Current carrying states in the disordered quantum anomalous Hall effect

doi:10.1088/1674-1056/ac5d2b

中国物理B ›› 2022, Vol. 31 ›› Issue (9): 97302-097302.doi: 10.1088/1674-1056/ac5d2b

Current carrying states in the disordered quantum anomalous Hall effect

Yi-Ming Dai(戴镒明)^1,2, Si-Si Wang(王思思)^1,2,3, Yan Yu(禹言)^4,5, Ji-Huan Guan(关济寰)^6,4, Hui-Hui Wang(王慧慧)^1,7,2, and Yan-Yang Zhang(张艳阳)^1,7,2,3,†

1 School of Physics and Materials Science, Guangzhou University, Guangzhou 510006, China;
2 Research Center for Advanced Information Materials, Guangzhou University, Guangzhou 510006, China;
3 School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China;
4 SKLSM, Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083, China;
5 School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China;
6 Beijing Academy of Quantum Information Sciences, Beijing 100193, China;
7 Huangpu Research and Graduate School of Guangzhou University, Guangzhou 510700, China

收稿日期:2022-01-13 修回日期:2022-03-04 接受日期:2022-03-14 出版日期:2022-08-19 发布日期:2022-09-03
通讯作者: Yan-Yang Zhang E-mail:yanyang@gzhu.edu.cn
基金资助:
This work was supported by the National Natural Science Foundation of China (Grant Nos. 11774336, 12104108, and 61427901) and the Starting Research Fund from Guangzhou University (Grant Nos. RQ2020082 and 62104360).

Current carrying states in the disordered quantum anomalous Hall effect

Yi-Ming Dai(戴镒明)^1,2, Si-Si Wang(王思思)^1,2,3, Yan Yu(禹言)^4,5, Ji-Huan Guan(关济寰)^6,4, Hui-Hui Wang(王慧慧)^1,7,2, and Yan-Yang Zhang(张艳阳)^1,7,2,3,†

1 School of Physics and Materials Science, Guangzhou University, Guangzhou 510006, China;
2 Research Center for Advanced Information Materials, Guangzhou University, Guangzhou 510006, China;
3 School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China;
4 SKLSM, Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083, China;
5 School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China;
6 Beijing Academy of Quantum Information Sciences, Beijing 100193, China;
7 Huangpu Research and Graduate School of Guangzhou University, Guangzhou 510700, China

Received:2022-01-13 Revised:2022-03-04 Accepted:2022-03-14 Online:2022-08-19 Published:2022-09-03
Contact: Yan-Yang Zhang E-mail:yanyang@gzhu.edu.cn
Supported by:
This work was supported by the National Natural Science Foundation of China (Grant Nos. 11774336, 12104108, and 61427901) and the Starting Research Fund from Guangzhou University (Grant Nos. RQ2020082 and 62104360).

摘要/Abstract

摘要： In a quantum Hall effect, flat Landau levels may be broadened by disorder. However, it has been found that in the thermodynamic limit, all extended (or current carrying) states shrink to one single energy value within each Landau level. On the other hand, a quantum anomalous Hall effect consists of dispersive bands with finite widths. We numerically investigate the picture of current carrying states in this case. With size scaling, the spectrum width of these states in each bulk band still shrinks to a single energy value in the thermodynamic limit, in a power law way. The magnitude of the scaling exponent at the intermediate disorder is close to that in the quantum Hall effects. The number of current carrying states obeys similar scaling rules, so that the density of states of current carrying states is finite. Other states in the bulk band are localized and may contribute to the formation of a topological Anderson insulator.

关键词: quantum anomalous Hall effect, Chern number, disordered system, localization

Abstract: In a quantum Hall effect, flat Landau levels may be broadened by disorder. However, it has been found that in the thermodynamic limit, all extended (or current carrying) states shrink to one single energy value within each Landau level. On the other hand, a quantum anomalous Hall effect consists of dispersive bands with finite widths. We numerically investigate the picture of current carrying states in this case. With size scaling, the spectrum width of these states in each bulk band still shrinks to a single energy value in the thermodynamic limit, in a power law way. The magnitude of the scaling exponent at the intermediate disorder is close to that in the quantum Hall effects. The number of current carrying states obeys similar scaling rules, so that the density of states of current carrying states is finite. Other states in the bulk band are localized and may contribute to the formation of a topological Anderson insulator.

Key words: quantum anomalous Hall effect, Chern number, disordered system, localization

中图分类号: (Weak or Anderson localization)

73.20.Fz

73.43.-f (Quantum Hall effects) 74.62.En (Effects of disorder)

Yi-Ming Dai(戴镒明), Si-Si Wang(王思思), Yan Yu(禹言), Ji-Huan Guan(关济寰), Hui-Hui Wang(王慧慧), and Yan-Yang Zhang(张艳阳). Current carrying states in the disordered quantum anomalous Hall effect[J]. 中国物理B, 2022, 31(9): 97302-097302.

参考文献

[1] Qi X L and Zhang S C 2011 Rev. Mod. Phys. 83 1057
[2] Hasan M Z and Kane C L 2011 Rev. Mod. Phys. 82 3045
[3] Klitzing K von, Dorda G and Pepper M 1980 Phys. Rev. Lett. 45 494
[4] Huo Y and Bhatt R N 1992 Phys. Rev. Lett. 68 1375
[5] Yang K and Bhatt R N 1996 Phys. Rev. Lett. 76 1316
[6] Yang K and Bhatt R N 1999 Phys. Rev. B 59 8144
[7] Yang K and Bhatt R N 1997 Phys. Rev. B 55 R1922(R)
[8] Xie X C, Wang X R and Xie X C 1998 Phys. Rev. Lett. 80 3563
[9] Furusaki A 1999 Phys. Rev. Lett. 82 604
[10] Haldane F D M 1988 Phys. Rev. Lett. 61 2015
[11] Liu C X Liu, Qi X L, Dai X, Fang Z and Zhang S C 2008 Phys. Rev. Lett. 101 146802
[12] Chang C Z, Zhang J, Feng X, Shen J, Zhang Z, Guo M, Li K, Ou Y, Wei P, Wang L L, Ji Z Q, Feng Y, Ji S, Chen X, Jia J, Dai X, Fang Z, Zhang S C, He K, Wang Y, Lu L, Ma X C and Xue Q K 2013 Science 340 167
[13] Bestwick A J, Fox E J, Kou X, Pan L, Wang K L and Goldhaber-Gordon D 2015 Phys. Rev. Lett. 114 187201
[14] Wang S W, Xiao D, Dou Z, Cao M, Zhao Y F, Samarth N, Chang C Z, Connolly M R and Smith C G 2020 Phys. Rev. Lett. 125 126801
[15] Li Z and Wang Z F 2020 Chin. Phys. B 29 107101
[16] Zhang Y Y, Chu R L, Zhang F C and Shen S Q 2012 Phys. Rev. B 85 035107
[17] Song Z G, Zhang Y Y, Song J T and Li S S 2016 Sci. Rep. 10 19018
[18] Wang S S, Zhang Y Y, Guan J H, Yu Y, Xia Y and Li S S 2019 Phys. Rev. B 99 125414
[19] Li H, Chen C Z, Jiang H and Xie X C 2021 Phys. Rev. Lett. 127 236402
[20] Zhang Z Q, Chen C Z, Wu Y, Jiang H, Liu J, Sun Q F and Xie X C 2021 Phys. Rev. B 103 075434
[21] Bernevig A, Hughes T and Zhang S C 2006 Science 314 1757
[22] Qi X L, Wu Y S and Zhang S C 2006 Phys. Rev. B 74 085308
[23] Boyers E, Crowley P J D, Chandran A and Sushkov A O 2020 Phys. Rev. Lett. 125 160505
[24] Xiao D, Chang M C and Niu Q 2010 Rev. Mod. Phys. 82 1959
[25] Halperin B I 1982 Phys. Rev. B 25 2185
[26] He Y, Jiang Y, Zhang T, Huang H, Fang C and Jin Z 2019 Chin. Phys. B 28 087102
[27] Liu J S, Han Y Z and Liu C S 2020 Chin. Phys. B 29 010302
[28] Bianco R and Resta R 2011 Phys. Rev. B 84 241106(R)
[29] Bianco R and Resta R 2013 Phys. Rev. Lett. 110 087202
[30] Marrazzo A and Resta R 2017 Phys. Rev. B 95 121114
[31] Ippoliti M and Bhatt R N 2020 Phys. Rev. Lett. 124 086602
[32] Qiao Z, Han Y, Zhang L, Wang K, Deng X and Jiang H 2016 Phys. Rev. Lett. 117 056802
[33] Abrahams E, Anderson P W, Licciardello D C and Ramakrishnan T V 1979 Phys. Rev. Lett. 42 673
[34] Zhang Y Y and Shen S Q 2013 Phys. Rev. B 88 195145
[35] Essin A M and Moore J E 2007 Phys. Rev. B 76 165307

Current carrying states in the disordered quantum anomalous Hall effect

Current carrying states in the disordered quantum anomalous Hall effect

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