When that axis is perpendicular to the layers, the valence band near the Fermi level shows spin splitting and valley polarization whose character—spin-valley coupling in AA stacking, valley splitting plus spin splitting in AB stacking—is captured by a compact effective Hamiltonian built on a massive Dirac dispersion. When the easy axis lies in the plane, spin and valley degeneracy returns. Because stacking can be changed by sliding one layer, sliding becomes a switch for spin, valley, and layer degrees of freedom, and an applied out-of-plane electric field continuously tunes the spin splitting, with valley polarization adjustable between −0.08 and +0.08 eV in the AA1 stacking. The authors also show Berry curvature of opposite sign at K and K', so a quantum valley Hall insulator can be achieved.

What carries the argument

The load-bearing object is the effective low-energy Hamiltonian H(k) = H0(k) + λ1(k) τ_z + λ2(k) s_z + λ3(k) τ_z s_z, where H0 describes a massive Dirac-like valence band, τ_z is the valley (K/K') pseudospin, s_z is the electron spin, and the λ terms quantify valley splitting, spin splitting, and spin-valley coupling. From first-principles fits the paper extracts λ values for each stacking; AA stackings with out-of-plane easy axis have λ3 ≈ 40.8 meV and λ1 = 0, while AB3 has λ1 = 11.7 meV and λ2 = 40.5 meV with λ3 = 0. This Hamiltonian converts the easy-axis direction, set by stacking, into a concrete spin/valley/layer texture. A second object is the Berry curvature, whose opposite-sign peak

What would settle it

Measure the easy axis of each stacking of bilayer YIBr (e.g., by magnetometry on mechanically exfoliated flakes or by angle-dependent Hall resistance) and compare spin-resolved valence bands at K and K' from ARPES against the predicted spin splitting and valley polarization; finding, for any stacking, an easy axis different from the computed one, or spin splitting when an in-plane easy axis is measured, would overturn the central claim. A cheaper first-principles check is to recompute the MAE with HSE or varied U and watch whether any stacking's easy axis flips.

Watch

Extended reading notes

Core claim

The central discovery is that the six high-symmetry stackings of antiferromagnetic bilayer Janus YIBr separate into two behaviors determined solely by the easy axis: out-of-plane easy axes (AA1, AA2, AB2) produce spin splitting and/or valley polarization in the top valence bands, while in-plane easy axes (AA3, AB1, AB3) leave spin and valley degenerate. The paper expresses this in an effective low-energy model H = H0 + λ1 τ_z + λ2 s_z + λ3 τ_z s_z, where H0 is a massive Dirac dispersion, and it shows that AA stackings have a pure spin-valley coupling term (λ3) while AB stackings have separate valley and spin terms (λ1, λ2). Berry curvature calculations give opposite signs at K and K', implyi

Load-bearing premise

The load-bearing premise is that the magnetic easy-axis directions computed with DFT+U (U = 2 eV) for the six stackings are correct; if a different functional or U flips any easy axis from out-of-plane to in-plane or vice versa, the correspondence between stacking, spin splitting, and valley polarization changes, and the sliding-control scheme loses its footing.

Editorial extensions

If this is right

  • Sliding one layer relative to the other (changing stacking) switches the easy axis between in-plane and out-of-plane, thereby turning spin splitting and valley polarization on or off.
  • With an out-of-plane easy axis, the valence band hole carries a coupled spin, valley, and layer label; for AA stacking, spin and valley are locked (λ3) while for AB stacking, valley polarization coexists with uniform spin splitting (λ1, λ2).
  • Berry curvature is opposite at K and K' and integrates to zero over the full Brillouin zone, so the system is a quantum valley Hall insulator whose valley Hall response can be switched by changing stacking.
  • An out-of-plane electric field of ±0.05 V/Å enhances spin splitting up to about 0.4 eV and, in AA1 stacking, continuously sweeps valley polarization between −0.08 and +0.08 eV, giving a control knob for hole spin, valley, and layer.
  • The fitted effective Hamiltonian reproduces the two valence bands for all six stackings, providing a transferable low-energy description for device-oriented modeling.

Reading between the lines

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

  • If the easy-axis–stacking correspondence holds in experiments, interlayer sliding would give a mechanically rewritable multistate memory where the stored bit is the spin/valley/layer configuration of the valence hole, not just a charge state.
  • The λ3 term in AA stackings resembles Ising-type spin-valley locking, suggesting that valley and spin degeneracies are lifted together; this could enable spin-filtered valley transport without an external magnetic field.
  • A natural test of the underlying mechanism is to apply the same DFT+U analysis to other Janus bilayers (e.g., YClBr or YIBr variants) and check whether the easy-axis/stacking rule and the sign of Berry curvature at K/K' always follow the inversion and mirror symmetries identified here.
  • Because the paper fits α and β separately along K–Γ and K–M directions with 120° symmetry, the hole effective mass is anisotropic; electric-field tuning could renormalize these masses, which might show up as transport anisotropy in experiments.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 6 minor

Summary. The manuscript reports a first-principles study of six stacking configurations of antiferromagnetic bilayer Janus YIBr, combining DFT with an effective low-energy model. It claims that stacking determines the magnetic easy axis, that out-of-plane easy axes produce spin splitting and/or valley polarization in the valence band, and that an external electric field can tune these properties. From the distribution of Berry curvature it also concludes that quantum valley Hall insulators can be achieved and controlled by stacking and electric field.

Significance. The systematic DFT dataset across six stackings—including magnetic anisotropy energies, spin/valley splittings, atom-resolved projections, and electric-field response—is a useful contribution to the study of Janus bilayer magnets. If the easy-axis-to-splitting correspondence is robust, the proposed dual control by sliding and electric field is an attractive idea for 2D spintronics/valleytronics. The topological claim, however, is not substantiated: the paper infers a quantum valley Hall effect from pointwise Berry curvature without computing a valley Chern number or demonstrating an insulating gap. The effective model also contains numerical inconsistencies that must be resolved. With these issues fixed, the paper could be a solid contribution; in its current form the central claims are only partially supported.

major comments (4)
  1. [Section III C, Eq. (2)] The effective-model parameters for AB3 are inconsistent with the DFT splittings reported in the same section. The text states that for AB structures with out-of-plane easy axis, the spin splitting is 17–24 meV and the K–K' energy difference is 80–81 meV. Later, λ1=11.7 meV and λ2=40.5 meV are assigned to AB3, where λ1 is explicitly defined as the valley splitting and λ2 as the spin splitting. These values disagree by roughly a factor of 7 and 2, respectively. Since Eq. (2) is introduced to 'describe' those same splittings, the model does not reproduce its own input data. Please correct either the reported splittings or the λ parameters, and show the effective-model eigenvalues against the DFT bands.
  2. [Section III D] The claim of a quantum valley Hall insulator is not supported by the presented evidence. The Berry curvature values at K (14 Ų or 7 Ų) and K' (−14 or −7 Ų) are pointwise quantities, not integrals. No valley-resolved Chern number is computed, no gap or Fermi-level analysis is given, and no edge-state calculation is shown. The statement that the BZ integral of the Berry curvature is zero only rules out a nonzero total Chern number; it does not establish a QVH insulator. Without a quantized valley Chern number and an insulating gap, the abstract's statement that 'quantum valley Hall insulators can be achieved' is an overreach. I recommend replacing this claim with 'large Berry curvature near K/K'' unless the topological invariant is computed.
  3. [Section III D, Eq. (2)] The effective Hamiltonian in Eq. (2) is fully diagonal in the τz, sz, and τzsz basis, with H0 a scalar. Such a model produces zero Berry curvature under the Kubo formula (Eq. (3)) because all interband velocity matrix elements vanish. The Berry curvature plots in Fig. 4 appear to come from the DFT wavefunctions, not from the effective model. If the authors intend the effective model to describe topological properties, they must include k-dependent off-diagonal terms that generate Berry curvature; otherwise the model is merely a band-fit and the topological discussion is disconnected from the model.
  4. [Section III A, Table I] The stacking-control narrative depends critically on the magnetic easy-axis directions determined from MAE at PBE+U with U=2 eV on Y. The U value is not justified or benchmarked, and MAE is known to be sensitive to the Hubbard U and exchange-correlation functional. A change in easy-axis ordering for even one stacking would alter the reported correlation between easy axis and spin/valley splitting. I ask the authors to provide the U dependence of the MAE (or at least a sensitivity check with, e.g., HSE06) for all six stackings, or to soften the conclusions accordingly.
minor comments (6)
  1. [Section III B] The references to Fig. 2 panels are swapped: the text says AA1/AB3 are shown in (a,c) and AA3/AB2 in (b,d), but the figure caption places AB2 in (c) and AB3 in (d).
  2. [Table I] The table caption and layout are ambiguous: ΔE values seem to combine relative energies for different magnetic states and directions. Please clarify the reference energy for each block (AFM and FM).
  3. [Section III D] The statement 'So the integral of the Berry curvature over the entire Brillouin zone is 0' is presented as a result, but no integration grid or numerical method is described. Please specify how this integral was evaluated.
  4. [Heading] The heading 'F. urther discussion' should read 'F. Further discussion'.
  5. [Section II] Write 10^{-6} eV instead of '10 −6 eV' in the convergence criteria.
  6. [Section III B] The phrase 'Dirac relativistic dispersion relation' for Eq. (1) is misleading; 'massive Dirac-like dispersion' is clearer, since the dispersion is not massless.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: central claims are DFT results; effective model is a descriptive fit, not a prediction from its own fitted inputs.

full rationale

The paper's central results (stacking-controlled easy axis from MAE, spin splitting/valley polarization, spin/atom-layer projections, Berry curvature signs) are obtained from first-principles DFT calculations, not from the effective model. The low-energy Hamiltonian H(k) in Eq. (2) is explicitly said to 'describe' the two valence bands; its parameters λ1, λ2, λ3 are taken from the measured splittings (e.g., 'λ3 is 40.8 meV', 'λ1 and λ2 are 11.7 meV and 40.5 meV'), and the electric-field term h(E)sz in Eq. (4) is likewise 'a linear function that describes the effect of external electric field on the spin split.' This is a fit, not a prediction, so the fitted-input-called-prediction pattern does not apply. The only self-citation is [22], cited among four references for the background statement that interlayer vdW interactions can introduce SOC from one layer to another; no load-bearing argument rests on it. A real but non-circular problem is in Section III.D, where 'the integral of the Berry curvature over the entire Brillouin zone is 0' is used to conclude 'There is a quantum valley Hall effect' without evaluating a quantized valley Chern number or edge states; that is an omitted proof/overclaim, not a circular derivation. Overall the derivation chain is self-contained: no equation reduces to an input and no claimed prediction is forced by a fit.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

The central claims rest on several fitted parameters (U, alpha, beta, lambdas, h(E)) and standard DFT/effective-model assumptions. No new physical entities are introduced, but the effective-model parameters are fit to the very data they describe.

free parameters (4)
  • Hubbard U (Y) = 2 eV
    Chosen by hand for DFT+U; no U-scan or justification given; affects band structure, MAE, and hence easy-axis determination.
  • alpha, beta in H0 = alpha 2.124-2.370 eV^2·Å^2 (K-Γ), 7.903-8.643 eV^2·Å^2 (K-M); beta 0.015-0.017 eV^2 (K-Γ), 0.255-0.294 eV^2 (K-M)
    Fitted directly to DFT valence bands; used to claim 'Dirac relativistic dispersion relation' and to compute effective masses.
  • lambda1, lambda2, lambda3 = e.g., AA2: lambda3=40.8 meV; AB3: lambda1=11.7 meV, lambda2=40.5 meV
    Extracted from the same DFT spin/valley splittings they are then used to describe, making the model descriptive rather than predictive.
  • h(E) linear coefficient = not given explicitly
    Linear function fitted to electric-field-dependent spin splittings in the same DFT dataset; used to claim electric-field control.
assumptions (4)
  • domain assumption PBE+U+DFT-D3 gives reliable ground states and band structures
    The entire study relies on this functional choice; no benchmark against experiment or higher-level theory is provided.
  • domain assumption MAE from total-energy differences with SOC determines the easy axis
    Easy-axis directions from Table I are taken as ground truth; all spin/valley conclusions hinge on this.
  • standard math Kubo formula applied to Kohn-Sham states gives physical Berry curvature
    Standard formula (Eq. 3) from linear-response theory; accepted in the field.
  • ad hoc to paper Massive Dirac form H0 = -sqrt(alpha k^2 + beta) is the correct ansatz
    The model form is asserted and then fitted; no derivation from symmetry or microscopic model is given.

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Cite this review

Pith. "Pith review of Spin-valley-layer coupling with dual control via stacking and electric field in antiferromagnetic bilayer Janus YIBr." pith.science (2026). https://pith.science/paper/CJCDEUFG

@misc{pith2026260717199,
  author       = {Pith},
  title        = {Pith review of: Spin-valley-layer coupling with dual control via stacking and electric field in antiferromagnetic bilayer Janus YIBr},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CJCDEUFG}},
  note         = {Machine review of arXiv:2607.17199}
}
read the original abstract

The modification and enhancement of antiferromagnetic two-dimensional semiconductor is considered crucial for realizing novel electronic properties and facilitating promising applications. For this purpose, we investigate six antiferromagnetic 2D bilayer Janus YIBr structures with different stacking variations by means of first-principles calculation and an effective low-energy model. The calculation of magnetic anisotropy energy shows that the direction of easy axis varies with different stacking. First-principles-calculated energy bands reveal that there is a Dirac relativistic dispersion relation in the valence band in a wide energy window of 0.3 eV at least. The calculations for spin, atom properties and Berry curvature description show that there is spin, valley and layer coupling with spin splitting, valley polarization and quantum valley Hall insulators can be achieved in the bilayer Janus structures. Further analyses of the effect of external electric field can be used to control spin, valley and layer of the hole near the Fermi level. These can be useful in future exploration for novel properties, control methods and more functionalities in bilayer Janus structures.

Figures

Figures reproduced from arXiv: 2607.17199 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_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (1 more)
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p006_6.png]

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Reference graph

Works this paper leans on

57 extracted references

  1. [1]

    K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science 306, 666 (2004)

    2004

  2. [2]

    A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, Rev. Mod. Phys. 81, 109 (2009)

    2009

  3. [3]

    -26.7906 0.0124 [100] -26.7900 0.0129

  4. [4]

    -26.7906 0.0124 [110] -26.7900 0.0129 AA3

  5. [5]

    -26.7904 0.0126 [100] -26.7899 0.0131

  6. [6]

    -26.7904 0.0126 [110] -26.7899 0.0131 AB1

  7. [7]

    -26.7910 0.0120 [100] -26.7887 0.0143

  8. [8]

    -26.7909 0.0121 [110] -26.7886 0.0144 AB2

Show all 57 references
  1. [9]

    -26.8010 0.0020 [100] -26.7998 0.0032

  2. [10]

    -26.8009 0.0021 [110] -26.7999 0.0031 AB3

  3. [11]

    -26.7911 0.0119 [100] -26.7901 0.0129

  4. [12]

    We also find that the energy dispersion relation of va- lence band near the Fermi surface is close to the massive Dirac relativistic dispersion relation

    -26.7911 0.0119 [110] -26.7901 0.0129 the Fermi level for the situation of out-of-plane easy axis and there is obvious valley polarization for the situation of AB stacking configuration. We also find that the energy dispersion relation of va- lence band near the Fermi surface ...

  5. [13]

    Zhang, H

    Z. Zhang, H. Sun, M. Dong, Y. Guo, and M. Zhao, npj Computational Materials 11, 277 (2025)

    2025

  6. [14]

    Zhang, X

    F. Zhang, X. Cheng, Z. Yin, C. Liu, L. Deng, Y. Qiao, Z. Shi, S. Zhang, J. Lin, Z. Liu, M. Ye, Y. Huang, X. Meng, C. Zhang, T. Okuda, K. Shimada, S. Cui, Y. Zhao, G.-H. Cao, S. Qiao, J. Liu, and C. Chen, Nature Physics 21, 760 (2025)

    2025

  7. [15]

    A. K. Geim, Science 324, 1530 (2009)

    2009

  8. [16]

    Islam, S

    A. Islam, S. Khan, J. J. Mim, M. F. Akter, M. S. Is- lam, S. Oliullah, and N. Hossain, Inorganic Chemistry Communications 174, 113980 (2025)

    2025

  9. [17]

    P. Han, J. Zhang, X. Chen, and J. Wang, Applied Physics Letters 126, 082901 (2025)

    2025

  10. [18]

    Bordoloi and S

    A. Bordoloi and S. Singh, Phys. Rev. B 110, 245421 (2024)

    2024

  11. [19]

    Tayran, Y

    C. Tayran, Y. Mogulkoc, and M. Çakmak, Materials Sci- ence in Semiconductor Processing 166, 107745 (2023)

    2023

  12. [20]

    V. V. Kulish and W. Huang, Journal of Materials Chem- istry C 5, 8734 (2017)

    2017

  13. [21]

    G. Wang, Y. Ma, H. Duan, R. Hu, Y. Tao, S. Yang, H. Zhong, J. Wang, D. Song, Y. Soh, T. Yu, B. Lei, Y. Xiong, P. Li, Y. Lu, and M. Tian, ACS Nano 20, 6052 (2026) , pMID: 41678376

    2026

  14. [22]

    X. Gao, Q. Liu, and G. Gao, Physical Chemistry Chem- ical Physics 28, 7393 (2026)

    2026

  15. [23]

    K. D. Belashchenko, Phys. Rev. Lett. 134, 086701 (2025)

    2025

  16. [24]

    Y. Wang, H. Sun, C. Wu, W. Zhang, S.-D. Guo, Y. She, and P. Li, Phys. Rev. B 111, 085432 (2025)

    2025

  17. [25]

    Guo, Y.-L

    S.-D. Guo, Y.-L. Tao, Z.-Y. Zhuo, G. Zhu, and Y. S. Ang, Phys. Rev. B 109, 134402 (2024)

    2024

  18. [26]

    C. Sun, Y. Sun, H. Ye, Y. Zhu, L. Chen, H. Li, G. P. Zhang, and J. Wang, Applied Physics Letters 127, 142903 (2025)

    2025

  19. [27]

    Guo, Frontiers of Physics 21, 025201 (2026)

    S.-D. Guo, Frontiers of Physics 21, 025201 (2026)

    2026

  20. [28]

    Hou and R

    Y. Hou and R. Wu, Advanced Functional Materials 35, e09453 (2025)

    2025

  21. [29]

    Y. Qi, J. Zhao, and H. Zeng, Phys. Rev. B 110, 014442 (2024)

    2024

  22. [30]

    J. Sun, X. Zheng, K. Jia, X. Fan, and T. Cao, Phys. Rev. B 113, 214438 (2026)

    2026

  23. [31]

    J. W. González, T. Brumme, E. S. Morell, and A. M. León, npj 2D Materials and Applications 10, 11 (2025)

    2025

  24. [32]

    S.-D. Guo, P. Li, and G. Wang, Phys. Rev. B 111, L140404 (2025)

    2025

  25. [33]

    W. Xun, X. Liu, Y. Zhang, Y.-Z. Wu, and P. Li, Applied Physics Letters 126, 161903 (2025)

    2025

  26. [34]

    Yu and B.-G

    B.-W. Yu and B.-G. Liu, iScience 28, 112818 (2025)

    2025

  27. [35]

    Y. Pan, Y. Bai, B. Wang, and J.-H. Cho, Applied Physics Letters 128, 162901 (2026)

    2026

  28. [36]

    J.-Y. Zhan, R. He, D. Wang, M.-D. He, N. Luo, J. Zeng, K.-Q. Chen, and L.-M. Tang, Phys. Rev. B 112, 024408 (2025)

    2025

  29. [37]

    P. E. Blöchl, Phys. Rev. B 50, 17953 (1994)

    1994

  30. [38]

    Kresse and J

    G. Kresse and J. Hafner, Phys. Rev. B 47, 558 (1993)

    1993

  31. [39]

    Y. Liu, J. Dong, G. Ni, and G. Gao, Phys. Rev. B 113, 014422 (2026)

    2026

  32. [40]

    J. He, H. Fu, Y. Xiong, J. Zhang, Z. Cheng, Z. Wu, and S. Ding, The Journal of Physical Chemistry Letters 16, 12911 (2025) , pMID: 41369679

    2025

  33. [41]

    X. Tian, Z. Zhang, L. Guan, X. Liu, X. Zhao, and L. Li, Phys. Rev. B 112, 035413 (2025)

    2025

  34. [42]

    Cao, S.-Y

    P. Cao, S.-Y. Xie, X.-B. Li, and Y. Jiang, Nano Letters 25, 10287 (2025) , pMID: 40539537

    2025

  35. [43]

    Bennett, G

    D. Bennett, G. Martínez-Carracedo, X. He, J. Ferrer, P. Ghosez, R. Comin, and E. Kaxiras, Phys. Rev. Lett. 133, 246703 (2024)

    2024

  36. [44]

    Liang, J

    Z. Liang, J. Zhang, C. Hua, Y. Wang, and F. Song, Phys. Rev. B 110, 085110 (2024)

    2024

  37. [45]

    Zhang, Y

    L. Zhang, Y. Liu, M. Wu, and G. Gao, Advanced Func- tional Materials 35, 2417857 (2025) . 8

    2025

  38. [46]

    Y. Wu, J. Tong, L. Deng, F. Luo, F. Tian, G. Qin, and X. Zhang, Nano Letters 23, 6226 (2023) , pMID: 37363831

    2023

  39. [47]

    X. Liu, A. P. Pyatakov, and W. Ren, Phys. Rev. Lett. 125, 247601 (2020)

    2020

  40. [48]

    Zhao and Y

    L. Zhao and Y. An, Journal of Alloys and Compounds 1071, 188798 (2026)

    2026

  41. [51]

    J. P. Perdew, K. Burke, and M. Ernzerhof, Physical re- view letters 77, 3865 (1996)

    1996

  42. [52]

    H. J. Monkhorst and J. D. Pack, Phys. Rev. B 13, 5188 (1976)

    1976

  43. [53]

    Bengtsson, Phys

    L. Bengtsson, Phys. Rev. B 59, 12301 (1999)

    1999

  44. [54]

    Neugebauer and M

    J. Neugebauer and M. Scheffler, Phys. Rev. B 46, 16067 (1992)

    1992

  45. [55]

    Grimme, J

    S. Grimme, J. Antony, S. Ehrlich, and H. Krieg, The Journal of Chemical Physics 132, 154104 (2010)

    2010

  46. [56]

    D. C. Hvazdouski, ￿. S. Baranava, E. A. Korznikova, A. A. Kistanov, and V. R. Stempitsky, 2D Materials 11, 025022 (2024)

    2024

  47. [57]

    D. J. Thouless, M. Kohmoto, M. P. Nightingale, and M. den Nijs, Phys. Rev. Lett. 49, 405 (1982)

    1982

  48. [100]

    -26.8019 0.0010 [100] -26.8004 0.0026

  49. [110]

    -26.8023 0.0007 [110] -26.8004 0.0025 AA2

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