-
1
-
-
0001032458
-
-
PRBMDO 1098-0121 10.1103/PhysRevB.14.2239
-
D. R. Hofstadter, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.14.2239 14, 2239 (1976).
-
(1976)
Phys. Rev. B
, vol.14
, pp. 2239
-
-
Hofstadter, D.R.1
-
2
-
-
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
-
3
-
-
4243734768
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.71.3697
-
Y. Hatsugai, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.71. 3697 71, 3697 (1993).
-
(1993)
Phys. Rev. Lett.
, vol.71
, pp. 3697
-
-
Hatsugai, Y.1
-
4
-
-
46949084674
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.101.010504
-
H. Li and F. D. M. Haldane, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.101.010504 101, 010504 (2008).
-
(2008)
Phys. Rev. Lett.
, vol.101
, pp. 010504
-
-
Li, H.1
Haldane, F.D.M.2
-
6
-
-
1642317682
-
-
PRBMDO 1098-0121 10.1103/PhysRevB.69.075111
-
S.-A. Cheong and C. L. Henley, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.69.075111 69, 075111 (2004).
-
(2004)
Phys. Rev. B
, vol.69
, pp. 075111
-
-
Cheong, S.-A.1
Henley, C.L.2
-
7
-
-
1642286641
-
-
PRBMDO 1098-0121 10.1103/PhysRevB.69.075112
-
S.-A. Cheong and C. L. Henley, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.69.075112 69, 075112 (2004).
-
(2004)
Phys. Rev. B
, vol.69
, pp. 075112
-
-
Cheong, S.-A.1
Henley, C.L.2
-
8
-
-
0037432902
-
-
1361-6447 10.1088/0305-4470/36/14/101
-
I. Peschel, J. Phys. A 1361-6447 10.1088/0305-4470/36/14/101 36, L205 (2003).
-
(2003)
J. Phys. A
, vol.36
, pp. 205
-
-
Peschel, I.1
-
9
-
-
84901050687
-
-
1742-5468 10.1088/1742-5468/2004/06/P06004
-
I. Peschel, J. Stat. Mech.: Theory Exp. 1742-5468 10.1088/1742-5468/2004/ 06/P06004 (2004) P06004.
-
J. Stat. Mech.: Theory Exp.
, vol.2004
, pp. 06004
-
-
Peschel, I.1
-
10
-
-
78651255443
-
-
PRBMDO 1098-0121 10.1103/PhysRevB.82.241102
-
A. M. Turner, Y. Zhang, and A. Vishwanath, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.82.241102 82, 241102 (2010).
-
(2010)
Phys. Rev. B
, vol.82
, pp. 241102
-
-
Turner, A.M.1
Zhang, Y.2
Vishwanath, A.3
-
11
-
-
79961239559
-
-
PRBMDO 1098-0121 10.1103/PhysRevB.83.245132
-
T. L. Hughes, E. Prodan, and B. A. Bernevig, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.83.245132 83, 245132 (2011).
-
(2011)
Phys. Rev. B
, vol.83
, pp. 245132
-
-
Hughes, T.L.1
Prodan, E.2
Bernevig, B.A.3
-
12
-
-
33746396593
-
General theorem relating the bulk topological number to edge states in two-dimensional insulators
-
DOI 10.1103/PhysRevB.74.045125
-
X.-L. Qi, Y.-S. Wu, and S.-C. Zhang, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.74.045125 74, 045125 (2006). (Pubitemid 44128419)
-
(2006)
Physical Review B - Condensed Matter and Materials Physics
, vol.74
, Issue.4
, pp. 045125
-
-
Qi, X.-L.1
Wu, Y.-S.2
Zhang, S.-C.3
-
13
-
-
36149021109
-
-
PHRVAO 0031-899X 10.1103/PhysRev.115.809
-
W. Kohn, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.115.809 115, 809 (1959).
-
(1959)
Phys. Rev.
, vol.115
, pp. 809
-
-
Kohn, W.1
-
14
-
-
79551589803
-
-
PRBMDO 1098-0121 10.1103/PhysRevB.83.035108
-
A. A. Soluyanov and D. Vanderbilt, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.83.035108 83, 035108 (2011).
-
(2011)
Phys. Rev. B
, vol.83
, pp. 035108
-
-
Soluyanov, A.A.1
Vanderbilt, D.2
-
15
-
-
80052421035
-
-
PRBMDO 1098-0121 10.1103/PhysRevB.84.075119
-
R. Yu, X. L. Qi, A. Bernevig, Z. Fang, and X. Dai, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.84.075119 84, 075119 (2011).
-
(2011)
Phys. Rev. B
, vol.84
, pp. 075119
-
-
Yu, R.1
Qi, X.L.2
Bernevig, A.3
Fang, Z.4
Dai, X.5
-
16
-
-
33846500082
-
Exponential localization of Wannier functions in insulators
-
DOI 10.1103/PhysRevLett.98.046402
-
C. Brouder, G. Panati, M. Calandra, C. Mourougane, and N. Marzari, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.046402 98, 046402 (2007). (Pubitemid 46168674)
-
(2007)
Physical Review Letters
, vol.98
, Issue.4
, pp. 046402
-
-
Brouder, C.1
Panati, G.2
Calandra, M.3
Mourougane, C.4
Marzari, N.5
-
17
-
-
71449093761
-
-
PRBMDO 1098-0121 10.1103/PhysRevB.80.153303
-
I. D. Rodríguez and G. Sierra, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.80.153303 80, 153303 (2009).
-
(2009)
Phys. Rev. B
, vol.80
, pp. 153303
-
-
Rodríguez, I.D.1
Sierra, G.2
-
19
-
-
36149023156
-
-
PHRVAO 0031-899X 10.1103/PhysRev.135.A685
-
J. D. Cloizeaux, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.135.A685 135, A685 (1964).
-
(1964)
Phys. Rev.
, vol.135
, pp. 685
-
-
Cloizeaux, J.D.1
-
20
-
-
84871038668
-
-
Since any projector squares to itself, each column is an eigenstate with eigenvalue 1. However, they are not normalized, nor are they orthogonal to each other (because no eigenstate with eigenvalue 0 is present). In fact, the construction of Wannier states is one way to orthonormalize these eigenstates.
-
Since any projector squares to itself, each column is an eigenstate with eigenvalue 1. However, they are not normalized, nor are they orthogonal to each other (because no eigenstate with eigenvalue 0 is present). In fact, the construction of Wannier states is one way to orthonormalize these eigenstates.
-
-
-
-
21
-
-
0002348163
-
-
SUSCAS 0039-6028 10.1016/0039-6028(84)90299-1
-
D. Thouless, Surf. Sci. SUSCAS 0039-6028 10.1016/0039-6028(84)90299-1 142, 147 (1984).
-
(1984)
Surf. Sci.
, vol.142
, pp. 147
-
-
Thouless, D.1
-
22
-
-
0013014735
-
-
NUPBBO 0550-3213 10.1016/0550-3213(89)90062-X
-
X. Wen and A. Zee, Nucl. Phys. B NUPBBO 0550-3213 10.1016/0550-3213(89) 90062-X 316, 641 (1989).
-
(1989)
Nucl. Phys. B
, vol.316
, pp. 641
-
-
Wen, X.1
Zee, A.2
-
23
-
-
0001248557
-
-
PRBMDO 1098-0121 10.1103/PhysRevB.39.11943
-
M. Kohmoto, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.39.11943 39, 11943 (1989).
-
(1989)
Phys. Rev. B
, vol.39
, pp. 11943
-
-
Kohmoto, M.1
-
24
-
-
80052769383
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.107.126803
-
X.-L. Qi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.107. 126803 107, 126803 (2011).
-
(2011)
Phys. Rev. Lett.
, vol.107
, pp. 126803
-
-
Qi, X.-L.1
-
25
-
-
0000186741
-
-
CMPHAY 0010-3616 10.1007/BF02193559
-
J. Provost and G. Vallee, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/BF02193559 76, 289 (1980).
-
(1980)
Commun. Math. Phys.
, vol.76
, pp. 289
-
-
Provost, J.1
Vallee, G.2
-
26
-
-
34548454416
-
Quantum critical scaling of the geometric tensors
-
DOI 10.1103/PhysRevLett.99.095701
-
L. Campos Venuti and P. Zanardi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.095701 99, 095701 (2007). (Pubitemid 47357773)
-
(2007)
Physical Review Letters
, vol.99
, Issue.9
, pp. 095701
-
-
Campos Venuti, L.1
Zanardi, P.2
|