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本文研究了各向同性square-octagon晶格在内禀自旋轨道耦合、Rashba自旋轨道耦合和交换场作用下的拓扑相变，同时引入陈数和自旋陈数对系统进行拓扑分类.系统在自旋轨道耦合和交换场的影响下会出现许多拓扑非平庸态，包括时间反演对称破缺的量子自旋霍尔态和量子反常霍尔态.特别的是，在时间反演对称破缺的量子自旋霍尔效应中，无能隙螺旋边缘态依然能够完好存在.调节交换场或者填充因子的大小会导致系统发生从时间反演对称破缺的量子自旋霍尔态到自旋过滤的量子反常霍尔态的拓扑相变.边缘态能谱和自旋谱的性质与陈数和自旋陈数的拓扑刻画完全一致.这些研究成果为自旋量子操控提供了一个有趣的途径.
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[1] Kane C L, Mele E J 2005 Phys. Rev. Lett. 95 226801
[2] Bernevig B A, Zhang S C 2005 Phys. Rev. Lett. 96 106802
[3] Hasan M Z, Kane C L 2010 Rev. Mod. Phys. 82 3045
[4] Qi X L, Zhang S C 2011 Rev. Mod. Phys. 83 1057
[5] Ren Y F, Qiao Z H, Niu Q 2016 Rep. Prog. Phys. 79 066501
[6] Kane C L, Mele E J 2005 Phys. Rev. Lett. 95 146802
[7] Moore J E, Balents L 2007 Phys. Rev. B 75 121306
[8] Prodan E 2009 Phys. Rev. B 80 125327
[9] Prodan E 2010 New J. Phys. 12 065003
[10] Sheng D N, Weng Z Y, Sheng L, Haldane F D M 2006 Phys. Rev. Lett. 97 036808
[11] Yang Y Y, Xu Z, Sheng L, Wang B G, Xing D Y, Sheng D N 2011 Phys. Rev. Lett. 107 066602
[12] Du L J, Knez I, Sullivan G, Du R R 2015 Phys. Rev. Lett. 114 096802
[13] Yao Y G, Ye F, Qi X L, Zhang S C, Fang Z 2007 Phys. Rev. B 75 041401
[14] Min H, Hill J E, Sinitsyn N A, Sahu B R, Kleinman L, MacDonald A H 2006 Phys. Rev. B 74 165310
[15] Liu C C, Jiang H, Yao Y 2011 Phys. Rev. B 84 195430
[16] Qiao Z, Yang S A, Feng W, Tse W K, Ding J, Yao Y, Wang J, Niu Q 2010 Phys. Rev. B 82 161414
[17] Qiao Z, Jiang H, Li X, Yao Y, Niu Q 2012 Phys. Rev. B 85 115439
[18] Zhang Z Y 2011 J. Phys. Condens. Matter 23 365801
[19] Chen M S, Wan S L 2012 J. Phys. Condens. Matter 24 325502
[20] Guo H M, Franz M 2009 Phys. Rev. B 80 113102
[21] Rüegg A, Wen J, Fiete G A 2010 Phys. Rev. B 81 205115
[22] Zhou T, Zhang J, Xue Y, Zhao B, Zhang H, Jiang H, Yang Z 2016 Phys. Rev. B 94 235449
[23] Kargarian M, Fiete G A 2010 Phys. Rev. B 82 085106
[24] Liu X P, Chen W C, Wang Y F, Gong C D 2013 J. Phys. Condens. Matter 25 305602
[25] Bao A, Tao H S, Liu H D, Zhang X Z, Liu W M 2015 Sci. Rep. 4 6918
[26] Bao A, Zhang X F, Zhang X Z 2015 Chin. Phys. B 24 050310
[27] Zhang L, Wang F 2017 Phys. Rev. Lett. 118 087201
[28] Kang Y T, Yang F, Yao D X 2017 arXiv: 1801.00220. https://arxiv.org/abs/1801.00220
[29] Yang Y, Yang J, Li X, Zhao Y 2018 Phys. Lett. A 382 723
[30] Panahi P S, Struck J, Hauke P, Bick A, Plenkers W, Meineke G, Becker C, Windpassinger P, Lewenstein M, Sengstock K 2011 Nat. Phys. 7 434
[31] Jo G B, Guzman J, Thomas C K, Hosur P, Vishwanath A, StamperKurn D M 2012 Phys. Rev. Lett. 108 045305
[32] He M R, Yu R, Zhu J 2012 Angew. Chem. 124 7864
[33] Fukui T, Hatsugai Y, Suzuki H 2005 J. Phys. Soc. Jpn. 74 1674
[34] Taillefumier M, Dugaev V K, Canals B, Lacroix C, Bruno P 2008 Phys. Rev. B 78 155330
[35] Hatsugai Y 1993 Phys. Rev. B 48 11851
[36] Hatsugai Y 1993 Phys. Rev. Lett. 71 3697
[37] Sun K, Fradkin E 2008 Phys. Rev. B 78 245122
[38] Goldman N, Beugeling W, Smith C M 2012 Europhys. Lett. 97 23003
[39] Beugeling W, Goldman N, Smith C M 2012 Phys. Rev. Lett. 86 075118
[40] Li H C, Sheng L, Shen R, Shao L B, Wang B G, Sheng D N, Xing D Y 2013 Phys. Rev. Lett. 110 266802
[41] Miao M, Yan Q, van de Walle C, Lou W, Li L, Chang K 2012 Phys. Rev. Lett. 109 186803
[42] Zhang D, Lou W, Miao M, Zhang S, Chang K 2013 Phys. Rev. Lett. 111 156402
[43] Jotzu G, Messer M, Desbuquois R, Lebrat M, Uehlinger T, Greif D, Esslinger T 2014 Nature 515 237
[44] Lin Y J, Compton R L, Jiménez-García K, Porto J V, Spielman I B 2009 Nature 462 628
[45] Lin Y J, Jiménez-García K, Spielman I B 2011 Nature 471 83
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