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Dephasing effects in topological insulators

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Abstract

Topological insulators, a class of typical topological materials in both two dimensions and three dimensions, are insulating in bulk and metallic at surface. The spin-momentum locked surface states and peculiar transport properties exhibit promising potential applications on quantum devices, which generate extensive interest in the last decade. Dephasing is the process of the loss of phase coherence, which inevitably exists in a realistic sample. In this review, we focus on recent progress in dephasing effects on the topological insulators. In general, there are two types of dephasing processes: normal dephasing and spin dephasing. In two-dimensional topological insulators, the phenomenologically numerical investigation shows that the longitudinal resistance plateaus is robust against normal dephasing but fragile with spin dephasing. Several microscopic mechanisms of spin dephasing are then discussed. In three-dimensional topological insulators, the helical surface states exhibit a helical spin texture due to the spin-momentum locking mechanism. Thus, normal dephasing has close connection to spin dephasing in this case, and gives rise to anomalous “gap-like” feature. Dephasing effects on properties of helical surface states are investigated.

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References

  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(6), 405 (1982)

    Article  ADS  Google Scholar 

  2. K. von Klitzing, G. Dorda, and M. Pepper, New method for high-accuracy determination of the fine-structure constant based on quantized Hall resistance, Phys. Rev. Lett. 45(6), 494 (1980)

    Article  ADS  Google Scholar 

  3. K. von Klitzing, 25 years of quantum Hall effects: A personal view on the discovery, physics and applications of this quantum effect, Séminaire Poincaré 2, 1 (2004)

    Google Scholar 

  4. 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(6), 405 (1982)

    Article  ADS  Google Scholar 

  5. M. Kohmoto, Topological invariant and the quantization of the Hall conductance, Ann. Phys. 160(2), 343 (1985)

    Article  ADS  MathSciNet  Google Scholar 

  6. F. D. M. Haldane, Model for a quantum Hall effect without Landau levels: Condensed-matter realization of the “parity anomaly”, Phys. Rev. Lett. 61(18), 2015 (1988)

    Article  ADS  MathSciNet  Google Scholar 

  7. 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, Science 340(6129), 167 (2013)

    Article  ADS  Google Scholar 

  8. C. L. Kane and E. J. Mele, Quantum spin Hall effect in graphene, Phys. Rev. Lett. 95(22), 226801 (2005)

    Article  ADS  Google Scholar 

  9. C. L. Kane and E. J. Mele, Z2 topological order and the quantum spin Hall effect, Phys. Rev. Lett. 95(14), 146802 (2005)

    Article  ADS  Google Scholar 

  10. H. Min, J. E. Hill, N. A. Sinitsyn, B. R. Sahu, L. Kleinman, and A. H. MacDonald, Intrinsic and Rashba spin–orbit interactions in graphene sheets, Phys. Rev. B 74, 165310 (2006)

    Article  ADS  Google Scholar 

  11. D. Huertas-Hernando, F. Guinea, and A. Brataas, Spin-orbit coupling in curved graphene, fullerenes, nanotubes, and nanotube caps, Phys. Rev. B 74(15), 155426 (2006)

    Article  ADS  Google Scholar 

  12. Y. G. Yao, F. Ye, X.-L. Qi, S.-C. Zhang, and Z. Fang, Spin-orbit gap of graphene: First-principles calculations, Phys. Rev. B 75, 041401(R) (2007)

    Article  ADS  Google Scholar 

  13. J. C. Boettger and S. B. Trickey, First-principles calculation of the spin–orbit splitting in graphene, Phys. Rev. B 75, 121402(R) (2007)

    Article  ADS  Google Scholar 

  14. M. Gmitra, S. Konschuh, C. Ertler, C. Ambrosch-Draxl, and J. Fabian, Band-structure topologies of graphene: Spin–orbit coupling effects from first principles, Phys. Rev. B 80(23), 235431 (2009)

    Article  ADS  Google Scholar 

  15. B. A. Bernevig and S. C. Zhang, Quantum spin Hall effect, Phys. Rev. Lett. 96(10), 106802 (2006)

    Article  ADS  Google Scholar 

  16. B. A. Bernevig, T. L. Hughes, and S. C. Zhang, Quantum spin Hall effect and topological phase transition in HgTe quantum wells, Science 314(5806), 1757 (2006)

    Article  ADS  Google Scholar 

  17. M. König, S. Wiedmann, C. Brune, A. Roth, H. Buhmann, L. W. Molenkamp, X. L. Qi, and S. C. Zhang, Quantum spin Hall insulator state in HgTe quantum wells, Science 318(5851), 766 (2007)

    Article  ADS  Google Scholar 

  18. I. Knez, R. R. Du, and G. Sullivan, Evidence for helical edge modes in inverted InAs/GaSb quantum wells, Phys. Rev. Lett. 107(13), 136603 (2011)

    Article  ADS  Google Scholar 

  19. S. Murakami, Quantum spin Hall effect and enhanced magnetic response by spin–orbit coupling, Phys. Rev. Lett. 97(23), 236805 (2006)

    Article  ADS  Google Scholar 

  20. C. C. Liu, W. F eng, and Y. Yao, Quantum spin Hall effect in silicene and two-dimensional germanium, Phys. Rev. Lett. 107(7), 076802 (2011)

    Article  ADS  Google Scholar 

  21. F. C. Chuang, L. Z. Yao, Z. Q. Huang, Y. T. Liu, C. H. Hsu, T. Das, H. Lin, and A. Bansil, Prediction of large-gap two-dimensional topological insulators consisting of bilayers of group III elements with Bi, Nano Lett. 14(5), 2505 (2014)

    Article  ADS  Google Scholar 

  22. J. J. Zhou, W. Feng, C. C. Liu, S. Guan, and Y. Yao, Large-Gap Quantum Spin Hall insulator in single layer bismuth monobromide Bi4Br4, Nano Lett. 14(8), 4767 (2014)

    Article  ADS  Google Scholar 

  23. W. Luo and H. J. Xiang, Room temperature quantum spin Hall insulators with a buckled square lattice, Nano Lett. 15(5), 3230 (2015)

    Article  ADS  Google Scholar 

  24. Y. D. Ma, L. Kou, A. Du, and T. Heine, Group 14 element-based noncentrosymmetric quantum spin Hall insulators with large bulk gap, Nano Res. 8(10), 3412 (2015)

    Article  Google Scholar 

  25. C. Si, J. Liu, Y. Xu, J. Wu, B.L. Gu, and W. Duan, Functionalized germanene as a prototype of large-gap two-dimensional topological insulators, Phys. Rev. B 89(11), 115429 (2014)

    Article  ADS  Google Scholar 

  26. Y. Xu, B. Yan, H. J. Zhang, J. Wang, G. Xu, P. Tang, W. Duan, and S. C. Zhang, Large-gap quantum spin Hall insulators in tin films, Phys. Rev. Lett. 111(13), 136804 (2013)

    Article  ADS  Google Scholar 

  27. Y. D. Ma, Y. Dai, L. Kou, T. Frauenheim, and T. Heine, Robust two-dimensional topological insulators in methyl-functionalized bismuth, antimony, and lead bilayer films, Nano Lett. 15(2), 1083 (2015)

    Article  ADS  Google Scholar 

  28. Z. G. Song, C. C. Liu, J. Yang, J. Han, M. Ye, B. Fu, Y. Yang, Q. Niu, J. Lu, and Y. Yao, Quantum spin Hall insulators and quantum valley Hall insulators of BiX/SbX (X = H, F, Cl and Br) monolayers with a record bulk band gap, NPG Asia Mater. 6(12), e147 (2014)

    Article  Google Scholar 

  29. H. M. Weng, X. Dai, and Z. Fang, Transition-metal pentatelluride ZrTe5 and HfTe5: A paradigm for large-gap quantum spin Hall insulators, Phys. Rev. X 4(1), 011002 (2014)

    Google Scholar 

  30. Y. D. Ma, L. Kou, X. Li, Y. Dai, S. C. Smith, and T. Heine, Quantum spin Hall effect and topological phase transition in two-dimensional square transition-metal dichalcogenides, Phys. Rev. B 92(8), 085427 (2015)

    Article  ADS  Google Scholar 

  31. Y. D. Ma, L. Kou, X. Li, Y. Dai, and T. Heine, Two-dimensional transition metal dichalcogenides with a hexagonal lattice: Room-temperature quantum spin Hall insulators, Phys. Rev. B 93(3), 035442 (2016)

    Article  ADS  Google Scholar 

  32. S. M. Nie, Z. Song, H. Weng, and Z. Fang, Quantum spin Hall effect in two-dimensional transition-metal dichalcogenide haeckelites, Phys. Rev. B 91(23), 235434 (2015)

    Article  ADS  Google Scholar 

  33. X. F. Qian, J. Liu, L. Fu, and J. Li, Quantum spin Hall effect in two-dimensional transition metal dichalcogenides, Science 346(6215), 1344 (2014)

    Article  ADS  Google Scholar 

  34. Y. D. Ma, L. Kou, X. Li, Y. Dai, and T. Heine, Room temperature quantum spin Hall states in two-dimensional crystals composed of pentagonal rings and their quantum wells, NPG Asia Mater. 8(4), e264 (2016)

    Article  Google Scholar 

  35. Z. F. Wang, N. Su, and F. Liu, Prediction of a two-dimensional organic topological insulator, Nano Lett. 13(6), 2842 (2013)

    Article  ADS  Google Scholar 

  36. B. Zhao, J. Zhang, W. Feng, Y. Yao, and Z. Yang, Quantum spin Hall and Z2 metallic states in an organic material, Phys. Rev. B 90(20), 201403 (2014)

    Article  ADS  Google Scholar 

  37. E. M. Spanton, K. C. Nowack, L. J. Du, G. Sullivan, R. R. Du, and K. A. Moler, Images of edge current in InAs/GaSb quantum wells, Phys. Rev. Lett. 113(2), 026804 (2014)

    Article  ADS  Google Scholar 

  38. L. J. Du, I. Knez, G. Sullivan, and R. R. Du, Robust helical edge transport in gated InAs/GaSb bilayers, Phys. Rev. Lett. 114(9), 096802 (2015)

    Article  ADS  Google Scholar 

  39. S. F. Wu, V. Fatemi, Q. D. Gibson, K. Watanabe, T. Taniguchi, R. J. Cava, and P. Jarillo-Herrero, Observation of the quantum spin Hall efft up to 100 kelvin in a monolayer crystal, Science 359(6371), 76 (2018)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  40. F. Reis, G. Li, L. Dudy, M. Bauernfeind, S. Glass, W. Hanke, R. Thomale, J. Schafer, and R. Claessen, Bismuthene on a SiC substrate: A candidate for a high-temperature quantum spin Hall material, Science 357(6348), 287 (2017)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  41. Z. Y. Fei, T. Palomaki, S. Wu, W. Zhao, X. Cai, B. Sun, P. Nguyen, J. Finney, X. Xu, and D. H. Cobden, Edge conduction in monolayer WTe2, Nat. Phys. 13(7), 677 (2017)

    Article  Google Scholar 

  42. S. J. Tang, C. Zhang, D. Wong, Z. Pedramrazi, H. Z. Tsai, C. Jia, B. Moritz, M. Claassen, H. Ryu, S. Kahn, J. Jiang, H. Yan, M. Hashimoto, D. Lu, R. G. Moore, C. C. Hwang, C. Hwang, Z. Hussain, Y. Chen, M. M. Ugeda, Z. Liu, X. Xie, T. P. Devereaux, M. F. Crommie, S. K. Mo, and Z. X. Shen, Quantum spin Hall state in monolayer 1T’-WTe2, Nat. Phys. 13(7), 683 (2017)

    Article  Google Scholar 

  43. A. Roth, C. Brne, H. Buhmann, L. W. Molenkamp, J. Maciejko, X. L. Qi, and S. C. Zhang, Nonlocal transport in the quantum spin Hall state, Science 325(5938), 294 (2009)

    Article  ADS  Google Scholar 

  44. I. Knez, C. T. Rettner, S. H. Yang, S. S. P. Parkin, L. J. Du, R. R. Du, and G. Sullivan, Observation of edge transport in the disordered regime of topologically insulating InAs/GaSb quantum wells, Phys. Rev. Lett. 112(2), 026602 (2014)

    Article  ADS  Google Scholar 

  45. J. J. Zhou, T. Zhou, S.-G. Cheng, H. Jiang, and Z. Q. Yang, Engineering topological quantum dot through planar magnetization in bismuthene, arxiv: 1812.11514 (2018)

    Google Scholar 

  46. L. Fu and C. L. Kane, Topological insulators with inversion symmetry, Phys. Rev. B 76(4), 045302 (2007)

    Article  ADS  Google Scholar 

  47. D. Hsieh, D. Qian, L. Wray, Y. Xia, Y. S. Hor, R. J. Cava, and M. Z. Hasan, A topological Dirac insulator in a quantum spin Hall phase, Nature 452(7190), 970 (2008)

    Article  ADS  Google Scholar 

  48. H. Zhang, C. X. Liu, X. L. Qi, X. Dai, Z. Fang, and S. C. Zhang, Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface, Nat. Phys. 5(6), 438 (2009)

    Article  Google Scholar 

  49. Y. Xia, D. Qian, D. Hsieh, L. Wray, A. Pal, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava, and M. Z. Hasan, Observation of a large-gap topological-insulator class with a single Dirac cone on the surface, Nat. Phys. 5(6), 398 (2009)

    Article  Google Scholar 

  50. D. Hsieh, Y. Xia, L. Wray, D. Qian, A. Pal, J. H. Dil, J. Osterwalder, F. Meier, G. Bihlmayer, C. L. Kane, Y. S. Hor, R. J. Cava, and M. Z. Hasan, Observation of unconventional quantum spin textures in topological insulators, Science 323(5916), 919 (2009)

    Article  ADS  Google Scholar 

  51. Y. L. Chen, J. G. Analytis, J. H. Chu, Z. K. Liu, S.K. Mo, X. L. Qi, H. J. Zhang, D. H. Lu, X. Dai, Z. Fang, S. C. Zhang, I. R. Fisher, Z. Hussain, and Z. X. Shen, Experimental realization of a three-dimensional topological insulator Bi2Te3, Science 325(5937), 178 (2009)

    Article  ADS  Google Scholar 

  52. J. S. Zhang, C. Z. Chang, Z. C. Zhang, J. Wen, X. Feng, K. Li, M. H. Liu, K. He, L. L. Wang, X. Chen, Q. K. Xue, X. C. Ma, and Y. Y. Wang, Band structure engineering in (Bi1−xSbx)2Te3 ternary topological insulators, Nat. Commun. 2(1), 574 (2011)

    Article  ADS  Google Scholar 

  53. D. Kim, S. Cho, N. P. Butch, P. Syers, K. Kirshenbaum, S. Adam, J. Paglione, and M. S. Fuhrer, Surface conduction of topological Dirac electrons in bulk insulating Bi Bi2Se3, Nat. Phys. 8(6), 459 (2012)

    Article  Google Scholar 

  54. Y. Xu, I. Miotkowski, C. Liu, J. F. Tian, H. Nam, N. Alidoust, J. N. Hu, C. K. Shih, M. Z. Hasan, and Y. P. Chen, Observation of topological surface state quantum Hall effect in an intrinsic three-dimensional topological insulator, Nat. Phys. 10(12), 956 (2014)

    Article  Google Scholar 

  55. D. A. Kozlov, Z. D. Kvon, E. B. Olshanetsky, N. N. Mikhailov, S. A. Dvoretsky, and D. Weiss, Transport properties of a 3D topological insulator based on a strained high-mobility HgTe film, Phys. Rev. Lett. 112(19), 196801 (2014)

    Article  ADS  Google Scholar 

  56. J. Liao, Y. B. Ou, X. Feng, S. Yang, C. J. Lin, W. M. Yang, K. H. Wu, K. He, X. C. Ma, Q. K. Xue, and Y. Q. Li, Observation of Anderson localization in ultrathin films of three-dimensional topological insulators, Phys. Rev. Lett. 114(21), 216601 (2015)

    Article  ADS  Google Scholar 

  57. H. C. Wang, H. W. Liu, C. Z. Chang, H. K. Zuo, Y. F. Zhao, Y. Sun, Z. C. Xia, K. He, X. C. Ma, X. C. Xie, Q. K. Xue, and J. Wang, Crossover between weak antilocalization and weak localization of bulk states in ultrathin Bi2Se3 films, Sci. Rep. 4(1), 5817 (2015)

    Article  Google Scholar 

  58. D. Hsieh, Y. Xia, D. Qian, L. Wray, J. H. Dil, F. Meier, J. Osterwalder, L. Patthey, J. G. Checkelsky, N. P. Ong, A. V. Fedorov, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava, and M. Z. Hasan, A tunable topological insulator in the spin helical Dirac transport regime, Nature 460(7259), 1101 (2009)

    Article  ADS  Google Scholar 

  59. L. Fu, Topological crystalline insulators, Phys. Rev. Lett. 106(10), 106802 (2011)

    Article  ADS  Google Scholar 

  60. C. K. Chiu, J. C. Y. Teo, A. P. Schnyder, and S. Ryu, Classification of topological quantum matter with symmetries, Rev. Mod. Phys. 88(3), 035005 (2016)

    Article  ADS  Google Scholar 

  61. S. Chakravarty and A. Schmid, Weak localization: The quasiclassical theory of electrons in a random potential, Phys. Rep. 140(4), 193 (1986)

    Article  ADS  Google Scholar 

  62. A. Stern, Y. Aharonov, and Y. Imry, Phase uncertainty and loss of interference: A general picture, Phys. Rev. A 41(7), 3436 (1990)

    Article  ADS  Google Scholar 

  63. H. Jiang, S. Cheng, Q. F. Sun, and X. C. Xie, Topological insulator: A new quantized spin Hall resistance robust to dephasing, Phys. Rev. Lett. 103(3), 036803 (2009)

    Article  ADS  Google Scholar 

  64. I. Zutic, J. Fabian, and S. Das Sarma, Spintronics: Fundamentals and applications, Rev. Mod. Phys. 76(2), 323 (2004)

    Article  ADS  Google Scholar 

  65. J. Fabian, A. Matos-Abiague, C. Ertler, P. Stano, and I. Zutic, Semiconductor spintronics, Acta Phys. Slovaca 57(4–5), 565 (2007)

    ADS  Google Scholar 

  66. T. L. Schmidt, S. Rachel, F. von Oppen, and L. I. Glazman, Inelastic electron backscattering in a generic helical edge channel, Phys. Rev. Lett. 108(15), 156402 (2012)

    Article  ADS  Google Scholar 

  67. J. I. Väyrynen, M. Goldstein, and L. I. Glazman, Helical edge resistance introduced by charge puddles, Phys. Rev. Lett. 110(21), 216402 (2013)

    Article  ADS  Google Scholar 

  68. J. C. Budich, F. Dolcini, P. Recher, and B. Trauzettel, Phonon-induced backscattering in helical edge states, Phys. Rev. Lett. 108(8), 086602 (2012)

    Article  ADS  Google Scholar 

  69. J. J. Qi, H. W. Liu, H. Jiang, and X. C. Xie, Effective spin dephasing mechanism in confined two-dimensional topological insulators, Sci. China Phys. Mech. Astron. 59(7), 677811 (2016)

    Article  Google Scholar 

  70. H. W. Liu, H. Jiang, Q. F. Sun, and X. C. Xie, Dephasing effect on backscattering of helical surface states in 3D topological insulators, Phys. Rev. Lett. 113(4), 046805 (2014)

    Article  ADS  Google Scholar 

  71. J. Liao, Y. B. Ou, H. W. Liu, K. He, X. C. Ma, Q. K. Xue, and Y. Q. Li, Enhanced electron dephasing in three-dimensional topological insulators, Nat. Commun. 8(1), 16071 (2017)

    Article  ADS  Google Scholar 

  72. C. Wu, B. A. Bernevig, and S. C. Zhang, Helical liquid and the edge of quantum spin Hall systems, Phys. Rev. Lett. 96(10), 106401 (2006)

    Article  ADS  Google Scholar 

  73. Q. F. Sun, J. Wang, and H. Guo, Quantum transport theory for nanostructures with Rashba spin–orbital interaction, Phys. Rev. B 71(16), 165310 (2005)

    Article  ADS  Google Scholar 

  74. Y. Meir and N. S. Wingreen, Landauer formula for the current through an interacting electron region, Phys. Rev. Lett. 68(16), 2512 (1992)

    Article  ADS  Google Scholar 

  75. A. P. Jauho, N. S. Wingreen, and Y. Meir, Time-dependent transport in interacting and noninteracting resonant-tunneling systems, Phys. Rev. B 50(8), 5528 (1994)

    Article  ADS  Google Scholar 

  76. S. Datta, Electronic Transport in Mesoscopic Systems, Cambridge: Cambridge University Press, 1995

    Book  Google Scholar 

  77. M. Büttiker, Role of quantum coherence in series resistors, Phys. Rev. B 33(5), 3020 (1986)

    Article  ADS  Google Scholar 

  78. Y. X. Xing, Q. F. Sun, and J. Wang, Inuence of dephasing on the quantum Hall effect and the spin Hall effect, Phys. Rev. B 77(11), 115346 (2008)

    Article  ADS  Google Scholar 

  79. E. J. Koop, B. J. van Wees, D. Reuter, A. D. Wieck, and C. H. van der Wal, Spin accumulation and spin relaxation in a large open quantum dot, Phys. Rev. Lett. 101(5), 056602 (2008)

    Article  ADS  Google Scholar 

  80. S. M. Frolov, A. Venkatesan, W. Yu, J. A. Folk, and W. Wegscheider, Electrical generation of pure spin currents in a two-dimensional electron gas, Phys. Rev. Lett. 102(11), 116802 (2009)

    Article  ADS  Google Scholar 

  81. Q. F. Sun, Y. X. Xing, and S. Q. Shen, Double quantum dot as detector of spin bias, Phys. Rev. B 77(19), 195313 (2008)

    Article  ADS  Google Scholar 

  82. Y. X. Xing, Q. F. Sun, and J. Wang, Spin bias measurement based on a quantum point contact, Appl. Phys. Lett. 93(14), 142107 (2008)

    Article  ADS  Google Scholar 

  83. Y. K. Kato, R. C. Myers, A. C. Gossard, and D. D. Awschalom, Observation of the spin Hall effect in Semiconductors, Science 306(5703), 1910 (2004)

    Article  ADS  Google Scholar 

  84. V. Sih, W. H. Lau, R. C. Myers, V. R. Horowitz, A. C. Gossard, and D. D. Awschalom, Generating spin currents in semiconductors with the spin Hall effect, Phys. Rev. Lett. 97(9), 096605 (2006)

    Article  ADS  Google Scholar 

  85. M. König, M. Baenninger, A. G. F. Garcia, N. Harjee, B. L. Pruitt, C. Ames, P. Leubner, C. Brüne, H. Buhmann, L. W. Molenkamp, and D. Goldhaber-Gordon, Spatially resolved study of backscattering in the quantum spin Hall state, Phys. Rev. X 3, 021003 (2013)

    Google Scholar 

  86. R. Jackiw and C. Rebbi, Solitons with fermion number 1/2, Phys. Rev. D 13(12), 3398 (1976)

    Article  ADS  MathSciNet  Google Scholar 

  87. F. Zhang, C. L. Kane, and E. J. Mele, Surface states of topological insulators, Phys. Rev. B 86(8), 081303 (2012)

    Article  ADS  Google Scholar 

  88. W. Y. Shan, J. Lu, H. Z. Lu, and S. Q. Shen, Vacancy-induced bound states in topological insulators, Phys. Rev. B 84(3), 035307 (2011)

    Article  ADS  Google Scholar 

  89. A. Ström, H. Johannesson, and G. I. Japaridze, Edge dynamics in a quantum spin Hall state: Effects from Rashba spin–orbit interaction, Phys. Rev. Lett. 104(25), 256804 (2010)

    Article  ADS  Google Scholar 

  90. J. Fabian and S. Das Sarma, Phonon-induced spin relaxation of conduction electrons in aluminum, Phys. Rev. Lett. 83(6), 1211 (1999)

    Article  ADS  Google Scholar 

  91. G. Grimvall, Electron–Phonon Interaction in Metals, North-Holland Pub, 1981

    Google Scholar 

  92. K. Saha and I. Garate, Phonon-induced topological insulation, Phys. Rev. B 89(20), 205103 (2014)

    Article  ADS  Google Scholar 

  93. E. Lhuillier, S. Keuleyan, and P. Guyot-Sionnest, Optical properties of HgTe colloidal quantum dots, Nanotechnology 23(17), 175705 (2012)

    Article  ADS  Google Scholar 

  94. A. Fasolino, E. Molinari, and J. C. Maan, Calculated superlattice and interface phonons of InAs/GaSb superlattices, Phys. Rev. B 33(12), 8889 (1986)

    Article  ADS  Google Scholar 

  95. D. Hernangómez-Pérez, J. Ulrich, S. Florens, and T. Champel, Spectral properties and local density of states of disordered quantum Hall systems with Rashba spin–orbit coupling, Phys. Rev. B 88(24), 245433 (2013)

    Article  ADS  Google Scholar 

  96. S. Y. Xu, Y. Xia, L. A. Wray, S. Jia, F. Meier, J. H. Dil, J. Osterwalder, B. Slomski, A. Bansil, H. Lin, R. J. Cava, and M. Z. Hasan, Topological phase transition and texture inversion in a tunable topological insulator, Science 332(6029), 560 (2011)

    Article  ADS  Google Scholar 

  97. T. Sato, K. Segawa, K. Kosaka, S. Souma, K. Nakayama, K. Eto, T. Minami, Y. Ando, and T. Takahashi, Unexpected mass acquisition of Dirac fermions at the quantum phase transition of a topological insulator, Nat. Phys. 7(11), 840 (2011)

    Article  Google Scholar 

  98. S. Y. Xu, M. Neupane, C. Liu, D. M. Zhang, A. Richardella, L. A. Wray, N. Alidoust, M. Leandersson, T. Balasubramanian, J. Snchez-Barriga, O. Rader, G. Landolt, B. Slomski, J. H. Dil, J. Osterwalder, T. R. Chang, H. T. Jeng, H. Lin, A. Bansil, N. Samarth, and M. Z. Hasan, Hedgehog spin texture and Berrys phase tuning in a magnetic topological insulator, Nat. Phys. 8(8), 616 (2012)

    Article  Google Scholar 

  99. S. Souma, M. Komatsu, M. Nomura, T. Sato, A. Takayama, T. Takahashi, K. Eto, K. Segawa, and Y. Ando, Spin polarization of gapped Dirac surface states near the topological phase transition in TlBi(S1−xSex)2, Phys. Rev. Lett. 109(18), 186804 (2012)

    Article  ADS  Google Scholar 

  100. B. L. Altshuler and A. G. Aronov, Electron–Electron Interactions in Disordered Systems, edited by A. L. Efros and M. Pollak, Elsevier, Amsterdam, 1985

  101. D. Belitz and S. Das Sarma, Inelastic phase-coherence time in thin metal films, Phys. Rev. B 36(14), 7701 (1987)

    Article  ADS  Google Scholar 

  102. V. B. Berestetskii, E. M. Lifshits, and L. P. Pitaevskii, Quantum Electrodynamics, Elsevier, Oxford, 1971

    Google Scholar 

  103. Y. Imry, Introduction to Mesoscopic Physics, Oxford University Press, 2008

    Google Scholar 

  104. B. L. Altshuler, A. G. Aronov, and D. E. Khmelnitsky, Effects of electron–electron collisions with small energy transfers on quantum localisation, J. Phys. C Solid State Phys. 15(36), 7367 (1982)

    Article  ADS  Google Scholar 

  105. B. I. Shklovskii and A. L. Efros, Electron Properties of Doped Semiconductors, Springer Science and Business Media, 2013

    Google Scholar 

  106. S. Malzard, C. Poli, and H. Schomerus, Topologically protected defect states in open photonic systems with non-Hermitian charge-conjugation and parity-time symmetry, Phys. Rev. Lett. 115(20), 200402 (2015)

    Article  ADS  Google Scholar 

  107. P. San-Jose, J. Cayao, E. Prada, and R. Aguado, Majorana bound states from exceptional points in non-topological superconductors, Sci. Rep. 6(1), 21427 (2016)

    Article  ADS  Google Scholar 

  108. T. E. Lee, Anomalous edge state in a non-Hermitian lattice, Phys. Rev. Lett. 116(13), 133903 (2016)

    Article  ADS  Google Scholar 

  109. D. Leykam, K. Y. Bliokh, C. Huang, Y. D. Chong, and F. Nori, Edge modes, degeneracies, and topological numbers in non-Hermitian systems, Phys. Rev. Lett. 118(4), 040401 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  110. Y. Xu, S. T. Wang, and L. M. Duan, Weyl exceptional rings in a three-dimensional dissipative cold atomic gas, Phys. Rev. Lett. 118(4), 045701 (2017)

    Article  ADS  Google Scholar 

  111. Z. P. Gong, Y. Ashida, K. Kawabata, K. Takasan, S. Higashikawa, and M. Ueda, Topological phases of non-Hermitian systems, Phys. Rev. X 8(3), 031079 (2018)

    Google Scholar 

  112. H. Jiang, C. Yang, and S. Chen, Topological invariants and phase diagrams for one-dimensional two-band non-Hermitian systems without chiral symmetry, Phys. Rev. A 98(5), 052116 (2018)

    Article  ADS  Google Scholar 

  113. S. Y. Yao and Z. Wang, Edge states and topological invariants of non-Hermitian systems, Phys. Rev. Lett. 121(8), 086803 (2018)

    Article  ADS  Google Scholar 

  114. S. Y. Yao, F. Song, and Z. Wang, Non-Hermitian Chern bands, Phys. Rev. Lett. 121(13), 136802 (2018)

    Article  ADS  Google Scholar 

  115. Private communication with Y. Y. Wang.

  116. F. Evers and A. D. Mirlin, Anderson transitions, Rev. Mod. Phys. 80(4), 1355 (2008)

    Article  ADS  Google Scholar 

  117. J. J. Qi, H. W. Liu, C. Z. Chen, H. Jiang, and X. C. Xie, Quantum to classical crossover under dephasing effects in a two-dimensional percolation model, arxiv: 1903.01764 (2019)

    Google Scholar 

  118. 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(16), 165316 (2009)

    Article  ADS  Google Scholar 

  119. D. W. Xu, J. J. Qi, J. Liu, X. C. Sacksteder, X. C. Xie, and H. Jiang, Phase structure of the topological Anderson insulator, Phys. Rev. B 85(19), 195140 (2012)

    Article  ADS  Google Scholar 

  120. C. Z. Chen, H. W. Liu, H. Jiang, Q. F. Sun, Z. Q. Wang, and X. C. Xie, Tunable Anderson metal-insulator transition in quantum spin-Hall insulators, Phys. Rev. B 91(21), 214202 (2015)

    Article  ADS  Google Scholar 

  121. C. Z. Chen, J. T. Song, H. Jiang, Q. F. Sun, Z. Q. Wang, and X. C. Xie, Disorder and metal-insulator transitions in Weyl semimetals, Phys. Rev. Lett. 115(24), 246603 (2015)

    Article  ADS  Google Scholar 

  122. C. Z. Chen, H. Liu, and X. C. Xie, Effects of random domains on the zero Hall plateau in the quantum anomalous Hall effect, Phys. Rev. Lett. 122(2), 026601 (2019)

    Article  ADS  Google Scholar 

  123. Y. Ando and L. Fu, Topological crystalline insulators and topological superconductors: From concepts to materials, Annu. Rev. Condens. Matter Phys. 6(1), 361 (2015)

    Article  ADS  Google Scholar 

  124. B. H. Yan and C. Felser, Topological materials: Weyl semimetals, Annu. Rev. Condens. Matter Phys. 8(1), 337 (2017)

    Article  ADS  Google Scholar 

  125. W. A. Benalcazar, B. A. Bernevig, and T. L. Hughes, Quantized electric multipole insulators, Science 357(6346), 61 (2017)

    Article  ADS  MathSciNet  MATH  Google Scholar 

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We are grateful to Y. Q. Li, Q. F. Sun and S. G. Cheng for collaboration and for their important contributions reviewed in this paper. This work was supported by the National Natural Science Foundation of China (Grant Nos. 11534001, 11822407, and 11674028), NBRPC (Grant Nos. 2017YFA0303301 and 2017YFA0304600), and NSF of Jiangsu Province, China (Grant No. BK20160007). H. Jiang was also funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions.

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Qi, J., Liu, H., Jiang, H. et al. Dephasing effects in topological insulators. Front. Phys. 14, 43403 (2019). https://doi.org/10.1007/s11467-019-0907-2

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