-
1
-
-
2342575465
-
-
10.1103/PhysRevLett.92.126603
-
J. Sinova, D. Culcer, Q. Niu, N. A. Sinitsyn, T. Jungwirth, and A. H. MacDonald, Phys. Rev. Lett. 92, 126603 (2004). 10.1103/PhysRevLett.92.126603
-
(2004)
Phys. Rev. Lett.
, vol.92
, pp. 126603
-
-
Sinova, J.1
Culcer, D.2
Niu, Q.3
Sinitsyn, N.A.4
Jungwirth, T.5
MacDonald, A.H.6
-
3
-
-
28844477796
-
-
10.1103/PhysRevLett.95.226801
-
C. L. Kane and E. J. Mele, Phys. Rev. Lett. 95, 226801 (2005). 10.1103/PhysRevLett.95.226801
-
(2005)
Phys. Rev. Lett.
, vol.95
, pp. 226801
-
-
Kane, C.L.1
Mele, E.J.2
-
5
-
-
3442880129
-
-
10.1103/PhysRevLett.49.405
-
D. J. Thouless, M. Kohmoto, M. P. Nightingale, and M. den Nijs, Phys. Rev. Lett. 49, 405 (1982). 10.1103/PhysRevLett.49.405
-
(1982)
Phys. Rev. Lett.
, vol.49
, pp. 405
-
-
Thouless, D.J.1
Kohmoto, M.2
Nightingale, M.P.3
Den Nijs, M.4
-
6
-
-
23544435097
-
-
10.1103/PhysRevB.25.2185
-
B. I. Halperin, Phys. Rev. B 25, 2185 (1982). 10.1103/PhysRevB.25.2185
-
(1982)
Phys. Rev. B
, vol.25
, pp. 2185
-
-
Halperin, B.I.1
-
7
-
-
4243734768
-
-
10.1103/PhysRevLett.71.3697
-
Y. Hatsugai, Phys. Rev. Lett. 71, 3697 (1993). 10.1103/PhysRevLett.71. 3697
-
(1993)
Phys. Rev. Lett.
, vol.71
, pp. 3697
-
-
Hatsugai, Y.1
-
8
-
-
33144489555
-
-
10.1103/PhysRevB.73.045322
-
C. Xu and J. E. Moore, Phys. Rev. B 73, 045322 (2006). 10.1103/PhysRevB.73.045322
-
(2006)
Phys. Rev. B
, vol.73
, pp. 045322
-
-
Xu, C.1
Moore, J.E.2
-
10
-
-
67649388540
-
-
Quantization is possible in some cases such as when the Hamiltonian is restricted to the set that commutes with sz.
-
Quantization is possible in some cases such as when the Hamiltonian is restricted to the set that commutes with sz.
-
-
-
-
11
-
-
28844477210
-
-
10.1103/PhysRevLett.95.146802
-
C. L. Kane and E. J. Mele, Phys. Rev. Lett. 95, 146802 (2005). 10.1103/PhysRevLett.95.146802
-
(2005)
Phys. Rev. Lett.
, vol.95
, pp. 146802
-
-
Kane, C.L.1
Mele, E.J.2
-
12
-
-
67649388538
-
-
For an introduction to the theory of fiber bundles and their applications in physics, see Ref.
-
For an introduction to the theory of fiber bundles and their applications in physics, see Ref.
-
-
-
-
13
-
-
33646635283
-
-
10.1016/0003-4916(85)90148-4
-
M. Kohmoto, Ann. Phys. 160, 343 (1985). 10.1016/0003-4916(85)90148-4
-
(1985)
Ann. Phys.
, vol.160
, pp. 343
-
-
Kohmoto, M.1
-
14
-
-
67649403749
-
-
We thank an anonymous referee for pointing this out.
-
We thank an anonymous referee for pointing this out.
-
-
-
-
15
-
-
67649397926
-
-
See, for instance, page 383 of Ref.
-
See, for instance, page 383 of Ref.
-
-
-
-
16
-
-
67649405177
-
-
Our analysis is therefore restricted to Hamiltonians which can be adiabatically continued to one whose filled bands have well-defined Chern numbers.
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Our analysis is therefore restricted to Hamiltonians which can be adiabatically continued to one whose filled bands have well-defined Chern numbers.
-
-
-
-
17
-
-
67649407886
-
-
In the case when the bands do not have well-defined Chern numbers, one may proceed by taking orthogonal linear combinations of them as in the case of a single pair of occupied bands.
-
In the case when the bands do not have well-defined Chern numbers, one may proceed by taking orthogonal linear combinations of them as in the case of a single pair of occupied bands.
-
-
-
-
18
-
-
67649409344
-
-
When the Chern numbers of the bands are not well defined, n is a label for the orthogonal linear combinations of occupied Bloch states discussed previously.
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When the Chern numbers of the bands are not well defined, n is a label for the orthogonal linear combinations of occupied Bloch states discussed previously.
-
-
-
-
20
-
-
67649397925
-
-
arXiv:cond-mat/0603271 (unpublished).
-
R. Roy, arXiv:cond-mat/0603271 (unpublished).
-
-
-
Roy, R.1
-
21
-
-
33746255952
-
-
10.1103/PhysRevLett.97.036808
-
D. N. Sheng, Z. Y. Weng, L. Sheng, and F. D. M. Haldane, Phys. Rev. Lett. 97, 036808 (2006). 10.1103/PhysRevLett.97.036808
-
(2006)
Phys. Rev. Lett.
, vol.97
, pp. 036808
-
-
Sheng, D.N.1
Weng, Z.Y.2
Sheng, L.3
Haldane, F.D.M.4
-
22
-
-
67650592439
-
-
10.1093/qmath/17.1.367
-
M. Atiyah, Q. J. Math. 17, 367 (1966). 10.1093/qmath/17.1.367
-
(1966)
Q. J. Math.
, vol.17
, pp. 367
-
-
Atiyah, M.1
-
23
-
-
33947198126
-
-
10.1103/PhysRevB.75.121403
-
T. Fukui and Y. Hatsugai, Phys. Rev. B 75, 121403 (R) (2007). 10.1103/PhysRevB.75.121403
-
(2007)
Phys. Rev. B
, vol.75
, pp. 121403
-
-
Fukui, T.1
Hatsugai, Y.2
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