1932

Abstract

The quantum anomalous Hall effect (QAHE) is a quantized Hall effect that occurs at zero magnetic field. Its mechanism and properties are different from those of conventional quantum Hall effects (QHEs) induced by magnetic field. The first theory of a QHE without a magnetic field was proposed in 1988. Yet, it has taken 25 years to be experimentally realized, which has now happened thanks to the development of the topological insulator—a conceptually new topological state of matter. Here, we review QAHE, beginning with the original theoretical idea and concluding with its final implementation using experimentally accessible materials. The current status and future direction of the field are also discussed.

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2018-03-10
2024-05-24
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Literature Cited

  1. Wen XG. 1.  2007. Quantum Field Theory of Many-body Systems: From the Origin of Sound to an Origin of Light and Electrons Oxford, UK: Oxford Univ. Press
  2. Tinkham M. 2.  2004. Introduction to Superconductivity New York: Dover Books. , 2nd ed..
  3. von Klitzing K, Dorda G, Peper M. 3.  1980. Phys. Rev. Lett. 45:494–97
  4. Tsui DC, Stormer HL, Gossard AC. 4.  1982. Phys. Rev. Lett. 48:1559–62
  5. Girvin SM. 5.  1990. The Quantum Hall Effect New York: Springer
  6. Thouless DJ, Kohmoto M, Nightingale MP, Nijs MD. 6.  1982. Phys. Rev. Lett. 49:405–8
  7. Avron JE, Osadchy D, Seiler R. 7.  2003. Phys. Today 56:38–42
  8. Bernevig BA, Hughes TL. 8.  2013. Topological Insulators and Topological Superconductors Princeton, NJ: Princeton Univ. Press
  9. Wen XG. 9.  2016. arXiv1610.03911
  10. Haldane FDM. 10.  1988. Phys. Rev. Lett. 61:2015–18
  11. Novoselov KS, Geim AK, Morozov SV, Jiang D, Zhang Y. 11.  et al. 2004. Science 306:666–69
  12. Nagaosa N, Sinova J, Onoda S, MacDonald AH, Ong NP. 12.  2010. Rev. Mod. Phys. 82:1539–92
  13. Onoda M, Nagaosa N. 13.  2003. Phys. Rev. Lett. 90:206601
  14. Kane CL, Mele EJ. 14.  2005. Phys. Rev. Lett. 95:146802
  15. Kane CL, Mele EJ. 15.  2005. Phys. Rev. Lett. 95:226801
  16. Bernevig BA, Zhang SC. 16.  2006. Phys. Rev. Lett. 96:106802
  17. Qi XL, Wu YS, Zhang SC. 17.  2006. Phys. Rev. B 74:085308
  18. Hasan MZ, Kane CL. 18.  2010. Rev. Mod. Phys. 82:3045–67
  19. Qi XL, Zhang SC. 19.  2011. Rev. Mod. Phys. 83:1057–110
  20. Fu L, Kane CL, Mele EJ. 20.  2007. Phys. Rev. Lett. 98:106803
  21. Moore JE, Balents L. 21.  2007. Phys. Rev. B 75:121306
  22. Roy R. 22.  2009. Phys. Rev. B 79:195321
  23. Yan B, Zhang SC. 23.  2012. Rep. Prog. Phys. 75:096501
  24. Bernevig BA, Hughes TL, Zhang SC. 24.  2006. Science 314:1757–61
  25. Liu CX, Hughes TL, Qi XL, Wang K, Zhang SC. 25.  2008. Phys. Rev. Lett. 100:236601
  26. König M, Wiedmann S, Brüne C, Roth A, Buhmann H. 26.  et al. 2007. Science 318:766–70
  27. Knez I, Du RR, Sullivan G. 27.  2011. Phys. Rev. Lett. 107:136603
  28. Nichele F, Suominen HJ, Kjaergaard M, Marcus CM, Sajadi E. 28.  et al. 2016. New J. Phys. 18:083005
  29. Fu L, Kane CL. 29.  2007. Phys. Rev. B 76:045302
  30. Hsieh D, Qian D, Wray L, Xia Y, Hor YS. 30.  et al. 2008. Nature 452:970–74
  31. Hsieh D, Xia Y, Wray L, Qian D, Pal A. 31.  et al. 2009. Science 323:919–22
  32. Zhang H, Liu CX, Qi XL, Dai X, Fang Z, Zhang SC. 32.  2009. Nat. Phys. 5:438–42
  33. Xia Y, Qian D, Hsieh D, Wray L, Pal A. 33.  et al. 2009. Nat. Phys. 5:398–402
  34. Chen YL, Analytis JG, Chu JH, Liu ZK, Mo SK. 34.  et al. 2009. Science 325:178–81
  35. Hsieh D, Xia Y, Qian D, Wray L, Dil H. 35.  et al. 2009. Nature 460:1101–5
  36. Liu CX, Qi XL, Dai X, Fang Z, Zhang SC. 36.  2008. Phys. Rev. Lett. 101:146802
  37. Qi XL, Hughes TL, Zhang SC. 37.  2008. Phys. Rev. B 78:195424
  38. Yu R, Zhang W, Zhang H J, Zhang SC, Dai X, Fang Z. 38.  2010. Science 329:61–64
  39. Nomura K, Nagaosa N. 39.  2011. Phys. Rev. Lett. 106:166802
  40. Buhmann H. 40.  2012. Bull. Am. Phys. Soc. 57:P27.1 http://meetings.aps.org/link/BAPS.2012.MAR.P27.1
  41. Liu CX, Zhang HJ, Yan B, Qi X-L, Frauenheim T. 41.  et al. 2010. Phys Rev B 81:041307
  42. Assaf BA, Cardinal T, Wei P, Katmis F, Moodera JS. 42.  et al. 2013. Appl. Phys. Lett. 102:012102
  43. Jiang Z, Chang CZ, Tang C, Zheng JG, Moodera JS. 43.  et al. 2016. AIP Adv 6:055809
  44. Katmis F, Lauter V, Nogueira FS, Assaf BA, Jamer ME. 44.  et al. 2016. Nature 533:513–16
  45. Dietl T, Ohno H, Matsukura F, Cibert J, Ferrand D. 45.  2000. Science 287:1019–22
  46. Ohno H. 46.  1998. Science 281:951–56
  47. Dietl T, Ohno H. 47.  2014. Rev. Mod. Phys. 86:187
  48. Zhang J, Chang CZ, Tang PZ, Zhang ZC, Feng X. 48.  et al. 2013. Science 339:1582–86
  49. Chien YJ. 49.  2007. Transition Metal-Doped Sb2Te3 and Bi2Te3 Diluted Magnetic Semiconductors PhD thesis, Univ. Michigan Ann Arbor:
  50. Hor YS, Roushan P, Beidenkopf H, Seo J, Qu D. 50.  et al. 2010. Phys. Rev. B 81:195203
  51. Chang CZ, Zhang J, Liu M, Zhang Z, Feng X. 51.  et al. 2013. Adv. Mater. 25:1065–70
  52. Li YY, Wang G, Zhu XG, Liu MH, Ye C. 52.  et al. 2010. Adv. Mater. 22:4002–7
  53. Song CL, Wang YL, Jiang YP, Zhang Y, Chang CZ. 53.  et al. 2010. Appl. Phys. Lett. 97:143118
  54. Zhang Y, He K, Chang CZ, Song CL, Wang LL. 54.  et al. 2010. Nat. Phys. 6:584–8
  55. Wang G, Zhu XG, Wen J, Chen X, He K. 55.  et al. 2010. Nano Res 3:874–80
  56. Wang G, Zhu XG, Sun YY, Li YY, Zhang T. 56.  et al. 2011. Adv. Mater. 2:2929–32
  57. Jiang YP, Sun YY, Chen M, Wang Y, Li Z. 57.  et al. 2012. Phys. Rev. Lett. 108:066809
  58. Zhang J, Chang CZ, Zhang ZC, Wen J, Feng X. 58.  et al. 2011. Nat. Commun. 2:574
  59. Li M, Chang CZ, Wu L, Tao J, Zhao W. 59.  et al. 2015. Phys. Rev. Lett. 114:146802
  60. Chang CZ, Zhang J, Feng X, Shen J, Zhang Z. 60.  et al. 2013. Science 340:167–70
  61. Chen J, Qin HJ, Yang F, Liu J, Guan T. 61.  et al. 2010. Phys. Rev. Lett. 105:176602
  62. Checkelsky JG, Yoshimi R, Tsukazaki A, Takahashi KS, Kozuka Y. 62.  et al. 2014. Nat. Phys. 10:731–36
  63. Kou X, Guo ST, Fan Y, Pan L, Lang M. 63.  et al. 2014. Phys. Rev. Lett. 113:137201
  64. Kandala A, Richardella A, Kempinger S, Liu CX, Samarth N. 64.  2015. Nat. Commun. 6:7434
  65. Checkelsky JG, Ye J, Onose Y, Iwasa Y, Tokura Y. 65.  2012. Nat. Phys. 8:729–33
  66. Jotzu G, Messer M, Desbuquois R, Lebrat M, Uehlinger T. 66.  et al. 2014. Nature 515:237–40
  67. Timm C. 67.  2003. J. Phys. Condens. Matter 15:R1865
  68. Das Sarma S, Hwang SH, Kaminski A. 68.  2003. Phys. Rev. B 67:155201
  69. Feng X, Feng Y, Wang J, Ou Y, Hao Z. 69.  et al. 2016. Adv. Mater. 28:6386–90
  70. Wang J, Lian B, Zhang SC. 70.  2015. Phys. Scr. T164:014003
  71. Lee I, Kima CK, Lee J, Billinge SJL, Zhong R. 71.  et al. 2015. PNAS 112:1316–21
  72. Lachman EO, Young AF, Richardella AR, Cuppens J, Naren HR. 72.  et al. 2015. Sci. Adv. 1:e1500740
  73. Liu M, Wang W, Richardella AR, Kandala A, Li J. 73.  et al. 2016. Sci. Adv. 2:e1600167
  74. Grauer S, Schreyeck S, Winnerlein M, Brunner K, Gould C. 74.  et al. 2015. Phys. Rev. B 92:201304
  75. Feng Y, Feng X, Ou Y, Wang J, Liu C. 75.  et al. 2015. Phys. Rev. Lett. 115:126801
  76. Kou X, Pan L, Wang J, Fan Y, Choi ES. 76.  et al. 2015. Nat. Commun. 6:8474
  77. Wang J, Lian B, Zhang SC. 77.  2014. Phys. Rev. B 89:085106
  78. Bestwick AJ, Fox EJ, Kou X, Pan L, Wang KL. 78.  2015. Phys. Rev. Lett. 114:187201
  79. Chang CZ, Zhao WW, Kim DY, Zhang HJ, Assaf BA. 79.  et al. 2015. Nat. Mater. 14:473–77
  80. Chang CZ, Zhao WW, Kim DY, Wei P, Jain JK. 80.  et al. 2015. Phys. Rev. Lett. 115:057206
  81. Li W, Claassen M, Chang CZ, Moritz B, Jia T. 81.  et al. 2016. Sci. Rep. 6:32732
  82. Mogi M, Yoshimi R, Tsukazaki A, Yasuda K, Kozuka Y. 82.  et al. 2015. Appl. Phys. Lett. 107:182401
  83. Ou Y, Liu C, Zhang L, Feng Y, Jiang G. 83.  et al. 2016. APL Mater 4:086101
  84. Ou Y, Liu C, Jiang G, Feng Y, Zhao D. 84.  et al. 2017. Adv. Mater. 30:1703062
  85. Qi S, Qiao Z, Deng X, Cubuk ED, Chen H. 85.  et al. 2016. Phys. Rev. Lett. 117:056804
  86. Han Y, Wan JG, Ge GX, Song FQ, Wang GH. 86.  2015. Sci. Rep. 5:16843
  87. Wang ZF, Liu Z, Liu F. 87.  2013. Phys. Rev. Lett. 110:196801
  88. Tang E, Mei JW, Wen XG. 88.  2011. Phys. Rev. Lett. 106:236802
  89. Lang M, Montazeri M, Onbasli MC, Kou X, Fan Y. 89.  et al. 2014. Nano Lett 14:3459–65
  90. Andriotis AN, Menon M. 90.  2013. Phys. Rev. B 87:155309
  91. Himpsel FJ, Ortega JE Mankey GJ, Willis RF. 91.  1998. Adv. Phys. 47:511–97
  92. Luo W, Qi XL. 92.  2013. Phys. Rev. B 87:085431
  93. Eremeev SV, Men'shov VN, Tugushev VV, Echenique PM, Chulkov EV. 93.  2013. Phys. Rev. B 88:144430
  94. Men'shov VN, Tugushev VV, Eremeev SV, Echenique PM, Chulkov EV. 94.  2013. Phys. Rev. B 88:224401
  95. Wang F, Ran Y. 95.  2011. Phys. Rev. B 84:241103R)
  96. Fang C, Gilbert MJ, Bernevig BA. 96.  2014. Phys. Rev. Lett. 112:046801
  97. Wang J, Lian B, Zhang H, Xu Y, Zhang SC. 97.  2013. Phys. Rev. Lett. 111:136801
  98. Wan X, Turner AM, Vishwanath A, Savrasov SY. 98.  2011. Phys. Rev. B 83:205101
  99. Burkov AA, Balents L. 99.  2011. Phys. Rev. Lett. 107:127205
  100. Xu G, Weng H, Wang Z, Dai X, Fang Z. 100.  2011. Phys. Rev. Lett. 107:186806
  101. Alicea J. 101.  2012. Rep. Prog. Phys. 75:076501
  102. Bonderson P, Das Sarma S, Freedman M, Nayak C. 102.  2010. arXiv1003.2856
  103. Qi XL, Hughes TL, Zhang SC. 103.  2012. Phys. Rev. B 82:184516
  104. Fu L, Kane CL. 104.  2009. Phys. Rev. Lett. 102:216403
  105. Akhmerov AR, Nilsson CN, Beenakker CWJ. 105.  2009. Phys. Rev. Lett. 102:216404
  106. Chung SB, Qi XL, Maciejko J, Zhang SC. 106.  2011. Phys. Rev. B 83:100512
  107. Wang J, Zhou Q, Lian B, Zhang SC. 107.  2015. Phys. Rev. B 92:064520
  108. He QL, Pan L, Stern AL, Burks E, Che X. 108.  et al. 2017. Science 357:294–99
  109. Alicea J, Fendley P. 109.  2016. Annu. Rev. Condens. Matter Phys. 7:119–39
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