Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
133 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Non-Hermitian Topology in Hermitian Topological Matter (2405.10015v2)

Published 16 May 2024 in cond-mat.mes-hall, hep-th, and quant-ph

Abstract: Non-Hermiticity gives rise to distinctive topological phenomena absent in Hermitian systems. However, connection between such intrinsic non-Hermitian topology and Hermitian topology has remained largely elusive. Here, considering the bulk and boundary as an environment and system, respectively, we demonstrate that anomalous boundary states in Hermitian topological insulators exhibit non-Hermitian topology. We study the self-energy capturing the particle exchange between the bulk and boundary, and show that it detects Hermitian topology in the bulk and induces non-Hermitian topology at the boundary. As an illustrative example, we reveal non-Hermitian topology and concomitant skin effect inherently embedded within chiral edge states of Chern insulators. We also identify the emergence of hinge states within effective non-Hermitian Hamiltonians at surfaces of three-dimensional topological insulators. Furthermore, we comprehensively classify our correspondence across all the tenfold symmetry classes of topological insulators and superconductors. Our work uncovers hidden connection between Hermitian and non-Hermitian topology, and provides an approach to identifying non-Hermitian topology in quantum matter.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (69)
  1. M. Z. Hasan and C. L. Kane, Colloquium: Topological insulators, Rev. Mod. Phys. 82, 3045 (2010).
  2. X.-L. Qi and S.-C. Zhang, Topological insulators and superconductors, Rev. Mod. Phys. 83, 1057 (2011).
  3. A. Altland and M. R. Zirnbauer, Nonstandard symmetry classes in mesoscopic normal-superconducting hybrid structures, Phys. Rev. B 55, 1142 (1997).
  4. A. Kitaev, Periodic table for topological insulators and superconductors, AIP Conf. Proc. 1134, 22 (2009).
  5. M. S. Rudner and L. S. Levitov, Topological Transition in a Non-Hermitian Quantum Walk, Phys. Rev. Lett. 102, 065703 (2009).
  6. Y. C. Hu and T. L. Hughes, Absence of topological insulator phases in non-Hermitian PT-symmetric Hamiltonians, Phys. Rev. B 84, 153101 (2011).
  7. H. Schomerus, Topologically protected midgap states in complex photonic lattices, Opt. Lett. 38, 1912 (2013).
  8. S. Longhi, D. Gatti, and G. D. Valle, Robust light transport in non-Hermitian photonic lattices, Sci. Rep. 5, 13376 (2015).
  9. T. E. Lee, Anomalous Edge State in a Non-Hermitian Lattice, Phys. Rev. Lett. 116, 133903 (2016).
  10. Y. Xu, S.-T. Wang, and L.-M. Duan, Weyl Exceptional Rings in a Three-Dimensional Dissipative Cold Atomic Gas, Phys. Rev. Lett. 118, 045701 (2017).
  11. H. Shen, B. Zhen, and L. Fu, Topological Band Theory for Non-Hermitian Hamiltonians, Phys. Rev. Lett. 120, 146402 (2018).
  12. K. Takata and M. Notomi, Photonic Topological Insulating Phase Induced Solely by Gain and Loss, Phys. Rev. Lett. 121, 213902 (2018).
  13. V. M. Martinez Alvarez, J. E. Barrios Vargas, and L. E. F. Foa Torres, Non-Hermitian robust edge states in one dimension: Anomalous localization and eigenspace condensation at exceptional points, Phys. Rev. B 97, 121401(R) (2018).
  14. S. Yao and Z. Wang, Edge States and Topological Invariants of Non-Hermitian Systems, Phys. Rev. Lett. 121, 086803 (2018).
  15. S. Yao, F. Song, and Z. Wang, Non-Hermitian Chern Bands, Phys. Rev. Lett. 121, 136802 (2018).
  16. A. McDonald, T. Pereg-Barnea, and A. A. Clerk, Phase-Dependent Chiral Transport and Effective Non-Hermitian Dynamics in a Bosonic Kitaev-Majorana Chain, Phys. Rev. X 8, 041031 (2018).
  17. C. H. Lee and R. Thomale, Anatomy of skin modes and topology in non-Hermitian systems, Phys. Rev. B 99, 201103(R) (2019).
  18. C. H. Lee, L. Li, and J. Gong, Hybrid Higher-Order Skin-Topological Modes in Nonreciprocal Systems, Phys. Rev. Lett. 123, 016805 (2019a).
  19. H. Zhou and J. Y. Lee, Periodic table for topological bands with non-Hermitian symmetries, Phys. Rev. B 99, 235112 (2019).
  20. L. Herviou, J. H. Bardarson, and N. Regnault, Defining a bulk-edge correspondence for non-Hermitian Hamiltonians via singular-value decomposition, Phys. Rev. A 99, 052118 (2019).
  21. H.-G. Zirnstein, G. Refael, and B. Rosenow, Bulk-Boundary Correspondence for Non-Hermitian Hamiltonians via Green Functions, Phys. Rev. Lett. 126, 216407 (2021).
  22. D. S. Borgnia, A. J. Kruchkov, and R.-J. Slager, Non-Hermitian Boundary Modes and Topology, Phys. Rev. Lett. 124, 056802 (2020).
  23. K. Yokomizo and S. Murakami, Non-Bloch Band Theory of Non-Hermitian Systems, Phys. Rev. Lett. 123, 066404 (2019).
  24. C. C. Wanjura, M. Brunelli, and A. Nunnenkamp, Topological framework for directional amplification in driven-dissipative cavity arrays, Nat. Commun. 11, 3149 (2020).
  25. K. Zhang, Z. Yang, and C. Fang, Correspondence between Winding Numbers and Skin Modes in Non-Hermitian Systems, Phys. Rev. Lett. 125, 126402 (2020).
  26. M. M. Denner, T. Neupert, and F. Schindler, Infernal and exceptional edge modes: non-Hermitian topology beyond the skin effect, J. Phys. Mater. 6, 045006 (2023).
  27. R. Okugawa, R. Takahashi, and K. Yokomizo, Second-order topological non-Hermitian skin effects, Phys. Rev. B 102, 241202(R) (2020).
  28. K. Kawabata, M. Sato, and K. Shiozaki, Higher-order non-Hermitian skin effect, Phys. Rev. B 102, 205118 (2020).
  29. Y. Fu, J. Hu, and S. Wan, Non-Hermitian second-order skin and topological modes, Phys. Rev. B 103, 045420 (2021).
  30. K. Kawabata, K. Shiozaki, and S. Ryu, Topological Field Theory of Non-Hermitian Systems, Phys. Rev. Lett. 126, 216405 (2021).
  31. K. Zhang, Z. Yang, and C. Fang, Universal non-Hermitian skin effect in two and higher dimensions, Nat. Commun. 13, 2496 (2022).
  32. X.-Q. Sun, P. Zhu, and T. L. Hughes, Geometric Response and Disclination-Induced Skin Effects in Non-Hermitian Systems, Phys. Rev. Lett. 127, 066401 (2021).
  33. K.-M. Kim and M. J. Park, Disorder-driven phase transition in the second-order non-Hermitian skin effect, Phys. Rev. B 104, L121101 (2021).
  34. D. Nakamura, T. Bessho, and M. Sato, Bulk-Boundary Correspondence in Point-Gap Topological Phases, Phys. Rev. Lett. 132, 136401 (2024).
  35. H.-Y. Wang, F. Song, and Z. Wang, Amoeba Formulation of Non-Bloch Band Theory in Arbitrary Dimensions, Phys. Rev. X 14, 021011 (2024).
  36. E. J. Bergholtz, J. C. Budich, and F. K. Kunst, Exceptional topology of non-Hermitian systems, Rev. Mod. Phys. 93, 015005 (2021).
  37. N. Okuma and M. Sato, Non-Hermitian Topological Phenomena: A Review, Annu. Rev. Condens. Matter Phys. 14, 83 (2023).
  38. V. V. Konotop, J. Yang, and D. A. Zezyulin, Nonlinear waves in 𝒫⁢𝒯𝒫𝒯\mathcal{PT}caligraphic_P caligraphic_T-symmetric systems, Rev. Mod. Phys. 88, 035002 (2016).
  39. V. Kozii and L. Fu, Non-Hermitian Topological Theory of Finite-Lifetime Quasiparticles: Prediction of Bulk Fermi Arc Due to Exceptional Point, arXiv:1708.05841 .
  40. M. Papaj, H. Isobe, and L. Fu, Nodal arc of disordered Dirac fermions and non-Hermitian band theory, Phys. Rev. B 99, 201107 (2019).
  41. H. Shen and L. Fu, Quantum Oscillation from In-Gap States and a Non-Hermitian Landau Level Problem, Phys. Rev. Lett. 121, 026403 (2018).
  42. T. Yoshida, R. Peters, and N. Kawakami, Non-Hermitian perspective of the band structure in heavy-fermion systems, Phys. Rev. B 98, 035141 (2018).
  43. M. R. Hirsbrunner, T. M. Philip, and M. J. Gilbert, Topology and observables of the non-Hermitian Chern insulator, Phys. Rev. B 100, 081104(R) (2019).
  44. P. A. McClarty and J. G. Rau, Non-Hermitian topology of spontaneous magnon decay, Phys. Rev. B 100, 100405(R) (2019).
  45. E. J. Bergholtz and J. C. Budich, Non-Hermitian Weyl physics in topological insulator ferromagnet junctions, Phys. Rev. Research 1, 012003(R) (2019).
  46. Y. Michishita and R. Peters, Equivalence of Effective Non-Hermitian Hamiltonians in the Context of Open Quantum Systems and Strongly Correlated Electron Systems, Phys. Rev. Lett. 124, 196401 (2020).
  47. N. Okuma and M. Sato, Non-Hermitian Skin Effects in Hermitian Correlated or Disordered Systems: Quantities Sensitive or Insensitive to Boundary Effects and Pseudo-Quantum-Number, Phys. Rev. Lett. 126, 176601 (2021).
  48. C. Lehmann, M. Schüler, and J. C. Budich, Dynamically Induced Exceptional Phases in Quenched Interacting Semimetals, Phys. Rev. Lett. 127, 106601 (2021).
  49. J. Cayao and M. Sato, Non-Hermitian phase-biased Josephson junctions, arXiv:2307.15472 .
  50. A. Wang, Z. Meng, and C. Q. Chen, Non-Hermitian topology in static mechanical metamaterials, Sci. Adv. 9, eadf7299 (2023).
  51. T. Bessho and M. Sato, Nielsen-Ninomiya Theorem with Bulk Topology: Duality in Floquet and Non-Hermitian Systems, Phys. Rev. Lett. 127, 196404 (2021).
  52. W. Zhu and J. Gong, Hybrid skin-topological modes without asymmetric couplings, Phys. Rev. B 106, 035425 (2022).
  53. W. Zhu and J. Gong, Photonic corner skin modes in non-Hermitian photonic crystals, Phys. Rev. B 108, 035406 (2023).
  54. Z. Ou, Y. Wang, and L. Li, Non-Hermitian boundary spectral winding, Phys. Rev. B 107, L161404 (2023).
  55. S. Datta, Electronic Transport in Mesoscopic Systems (Cambridge University Press, Cambridge, England, 1995).
  56. N. Moiseyev, Non-Hermitian Quantum Mechanics (Cambridge University Press, Cambridge, England, 2011).
  57. N. Hatano and D. R. Nelson, Localization Transitions in Non-Hermitian Quantum Mechanics, Phys. Rev. Lett. 77, 570 (1996).
  58. N. Hatano and D. R. Nelson, Vortex pinning and non-Hermitian quantum mechanics, Phys. Rev. B 56, 8651 (1997).
  59. N. Hatano, What is the resonant state in open quantum systems?, J. Phys.: Conf. Ser. 2038, 012013 (2021).
  60. W. P. Su, J. R. Schrieffer, and A. J. Heeger, Solitons in Polyacetylene, Phys. Rev. Lett. 42, 1698 (1979).
  61. η=1/L𝜂1𝐿\eta=1/\sqrt{L}italic_η = 1 / square-root start_ARG italic_L end_ARG is chosen to be much larger than the level spacing ∼1/Lsimilar-toabsent1𝐿\sim 1/L∼ 1 / italic_L but much smaller than the macroscopic energy scale ∼1similar-toabsent1\sim 1∼ 1.
  62. 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).
  63. X.-L. Qi, T. L. Hughes, and S.-C. Zhang, Topological field theory of time-reversal invariant insulators, Phys. Rev. B 78, 195424 (2008).
  64. S. Datta, Quantum Transport (Cambridge University Press, Cambridge, England, 2005).
  65. 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).
  66. K. Fujikawa and H. Suzuki, Path Integrals and Quantum Anomalies (Oxford University Press, Oxford, 2004).
  67. L. H. Karsten, Lattice fermions in euclidean space-time, Phys. Lett. B 104, 315 (1981).
  68. S. Lieu, M. McGinley, and N. R. Cooper, Tenfold Way for Quadratic Lindbladians, Phys. Rev. Lett. 124, 040401 (2020).
  69. B. C. Shin, A formula for Eigenpairs of certain symmetric tridiagonal matrices, Bull. Aust. Math. Soc. 55, 249 (1997).

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now
X Twitter Logo Streamline Icon: https://streamlinehq.com

Tweets