-
1
-
-
28844477210
-
Z2 topological order and the quantum spin hall effect
-
DOI 10.1103/PhysRevLett.95.146802, 146802
-
C. L. Kane and E. J. Mele, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.146802 95, 146802 (2005). (Pubitemid 41777602)
-
(2005)
Physical Review Letters
, vol.95
, Issue.14
, pp. 1-4
-
-
Kane, C.L.1
Mele, E.J.2
-
2
-
-
33847795859
-
Topological insulators in three dimensions
-
DOI 10.1103/PhysRevLett.98.106803
-
L. Fu, C. L. Kane, and E. J. Mele, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.106803 98, 106803 (2007). (Pubitemid 46393379)
-
(2007)
Physical Review Letters
, vol.98
, Issue.10
, pp. 106803
-
-
Fu, L.1
Kane, C.L.2
Mele, E.J.3
-
3
-
-
34347373900
-
-
PRBMDO 1098-0121 10.1103/PhysRevB.76.045302
-
L. Fu and C. L. Kane, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.76. 045302 76, 045302 (2007).
-
(2007)
Phys. Rev. B
, vol.76
, pp. 045302
-
-
Fu, L.1
Kane, C.L.2
-
4
-
-
35348905692
-
-
PRBMDO 1098-0121 10.1103/PhysRevB.76.165307
-
A. M. Essin and J. E. Moore, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.76.165307 76, 165307 (2007).
-
(2007)
Phys. Rev. B
, vol.76
, pp. 165307
-
-
Essin, A.M.1
Moore, J.E.2
-
5
-
-
33947696243
-
-
PRBMDO 1098-0121 10.1103/PhysRevB.75.121306
-
J. E. Moore and L. Balents, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.75.121306 75, 121306 (2007).
-
(2007)
Phys. Rev. B
, vol.75
, pp. 121306
-
-
Moore, J.E.1
Balents, L.2
-
6
-
-
3442880129
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.49.405
-
D. J. Thouless, M. Kohmoto, M. P. Nightingale, and M. den Nijs, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.49.405 49, 405 (1982).
-
(1982)
Phys. Rev. Lett.
, vol.49
, pp. 405
-
-
Thouless, D.J.1
Kohmoto, M.2
Nightingale, M.P.3
Den Nijs, M.4
-
7
-
-
0000225270
-
-
APNYA6 0003-4916 10.1016/0003-4916(85)90149-6
-
M. Kohmoto, Ann. Phys. (NY) APNYA6 0003-4916 10.1016/0003-4916(85)90149-6 160, 355 (1985).
-
(1985)
Ann. Phys. (NY)
, vol.160
, pp. 355
-
-
Kohmoto, M.1
-
8
-
-
57249110726
-
-
PRBMDO 1098-0121 10.1103/PhysRevB.78.195125
-
A. P. Schnyder, S. Ryu, A. Furusaki, and A. W. W. Ludwig, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.78.195125 78, 195125 (2008).
-
(2008)
Phys. Rev. B
, vol.78
, pp. 195125
-
-
Schnyder, A.P.1
Ryu, S.2
Furusaki, A.3
Ludwig, A.W.W.4
-
9
-
-
78651343064
-
-
edited by V. Lebedev and M. Feigelman (AIP, New York
-
A. Kitaev, Advances in Theoretical Physics: Landau Memorial Conference, AIP Conf. Proc. No. 1134, edited by, V. Lebedev, and, M. Feigelman, (AIP, New York, 2009), p. 22.
-
(2009)
Advances in Theoretical Physics: Landau Memorial Conference
, pp. 22
-
-
Kitaev, A.1
-
10
-
-
65649114938
-
-
AIP, New York
-
A. P. Schnyder, S. Ryu, A. Furusaki, A. W. W. Ludwig, Advances in Theoretical Physics: Landau Memorial Conference, AIP Conf. Proc. No. 1134 (AIP, New York, 2009), p. 10.
-
(2009)
Advances in Theoretical Physics: Landau Memorial Conference
, pp. 10
-
-
Schnyder, A.P.1
Ryu, S.2
Furusaki, A.3
Ludwig, A.W.W.4
-
11
-
-
0030515852
-
-
JMAPAQ 0022-2488 10.1063/1.531675
-
M. R. Zirnbauer, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.531675 37, 4986 (1996).
-
(1996)
J. Math. Phys.
, vol.37
, pp. 4986
-
-
Zirnbauer, M.R.1
-
12
-
-
0000023684
-
-
PRBMDO 1098-0121 10.1103/PhysRevB.55.1142
-
A. Altland and M. R. Zirnbauer, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.55.1142 55, 1142 (1997).
-
(1997)
Phys. Rev. B
, vol.55
, pp. 1142
-
-
Altland, A.1
Zirnbauer, M.R.2
-
13
-
-
42949106486
-
A topological Dirac insulator in a quantum spin Hall phase
-
DOI 10.1038/nature06843, PII NATURE06843
-
D. Hsieh, D. Qian, L. Wray, Y. Xia, Y. S. Hor, R. J. Cava, and M. Z. Hasan, Nature (London) NATUAS 0028-0836 10.1038/nature06843 452, 970 (2008). (Pubitemid 351606144)
-
(2008)
Nature
, vol.452
, Issue.7190
, pp. 970-974
-
-
Hsieh, D.1
Qian, D.2
Wray, L.3
Xia, Y.4
Hor, Y.S.5
Cava, R.J.6
Hasan, M.Z.7
-
14
-
-
60149088445
-
-
J., SCIEAS 0036-8075 10.1126/science.1167733
-
D. Hsieh, Y. Xia, L. Wray, D. Qian, A. Pal, J. H. Dil, J. Osterwalde R. Meier, G. Bihknayer, C. L. Kane, Y. Hor, R. Cava, and M. Hasan, Science SCIEAS 0036-8075 10.1126/science.1167733 323, 919 (2009).
-
(2009)
Science
, vol.323
, pp. 919
-
-
Hsieh, D.1
Xia, Y.2
Wray, L.3
Qian, D.4
Pal, A.5
Dil, J.H.6
Meier, O.R.7
Bihknayer, G.8
Kane, C.L.9
Hor, Y.10
Cava, R.11
Hasan, M.12
-
15
-
-
67650262991
-
-
SCIEAS 1745-2473 10.1038/nphys1274
-
Y. Xia, D. Qian, D. Hsieh, L. Wray, A. Pal, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava, and M. Z. Hasan, Nature Phys. SCIEAS 1745-2473 10.1038/nphys1274 5, 398 (2009).
-
(2009)
Nature Phys.
, vol.5
, pp. 398
-
-
Xia, Y.1
Qian, D.2
Hsieh, D.3
Wray, L.4
Pal, A.5
Lin, H.6
Bansil, A.7
Grauer, D.8
Hor, Y.S.9
Cava, R.J.10
Hasan, M.Z.11
-
16
-
-
69349084799
-
-
NATUAS 0028-0836 10.1038/nature08234
-
D. Hsieh, Y. Xia, D. Qian, L. Wray, J. H. Dil, F. Meier, J. Osterwalder, L. Patthey, J. G. Checkelsky, N. P. Ong, A. V. Fedorov, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava, and M. Z. Hasan, Nature (London) NATUAS 0028-0836 10.1038/nature08234 460, 1101 (2009).
-
(2009)
Nature (London)
, vol.460
, pp. 1101
-
-
Hsieh, D.1
Xia, Y.2
Qian, D.3
Wray, L.4
Dil, J.H.5
Meier, F.6
Osterwalder, J.7
Patthey, L.8
Checkelsky, J.G.9
Ong, N.P.10
Fedorov, A.V.11
Lin, H.12
Bansil, A.13
Grauer, D.14
Hor, Y.S.15
Cava, R.J.16
Hasan, M.Z.17
-
17
-
-
67650456298
-
-
SCIEAS 0036-8075 10.1126/science.1173034
-
Y. L. Chen, J. G. Analytis, J.-H. Chu, Z. K. Liu, S.-K. Mo, X. L. Qi, H. J. Zhang, D. H. Lu, X. Dai, Z. Fang, S. C. Zhang, I. R. Fisher, Z. Hussain, and Z.-X. Shen, Science SCIEAS 0036-8075 10.1126/science.1173034 325, 178 (2009).
-
(2009)
Science
, vol.325
, pp. 178
-
-
Chen, Y.L.1
Analytis, J.G.2
Chu, J.-H.3
Liu, Z.K.4
Mo, S.-K.5
Qi, X.L.6
Zhang, H.J.7
Lu, D.H.8
Dai, X.9
Fang, Z.10
Zhang, S.C.11
Fisher, I.R.12
Hussain, Z.13
Shen, Z.-X.14
-
18
-
-
57249108445
-
-
PRBMDO 1098-0121 10.1103/PhysRevB.78.195424
-
X.-L. Qi, T. L. Hughes, and S.-C. Zhang, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.78.195424 78, 195424 (2008).
-
(2008)
Phys. Rev. B
, vol.78
, pp. 195424
-
-
Qi, X.-L.1
Hughes, T.L.2
Zhang, S.-C.3
-
19
-
-
65549133453
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.102.146805
-
A. M. Essin, J. E. Moore, and D. Vanderbilt, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.102.146805 102, 146805 (2009).
-
(2009)
Phys. Rev. Lett.
, vol.102
, pp. 146805
-
-
Essin, A.M.1
Moore, J.E.2
Vanderbilt, D.3
-
20
-
-
7444237833
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.58.1799
-
F. Wilczek, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.58.1799 58, 1799 (1987).
-
(1987)
Phys. Rev. Lett.
, vol.58
, pp. 1799
-
-
Wilczek, F.1
-
21
-
-
77954827546
-
-
NJOPFM 1367-2630 10.1088/1367-2630/12/6/065010
-
S. Ryu, A. Schnyder, A. Furusaki, and A. W. W. Ludwig, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/12/6/065010 12, 065010 (2010).
-
(2010)
New J. Phys.
, vol.12
, pp. 065010
-
-
Ryu, S.1
Schnyder, A.2
Furusaki, A.3
Ludwig, A.W.W.4
-
22
-
-
78650032048
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.105.246809
-
See, for example, J. Maciejko, X.-L. Qi, A. Karch, and S.-C. Zhang, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.105.246809 105, 246809 (2010);
-
(2010)
Phys. Rev. Lett.
, vol.105
, pp. 246809
-
-
MacIejko, J.1
Qi, X.-L.2
Karch, A.3
Zhang, S.-C.4
-
23
-
-
79961109519
-
-
1098-0121 10.1103/PhysRevB.83.195139
-
B. Swingle, M. Barkeshli, J. McGreevy, and T. Senthil, Phys. Rev. B 1098-0121 10.1103/PhysRevB.83.195139 83, 195139 (2011).
-
(2011)
Phys. Rev. B
, vol.83
, pp. 195139
-
-
Swingle, B.1
Barkeshli, M.2
McGreevy, J.3
Senthil, T.4
-
24
-
-
0001106242
-
-
PRBMDO 1098-0121 10.1103/PhysRevB.50.7526
-
A. W. W. Ludwig, M. P. A. Fisher, R. Shankar, and G. Grinstein, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.50.7526 50, 7526 (1994).
-
(1994)
Phys. Rev. B
, vol.50
, pp. 7526
-
-
Ludwig, A.W.W.1
Fisher, M.P.A.2
Shankar, R.3
Grinstein, G.4
-
25
-
-
77954827655
-
-
PRBMDO 1098-0121 10.1103/PhysRevB.81.045120
-
P. Hosur, S. Ryu, and A. Vishwanath, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.81.045120 81, 045120 (2010).
-
(2010)
Phys. Rev. B
, vol.81
, pp. 045120
-
-
Hosur, P.1
Ryu, S.2
Vishwanath, A.3
-
28
-
-
65649116620
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.102.196804
-
A. P. Schnyder, S. Ryu, and A. W. W. Ludwig, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.102.196804 102, 196804 (2009).
-
(2009)
Phys. Rev. Lett.
, vol.102
, pp. 196804
-
-
Schnyder, A.P.1
Ryu, S.2
Ludwig, A.W.W.3
-
31
-
-
0000144241
-
-
PHRVAO 0031-899X 10.1103/PhysRev.135.A1505
-
J. M. Luttinger, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.135.A1505 135, A1505 (1964).
-
(1964)
Phys. Rev.
, vol.135
, pp. 1505
-
-
Luttinger, J.M.1
-
32
-
-
0034339791
-
-
CQGRDG 0264-9381 10.1088/0264-9381/17/19/311
-
S. J. Clark and R. W. Tucker, Class. Quantum Grav. CQGRDG 0264-9381 10.1088/0264-9381/17/19/311 17, 4125 (2000).
-
(2000)
Class. Quantum Grav.
, vol.17
, pp. 4125
-
-
Clark, S.J.1
Tucker, R.W.2
-
33
-
-
0003482664
-
-
See, e.g., Institute of Physics, Bristol
-
See, e.g., M. Nakahara, Geometry, Topology and Physics (Institute of Physics, Bristol, 1998).
-
(1998)
Geometry, Topology and Physics
-
-
Nakahara, M.1
-
36
-
-
0000049832
-
-
CQGRDG 1098-0121 10.1103/PhysRevB.61.10267
-
N. Read and Dmitry Green, Phys. Rev. B CQGRDG 1098-0121 10.1103/PhysRevB.61.10267 61, 10267 (2000).
-
(2000)
Phys. Rev. B
, vol.61
, pp. 10267
-
-
Read, N.1
Green, D.2
-
37
-
-
0002648075
-
-
Stanford University Press, Stanford, CA
-
See, e.g., M. H. Freedman and R. Kirby, Proceedings of the Symposium on Pure Mathematics (Stanford University Press, Stanford, CA, 1976), Pt. 2, pp. 85-97;
-
(1976)
Proceedings of the Symposium on Pure Mathematics
, pp. 85-97
-
-
Freedman, M.H.1
Kirby, R.2
-
39
-
-
41549146655
-
-
PRBMDO 1098-0121 10.1103/PhysRevB.77.144504
-
J. Goryo, M. Kohmoto, and Y.-S. Wu, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.77.144504 77, 144504 (2008).
-
(2008)
Phys. Rev. B
, vol.77
, pp. 144504
-
-
Goryo, J.1
Kohmoto, M.2
Wu, Y.-S.3
-
40
-
-
0038201996
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.90.167204
-
F. Meier and D. Loss, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90.167204 90, 167204 (2003).
-
(2003)
Phys. Rev. Lett.
, vol.90
, pp. 167204
-
-
Meier, F.1
Loss, D.2
-
41
-
-
84863420838
-
-
We will give a brief explanation of the relevant concepts below. See also Refs. 33,35,43, and 54.
-
We will give a brief explanation of the relevant concepts below. See also Refs. 33,35,43, and 54.
-
-
-
-
42
-
-
0002185817
-
-
APNYA6 0003-4916 10.1016/0003-4916(85)90087-9
-
L. Alvarez-Gaumé and P. Ginsparg, Ann. Phys. (NY) APNYA6 0003-4916 10.1016/0003-4916(85)90087-9 161, 423 (1985).
-
(1985)
Ann. Phys. (NY)
, vol.161
, pp. 423
-
-
Alvarez-Gaumé, L.1
Ginsparg, P.2
-
43
-
-
84863408869
-
-
Z. Wang, X.-L. Qi, and S.-C. Zhang, e-print arXiv: 1011.0586
-
in Z. Wang, X.-L. Qi, and S.-C. Zhang, e-print arXiv: 1011.0586.
-
-
-
-
44
-
-
77956910978
-
-
PYLBAJ 0370-2693 10.1016/j.physletb.2010.08.019
-
S. Ryu and T. Takayanagi, Phys. Lett. B PYLBAJ 0370-2693 10.1016/j.physletb.2010.08.019 693, 175 (2010).
-
(2010)
Phys. Lett. B
, vol.693
, pp. 175
-
-
Ryu, S.1
Takayanagi, T.2
-
45
-
-
78650987473
-
-
1550-7998 10.1103/PhysRevD.82.086014
-
S. Ryu and T. Takayanagi, Phys. Rev. D 1550-7998 10.1103/PhysRevD.82. 086014 82, 086014 (2010).
-
(2010)
Phys. Rev. D
, vol.82
, pp. 086014
-
-
Ryu, S.1
Takayanagi, T.2
-
46
-
-
41749121692
-
-
PRBMDO 1098-0121 10.1103/PhysRevB.77.165108
-
M. S. Foster and A. W. W. Ludwig, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.77.165108 77, 165108 (2008).
-
(2008)
Phys. Rev. B
, vol.77
, pp. 165108
-
-
Foster, M.S.1
Ludwig, A.W.W.2
-
47
-
-
0010190678
-
-
NUPBBO 0550-3213 10.1016/0550-3213(84)90066-X
-
L. Alvarez-Gaumé and E. Witten, Nucl. Phys. B NUPBBO 0550-3213 10.1016/0550-3213(84)90066-X 234, 269 (1983).
-
(1983)
Nucl. Phys. B
, vol.234
, pp. 269
-
-
Alvarez-Gaumé, L.1
Witten, E.2
-
48
-
-
75849118012
-
-
0031-9007 10.1103/PhysRevLett.104.057001
-
Y. S. Hor, A. J. Williams, J. G. Checkelsky, P. Roushan, J. Seo, Q. Xu, H. W. Zandbergen, A. Yazdani, N. P. Ong, and R. J. Cava, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.104.057001 104, 057001 (2010).
-
(2010)
Phys. Rev. Lett.
, vol.104
, pp. 057001
-
-
Hor, Y.S.1
Williams, A.J.2
Checkelsky, J.G.3
Roushan, P.4
Seo, J.5
Xu, Q.6
Zandbergen, H.W.7
Yazdani, A.8
Ong, N.P.9
Cava, R.J.10
-
49
-
-
77955948515
-
-
0031-9007 10.1103/PhysRevLett.105.097001
-
L. Fu and E. Berg, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.105. 097001 105, 097001 (2010).
-
(2010)
Phys. Rev. Lett.
, vol.105
, pp. 097001
-
-
Fu, L.1
Berg, E.2
-
50
-
-
77955218335
-
-
1098-0121 10.1103/PhysRevB.81.134509
-
L. Fidkowski and A. Kitaev, Phys. Rev. B 1098-0121 10.1103/PhysRevB.81. 134509 81, 134509 (2010).
-
(2010)
Phys. Rev. B
, vol.81
, pp. 134509
-
-
Fidkowski, L.1
Kitaev, A.2
-
51
-
-
79961067002
-
-
1098-0121 10.1103/PhysRevB.83.075103
-
L. Fidkowski and A. Kitaev, Phys. Rev. B 1098-0121 10.1103/PhysRevB.83. 075103 83, 075103 (2011).
-
(2011)
Phys. Rev. B
, vol.83
, pp. 075103
-
-
Fidkowski, L.1
Kitaev, A.2
-
52
-
-
79961064168
-
-
1098-0121 10.1103/PhysRevB.83.075102
-
A. M. Turner, F. Pollmann, and E. Berg, Phys. Rev. B 1098-0121 10.1103/PhysRevB.83.075102 83, 075102 (2011).
-
(2011)
Phys. Rev. B
, vol.83
, pp. 075102
-
-
Turner, A.M.1
Pollmann, F.2
Berg, E.3
-
53
-
-
71449101812
-
-
PRBMDO 1098-0121 10.1103/PhysRevB.80.155131
-
Z.-C. Gu and X.-G. Wen, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.80.155131 80, 155131 (2009);
-
(2009)
Phys. Rev. B
, vol.80
, pp. 155131
-
-
Gu, Z.-C.1
Wen, X.-G.2
-
54
-
-
79551610647
-
-
PRBMDO 1098-0121 10.1103/PhysRevB.83.035107
-
X. Chen, Z.-C. Gu, and X.-G. Wen, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.83.035107 83, 035107 (2011);
-
(2011)
Phys. Rev. B
, vol.83
, pp. 035107
-
-
Chen, X.1
Gu, Z.-C.2
Wen, X.-G.3
-
55
-
-
84863420839
-
-
F. Pollmann, E. Berg, A. M. Turner, and M. Oshikawa, e-print arXiv: 0909.4059
-
F. Pollmann, E. Berg, A. M. Turner, and M. Oshikawa, e-print arXiv: 0909.4059.
-
-
-
|