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arxiv: 2604.05588 · v1 · submitted 2026-04-07 · ❄️ cond-mat.mes-hall

Robust quantized thermal conductance of Majorana floating edge bands in d-wave superconductors

Yanmiao Han , Yu-Hao Wan , Zhaoqin Cao , Rundong Zhao , Qing-Feng Sun This is my paper

Pith reviewed 2026-05-10 19:09 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall
keywords Majorana edge bandsquantized thermal conductanced-wave superconductorsquantum anomalous Hall insulatortopological superconductivityBogoliubov-de Gennes modelnonequilibrium Green's function
0
0 comments X

The pith

Floating Majorana edge bands produce quantized thermal conductance in time-reversal-breaking superconductors.

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

The paper identifies floating Majorana edge bands as isolated counterpropagating Majorana modes that detach from the bulk continuum in two-dimensional superconductors that break time-reversal symmetry. These bands arise from anisotropic Wilson masses in a two-band Bogoliubov-de Gennes model and appear microscopically when a quantum anomalous Hall insulator is placed in contact with a d-wave superconductor. Their transport signature is a quantized total thermal conductance in two-terminal devices together with a robust half-quantized plateau in four-terminal geometries. The response remains stable against moderate long-range disorder, finite temperature, and nonzero chemical potential, providing a route to helical-like Majorana transport without time-reversal symmetry.

Core claim

Floating Majorana edge bands form isolated, momentum-separated counterpropagating Majorana modes detached from the bulk continuum. In a quantum anomalous Hall insulator proximitized by a d-wave superconductor, these bands produce a quantized total thermal conductance in two-terminal devices and a robust half-quantized plateau in four-terminal geometries that distinguishes them from chiral N=±2 quantum anomalous Hall phases.

What carries the argument

Floating Majorana edge bands (FMEBs): momentum-separated counterpropagating Majorana modes that remain detached from the bulk continuum and carry the thermal transport.

If this is right

  • Quantized total thermal conductance appears in two-terminal devices.
  • A robust half-quantized plateau forms in four-terminal geometries.
  • The signatures cleanly separate floating Majorana edge bands from chiral N=±2 quantum anomalous Hall phases.
  • Thermal response stays stable under finite temperature, moderate long-range disorder, and finite chemical potential.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar bands may appear in other pairings or material stacks that produce anisotropic masses.
  • The half-quantized plateau offers an experimental handle for detecting helical-like Majorana transport in non-time-reversal-symmetric platforms.
  • Stability under disorder suggests these modes could be used in devices where conventional chiral or helical edges would be disrupted.

Load-bearing premise

The isolated counterpropagating modes appear only when anisotropic Wilson masses are realized in the two-band Bogoliubov-de Gennes model of a quantum anomalous Hall insulator proximitized by a d-wave superconductor.

What would settle it

Absence of the half-quantized thermal conductance plateau in four-terminal measurements under moderate disorder would rule out the claimed isolation and robustness of the floating Majorana edge bands.

Figures

Figures reproduced from arXiv: 2604.05588 by Qing-Feng Sun, Rundong Zhao, Yanmiao Han, Yu-Hao Wan, Zhaoqin Cao.

Figure 1
Figure 1. Figure 1: FIG. 1. Bulk and edge spectra of the anisotropic BdG-QWZ [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Realization of FMEBs in a QAH insulator proximitized by [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Two-terminal transport signatures across the QAH-FMEB [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Four-terminal transport response distinguishing the QAH [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Robustness of FMEB thermal conductance against disorder. [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Temperature dependence of thermal transport in the FMEB [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Effect of finite chemical potential on FMEB thermal trans [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Winding number characterization of the two Majorana [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗
read the original abstract

We propose and characterize a new class of Majorana boundary states, i.e., floating Majorana edge bands (FMEBs), which emerge in two-dimensional (2D) superconductors that break time-reversal symmetry yet host helical-like transport. In contrast to conventional chiral or helical edge modes, FMEBs form isolated, momentum-separated counterpropagating Majorana modes detached from the bulk continuum. We identify a minimal mechanism for their emergence via anisotropic Wilson masses in a two-band Bogoliubov-de Gennes (BdG) model, and demonstrate their microscopic realization in a quantum anomalous Hall (QAH) insulator proximitized by a $d$-wave superconductor. Using nonequilibrium Green's function (NEGF) simulations, we uncover clear transport fingerprints: a quantized total thermal conductance in two-terminal devices, and a robust half-quantized plateau in four-terminal geometries that cleanly distinguishes FMEBs from chiral $\mathcal{N}= \pm 2$ QAH phases. This thermal response remains remarkably stable under finite temperature, moderate long-range disorder, and finite chemical potential. Our findings establish FMEBs as an experimentally accessible route toward helical-like Majorana transport in systems without time-reversal symmetry, with direct implications for topological quantum computation.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript proposes floating Majorana edge bands (FMEBs) as a new class of isolated, momentum-separated counterpropagating Majorana modes in time-reversal symmetry breaking 2D superconductors. These emerge via anisotropic Wilson masses in a two-band BdG model microscopically realized by proximitizing a QAH insulator with d-wave superconductivity. NEGF transport simulations are used to demonstrate a quantized total thermal conductance in two-terminal geometries and a robust half-quantized plateau in four-terminal setups that distinguishes FMEBs from chiral N=±2 QAH phases, with the signatures remaining stable under finite temperature, moderate disorder, and finite chemical potential.

Significance. If the isolation of the FMEBs from the bulk continuum holds and the transport quantization is not an artifact, the work identifies a new mechanism for helical-like Majorana transport without TRS, offering clear experimental fingerprints via thermal conductance that could be relevant for topological quantum computation. The use of NEGF to extract falsifiable transport predictions is a positive aspect of the numerical approach.

major comments (2)
  1. [BdG model and microscopic realization] The central claim that FMEBs remain detached from the bulk continuum (producing the reported quantized conductances) rests on anisotropic Wilson masses in the two-band BdG model. However, d-wave pairing is nodal and momentum-dependent; the manuscript must demonstrate explicitly that the anisotropy opens a full gap at all Brillouin-zone momenta where the floating bands exist and prevents hybridization. Without the bulk dispersion or DOS shown for the microscopic QAH+d-wave realization, the NEGF signatures alone do not establish isolation (see the sections on the minimal mechanism and microscopic realization).
  2. [NEGF transport simulations] The two-terminal quantized thermal conductance and four-terminal half-quantized plateau are load-bearing for distinguishing FMEBs from chiral phases. The NEGF results should include convergence checks with respect to system size, lead coupling, and disorder averaging, as finite-size effects or partial spectral overlap could mimic quantization without true isolation of counterpropagating modes.
minor comments (1)
  1. [Abstract and introduction] Clarify the precise definition of 'floating' in the introduction, as the term is used to emphasize detachment from the bulk but could be confused with other edge-state terminology.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive evaluation of our work and for the detailed comments, which help clarify the presentation of our results. We address each major comment below and have revised the manuscript to incorporate the requested demonstrations and checks.

read point-by-point responses

  1. Referee: [BdG model and microscopic realization] The central claim that FMEBs remain detached from the bulk continuum (producing the reported quantized conductances) rests on anisotropic Wilson masses in the two-band BdG model. However, d-wave pairing is nodal and momentum-dependent; the manuscript must demonstrate explicitly that the anisotropy opens a full gap at all Brillouin-zone momenta where the floating bands exist and prevents hybridization. Without the bulk dispersion or DOS shown for the microscopic QAH+d-wave realization, the NEGF signatures alone do not establish isolation (see the sections on the minimal mechanism and microscopic realization).

    Authors: We agree that explicit confirmation of the bulk gap is required to rigorously establish isolation of the FMEBs. In the revised manuscript we add the bulk dispersion and density-of-states plots for both the minimal two-band BdG model (with anisotropic Wilson masses) and the microscopic QAH+d-wave realization. These figures show that the anisotropy produces a full gap at all Brillouin-zone momenta relevant to the floating bands, with no spectral overlap or hybridization channels to the bulk continuum. The added data directly support the NEGF transport results and confirm that the observed quantization originates from truly detached counterpropagating Majorana modes. revision: yes

  2. Referee: [NEGF transport simulations] The two-terminal quantized thermal conductance and four-terminal half-quantized plateau are load-bearing for distinguishing FMEBs from chiral phases. The NEGF results should include convergence checks with respect to system size, lead coupling, and disorder averaging, as finite-size effects or partial spectral overlap could mimic quantization without true isolation of counterpropagating modes.

    Authors: We appreciate the referee’s emphasis on numerical convergence. The revised manuscript now includes explicit checks: thermal conductance versus system size (up to substantially larger lattices), versus lead-coupling strength, and averaged over an increased number of disorder realizations. These additional results demonstrate that the two-terminal quantization and four-terminal half-quantized plateau converge to the reported values and remain stable, excluding finite-size artifacts or incomplete averaging as explanations. The distinction from chiral N=±2 phases is thereby reinforced. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained numerical simulation of explicitly defined BdG model

full rationale

The paper defines a two-band BdG model incorporating anisotropic Wilson masses as the minimal mechanism for FMEBs, then computes transport signatures (quantized thermal conductance, half-quantized plateaus) directly via NEGF simulations on that model. No load-bearing self-citations, no parameters fitted to data and renamed as predictions, and no ansatz or uniqueness theorem imported from prior author work. The results follow from solving the stated Hamiltonian without any step reducing by construction to its own inputs; the central claims rest on explicit numerical output rather than circular redefinition.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

The proposal rests on the standard BdG formalism and NEGF transport method plus the introduction of anisotropic Wilson masses whose microscopic origin is asserted but not independently derived.

axioms (2)
  • standard math Bogoliubov-de Gennes mean-field description of superconductivity
    Invoked to model the proximitized system.
  • standard math Nonequilibrium Green's function formalism for thermal transport
    Used to compute conductance.
invented entities (1)
  • Floating Majorana edge bands (FMEBs) no independent evidence
    purpose: Isolated counterpropagating Majorana modes detached from bulk continuum
    New postulated boundary states introduced to explain the transport phenomenology.

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Reference graph

Works this paper leans on

71 extracted references · 71 canonical work pages

  1. [1]

    Frolov, M

    S. Frolov, M. Manfra, and J. Sau, Topological superconductiv- ity in hybrid devices, Nat. Phys.16, 718 (2020)

    work page 2020

  2. [2]

    Sato and Y

    M. Sato and Y . Ando, Topological superconductors: a review, Rep. Prog. Phys.80, 076501 (2017)

    work page 2017

  3. [3]

    D. Zhu, T. Jaako, Q. He, and P. Rabl, Quantum computing with superconducting circuits in the picosecond regime, Phys. Rev. Appl.16, 014024 (2021)

    work page 2021

  4. [4]

    D. A. Ivanov, Non-abelian statistics of half-quantum vortices in p-wave superconductors, Phys. Rev. Lett.86, 268 (2001)

    work page 2001

  5. [6]

    A. Y . Kitaev, Unpaired majorana fermions in quantum wires, Physics-Uspekhi44, 131 (2001)

    work page 2001

  6. [7]

    Alicea, New directions in the pursuit of majorana fermions in solid state systems, Rep

    J. Alicea, New directions in the pursuit of majorana fermions in solid state systems, Rep. Prog. Phys.75, 076501 (2012)

    work page 2012

  7. [8]

    C. W. Beenakker, Search for majorana fermions in supercon- ductors, Annu. Rev. Condens. Matter Phys.4, 113 (2013)

    work page 2013

  8. [9]

    Y . Han, Y . Yang, J. Cui, and R. Zhao, The impact of single- photon loss on symmetry breaking quantum error correction, Phys. Scr.100, 055101 (2025)

    work page 2025

  9. [10]

    Prada, P

    E. Prada, P. San-Jose, M. W. A. de Moor, A. Geresdi, E. J. H. Lee, J. Klinovaja, D. Loss, J. Nyg ˚ard, R. Aguado, and L. P. Kouwenhoven, From andreev to majorana bound states in hy- brid superconductor–semiconductor nanowires, Nat. Rev. Phys. 2, 575 (2020)

    work page 2020

  10. [11]

    S. Deng, L. Viola, and G. Ortiz, Majorana modes in time- reversal invariants-wave topological superconductors, Phys. Rev. Lett.108, 036803 (2012)

    work page 2012

  11. [12]

    Zhang, W

    R.-X. Zhang, W. S. Cole, and S. Das Sarma, Helical hinge ma- jorana modes in iron-based superconductors, Phys. Rev. Lett. 122, 187001 (2019)

    work page 2019

  12. [13]

    Read and D

    N. Read and D. Green, Paired states of fermions in two di- mensions with breaking of parity and time-reversal symmetries and the fractional quantum hall effect, Phys. Rev. B61, 10267 (2000)

    work page 2000

  13. [14]

    Wang and B

    J. Wang and B. Lian, Multiple chiral majorana fermion modes and quantum transport, Phys. Rev. Lett.121, 256801 (2018)

    work page 2018

  14. [15]

    Z.-X. Li, C. Chan, and H. Yao, Realizing majorana zero modes by proximity effect between topological insulators andd-wave high-temperature superconductors, Phys. Rev. B91, 235143 (2015)

    work page 2015

  15. [16]

    Zareapour, A

    P. Zareapour, A. Hayat, S. Y . Yang, D. Zhao, M. Kreshchuk, N. Jain, Z. Xu, G. Yang, G. Gu, X. Jia, L. Kisslinger, L. Krusin-Elbaum, A. Tsvelik, T. Valla, M. M. Qazilbash, D. N. Basov, L. H. Greene, S. Krishnamoorthy, Y . Kedem, Y . Luba- shevsky, K. West, B. Pang, and J. Wei, Proximity-induced high-temperature superconductivity in the topological insula-...

    work page 2012

  16. [17]

    M.-X. Wang, C. Liu, J.-P. Xu, F. Yang, L. Miao, M.-Y . Yao, C. Gao, C. Shen, X. Ma, X. Chen,et al., The coexistence of superconductivity and topological order in the bi2se3 thin films, Science336, 52 (2012)

    work page 2012

  17. [18]

    H. Zhao, B. Rachmilowitz, Z. Ren, R. Han, J. Schneeloch, R. Zhong, G. Gu, Z. Wang, and I. Zeljkovi ´c, Superconducting proximity effect in a topological insulator using fe(te,se), Phys. Rev. B97, 224504 (2018)

    work page 2018

  18. [19]

    Fu and C

    L. Fu and C. L. Kane, Superconducting proximity effect and majorana fermions at the surface of a topological insulator, Phys. Rev. Lett.100, 096407 (2008)

    work page 2008

  19. [20]

    R. M. Lutchyn, J. D. Sau, and S. D. Sarma, Majorana fermions and a topological phase transition in semiconductor– superconductor heterostructures, Phys. Rev. Lett105, 077001 (2010)

    work page 2010

  20. [21]

    Y . Oreg, G. Refael, and F. von Oppen, Helical liquids and ma- jorana bound states in quantum wires, Phys. Rev. Lett105, 177002 (2010)

    work page 2010

  21. [22]

    X.-L. Qi, T. L. Hughes, and S.-C. Zhang, Chiral topological superconductor from the quantum hall state, Phys. Rev. B82, 184516 (2010)

    work page 2010

  22. [23]

    Zhang, Y

    H. Zhang, Y . Xu, J. Wang, K. Chang, and S.-C. Zhang, Quan- tum spin hall and quantum anomalous hall states realized in junction quantum wells, Phys. Rev. Lett.112, 216803 (2014)

    work page 2014

  23. [24]

    S. Hart, H. Ren, T. Wagner, P. Leubner, M. M ¨uhlbauer, C. Br¨une, H. Buhmann, L. W. Molenkamp, and A. Yacoby, In- duced superconductivity in the quantum spin hall edge, Nat. Phys.10, 638 (2014)

    work page 2014

  24. [25]

    V . S. Pribiag, A. J. A. Beukman, F. Qu, M. C. Cassidy, C. Char- pentier, W. Wegscheider, and L. P. Kouwenhoven, Edge-mode 11 superconductivity in a two-dimensional topological insulator, Nat. Nanotechnol.10, 593 (2015)

    work page 2015

  25. [26]

    Q. L. He, L. Pan, A. L. Stern, E. C. Burks, X. Che, G. Yin, J. Wang, B. Lian, Q. Zhou, E. S. Choi, K. Murata, X. Kou, Z. Chen, T. Nie, Q. Shao, Y . Fan, S.-C. Zhang, J. Xia, and K. L. Wang, Chiral majorana fermion modes in a quantum anoma- lous hall insulator–superconductor structure, Science357, 294 (2017), retracted

    work page 2017

  26. [27]

    Kayyalha, D

    M. Kayyalha, D. Xiao, R. Zhang, Y . Shin, J. Jiang, K. M. Fijalkowski, S. Mandal, M. Winnerlein, C. Gould, K. Brun- ner, S. Grauer, J. Liao, F. Schuba, S. M ¨uhlbauer, I. Siddiqi, G. Bauer, F. Amet, L. W. Molenkamp, C.-Z. Li, J. Wang, C.-X. Liu, and C.-Z. Chang, Absence of evidence for chiral majorana modes in quantum anomalous hall–superconductor structu...

    work page 2020

  27. [28]

    Huang, F

    Y . Huang, F. Setiawan, and J. D. Sau, Disorder-induced half- integer quantized conductance plateau in quantum anoma- lous hall insulator–superconductor structures, Phys. Rev. B97, 100501 (2018)

    work page 2018

  28. [29]

    Ji and X.-G

    W. Ji and X.-G. Wen, 1 2(e2/h)conductance plateau without 1d chiral majorana fermions, Phys. Rev. Lett.120, 107002 (2018)

    work page 2018

  29. [30]

    Lian, X.-Q

    B. Lian, X.-Q. Sun, A. Vaezi, X.-L. Qi, and S.-C. Zhang, Topological quantum computation based on chiral majorana fermions, Proc. Natl. Acad. Sci. U.S.A.115, 10938 (2018)

    work page 2018

  30. [31]

    J. Shen, J. Lyu, J. Z. Gao, Y .-M. Xie, C.-Z. Chen, C.-W. Cho, O. Atanov, Z. Chen, K. Liu, Y . J. Hu, K. Y . Yip, S. K. Goh, Q. L. He, L. Pan, K. L. Wang, K. T. Law, and R. Lortz, Spectroscopic fingerprint of chiral majorana modes at the edge of a quantum anomalous hall insulator/superconductor heterostructure, Proc. Natl. Acad. Sci. U.S.A.117, 16267 (2020)

    work page 2020

  31. [32]

    Banerjee, M

    M. Banerjee, M. Heiblum, V . Umansky, D. E. Feldman, Y . Oreg, and A. Stern, Observation of half-integer thermal hall conductance, Nature559, 205 (2018)

    work page 2018

  32. [33]

    Yokoi, S

    T. Yokoi, S. Ma, Y . Kasahara, S. Kasahara, T. Shibauchi, H. Tanaka, N. Kurita, J. Nasu, Y . Motome, C. Hickey, S. Trebst, and Y . Matsuda, Half-integer quantized anomalous thermal hall effect in the kitaev materialα-rucl 3, Science373, 568 (2021)

    work page 2021

  33. [34]

    S. H. Simon, Interpretation of thermal conductance of theν= 5/2edge, Phys. Rev. B97, 121406 (2018)

    work page 2018

  34. [35]

    A. Topp, R. Queiroz, A. Gr ¨uneis, L. M ¨uchler, A. Rost, A. Varykhalov, D. Marchenko, M. Krivenkov, F. Rodolakis, J. L. McChesney, B. V . Lotsch, L. M. Schoop, and C. R. Ast, Surface floating 2d bands in layered nonsymmorphic semimet- als: Zrsis and related compounds, Phys. Rev. X7, 041073 (2017)

    work page 2017

  35. [36]

    Zhu, T.-R

    Z. Zhu, T.-R. Chang, C.-Y . Huang, H. Pan, X.-A. Nie, X.-Z. Wang, Z.-T. Jin, S.-Y . Xu, S.-M. Huang, D.-D. Guan, S. Wang, Y .-Y . Li, C. Liu, D. Qian, W. Ku, F. Song, H. Lin, H. Zheng, and J.-F. Jia, Quasiparticle interference and nonsymmorphic effect on a floating band surface state of zrsise, Nat. Commun.9, 4153 (2018)

    work page 2018

  36. [37]

    S. Ma, Y . Ma, W. Gao, H. Yu, Q. Cheng, and T. J. Cui, Asym- metric frequency multiplexing topological devices based on a floating edge band, Photon. Res.12, 1728 (2024)

    work page 2024

  37. [38]

    Li and S.-B

    Y .-Y . Li and S.-B. Zhang, Floating edge bands in the bernevig- hughes-zhang model with altermagnetism, Phys. Rev. B111, 045106 (2025)

    work page 2025

  38. [39]

    ˇSmejkal, J

    L. ˇSmejkal, J. Sinova, and T. Jungwirth, Emerging research landscape of altermagnetism, Phys. Rev. X12, 040501 (2022)

    work page 2022

  39. [40]

    Krempask ´y, L

    J. Krempask ´y, L. ˇSmejkal,et al., Altermagnetic lifting of kramers spin degeneracy, Nature626, 517 (2024)

    work page 2024

  40. [41]

    S. Lee, J. Kapeghian, S. Park,et al., Broken kramers degener- acy in altermagnetic mnte, Phys. Rev. Lett.132, 036702 (2024)

    work page 2024

  41. [43]

    Nakamura, K

    D. Nakamura, K. Shiozaki, K. Shimomura, M. Sato, and K. Kawabata, Non-hermitian origin of detachable boundary states in topological insulators, Phys. Rev. Lett.135, 096601 (2025)

    work page 2025

  42. [44]

    J. Ma, C. Ouyang, Y . Yang, D. Wang, H. Li, L. Niu, Y . Liu, Q. Xu, Y . Li, Z. Tian,et al., Asymmetric frequency multiplex- ing topological devices based on a floating edge band, Photon. Res.12, 1201 (2024)

    work page 2024

  43. [45]

    Yang, Z.-Z

    W.-J. Yang, Z.-Z. Yang, X.-Y . Zou, and J.-C. Cheng, Charac- terization and experimental demonstration of corner states of boundary-obstructed topological insulators in a honeycomb lat- tice, Phys. Rev. B107, 174101 (2023)

    work page 2023

  44. [46]

    L. Wang, Y . Jiang, J. Liu, S. Zhang, J. Li, P. Liu, Y . Sun, H. Weng, and X.-Q. Chen, Two-dimensional obstructed atomic insulators with fractional corner charge in theM A 2Z4 family, Phys. Rev. B106, 155144 (2022)

    work page 2022

  45. [47]

    J. Wang, Q. Zhou, B. Lian, and S.-C. Zhang, Chiral topologi- cal superconductor and half-integer conductance plateau from quantum anomalous hall plateau transition, Phys. Rev. B92, 064520 (2015)

    work page 2015

  46. [48]

    Zhang, Z

    Y .-T. Zhang, Z. Hou, X. C. Xie, and Q.-F. Sun, Quantum perfect crossed andreev reflection in top-gated quantum anomalous hall insulator–superconductor junctions, Phys. Rev. B95, 245433 (2017)

    work page 2017

  47. [49]

    Y .-H. Li, J. Liu, H. Liu, H. Jiang, Q.-F. Sun, and X. C. Xie, Noise signatures for determining chiral majorana fermion modes, Phys. Rev. B98, 045141 (2018)

    work page 2018

  48. [50]

    Qi and S.-C

    X.-L. Qi and S.-C. Zhang, Topological insulators and supercon- ductors, Rev. Mod. Phys.83, 1057 (2011)

    work page 2011

  49. [51]

    Q. Yan, H. Li, J. Zeng, Q.-F. Sun, and X. Xie, A majorana perspective on understanding and identifying axion insulators, Commun. Phys.4, 239 (2021)

    work page 2021

  50. [52]

    J. K. Asb ´oth, L. Oroszl ´any, and A. P ´alyi,A short course on topological insulators, V ol. 919 (Springer, 2016)

    work page 2016

  51. [53]

    Yan, Y .-F

    Q. Yan, Y .-F. Zhou, and Q.-F. Sun, Electrically tunable chiral majorana edge modes in quantum anomalous hall insulator– topological superconductor systems, Phys. Rev. B100, 235407 (2019)

    work page 2019

  52. [54]

    Wan and Q.-F

    Y .-H. Wan and Q.-F. Sun, Magnetization-induced phase transi- tions on the surface of three-dimensional topological insulators, Phys. Rev. B109, 045418 (2024)

    work page 2024

  53. [55]

    Wan and Q.-F

    Y .-H. Wan and Q.-F. Sun, Altermagnetism-induced parity anomaly in weak topological insulators, Phys. Rev. B111, 045407 (2025)

    work page 2025

  54. [56]

    H. Li, H. Jiang, Q.-F. Sun, and X. Xie, Emergent energy dissi- pation in quantum limit, Sci. Bull.69, 1221 (2024)

    work page 2024

  55. [57]

    Wan, P.-Y

    Y .-H. Wan, P.-Y . Liu, and Q.-F. Sun, Quantum Anomalous Hall Effect in Ferromagnetic Metals, Phys. Rev. Lett.135, 186302 (2025)

    work page 2025

  56. [58]

    N.-X. Yang, Q. Yan, and Q.-F. Sun, Half-integer quantized ther- mal conductance plateau in chiral topological superconductor systems, Phys. Rev. B105, 125414 (2022)

    work page 2022

  57. [59]

    Kawarabayashi, Y

    T. Kawarabayashi, Y . Hatsugai, and H. Aoki, Quantum hall plateau transition in graphene with spatially correlated random hopping, Phys. Rev. Lett.103, 156804 (2009)

    work page 2009

  58. [60]

    Cheng, H

    S.-g. Cheng, H. Zhang, and Q.-f. Sun, Effect of electron- hole inhomogeneity on specular andreev reflection and an- dreev retroreflection in a graphene-superconductor hybrid sys- tem, Phys. Rev. B83, 235403 (2011)

    work page 2011

  59. [61]

    Yang, Y .-F

    N.-X. Yang, Y .-F. Zhou, P. Lv, and Q.-F. Sun, Gate voltage con- trolled thermoelectric figure of merit in three-dimensional topo- 12 logical insulator nanowires, Phys. Rev. B97, 235435 (2018)

    work page 2018

  60. [62]

    Wan, P.-Y

    Y .-H. Wan, P.-Y . Liu, and Q.-F. Sun, Classification of chern numbers based on high-symmetry points, Phys. Rev. B111, L161410 (2025)

    work page 2025

  61. [63]

    Wan, P.-Y

    Y .-H. Wan, P.-Y . Liu, and Q.-F. Sun, Interplay of altermag- netic order and wilson mass in the dirac equation: Helical edge states without time-reversal symmetry, Phys. Rev. B112, 115412 (2025)

    work page 2025

  62. [64]

    Chang, J

    C.-Z. Chang, J. Zhang, X. Feng, J. Shen, Z. Zhang, M. Guo, K. Li, Y . Ou, P. Wei, L.-L. Wang, Z.-Q. Ji, Y . Feng, S. Ji, X. Chen, J. Jia, X. Dai, Z. Fang, S.-C. Zhang, K. He, Y . Wang, L. Lu, X.-C. Ma, and Q.-K. Xue, Experimental observation of the quantum anomalous hall effect in a magnetic topological insulator, Science340, 167 (2013)

    work page 2013

  63. [65]

    Y . Deng, Y . Yu, M. Z. Shi, Z. Guo, Z. Xu, J. Wang, X. H. Chen, and Y . Zhang, Quantum anomalous hall effect in intrinsic mag- netic topological insulator mnbi2te4, Science367, 895 (2020)

    work page 2020

  64. [66]

    Zareapour, A

    P. Zareapour, A. Hayat, S. Y . F. Zhao, M. Kreshchuk, A. Jain, D. C. Kwok, N. Lee, S.-W. Cheong, Z. Xu, A. Yang,et al., Proximity-induced high-temperature superconductivity in the topological insulators bi2se3 and bi2te3, Nat. Commun.3, 1056 (2012)

    work page 2012

  65. [67]

    A. Uday, G. Lippertz, K. Moors, H. F. Legg, R. Joris, A. Bliesener, L. M. Pereira, A. Taskin, and Y . Ando, Induced superconducting correlations in a quantum anomalous hall in- sulator, Nat. Phys.20, 1589 (2024)

    work page 2024

  66. [68]

    A. M. Black-Schaffer and A. V . Balatsky, Proximity-induced unconventional superconductivity in topological insulators, Phys. Rev. B87, 220506 (2013)

    work page 2013

  67. [69]

    Li, S.-P

    W.-J. Li, S.-P. Chao, and T.-K. Lee, Theoretical study of large proximity-induceds-wave-like pairing from ad-wave super- conductor, Phys. Rev. B93, 035140 (2016)

    work page 2016

  68. [70]

    Altland, P

    A. Altland, P. W. Brouwer, J. Dieplinger, M. S. Foster, M. Moreno-Gonzalez, and L. Trifunovic, Fragility of surface states in non-wigner-dyson topological insulators, Phys. Rev. X 14, 011057 (2024)

    work page 2024

  69. [71]

    Shiozaki, D

    K. Shiozaki, D. Nakamura, K. Shimomura, M. Sato, and K. Kawabata,k-theory classification of wannier localizability and detachable topological boundary states, Phys. Rev. B112, 075152 (2025)

    work page 2025

  70. [72]

    S. Ryu, A. P. Schnyder, A. Furusaki, and A. W. Ludwig, Topo- logical insulators and superconductors: tenfold way and dimen- sional hierarchy, New J. Phys.12, 065010 (2010)

    work page 2010

  71. [73]

    X.-L. Qi, T. L. Hughes, S. Raghu, and S.-C. Zhang, Time- reversal-invariant topological superconductors and superfluids in two and three dimensions, Phys. Rev. Lett.102, 187001 (2009)

    work page 2009