Special Issue:
TOPICAL REVIEW — Topological insulator
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TOPICAL REVIEW—Topological insulator |
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Spin Chern numbers and time-reversal-symmetry-broken quantum spin Hall effect |
Sheng Li (盛利)a, Li Hui-Chao (李会超)a, Yang Yun-You (杨运友)a, Sheng Dong-Ning (盛冬宁)b, Xing Ding-Yu (邢定钰)a |
a National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China;
b Department of Physics and Astronomy, California State University, Northridge, California 91330, USA |
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Abstract The quantum spin Hall (QSH) effect is considered to be unstable to perturbations violating the time-reversal (TR) symmetry. We review some recent developments in the search of the QSH effect in the absence of the TR symmetry. The possibility to realize a robust QSH effect by artificial removal of the TR symmetry of the edge states is explored. As a useful tool to characterize topological phases without the TR symmetry, the spin-Chern number theory is introduced.
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Received: 17 April 2013
Accepted manuscript online:
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PACS:
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72.25.-b
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(Spin polarized transport)
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73.43.-f
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(Quantum Hall effects)
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73.20.At
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(Surface states, band structure, electron density of states)
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73.50.-h
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(Electronic transport phenomena in thin films)
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Fund: Project supported by the National Basic Research Program of China (Grant Nos. 2009CB929504, 2011CB922103, and 2010CB923400), the National Natural Science Foundation of China (Grant Nos. 11225420, 11074110, 11174125, 11074109, and 91021003), the Priority Academic Program Development of Jiangsu Higher Education Institutions, China, the US NSF (Grant Nos. DMR-0906816 and DMR-1205734), and Princeton MRSEC (Grant No. DMR-0819860). |
Corresponding Authors:
Sheng Dong-Ning, Xing Ding-Yu
E-mail: shengli@nju.edu.cn; dyxing@nju.edu.cn
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Cite this article:
Sheng Li (盛利), Li Hui-Chao (李会超), Yang Yun-You (杨运友), Sheng Dong-Ning (盛冬宁), Xing Ding-Yu (邢定钰) Spin Chern numbers and time-reversal-symmetry-broken quantum spin Hall effect 2013 Chin. Phys. B 22 067201
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[1] |
Kane C L and Mele E J 2005 Phys. Rev. Lett. 95 226801
|
[2] |
Bernevig B A and Zhang S C 2006 Phys. Rev. Lett. 96 106802
|
[3] |
König M, Wiedmann S, Brüne C, Roth A, Buhmann H, Molenkamp LW, Qi X L and Zhang S C 2007 Science 318 766
|
[4] |
Bernevig B A, Hughes T L and Zhang S C 2006 Science 314 1757
|
[5] |
Haldane F D M 1988 Phys. Rev. Lett. 61 2015
|
[6] |
Sheng L, Sheng D N, Ting C S and Haldane F D M 2005 Phys. Rev.Lett. 95 136602
|
[7] |
Wu C, Bernevig B A and Zhang S C 2006 Phys. Rev. Lett. 96 106401
|
[8] |
Kane C L and Mele E J 2005 Phys. Rev. Lett. 95 146802
|
[9] |
Sheng D N, Weng Z Y, Sheng L and Haldane F D M 2006 Phys. Rev.Lett. 97 036808
|
[10] |
Prodan E 2009 Phys. Rev. B 80 125327
|
[11] |
Li H C, Sheng L, Sheng D N and Xing D Y 2010 Phys. Rev. B 82165104
|
[12] |
Moore J E and Balents L 2007 Phys. Rev. B 75 121306
|
[13] |
Fu L and Kane C L 2007 Phys. Rev. B 76 045302
|
[14] |
Fu L, Kane C L and Mele E J 2007 Phys. Rev. Lett. 98 106803
|
[15] |
Zhang H J, Liu C X, Qi X L, Dai X, Fang Z and Zhang S C 2009 Nat.Phys. 5 438
|
[16] |
Hasan M Z and Kane C L 2010 Rev. Mod. Phys. 82 3045
|
[17] |
Qi X L and Zhang S C 2010 Phys. Today 63 33
|
[18] |
Fu L and Kane C L 2008 Phys. Rev. Lett. 100 096407
|
[19] |
Qi X L, Hughes T and Zhang S C 2008 Phys. Rev. B 78 195424
|
[20] |
Essin A M, Moore J E and Vanderbilt D 2009 Phys. Rev. Lett. 102146805
|
[21] |
Hsieh D, Qian D, Wray L, Xia Y, Hor Y S, Cava R J and Hasan M Z2008 Nature 452 970
|
[22] |
Hsieh D, Xia Y, Wray L, Qian D, Pal A, Dil J H, Osterwalder J, MeierF, Bihlmayer G, Kane C L, Hor Y S, Cava R J and Hasan M Z 2009Science 323 919
|
[23] |
Xia Y, Qian D, Hsieh D, Wray L, Pal A, Lin H, Bansil A, Grauer D,Hor Y S, Cava R J and Hasan M Z 2009 Nat. Phys. 5 398
|
[24] |
Chen Y L, Analytis J G, Chu J H, Liu Z K, Mo S K, Qi X L, Zhang HJ, Lu D H, Dai X, Fang Z, Zhang S C, Fisher I R, Hussain Z and ShenZ X 2009 Science 325 178
|
[25] |
Roushan P, Seo J, Parker C V, Hor Y S, Hsieh D, Qian D, RichardellaA, Hasan M Z, Cava R J and Yazdani A 2009 Nature 460 1106
|
[26] |
Zhang T, Cheng P, Chen X, Jia J F, Ma X C, He K, Wang L L, ZhangH J, Dai X, Fang Z, Xie X C and Xue Q K 2009 Phys. Rev. Lett. 103266803
|
[27] |
Jiang H, Cheng S, Sun Q F and Xie X C 2009 Phys. Rev. Lett. 103036803
|
[28] |
Laughlin R B 1981 Phys. Rev. B 23 5632
|
[29] |
Fu L and Kane C L 2006 Phys. Rev. B 74 195312
|
[30] |
Yang Y, Xu Z, Sheng L, Wang B G, Xing D Y and Sheng D N 2011Phys. Rev. Lett. 107 066602
|
[31] |
Qi X L, Wu Y S and Zhang S C 2006 Phys. Rev. B 74 085308
|
[32] |
Qi X L, Hughes T L and Zhang S C 2008 Phys. Rev. B 78 195424
|
[33] |
Liu C X, Qi X L, Dai X, Fang Z and Zhang S C 2008 Phys. Rev. Lett.101 146802
|
[34] |
Yu R, ZhangW, Zhang H J, Zhang S C, Dai X and Fang Z 2010 Science329 61
|
[35] |
Qiao Z H, Yang S Y A, Feng W X, Tse W K, Ding J, Yao Y G, WangJ and Niu Q 2010 Phys. Rev. B 82 161414
|
[36] |
Chang C Z, et al. 2013 Science 399 1582
|
[37] |
Xu Z, Sheng L, Xing D Y, Prodan E and Sheng D N 2012 Phys. Rev. B85 075115
|
[38] |
Xu Z, Sheng L, Shen R,Wang B and Xing D Y 2013 J. Phys.: Condens.Matter 25 065501
|
[39] |
Li H C, Sheng L and Xing D Y 2012 Phys. Rev. Lett. 108 196806
|
[40] |
Li H C, Sheng L, Shen R, Shao L B, Wang B G, Sheng D N and XingD Y 2013 cond-mat/1301.6460
|
[41] |
Shan W Y, Lu H Z and Shen S Q 2010 New J. Phys. 12 043048
|
[42] |
Lu H Z, Shan W Y, Yao W, Niu Q and Shen S Q 2010 Phys. Rev. B 81115407
|
[43] |
Brüne C, Liu C X, Novik E G, Hankiewicz E M, Buhmann H, Chen YL, Qi X L, Shen Z X, Zhang S C and Molenkamp LW2011 Phys. Rev.Lett. 106 126803
|
[44] |
Sheng L, Xing D Y, Sheng D N and Ting C S 1997 Phys. Rev. Lett. 791710
|
[45] |
Liu Q, Liu C X, Xu C K, Qi X L and Zhang S C 2009 Phys. Rev. Lett.102 156603
|
[46] |
König M, Buhmann H, Molenkamp L W, Hughes T, Liu C X, Qi X Land Zhang S C 2008 J. Phys. Soc. Jpn. 77 031007
|
[47] |
Smith D L and Mailhiot C 1990 Rev. Mod. Phys. 62 173
|
[48] |
Yang Y, Li H, Sheng L, Shen R, Sheng D N and Xing D Y 2013 condmat/1301.1618
|
[49] |
Wan X, Turner A M, Vishwanath A and Savrasov S Y 2011 Phys. Rev.B 83 205101
|
[50] |
Burkov A A and Balents L 2011 Phys. Rev. Lett. 107 127205
|
[51] |
Sun K, Liu W V, Hemmerich A and Sarma S D 2011 Nat. Phys. 8 67
|
[52] |
Fang C, Gilbert M J, Dai X and Bernevig B A 2012 Phys. Rev. Lett.108 266802
|
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