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Chiral edge state coupling theory of transport in quantum anomalous Hall insulators

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Abstract

The quantum anomalous Hall effect is characterized by a quantized Hall resistance with a vanishing longitudinal resistance. Many experiments reported the quantization of the Hall resistance, which is always accompanied by a non-vanishing longitudinal resistance that is several kΩ. Meanwhile, the non-vanishing longitudinal resistance exhibits a universal exponential decay with the increase in magnetic field. We propose that the coupling of chiral edge states, which has not been properly evaluated in the previous theories, can give rise to the non-vanishing longitudinal resistance. The coupling between the chiral edges states along the opposite boundaries can be assisted by magnetic domains or defects inside the sample bulk, which has been already identified in recent experiments. Our theory provides a potential mechanism to understand the experimental result in both magnetic topological insulator and moiré superlattice systems.

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References

  1. 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, Science 340, 167 (2013).

    Article  ADS  Google Scholar 

  2. N. Nagaosa, J. Sinova, S. Onoda, A. H. MacDonald, and N. P. Ong, Rev. Mod. Phys. 82, 1539 (2010).

    Article  ADS  Google Scholar 

  3. R. Yu, W. Zhang, H. J. Zhang, S. C. Zhang, X. Dai, and Z. Fang, Science 329, 61 (2010).

    Article  ADS  Google Scholar 

  4. C. X. Liu, S. C. Zhang, and X. L. Qi, Annu. Rev. Condens. Matter Phys. 7, 301 (2016).

    Article  ADS  Google Scholar 

  5. C. Z. Chang, C. X. Liu, and A. H. MacDonald, Rev. Mod. Phys. 95, 011002 (2023).

    Article  ADS  Google Scholar 

  6. H. Chi, and J. S. Moodera, APL Mater. 10, 090903 (2022).

    Article  ADS  Google Scholar 

  7. W. B. Dai, H. Li, D. H. Xu, C. Z. Chen, and X. C. Xie, Phys. Rev. B 106, 245425 (2022).

    Article  ADS  Google Scholar 

  8. T. Devakul, and L. Fu, Phys. Rev. X 12, 021031 (2022).

    Google Scholar 

  9. J. Henk, M. Flieger, I. V. Maznichenko, I. Mertig, A. Ernst, S. V. Eremeev, and E. V. Chulkov, Phys. Rev. Lett. 109, 076801 (2012).

    Article  ADS  Google Scholar 

  10. H. Jiang, Z. Qiao, H. Liu, and Q. Niu, Phys. Rev. B 85, 045445 (2012).

    Article  ADS  Google Scholar 

  11. K. Jiang, S. Zhou, X. Dai, and Z. Wang, Phys. Rev. Lett. 120, 157205 (2018).

    Article  ADS  Google Scholar 

  12. J. Jiang, D. Xiao, F. Wang, J. H. Shin, D. Andreoli, J. Zhang, R. Xiao, Y. F. Zhao, M. Kayyalha, L. Zhang, K. Wang, J. Zang, C. Liu, N. Samarth, M. H. W. Chan, and C. Z. Chang, Nat. Mater. 19, 732 (2020).

    Article  ADS  Google Scholar 

  13. M. Kawamura, M. Mogi, R. Yoshimi, T. Morimoto, K. S. Takahashi, A. Tsukazaki, N. Nagaosa, M. Kawasaki, and Y. Tokura, Nat. Phys. 19, 333 (2023).

    Article  Google Scholar 

  14. Y. H. Li, and R. Cheng, Phys. Rev. Lett. 126, 026601 (2021).

    Article  ADS  Google Scholar 

  15. Z. Li, Y. Han, and Z. Qiao, Phys. Rev. Lett. 129, 036801 (2022).

    Article  ADS  Google Scholar 

  16. S. Li, T. Liu, C. Liu, Y. Wang, H. Z. Lu, and X. C. Xie, Natl. Sci. Rev. nwac296 (2023).

  17. X. Liu, H. C. Hsu, and C. X. Liu, Phys. Rev. Lett. 111, 086802 (2013).

    Article  ADS  Google Scholar 

  18. F. Qin, C. H. Lee, and R. Chen, Phys. Rev. B 106, 235405 (2022).

    Article  ADS  Google Scholar 

  19. Y. Okazaki, T. Oe, M. Kawamura, R. Yoshimi, S. Nakamura, S. Takada, M. Mogi, K. S. Takahashi, A. Tsukazaki, M. Kawasaki, Y. Tokura, and N. H. Kaneko, Nat. Phys. 18, 25 (2022).

    Article  Google Scholar 

  20. H. Polshyn, J. Zhu, M. A. Kumar, Y. Zhang, F. Yang, C. L. Tschirhart, M. Serlin, K. Watanabe, T. Taniguchi, A. H. MacDonald, and A. F. Young, Nature 588, 66 (2020).

    Article  ADS  Google Scholar 

  21. S. Qi, Z. Qiao, X. Deng, E. D. Cubuk, H. Chen, W. Zhu, E. Kaxiras, S. B. Zhang, X. Xu, and Z. Zhang, Phys. Rev. Lett. 117, 056804 (2016).

    Article  ADS  Google Scholar 

  22. J. X. Qiu, C. Tzschaschel, J. Ahn, A. Gao, H. Li, X. Y. Zhang, B. Ghosh, C. Hu, Y. X. Wang, Y. F. Liu, D. Bérubé, T. Dinh, Z. Gong, S. W. Lien, S. C. Ho, B. Singh, K. Watanabe, T. Taniguchi, D. C. Bell, H. Z. Lu, A. Bansil, H. Lin, T. R. Chang, B. B. Zhou, Q. Ma, A. Vishwanath, N. Ni, and S. Y. Xu, Nat. Mater. 22, 583 (2023).

    Article  ADS  Google Scholar 

  23. J. Wang, B. Lian, H. Zhang, Y. Xu, and S. C. Zhang, Phys. Rev. Lett. 111, 136801 (2013).

    Article  ADS  Google Scholar 

  24. J. Wang, B. Lian, and S. C. Zhang, Phys. Rev. Lett. 115, 036805 (2015).

    Article  ADS  Google Scholar 

  25. S. W. Wang, D. Xiao, Z. Dou, M. Cao, Y. F. Zhao, N. Samarth, C. Z. Chang, M. R. Connolly, and C. G. Smith, Phys. Rev. Lett. 125, 126801 (2020).

    Article  ADS  Google Scholar 

  26. P. Wang, J. Ge, J. Li, Y. Liu, Y. Xu, and J. Wang, Innovation 2, 100098 (2021).

    Google Scholar 

  27. Y. Wang, X. M. Ma, Z. Hao, Y. Cai, H. Rong, F. Zhang, W. Chen, C. Zhang, J. Lin, Y. Zhao, C. Liu, Q. Liu, and C. Chen, Natl. Sci. Rev. nwad066 (2023).

  28. J. Wu, J. Liu, and X. J. Liu, Phys. Rev. Lett. 113, 136403 (2014).

    Article  ADS  Google Scholar 

  29. D. Xiao, J. Jiang, J. H. Shin, W. Wang, F. Wang, Y. F. Zhao, C. Liu, W. Wu, M. H. W. Chan, N. Samarth, and C. Z. Chang, Phys. Rev. Lett. 120, 056801 (2018).

    Article  ADS  Google Scholar 

  30. R. Chen, H. P. Sun, and B. Zhou, Phys. Rev. B 107, 125304 (2023).

    Article  ADS  Google Scholar 

  31. Y. F. Zhao, R. Zhang, R. Mei, L. J. Zhou, H. Yi, Y. Q. Zhang, J. Yu, R. Xiao, K. Wang, N. Samarth, M. H. W. Chan, C. X. Liu, and C. Z. Chang, Nature 588, 419 (2020).

    Article  ADS  Google Scholar 

  32. Y. F. Zhao, R. Zhang, L. J. Zhou, R. Mei, Z. J. Yan, M. H. W. Chan, C. X. Liu, and C. Z. Chang, Phys. Rev. Lett. 128, 216801 (2022).

    Article  ADS  Google Scholar 

  33. C. Z. Chen, J. Qi, D. H. Xu, and X. C. Xie, Sci. China-Phys. Mech. Astron. 64, 127211 (2021).

    Article  ADS  Google Scholar 

  34. J. Qi, H. Liu, C. Z. Chen, H. Jiang, and X. C. Xie, Sci. China-Phys. Mech. Astron. 63, 227811 (2020).

    Article  ADS  Google Scholar 

  35. J. G. Checkelsky, R. Yoshimi, A. Tsukazaki, K. S. Takahashi, Y. Kozuka, J. Falson, M. Kawasaki, and Y. Tokura, Nat. Phys. 10, 731 (2014).

    Article  Google Scholar 

  36. X. Kou, S. T. Guo, Y. Fan, L. Pan, M. Lang, Y. Jiang, Q. Shao, T. Nie, K. Murata, J. Tang, Y. Wang, L. He, T. K. Lee, W. L. Lee, and K. L. Wang, Phys. Rev. Lett. 113, 137201 (2014).

    Article  ADS  Google Scholar 

  37. A. J. Bestwick, E. J. Fox, X. Kou, L. Pan, K. L. Wang, and D. Goldhaber-Gordon, Phys. Rev. Lett. 114, 187201 (2015).

    Article  ADS  Google Scholar 

  38. T. Li, S. Jiang, B. Shen, Y. Zhang, L. Li, Z. Tao, T. Devakul, K. Watanabe, T. Taniguchi, L. Fu, J. Shan, and K. F. Mak, Nature 600, 641 (2021).

    Article  ADS  Google Scholar 

  39. C. Z. Chang, W. Zhao, D. Y. Kim, H. Zhang, B. A. Assaf, D. Heiman, S. C. Zhang, C. Liu, M. H. W. Chan, and J. S. Moodera, Nat. Mater. 14, 473 (2015).

    Article  ADS  Google Scholar 

  40. W. Wang, Y. Ou, C. Liu, Y. Wang, K. He, Q. K. Xue, and W. Wu, Nat. Phys. 14, 791 (2018).

    Article  Google Scholar 

  41. J. Wang, B. Lian, H. Zhang, and S. C. Zhang, Phys. Rev. Lett. 111, 086803 (2013).

    Article  ADS  Google Scholar 

  42. W. Lin, Y. Feng, Y. Wang, Z. Lian, H. Li, Y. Wu, C. Liu, Y. Wang, J. Zhang, Y. Wang, X. Zhou, and J. Shen, Phys. Rev. B 105, 165411 (2022).

    Article  ADS  Google Scholar 

  43. G. Lippertz, A. Bliesener, A. Uday, L. M. C. Pereira, A. A. Taskin, and Y. Ando, Phys. Rev. B 106, 045419 (2022).

    Article  ADS  Google Scholar 

  44. I. T. Rosen, M. P. Andersen, L. K. Rodenbach, L. Tai, P. Zhang, K. L. Wang, M. A. Kastner, and D. Goldhaber-Gordon, Phys. Rev. Lett. 129, 246602 (2022).

    Article  ADS  Google Scholar 

  45. E. J. Fox, I. T. Rosen, Y. Yang, G. R. Jones, R. E. Elmquist, X. Kou, L. Pan, K. L. Wang, and D. Goldhaber-Gordon, Phys. Rev. B 98, 075145 (2018).

    Article  ADS  Google Scholar 

  46. L. K. Rodenbach, I. T. Rosen, E. J. Fox, P. Zhang, L. Pan, K. L. Wang, M. A. Kastner, and D. Goldhaber-Gordon, APL Mater. 9, 081116 (2021).

    Article  ADS  Google Scholar 

  47. K. M. Fijalkowski, N. Liu, P. Mandal, S. Schreyeck, K. Brunner, C. Gould, and L. W. Molenkamp, Nat. Commun. 12, 5599 (2021).

    Article  ADS  Google Scholar 

  48. K. He, Physics 8, 41 (2015).

    Article  Google Scholar 

  49. B. Zhou, H. Z. Lu, R. L. Chu, S. Q. Shen, and Q. Niu, Phys. Rev. Lett. 101, 246807 (2008).

    Article  ADS  Google Scholar 

  50. R. Chen, and B. Zhou, Chin. Phys. B 25, 067204 (2016).

    Article  Google Scholar 

  51. H. Jiang, H. Liu, J. Feng, Q. Sun, and X. C. Xie, Phys. Rev. Lett. 112, 176601 (2014).

    Article  ADS  Google Scholar 

  52. J. Linder, T. Yokoyama, and A. Sudbø, Phys. Rev. B 80, 205401 (2009).

    Article  ADS  Google Scholar 

  53. Y. Zhang, K. He, C. Z. Chang, C. L. Song, L. L. Wang, X. Chen, J. F. Jia, Z. Fang, X. Dai, W. Y. Shan, S. Q. Shen, Q. Niu, X. L. Qi, S. C. Zhang, X. C. Ma, and Q. K. Xue, Nat. Phys. 6, 584 (2010).

    Article  Google Scholar 

  54. H. Z. Lu, W. Y. Shan, W. Yao, Q. Niu, and S. Q. Shen, Phys. Rev. B 81, 115407 (2010).

    Article  ADS  Google Scholar 

  55. C. X. Liu, H. J. Zhang, B. Yan, X. L. Qi, T. Frauenheim, X. Dai, Z. Fang, and S. C. Zhang, Phys. Rev. B 81, 041307 (2010).

    Article  ADS  Google Scholar 

  56. K. I. Imura, M. Okamoto, Y. Yoshimura, Y. Takane, and T. Ohtsuki, Phys. Rev. B 86, 245436 (2012).

    Article  ADS  Google Scholar 

  57. Y. Takane, J. Phys. Soc. Jpn. 85, 124711 (2016).

    Article  ADS  Google Scholar 

  58. R. Chen, D. H. Xu, and B. Zhou, Phys. Rev. B 95, 245305 (2017).

    Article  ADS  Google Scholar 

  59. Z. Wang, Y. Sun, X. Q. Chen, C. Franchini, G. Xu, H. Weng, X. Dai, and Z. Fang, Phys. Rev. B 85, 195320 (2012).

    Article  ADS  Google Scholar 

  60. Z. Wang, H. Weng, Q. Wu, X. Dai, and Z. Fang, Phys. Rev. B 88, 125427 (2013).

    Article  ADS  Google Scholar 

  61. X. Xiao, S. A. Yang, Z. Liu, H. Li, and G. Zhou, Sci. Rep. 5, 7898 (2015).

    Article  ADS  Google Scholar 

  62. H. Pan, M. Wu, Y. Liu, and S. A. Yang, Sci. Rep. 5, 14639 (2015).

    Article  ADS  Google Scholar 

  63. T. Schumann, L. Galletti, D. Kealhofer, H. Kim, M. Goyal, and S. Stemmer, Phys. Rev. Lett. 120, 016801 (2018).

    Article  ADS  Google Scholar 

  64. J. L. Collins, A. Tadich, W. Wu, L. C. Gomes, J. N. B. Rodrigues, C. Liu, J. Hellerstedt, H. Ryu, S. Tang, S. K. Mo, S. Adam, S. A. Yang, M. S. Fuhrer, and M. T. Edmonds, Nature 564, 390 (2018).

    Article  ADS  Google Scholar 

  65. G. Qiu, P. Zhang, P. Deng, S. K. Chong, L. Tai, C. Eckberg, and K. L. Wang, Phys. Rev. Lett. 128, 217704 (2022).

    Article  ADS  Google Scholar 

  66. L. J. Zhou, R. Mei, Y. F. Zhao, R. Zhang, D. Zhuo, Z. J. Yan, W. Yuan, M. Kayyalha, M. H. W. Chan, C. X. Liu, and C. Z. Chang, Phys. Rev. Lett. 130, 086201 (2023).

    Article  ADS  Google Scholar 

  67. P. Deng, C. Eckberg, P. Zhang, G. Qiu, E. Emmanouilidou, G. Yin, S. K. Chong, L. Tai, N. Ni, and K. L. Wang, Nat. Commun. 13, 4246 (2022).

    Article  ADS  Google Scholar 

  68. H. Z. Lu, A. Zhao, and S. Q. Shen, Phys. Rev. Lett. 111, 146802 (2013).

    Article  ADS  Google Scholar 

  69. W. Y. Shan, H. Z. Lu, and S. Q. Shen, New J. Phys. 12, 043048 (2010).

    Article  ADS  Google Scholar 

  70. C. X. Liu, X. L. Qi, H. J. Zhang, X. Dai, Z. Fang, and S. C. Zhang, Phys. Rev. B 82, 045122 (2010).

    Article  ADS  Google Scholar 

  71. H. P. Sun, C. A. Li, S. J. Choi, S. B. Zhang, H. Z. Lu, and B. Trauzettel, Phys. Rev. Res. 5, 013179 (2023).

    Article  Google Scholar 

  72. R. Landauer, Philos. Mag. 21, 863 (1970).

    Article  ADS  Google Scholar 

  73. M. Büttiker, Phys. Rev. B 38, 9375 (1988).

    Article  ADS  Google Scholar 

  74. D. S. Fisher, and P. A. Lee, Phys. Rev. B 23, 6851 (1981).

    Article  ADS  MathSciNet  Google Scholar 

  75. A. MacKinnon, Z. Phys. B-Cond. Matter 59, 385 (1985).

    Article  Google Scholar 

  76. G. Metalidis, and P. Bruno, Phys. Rev. B 72, 235304 (2005).

    Article  ADS  Google Scholar 

  77. H. Jiang, L. Wang, Q. Sun, and X. C. Xie, Phys. Rev. B 80, 165316 (2009).

    Article  ADS  Google Scholar 

  78. M. Mogi, M. Kawamura, A. Tsukazaki, R. Yoshimi, K. S. Takahashi, M. Kawasaki, and Y. Tokura, Sci. Adv. 3, eaao1669 (2017).

    Article  Google Scholar 

  79. S. Grauer, K. M. Fijalkowski, S. Schreyeck, M. Winnerlein, K. Brunner, R. Thomale, C. Gould, and L. W. Molenkamp, Phys. Rev. Lett. 118, 246801 (2017).

    Article  ADS  Google Scholar 

  80. C. Z. Chang, W. Zhao, J. Li, J. K. Jain, C. Liu, J. S. Moodera, and M. H. W. Chan, Phys. Rev. Lett. 117, 126802 (2016).

    Article  ADS  Google Scholar 

  81. Y. Feng, X. Feng, Y. Ou, J. Wang, C. Liu, L. Zhang, D. Zhao, G. Jiang, S. C. Zhang, K. He, X. Ma, Q. K. Xue, and Y. Wang, Phys. Rev. Lett. 115, 126801 (2015).

    Article  ADS  Google Scholar 

  82. C. Z. Chen, J. J. He, D. H. Xu, and K. T. Law, Phys. Rev. B 96, 041118 (2017).

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Department of Physics, Hubei University, Wuhan, 430062, China

    Rui Chen & Bin Zhou

  2. Institute for Theoretical Physics and Astrophysics, University of Würzburg, Würzburg, 97074, Germany

    Hai-Peng Sun

  3. Department of Physics and Chongqing Key Laboratory for Strongly Coupled Physics, Chongqing University, Chongqing, 400044, China

    Dong-Hui Xu

  4. Center of Quantum Materials and Devices, Chongqing University, Chongqing, 400044, China

    Dong-Hui Xu

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  1. Rui Chen
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  2. Hai-Peng Sun
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  3. Bin Zhou
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Correspondence to Bin Zhou or Dong-Hui Xu.

Additional information

Dong-Hui Xu was supported by the National Natural Science Foundation of China (Grant Nos. 12074108, and 12147102) and Natural Science Foundation of Chongqing (Grant No. CSTB2022NSCQ-MSX0568). Bin Zhou was supported by the National Natural Science Foundation of China (Grant No. 12074107), the Program of Outstanding Young and Middle-aged Scientific and Technological Innovation Team of Colleges and Universities in Hubei Province (Grant No. T2020001), and the Innovation Group Project of the Natural Science Foundation of Hubei Province of China (Grant No. 2022CFA012). Hai-Peng Sun was supported by the Würzburg-Dresden Cluster of Excellence ct.qmat, EXC2147 (Grant No. 390858490), and the Deutsche Forschungsgemeinschaft (Grant No. SFB 1170).

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Chen, R., Sun, HP., Zhou, B. et al. Chiral edge state coupling theory of transport in quantum anomalous Hall insulators. Sci. China Phys. Mech. Astron. 66, 287211 (2023). https://doi.org/10.1007/s11433-023-2115-7

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