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arxiv: 2501.10998 · v2 · submitted 2025-01-19 · ❄️ cond-mat.supr-con

Pseudo-spin-polarized topological superconductivity in kagome RbV₃Sb₅

Xilin Feng , Zi-Ting Sun , Ben-Chuan Lin , K. T. Law This is my paper

Pith reviewed 2026-05-23 05:08 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con
keywords topological superconductivitykagome latticeRbV3Sb5pseudo-spin polarizationMajorana flat bandstime-reversal symmetry breakingnodal superconductorpairing symmetry
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The pith

RbV3Sb5 is a nodal topological superconductor with pseudo-spin-polarized Cooper pairs that induce magnetic hysteresis.

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

The paper argues that magnetic hysteresis observed in the superconducting state of RbV3Sb5 arises because the material realizes a specific pairing symmetry. This symmetry produces a nodal topological superconductor in which Cooper pairs carry pseudo-spin polarization. The polarized domains behave like ferromagnetic domains, generating the measured hysteresis while also breaking time-reversal symmetry. The same state hosts Majorana flat-band modes localized at the sample boundaries. These modes are predicted to appear in tunneling spectra, linking the hysteresis data directly to a topological phase.

Core claim

In this work, we propose that RbV₃Sb₅ is a nodal topological superconductor with pseudo-spin-polarized Cooper pairs. The pseudo-spin-polarized superconducting domains resemble the properties of ferromagnetic domains and induce hysteresis. Moreover, the nodal topological superconducting state possesses Majorana flat band modes at the sample boundary, which can be detected by tunneling experiments.

What carries the argument

Pseudo-spin-polarized nodal topological pairing symmetry, selected by the combination of magnetic hysteresis data and crystalline symmetry constraints.

If this is right

  • Pseudo-spin-polarized domains produce ferromagnetic-like hysteresis in magnetoresistance within the superconducting state.
  • Majorana flat-band modes appear at the sample boundaries of the nodal topological superconductor.
  • These boundary modes are accessible to tunneling spectroscopy experiments.
  • The state spontaneously breaks time-reversal symmetry while remaining consistent with the measured crystalline symmetries.

Where Pith is reading between the lines

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

  • The same pairing mechanism could appear in the related compounds KV3Sb5 and CsV3Sb5 under similar experimental conditions.
  • External fields might switch the domains, offering a route to control edge modes without conventional magnetism.
  • Confirmation of the flat bands would connect kagome superconductivity to proposals for Majorana-based quantum information.
  • The hysteresis arises purely from the superconducting order parameter rather than from localized magnetic moments.

Load-bearing premise

The observed magnetic hysteresis together with the material's crystalline symmetry uniquely selects the pseudo-spin-polarized nodal topological pairing over other possible symmetries.

What would settle it

Tunneling spectroscopy on sample edges that shows no Majorana flat bands, or magnetoresistance data that lacks hysteresis once the proposed pairing is ruled out by independent probes.

Figures

Figures reproduced from arXiv: 2501.10998 by Ben-Chuan Lin, K. T. Law, Xilin Feng, Zi-Ting Sun.

Figure 1
Figure 1. Figure 1: FIG. 1. (a). The hysteresis behavior of a ferromagnetic material. [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a). The real space structure of the kagome lattice plane [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a). The upper critical fields, calculated from the gap equa [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Edge Majorana flat band and tunneling conductance in [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. The band near the Fermi surface, projected from the 4-orbital minimal model, is shown as the blue line. The orange line represents the [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. The open boundary calculation of the nodal superconductivity. During this calculation, the amplitude of the gap [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. The open boundary spectrum under finite x-axis magnetic field, (a). [PITH_FULL_IMAGE:figures/full_fig_p013_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. The open boundary spectrum under finite y-aix magnetic field, (a). [PITH_FULL_IMAGE:figures/full_fig_p014_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. (a). In addition to the zero-bias peak, the tunneling conductance at the zero-field case shows two small peaks at electron energies [PITH_FULL_IMAGE:figures/full_fig_p015_9.png] view at source ↗
read the original abstract

Kagome superconductors AV$_3$Sb$_5$ (A=K, Rb, Cs) have sparked considerable interest due to the presence of several intertwined symmetry-breaking phases within a single material. Interestingly, in a recent experiment, magnetic hysteresis was observed in the superconducting state through magnetoresistance measurements in RbV$_{3}$Sb$_{5}$ [Nature Comm \textbf{17}, 1310 (2026)], providing strong evidence of a spontaneous time-reversal symmetry breaking superconducting state. The magnetic hysteresis, combined with crystalline symmetry, imposes strong constraints on the possible pairing symmetries of the superconducting state. In this work, we propose that RbV$_3$Sb$_5$ is a nodal topological superconductor with pseudo-spin-polarized Cooper pairs. The pseudo-spin-polarized superconducting domains resemble the properties of ferromagnetic domains and induce hysteresis. Moreover, the nodal topological superconducting state possesses Majorana flat band modes at the sample boundary, which can be detected by tunneling experiments.

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

3 major / 1 minor

Summary. The manuscript proposes that RbV₃Sb₅ realizes a nodal topological superconducting state with pseudo-spin-polarized Cooper pairs. Observed magnetic hysteresis in magnetoresistance is attributed to domains of this state that mimic ferromagnetic domains; the state is selected by constraints from the hysteresis data together with kagome crystalline symmetry, and the nodal topology is predicted to produce Majorana flat bands at sample boundaries detectable by tunneling spectroscopy.

Significance. If substantiated, the identification would link a concrete experimental signature (hysteresis) to a specific pairing symmetry in the AV₃Sb₅ family and supply a falsifiable prediction for Majorana modes. The proposal rests on symmetry-based selection rather than microscopic calculation, so its impact hinges on whether the symmetry argument uniquely isolates the claimed state.

major comments (3)
  1. [Abstract] Abstract: the assertion that 'magnetic hysteresis, combined with crystalline symmetry, imposes strong constraints on the possible pairing symmetries' and selects the pseudo-spin-polarized nodal state is unsupported; no enumeration of D₆ₕ (or subgroup) irreps, their TRS properties, or explicit exclusion of other TRS-breaking candidates (e.g., chiral d+id or E₂g states) is provided.
  2. [Abstract] Abstract and introduction: the mapping from pseudo-spin polarization to an effective spontaneous magnetization capable of producing observable domain hysteresis is stated but not derived; no model or effective Hamiltonian is shown that converts the pseudo-spin texture into a net magnetic moment.
  3. [Abstract] The central claim that the observed hysteresis uniquely selects the proposed state therefore remains a hypothesis rather than a demonstrated result; an explicit irrep table or symmetry-allowed order-parameter analysis is required to secure the selection.
minor comments (1)
  1. [Abstract] The citation 'Nature Comm 17, 1310 (2026)' refers to a future publication; please confirm the correct reference details.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful and constructive report. The comments correctly identify that the symmetry-based selection argument would be strengthened by explicit enumeration and derivation. We will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the assertion that 'magnetic hysteresis, combined with crystalline symmetry, imposes strong constraints on the possible pairing symmetries' and selects the pseudo-spin-polarized nodal state is unsupported; no enumeration of D₆ₕ (or subgroup) irreps, their TRS properties, or explicit exclusion of other TRS-breaking candidates (e.g., chiral d+id or E₂g states) is provided.

    Authors: We agree that an explicit irrep table is needed to make the selection rigorous. In the revised manuscript we will add a table enumerating the relevant D₆ₕ (and subgroup) irreps, their time-reversal properties, and a step-by-step exclusion of other TRS-breaking candidates (including chiral d+id and E₂g) using the observed hysteresis together with the kagome lattice symmetries. revision: yes

  2. Referee: [Abstract] Abstract and introduction: the mapping from pseudo-spin polarization to an effective spontaneous magnetization capable of producing observable domain hysteresis is stated but not derived; no model or effective Hamiltonian is shown that converts the pseudo-spin texture into a net magnetic moment.

    Authors: The manuscript currently states the resemblance to ferromagnetic domains but does not derive the effective magnetization. We will add a short effective-model section (or appendix) that starts from the pseudo-spin texture of the proposed pairing and shows how it generates a net orbital or spin magnetization sufficient to produce the observed hysteresis. revision: yes

  3. Referee: [Abstract] The central claim that the observed hysteresis uniquely selects the proposed state therefore remains a hypothesis rather than a demonstrated result; an explicit irrep table or symmetry-allowed order-parameter analysis is required to secure the selection.

    Authors: We accept that the uniqueness claim requires the explicit analysis requested. The revised version will contain the irrep table and order-parameter analysis that together demonstrate why the pseudo-spin-polarized nodal state is the only symmetry-allowed candidate consistent with the hysteresis data. revision: yes

Circularity Check

0 steps flagged

No circularity: proposal rests on external hysteresis data plus symmetry constraints

full rationale

The paper's central claim selects the pseudo-spin-polarized nodal state from observed magnetoresistance hysteresis (cited to an external 2026 Nature Comm experiment) combined with kagome crystalline symmetry. No equations or text reduce a prediction to a fitted input by construction, no self-citation chain bears the load, and no uniqueness theorem is imported from the authors' prior work. The derivation chain is therefore self-contained against the external benchmark and does not match any enumerated circularity pattern.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

The central claim rests on interpreting an external experiment as evidence of spontaneous TRS breaking and on introducing the pseudo-spin-polarization concept to satisfy symmetry constraints; no free parameters are stated, but the pairing symmetry selection is an unverified domain assumption.

axioms (2)
  • domain assumption Magnetic hysteresis in the superconducting state of RbV₃Sb₅ indicates spontaneous time-reversal symmetry breaking.
    Drawn directly from the cited Nature Comm. experiment and used to constrain pairing.
  • domain assumption Crystalline symmetry together with the hysteresis observation restricts possible superconducting pairing symmetries to the nodal topological pseudo-spin-polarized state.
    Stated in the abstract as imposing strong constraints that select the proposed state.
invented entities (1)
  • pseudo-spin-polarized Cooper pairs no independent evidence
    purpose: To produce superconducting domains that mimic ferromagnetic domains and thereby generate the observed magnetic hysteresis.
    New concept introduced in the proposal to reconcile the experimental hysteresis with topological nodal superconductivity.

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Reference graph

Works this paper leans on

86 extracted references · 86 canonical work pages · 1 internal anchor

  1. [1]

    S. Wang, X. Feng, J.-Z. Fang, J.-P. Peng, Z.-T. Sun, J.-J. Yang, J. Liu, J.-J. Zhao, J.-K. Wang, X.-J. Liu, Z.-N. Wu, S. Sun, N. Kang, X.-S. Wu, Z. Zhang, X. Fu, K. T. Law, B.-C. Lin, and D. Yu, Spin-polarized p-wave superconductivity in the kagome material RbV3Sb5 (2024), arXiv:2405.12592 [cond-mat.str-el]

    work page arXiv 2024

  2. [2]

    B. R. Ortiz, L. C. Gomes, J. R. Morey, M. Winiarski, M. Bor- delon, J. S. Mangum, I. W. Oswald, J. A. Rodriguez-Rivera, J. R. Neilson, S. D. Wilson,et al., Physical Review Materials3, 094407 (2019)

    work page 2019

  3. [3]

    B. R. Ortiz, S. M. Teicher, Y . Hu, J. L. Zuo, P. M. Sarte, E. C. Schueller, A. M. Abeykoon, M. J. Krogstad, S. Rosenkranz, R. Osborn, et al., Physical Review Letters 125, 247002 (2020)

    work page 2020

  4. [4]

    J.-X. Yin, B. Lian, and M. Z. Hasan, Nature 612, 647 (2022)

    work page 2022

  5. [5]

    Y . Wang, H. Wu, G. T. McCandless, J. Y . Chan, and M. N. Ali, Nat Rev Phys 5, 635–658 (2023)

    work page 2023

  6. [6]

    Guguchia, R

    Z. Guguchia, R. Khasanov, and H. Luetkens, npj Quantum Ma- terials 8, 41 (2023)

    work page 2023

  7. [7]

    Jiang, J.-X

    Y .-X. Jiang, J.-X. Yin, M. M. Denner, N. Shumiya, B. R. Ortiz, G. Xu, Z. Guguchia, J. He, M. S. Hossain, X. Liu,et al., Nature materials 20, 1353 (2021)

    work page 2021

  8. [8]

    L. Yu, C. Wang, Y . Zhang, M. Sander, S. Ni, Z. Lu, S. Ma, Z. Wang, Z. Zhao, H. Chen, et al. , arXiv preprint arXiv:2107.10714 (2021)

    work page arXiv 2021

  9. [9]

    S.-Y . Yang, Y . Wang, B. R. Ortiz, D. Liu, J. Gayles, E. Derunova, R. Gonzalez-Hernandez, L. ˇSmejkal, Y . Chen, S. S. Parkin, et al., Science advances 6, eabb6003 (2020)

    work page 2020

  10. [10]

    F. Yu, T. Wu, Z. Wang, B. Lei, W. Zhuo, J. Ying, and X. Chen, Physical Review B 104, L041103 (2021)

    work page 2021

  11. [11]

    X. Feng, K. Jiang, Z. Wang, and J. Hu, Science bulletin 66, 1384 (2021)

    work page 2021

  12. [12]

    X. Feng, Y . Zhang, K. Jiang, and J. Hu, Physical Review B104, 165136 (2021). 6

    work page 2021

  13. [13]

    Lin and R

    Y .-P. Lin and R. M. Nandkishore, Physical Review B 104, 045122 (2021)

    work page 2021

  14. [14]

    M. M. Denner, R. Thomale, and T. Neupert, Physical Review Letters 127, 217601 (2021)

    work page 2021

  15. [15]

    M. H. Christensen, T. Birol, B. M. Andersen, and R. M. Fer- nandes, Physical Review B 104, 214513 (2021)

    work page 2021

  16. [16]

    Wagner, C

    G. Wagner, C. Guo, P. J. Moll, T. Neupert, and M. H. Fischer, Physical Review B 108, 125136 (2023)

    work page 2023

  17. [17]

    S. Wu, B. R. Ortiz, H. Tan, S. D. Wilson, B. Yan, T. Birol, and G. Blumberg, Physical Review B 105, 155106 (2022)

    work page 2022

  18. [18]

    Y . Wang, T. Wu, Z. Li, K. Jiang, and J. Hu, Physical Review B 107, 184106 (2023)

    work page 2023

  19. [19]

    Y . Xu, Z. Ni, Y . Liu, B. R. Ortiz, Q. Deng, S. D. Wilson, B. Yan, L. Balents, and L. Wu, Nature physics 18, 1470 (2022)

    work page 2022

  20. [20]

    H. Li, H. Zhao, B. R. Ortiz, T. Park, M. Ye, L. Balents, Z. Wang, S. D. Wilson, and I. Zeljkovic, Nature Physics 18, 265 (2022)

    work page 2022

  21. [21]

    Grandi, A

    F. Grandi, A. Consiglio, M. A. Sentef, R. Thomale, and D. M. Kennes, Physical Review B 107, 155131 (2023)

    work page 2023

  22. [22]

    Tazai, Y

    R. Tazai, Y . Yamakawa, and H. Kontani, Nature Communica- tions 14, 7845 (2023)

    work page 2023

  23. [23]

    Jiang, H

    Z. Jiang, H. Ma, W. Xia, Z. Liu, Q. Xiao, Z. Liu, Y . Yang, J. Ding, Z. Huang, J. Liu, et al., Nano Letters 23, 5625 (2023)

    work page 2023

  24. [24]

    X. Wu, T. Schwemmer, T. M ¨uller, A. Consiglio, G. Sangio- vanni, D. Di Sante, Y . Iqbal, W. Hanke, A. P. Schnyder, M. M. Denner, et al., Physical review letters 127, 177001 (2021)

    work page 2021

  25. [25]

    B. R. Ortiz, P. M. Sarte, E. M. Kenney, M. J. Graf, S. M. Te- icher, R. Seshadri, and S. D. Wilson, Physical Review Materials 5, 034801 (2021)

    work page 2021

  26. [26]

    C. Mu, Q. Yin, Z. Tu, C. Gong, H. Lei, Z. Li, and J. Luo, Chi- nese Physics Letters 38, 077402 (2021)

    work page 2021

  27. [27]

    Q. Yin, Z. Tu, C. Gong, Y . Fu, S. Yan, and H. Lei, Chinese Physics Letters 38, 037403 (2021)

    work page 2021

  28. [28]

    S. Ni, S. Ma, Y . Zhang, J. Yuan, H. Yang, Z. Lu, N. Wang, J. Sun, Z. Zhao, D. Li, et al. , Chinese Physics Letters 38, 057403 (2021)

    work page 2021

  29. [29]

    H. Zhao, H. Li, B. R. Ortiz, S. M. Teicher, T. Park, M. Ye, Z. Wang, L. Balents, S. D. Wilson, and I. Zeljkovic, Nature 599, 216 (2021)

    work page 2021

  30. [30]

    C. Zhao, L. Wang, W. Xia, Q. Yin, J. Ni, Y . Huang, C. Tu, Z. Tao, Z. Tu, C. Gong,et al., arXiv preprint arXiv:2102.08356 (2021)

    work page arXiv 2021

  31. [31]

    Q. Wang, P. Kong, W. Shi, C. Pei, C. Wen, L. Gao, Y . Zhao, Q. Yin, Y . Wu, G. Li, et al., Advanced Materials 33, 2102813 (2021)

    work page 2021

  32. [32]

    A. T. Rømer, S. Bhattacharyya, R. Valent ´ı, M. H. Christensen, and B. M. Andersen, Phys. Rev. B 106, 174514 (2022)

    work page 2022

  33. [33]

    Y .-M. Wu, P. Nosov, A. A. Patel, and S. Raghu, Physical Re- view Letters 130, 026001 (2023)

    work page 2023

  34. [34]

    J.-T. Jin, K. Jiang, H. Yao, and Y . Zhou, Physical Review Let- ters 129, 167001 (2022)

    work page 2022

  35. [35]

    Zhou and Z

    S. Zhou and Z. Wang, Nature Communications13, 7288 (2022)

    work page 2022

  36. [36]

    Schwemmer, H

    T. Schwemmer, H. Hohmann, M. D¨urrnagel, J. Potten, J. Beyer, S. Rachel, Y .-M. Wu, S. Raghu, T. M ¨uller, W. Hanke, et al., arXiv preprint arXiv:2302.08517 (2023)

    work page arXiv 2023

  37. [37]

    Y . Gu, Y . Zhang, X. Feng, K. Jiang, and J. Hu, Phys. Rev. B 105, L100502 (2022)

    work page 2022

  38. [38]

    Y .-M. Xie, B. T. Zhou, and K. T. Law, Physical Review Letters 125, 107001 (2020)

    work page 2020

  39. [39]

    Zhang, Y .-M

    E. Zhang, Y .-M. Xie, Y . Fang, J. Zhang, X. Xu, Y .-C. Zou, P. Leng, X.-J. Gao, Y . Zhang, L. Ai, et al., Nature Physics 19, 106 (2023)

    work page 2023

  40. [40]

    Including three parts, I

    The Supplementray material of ”Odd-parity topological super- conductivity in kagome metal RbV3Sb5”. Including three parts, I. Model Hamiltonian of RbV3Sb5, II. Linearized gap equation in MCBB representation, III. Topological superconductivity

    work page

  41. [41]

    Yip, Phys

    S.-K. Yip, Phys. Rev. B 87, 104505 (2013)

    work page 2013

  42. [42]

    Fu, Physical review letters 115, 026401 (2015)

    L. Fu, Physical review letters 115, 026401 (2015)

    work page 2015

  43. [43]

    Pseudospin bases for a model of Cu:Bi$_2$Se$_3$

    S. Yip, arXiv preprint arXiv:1609.04152 (2016)

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  44. [44]

    M. H. Fischer, M. Sigrist, D. F. Agterberg, and Y . Yanase, An- nual Review of Condensed Matter Physics 14, 153 (2023)

    work page 2023

  45. [45]

    L. Jiao, S. Howard, S. Ran, Z. Wang, J. O. Rodriguez, M. Sigrist, Z. Wang, N. P. Butch, and V . Madhavan, Nature 579, 523 (2020)

    work page 2020

  46. [46]

    I. M. Hayes, D. S. Wei, T. Metz, J. Zhang, Y . S. Eo, S. Ran, S. R. Saha, J. Collini, N. P. Butch, D. F. Agterberg, et al., Science 373, 797 (2021)

    work page 2021

  47. [47]

    Aoki, J.-P

    D. Aoki, J.-P. Brison, J. Flouquet, K. Ishida, G. Knebel, Y . Tokunaga, and Y . Yanase, Journal of Physics: Condensed Matter 34, 243002 (2022)

    work page 2022

  48. [48]

    Ishihara, M

    K. Ishihara, M. Roppongi, M. Kobayashi, K. Imamura, Y . Mizukami, H. Sakai, P. Opletal, Y . Tokiwa, Y . Haga, K. Hashimoto, et al., Nature Communications 14, 2966 (2023)

    work page 2023

  49. [49]

    Guguchia, C

    Z. Guguchia, C. Mielke III, D. Das, R. Gupta, J.-X. Yin, H. Liu, Q. Yin, M. H. Christensen, Z. Tu, C. Gong, et al., Nature com- munications 14, 153 (2023)

    work page 2023

  50. [50]

    M. S. Hossain, Q. Zhang, E. S. Choi, D. Ratkovski, B. L¨uscher, Y . Li, Y .-X. Jiang, M. Litskevich, Z.-J. Cheng, J.-X. Yin,et al., arXiv preprint arXiv:2411.15333 (2024)

    work page arXiv 2024

  51. [51]

    Frigeri, D

    P. Frigeri, D. Agterberg, A. Koga, and M. Sigrist, Physical Re- view Letters 92, 097001 (2004)

    work page 2004

  52. [52]

    Sigrist, in AIP Conference Proceedings, V ol

    M. Sigrist, in AIP Conference Proceedings, V ol. 1162 (Ameri- can Institute of Physics, 2009) pp. 55–96

    work page 2009

  53. [53]

    Lawrence and S

    W. Lawrence and S. Doniach, in Proceedings of the 12th In- ternational Conference on Low Temperature Physics (1971) p. 361

    work page 1971

  54. [54]

    R. A. Klemm, A. Luther, and M. Beasley, Physical Review B 12, 877 (1975)

    work page 1975

  55. [55]

    Ruggiero, T

    S. Ruggiero, T. Barbee Jr, and M. Beasley, Physical Review Letters 45, 1299 (1980)

    work page 1980

  56. [56]

    Sato and S

    M. Sato and S. Fujimoto, Physical Review B79, 094504 (2009)

    work page 2009

  57. [57]

    M. Z. Hasan and C. L. Kane, Reviews of modern physics 82, 3045 (2010)

    work page 2010

  58. [58]

    J. D. Sau, R. M. Lutchyn, S. Tewari, and S. D. Sarma, Physical review letters 104, 040502 (2010)

    work page 2010

  59. [59]

    Alicea, Physical Review B 81, 125318 (2010)

    J. Alicea, Physical Review B 81, 125318 (2010)

    work page 2010

  60. [60]

    Y . Oreg, G. Refael, and F. V on Oppen, Physical review letters 105, 177002 (2010)

    work page 2010

  61. [61]

    A. P. Schnyder and S. Ryu, Physical Review B 84, 060504 (2011)

    work page 2011

  62. [62]

    Qi and S.-C

    X.-L. Qi and S.-C. Zhang, Reviews of Modern Physics83, 1057 (2011)

    work page 2011

  63. [63]

    Alicea, Reports on progress in physics 75, 076501 (2012)

    J. Alicea, Reports on progress in physics 75, 076501 (2012)

    work page 2012

  64. [64]

    Beenakker, Annu

    C. Beenakker, Annu. Rev. Condens. Matter Phys.4, 113 (2013)

    work page 2013

  65. [65]

    A. P. Schnyder and P. M. Brydon, Journal of Physics: Con- densed Matter 27, 243201 (2015)

    work page 2015

  66. [66]

    B. T. Zhou, N. F. Yuan, H.-L. Jiang, and K. T. Law, Physical Review B 93, 180501 (2016)

    work page 2016

  67. [67]

    M. R. Zirnbauer, Journal of Mathematical Physics 37, 4986 (1996)

    work page 1996

  68. [68]

    Altland and M

    A. Altland and M. R. Zirnbauer, Physical Review B 55, 1142 (1997)

    work page 1997

  69. [69]

    Matsuura, P.-Y

    S. Matsuura, P.-Y . Chang, A. P. Schnyder, and S. Ryu, New Journal of Physics 15, 065001 (2013)

    work page 2013

  70. [70]

    C.-K. Chiu, J. C. Teo, A. P. Schnyder, and S. Ryu, Reviews of Modern Physics 88, 035005 (2016)

    work page 2016

  71. [71]

    Sato and Y

    M. Sato and Y . Ando, Reports on Progress in Physics 80, 076501 (2017)

    work page 2017

  72. [72]

    D. S. Fisher and P. A. Lee, Physical Review B 23, 6851 (1981). 7

    work page 1981

  73. [73]

    P. A. Lee and D. S. Fisher, Physical Review Letters 47, 882 (1981)

    work page 1981

  74. [74]

    Sun and X

    Q.-f. Sun and X. Xie, Journal of Physics: Condensed Matter 21, 344204 (2009)

    work page 2009

  75. [75]

    J. Liu, A. C. Potter, K. T. Law, and P. A. Lee, Physical review letters 109, 267002 (2012)

    work page 2012

  76. [76]

    K. T. Law, P. A. Lee, and T. K. Ng, Physical review letters103, 237001 (2009)

    work page 2009

  77. [77]

    Wimmer, A

    M. Wimmer, A. Akhmerov, J. Dahlhaus, and C. Beenakker, New Journal of Physics 13, 053016 (2011)

    work page 2011

  78. [78]

    Kohn and J

    W. Kohn and J. Luttinger, Physical Review Letters 15, 524 (1965)

    work page 1965

  79. [79]

    Ghazaryan, T

    A. Ghazaryan, T. Holder, M. Serbyn, and E. Berg, Physical re- view letters 127, 247001 (2021)

    work page 2021

  80. [80]

    You and A

    Y .-Z. You and A. Vishwanath, Physical Review B105, 134524 (2022)

    work page 2022

Showing first 80 references.