- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Disorder-induced topological phases in a two-dimensional Chern insulator with strong magnetic disorder

Devesh Vaish1,* and Michael Potthoff1,2,†

  • *Contact author: devesh.r.vaish@jyu.fi
  • †Contact author: michael.potthoff@uni-hamburg.de
PDF

Phys. Rev. Research 8, 023312 – Published 17 June, 2026

DOI: https://doi.org/10.1103/fjnq-k1wq

Abstract

Strong directional disorder in local magnetic moments coupled to a Chern insulator gives rise to topological phases that cannot be realized in any clean system and are therefore genuinely disorder driven. We demonstrate this in a spinful Qi-Wu-Zhang model of a two-dimensional Chern insulator coupled to disordered classical spins of unit length. The topological phase diagram is computed numerically using two complementary approaches: twisted boundary conditions and the topological Hamiltonian technique. Our results show that strong disorder can act as a fundamental topological mechanism rather than merely a perturbation. For strong exchange coupling, tuning the mass parameter reveals a transition between phases with different Chern numbers C. Remarkably, this transition is driven by zeros, rather than poles, of the disorder-averaged Green’s function crossing the chemical potential, and has no analog in any clean system. We further identify a strong-coupling phase with C=0 that is nonetheless topologically nontrivial, characterized by a distinct Chern number C(S)≠0 over the manifold of classical spin configurations. This phase is also disorder driven, as C(S)=0 in the clean limit.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (62)

  1. D. J. Thouless, M. Kohmoto, M. P. Nightingale, and M. den Nijs, Quantized Hall conductance in a two-dimensional periodic potential, Phys. Rev. Lett. 49, 405 (1982).
  2. J. E. Avron, R. Seiler, and B. Simon, Homotopy and quantization in condensed matter physics, Phys. Rev. Lett. 51, 51 (1983).
  3. B. Simon, Holonomy, the quantum adiabatic theorem, and Berry’s phase, Phys. Rev. Lett. 51, 2167 (1983).
  4. C. L. Kane and E. J. Mele, Z2 topological order and the quantum spin Hall effect, Phys. Rev. Lett. 95, 146802 (2005).
  5. M. Z. Hasan and C. L. Kane, Colloquium: Topological insulators, Rev. Mod. Phys. 82, 3045 (2010).
  6. X.-L. Qi and S.-C. Zhang, Topological insulators and superconductors, Rev. Mod. Phys. 83, 1057 (2011).
  7. C.-K. Chiu, J. C. Y. Teo, A. P. Schnyder, and S. Ryu, Classification of topological quantum matter with symmetries, Rev. Mod. Phys. 88, 035005 (2016).
  8. F. D. M. Haldane, Model for a quantum Hall effect without Landau levels: Condensed-matter realization of the “parity anomaly”, Phys. Rev. Lett. 61, 2015 (1988).
  9. S. Rachel, Interacting topological insulators: A review, Rep. Prog. Phys. 81, 116501 (2018).
  10. P. W. Anderson, Absence of diffusion in certain random lattices, Phys. Rev. 109, 1492 (1958).
  11. E. Abrahams, P. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan, Scaling theory of localization: Absence of quantum diffusion in two dimensions, Phys. Rev. Lett. 42, 673 (1979).
  12. P. W. Anderson, D. J. Thouless, E. Abrahams, and D. S. Fisher, New method for a scaling theory of localization, Phys. Rev. B 22, 3519 (1980).
  13. Q. Niu, D. J. Thouless, and Y.-S. Wu, Quantized Hall conductance as a topological invariant, Phys. Rev. B 31, 3372 (1985).
  14. R. Tao and Y.-S. Wu, Gauge invariance and fractional quantum Hall effect, Phys. Rev. B 30, 1097 (1984).
  15. J. E. Avron and R. Seiler, Quantization of the Hall conductance for general, multiparticle Schrödinger Hamiltonians, Phys. Rev. Lett. 54, 259 (1985).
  16. L. Lin, Y. Ke, L. Zhang, and C. Lee, Calculations of the Chern number: Equivalence of real-space and twisted-boundary-condition formulas, Phys. Rev. B 108, 174204 (2023).
  17. J. Bellissard, A. van Elst, and H. Schulz‐Baldes, The noncommutative geometry of the quantum Hall effect, J. Math. Phys. 35, 5373 (1994).
  18. E. Prodan, Disordered topological insulators: A non-commutative geometry perspective, J. Phys. A 44, 113001 (2011).
  19. E. Prodan, T. L. Hughes, and B. A. Bernevig, Entanglement spectrum of a disordered topological Chern insulator, Phys. Rev. Lett. 105, 115501 (2010).
  20. E. Prodan, Non-commutative tools for topological insulators, New J. Phys. 12, 065003 (2010).
  21. T. A. Loring and M. B. Hastings, Disordered topological insulators via C*-algebras, Europhys. Lett. 92, 67004 (2010).
  22. M. B. Hastings and T. A. Loring, Almost commuting matrices, localized Wannier functions, and the quantum Hall effect, J. Math. Phys. 51, 015214 (2010).
  23. T. A. Loring, K-theory and pseudospectra for topological insulators, Ann. Phys. 356, 383 (2015).
  24. J. Li, R.-L. Chu, J. K. Jain, and S.-Q. Shen, Topological Anderson insulator, Phys. Rev. Lett. 102, 136806 (2009).
  25. B. A. Bernevig, T. L. Hughes, and S.-C. Zhang, Quantum spin Hall effect and topological phase transition in HgTe quantum wells, Science 314, 1757 (2006).
  26. C. W. Groth, M. Wimmer, A. R. Akhmerov, J. Tworzydło, and C. W. J. Beenakker, Theory of the topological Anderson insulator, Phys. Rev. Lett. 103, 196805 (2009).
  27. H. Jiang, L. Wang, Q.-f. Sun, and X. C. Xie, Numerical study of the topological Anderson insulator in HgTe/CdTe quantum wells, Phys. Rev. B 80, 165316 (2009).
  28. A. Yamakage, K. Nomura, K.-I. Imura, and Y. Kuramoto, Disorder-induced multiple transition involving Z2 topological insulator, J. Phys. Soc. Jpn. 80, 053703 (2011).
  29. H.-M. Guo, G. Rosenberg, G. Refael, and M. Franz, Topological Anderson insulator in three dimensions, Phys. Rev. Lett. 105, 216601 (2010).
  30. R. Bianco and R. Resta, Mapping topological order in coordinate space, Phys. Rev. B 84, 241106 (2011).
  31. G.-G. Liu, Y. Yang, X. Ren, H. Xue, X. Lin, Y.-H. Hu, H.-x. Sun, B. Peng, P. Zhou, Y. Chong, and B. Zhang, Topological Anderson insulator in disordered photonic crystals, Phys. Rev. Lett. 125, 133603 (2020).
  32. Q. Lin, T. Li, L. Xiao, K. Wang, W. Yi, and P. Xue, Observation of non-Hermitian topological Anderson insulator in quantum dynamics, Nat. Commun. 13, 3229 (2022).
  33. E. Prodan, Three-dimensional phase diagram of disordered HgTe/CdTe quantum spin-Hall wells, Phys. Rev. B 83, 195119 (2011).
  34. X.-L. Qi, Y.-S. Wu, and S.-C. Zhang, Topological quantization of the spin Hall effect in two-dimensional paramagnetic semiconductors, Phys. Rev. B 74, 085308 (2006).
  35. K. Ishikawa and T. Matsuyama, Magnetic field induced multi-component QED3 and quantum Hall effect, Z. Phys. C 33, 41 (1986).
  36. G. E. Volovik, The Universe in a Helium Droplet (Oxford University Press, New York, 2003).
  37. Z. Wang and S.-C. Zhang, Simplified topological invariants for interacting insulators, Phys. Rev. X 2, 031008 (2012).
  38. S. Michel, A. Fünfhaus, R. Quade, R. Valentí, and M. Potthoff, Bound states and local topological phase diagram of classical impurity spins coupled to a Chern insulator, Phys. Rev. B 109, 155116 (2024).
  39. A. Altland and M. R. Zirnbauer, Nonstandard symmetry classes in mesoscopic normal-superconducting hybrid structures, Phys. Rev. B 55, 1142 (1997).
  40. S. Ryu, A. P. Schnyder, A. Furusaki, and A. W. W. Ludwig, Topological insulators and superconductors: Tenfold way and dimensional hierarchy, New J. Phys. 12, 065010 (2010).
  41. K. Kudo, H. Watanabe, T. Kariyado, and Y. Hatsugai, Many-body Chern number without integration, Phys. Rev. Lett. 122, 146601 (2019).
  42. Y. Xue and E. Prodan, Quantum criticality at the Chern-to-normal insulator transition, Phys. Rev. B 87, 115141 (2013).
  43. Y. V. Fyodorov and A. D. Mirlin, Analytical derivation of the scaling law for the inverse participation ratio in quasi-one-dimensional disordered systems, Phys. Rev. Lett. 69, 1093 (1992).
  44. M. Potthoff and M. Balzer, Self-energy-functional theory for systems of interacting electrons with disorder, Phys. Rev. B 75, 125112 (2007).
  45. P. Tscheppe, M. Klett, H. Menke, S. Andergassen, N. Enderlein, P. Hansmann, and T. Schäfer, Coherent cellular dynamical mean-field theory: A real-space quantum embedding approach to disorder in strongly correlated electron systems, New J. Phys. 27, 123504 (2025).
  46. V. Gurarie, Single-particle Green’s functions and interacting topological insulators, Phys. Rev. B 83, 085426 (2011).
  47. N. Wagner, L. Crippa, A. Amaricci, P. Hansmann, M. Klett, E. J. König, T. Schäfer, D. D. Sante, J. Cano, A. J. Millis, A. Georges, and G. Sangiovanni, Mott insulators with boundary zeros, Nat. Commun. 14, 7531 (2023).
  48. M. Nakahara, Geometry, Topology, and Physics (Institute of Physics Publishing, Bristol, 1998).
  49. S. Michel and M. Potthoff, Spin Berry curvature of the Haldane model, Phys. Rev. B 106, 235423 (2022).
  50. P. A. M. Dirac, Quantised singularities in the electromagnetic field, Proc. R. Soc. London A 133, 60 (1931).
  51. M. V. Berry, Quantal phase factors accompanying adiabatic changes, Proc. R. Soc. London A 392, 45 (1984).
  52. J. Ye, Y. B. Kim, A. J. Millis, B. I. Shraiman, P. Majumdar, and Z. Tešanović, Berry phase theory of the anomalous Hall effect: Application to colossal magnetoresistance manganites, Phys. Rev. Lett. 83, 3737 (1999).
  53. K. Ohgushi, S. Murakami, and N. Nagaosa, Spin anisotropy and quantum Hall effect in the kagomé lattice: Chiral spin state based on a ferromagnet, Phys. Rev. B 62, R6065 (2000).
  54. Y. Akagi and Y. Motome, Spin chirality ordering and anomalous Hall effect in the ferromagnetic Kondo lattice model on a triangular lattice, J. Phys. Soc. Jpn. 79, 083711 (2010).
  55. H. Ishizuka and N. Nagaosa, Spin chirality induced skew scattering and anomalous Hall effect in chiral magnets, Sci. Adv. 4, eaap9962 (2018).
  56. Y.-P. Huang, J.-W. Dong, P. Kotetes, and S. Zhou, Antiferromagnetic chiral spin density wave and strain-induced Chern insulator in the square lattice Hubbard model with frustration, Phys. Rev. B 102, 195120 (2020).
  57. M. Tomé and H. D. Rosales, Topological phase transition driven by magnetic field and topological Hall effect in an antiferromagnetic skyrmion lattice, Phys. Rev. B 103, L020403 (2021).
  58. S. Divic, H. Ling, T. Pereg-Barnea, and A. Paramekanti, Magnetic skyrmion crystal at a topological insulator surface, Phys. Rev. B 105, 035156 (2022).
  59. S. Hayami, Chern insulating state with double-q ordering wave vectors at the Brillouin zone boundary, Phys. Rev. B 108, 094416 (2023).
  60. K. K. Kesharpu, E. A. Kochetov, and A. Ferraz, Topological Hall effect induced by classical large-spin background: su(2) path-integral approach, Phys. Rev. B 107, 155146 (2023).
  61. Y. Zhou, S. Li, X. Liang, and Y. Zhou, Topological spin textures: Basic physics and devices, Adv. Mater. 37, 2312935 (2025).
  62. D. Vaish and M. Potthoff, Disorder-induced topological phases in a two-dimensional Chern insulator with strong magnetic disorder [Data set], Zenodo, 2026, https://doi.org/10.5281/zenodo.20118934.

Outline

Information

Phys. Rev. Research 8, 023312– Published 17 June, 2026
  • Received 18 February 2026
  • Accepted 9 May 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation