-
2
-
-
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
-
3
-
-
45849155239
-
-
10.1103/PhysRevLett.89.077002
-
S. Ryu and Y. Hatsugai, Phys. Rev. Lett. 89, 077002 (2002). 10.1103/PhysRevLett.89.077002
-
(2002)
Phys. Rev. Lett.
, vol.89
, pp. 077002
-
-
Ryu, S.1
Hatsugai, Y.2
-
6
-
-
38949129028
-
-
10.1126/science.1148047
-
M. König, S. Wiedmann, C. Brüne, A. Roth, H. Buhmann, L. W. Molenkamp, X.-L. Qi, and S.-C. Zhang, Science 318, 766 (2007). 10.1126/science.1148047
-
(2007)
Science
, vol.318
, pp. 766
-
-
König, M.1
Wiedmann, S.2
Brüne, C.3
Roth, A.4
Buhmann, H.5
Molenkamp, L.W.6
Qi, X.-L.7
Zhang, S.-C.8
-
7
-
-
42949106486
-
-
10.1038/nature06843
-
D. Hsieh, D. Qian, L. Wray, Y. Xia, Y. S. Hor, R. J. Cava, and M. Z. Hasan, Nature (London) 452, 970 (2008). 10.1038/nature06843
-
(2008)
Nature (London)
, vol.452
, pp. 970
-
-
Hsieh, D.1
Qian, D.2
Wray, L.3
Xia, Y.4
Hor, Y.S.5
Cava, R.J.6
Hasan, M.Z.7
-
8
-
-
78651343064
-
-
AIP Conf. Proc. No. 1134 (AIP, New York
-
A. Kitaev, Advances in Theoretical Physics: Landau Memorial Conference Chernogolokova (Russia), 22-26 June 2008, AIP Conf. Proc. No. 1134 (AIP, New York, 2009), p. 22.
-
(2009)
Advances in Theoretical Physics: Landau Memorial Conference Chernogolokova (Russia), 22-26 June 2008
, pp. 22
-
-
Kitaev, A.1
-
9
-
-
57249110726
-
-
10.1103/PhysRevB.78.195125
-
A. P. Schnyder, S. Ryu, A. Furusaki, and A. W. W. Ludwig, Phys. Rev. B 78, 195125 (2008). 10.1103/PhysRevB.78.195125
-
(2008)
Phys. Rev. B
, vol.78
, pp. 195125
-
-
Schnyder, A.P.1
Ryu, S.2
Furusaki, A.3
Ludwig, A.W.W.4
-
11
-
-
33750926079
-
-
10.1103/PhysRevB.74.195312
-
L. Fu and C. L. Kane, Phys. Rev. B 74, 195312 (2006). 10.1103/PhysRevB.74.195312
-
(2006)
Phys. Rev. B
, vol.74
, pp. 195312
-
-
Fu, L.1
Kane, C.L.2
-
12
-
-
21744448915
-
-
10.1143/JPSJ.74.1214
-
R. Shindou, J. Phys. Soc. Jpn. 74, 1214 (2005). 10.1143/JPSJ.74.1214
-
(2005)
J. Phys. Soc. Jpn.
, vol.74
, pp. 1214
-
-
Shindou, R.1
-
15
-
-
33644561837
-
-
10.1103/PhysRevB.27.6083
-
D. J. Thouless, Phys. Rev. B 27, 6083 (1983). 10.1103/PhysRevB.27.6083
-
(1983)
Phys. Rev. B
, vol.27
, pp. 6083
-
-
Thouless, D.J.1
-
16
-
-
0001593798
-
-
10.1088/0305-4470/17/12/016
-
Q. Niu and D. J. Thouless, J. Phys. A 17, 2453 (1984). 10.1088/0305-4470/17/12/016
-
(1984)
J. Phys. A
, vol.17
, pp. 2453
-
-
Niu, Q.1
Thouless, D.J.2
-
17
-
-
77957118111
-
-
10.1103/PhysRevA.82.033429
-
T. Kitagawa, M. S. Rudner, E. Berg, and E. Demler, Phys. Rev. A 82, 033429 (2010). 10.1103/PhysRevA.82.033429
-
(2010)
Phys. Rev. A
, vol.82
, pp. 033429
-
-
Kitagawa, T.1
Rudner, M.S.2
Berg, E.3
Demler, E.4
-
18
-
-
3042690839
-
-
10.1088/1367-2630/5/1/356
-
D. Jaksch and P. Zoller, New J. Phys. 5, 56 (2003). 10.1088/1367-2630/5/ 1/356
-
(2003)
New J. Phys.
, vol.5
, pp. 56
-
-
Jaksch, D.1
Zoller, P.2
-
20
-
-
33845390735
-
-
10.1103/PhysRevLett.97.240401
-
S.-L. Zhu, H. Fu, C.-J. Wu, S.-C. Zhang, and L.-M. Duan, Phys. Rev. Lett. 97, 240401 (2006). 10.1103/PhysRevLett.97.240401
-
(2006)
Phys. Rev. Lett.
, vol.97
, pp. 240401
-
-
Zhu, S.-L.1
Fu, H.2
Wu, C.-J.3
Zhang, S.-C.4
Duan, L.-M.5
-
21
-
-
68849124652
-
-
10.1103/PhysRevA.79.011604
-
K. J. Günter, M. Cheneau, T. Yefsah, S. P. Rath, and J. Dalibard, Phys. Rev. A 79, 011604 (2009). 10.1103/PhysRevA.79.011604
-
(2009)
Phys. Rev. A
, vol.79
, pp. 011604
-
-
Günter, K.J.1
Cheneau, M.2
Yefsah, T.3
Rath, S.P.4
Dalibard, J.5
-
22
-
-
66749129585
-
-
10.1103/PhysRevA.79.063613
-
I. B. Spielman, Phys. Rev. A 79, 063613 (2009). 10.1103/PhysRevA.79. 063613
-
(2009)
Phys. Rev. A
, vol.79
, pp. 063613
-
-
Spielman, I.B.1
-
23
-
-
27144502377
-
-
10.1103/PhysRevLett.95.010403
-
K. Osterloh, M. Baig, L. Santos, P. Zoller, and M. Lewenstein, Phys. Rev. Lett. 95, 010403 (2005). 10.1103/PhysRevLett.95.010403
-
(2005)
Phys. Rev. Lett.
, vol.95
, pp. 010403
-
-
Osterloh, K.1
Baig, M.2
Santos, L.3
Zoller, P.4
Lewenstein, M.5
-
24
-
-
74949096195
-
-
10.1103/PhysRevLett.104.033903
-
J. Otterbach, J. Ruseckas, R. G. Unanyan, G. Juzeliunas, and M. Fleischhauer, Phys. Rev. Lett. 104, 033903 (2010). 10.1103/PhysRevLett.104. 033903
-
(2010)
Phys. Rev. Lett.
, vol.104
, pp. 033903
-
-
Otterbach, J.1
Ruseckas, J.2
Unanyan, R.G.3
Juzeliunas, G.4
Fleischhauer, M.5
-
25
-
-
62149095055
-
-
10.1103/PhysRevB.79.081406
-
T. Oka and H. Aoki, Phys. Rev. B 79, 081406 (2009) see also erratum. 10.1103/PhysRevB.79.081406
-
(2009)
Phys. Rev. B
, vol.79
, pp. 081406
-
-
Oka, T.1
Aoki, H.2
-
26
-
-
77954111277
-
-
10.1103/PhysRevLett.105.017401
-
J.-i. Inoue and A. Tanaka, Phys. Rev. Lett. 105, 017401 (2010). 10.1103/PhysRevLett.105.017401
-
(2010)
Phys. Rev. Lett.
, vol.105
, pp. 017401
-
-
Inoue, J.-I.1
Tanaka, A.2
-
28
-
-
36149022366
-
-
10.1103/PhysRev.138.B979
-
J. H. Shirley, Phys. Rev. 138, B979 (1965). 10.1103/PhysRev.138.B979
-
(1965)
Phys. Rev.
, vol.138
, pp. 979
-
-
Shirley, J.H.1
-
29
-
-
78650821154
-
-
1 is invariant under such similarity transformations, and therefore, is independent of the choice of basis.
-
1 is invariant under such similarity transformations, and therefore, is independent of the choice of basis.
-
-
-
-
30
-
-
78650839764
-
-
k,α } such that they become smooth as a function of crystal momentum k.
-
k,α } such that they become smooth as a function of crystal momentum k.
-
-
-
-
31
-
-
78650837993
-
-
When the system is finite, and thus, crystal momenta are discrete, the notion of quasienergy winding becomes ill defined. However, one can make the concept of winding numbers meaningful again by defining the topological invariant through twisted boundary conditions as described in Appendix .
-
When the system is finite, and thus, crystal momenta are discrete, the notion of quasienergy winding becomes ill defined. However, one can make the concept of winding numbers meaningful again by defining the topological invariant through twisted boundary conditions as described in Appendix.
-
-
-
-
32
-
-
39249085192
-
-
10.1103/PhysRevLett.87.070601;
-
H. Schanz, M.-F. Otto, R. Ketzmerick, and T. Dittrich, Phys. Rev. Lett. 87, 070601 (2001) 10.1103/PhysRevLett.87.070601
-
(2001)
Phys. Rev. Lett.
, vol.87
, pp. 070601
-
-
Schanz, H.1
Otto, M.-F.2
Ketzmerick, R.3
Dittrich, T.4
-
34
-
-
0003482664
-
-
Graduate Student Series in Physics, 2nd ed. (Taylor & Francis, London, 10.1201/9781420056945
-
M. Nakahara, Geometry, Topology and Physics, Graduate Student Series in Physics, 2nd ed. (Taylor & Francis, London, 2003). 10.1201/9781420056945
-
(2003)
Geometry, Topology and Physics
-
-
Nakahara, M.1
-
35
-
-
78650831669
-
-
If the quasienergy spectrum is gapped, it is always possible to continuously deform the spectrum so that all of the bands become flat (i.e., independent of the crystal momentum) and degenerate. After this deformation, the evolution operator becomes proportional to unity for all k. Such an evolution operator is clearly topologically trivial. On the other hand, if the quasienergy spectrum is gapless, this procedure cannot be carried out because the spectrum has to be periodic in k throughout the deformation.
-
If the quasienergy spectrum is gapped, it is always possible to continuously deform the spectrum so that all of the bands become flat (i.e., independent of the crystal momentum) and degenerate. After this deformation, the evolution operator becomes proportional to unity for all k. Such an evolution operator is clearly topologically trivial. On the other hand, if the quasienergy spectrum is gapless, this procedure cannot be carried out because the spectrum has to be periodic in k throughout the deformation.
-
-
-
-
36
-
-
78650841125
-
-
In particular, there is no quasienergy winding at λ∼1, and all the homotopy classes of the Floquet operator are trivial.
-
In particular, there is no quasienergy winding at λ ∼ 1, and all the homotopy classes of the Floquet operator are trivial.
-
-
-
-
37
-
-
78650809442
-
-
More general Hamiltonians with two bands can have a sublattice- independent energy shift but determinant of evolution operators resulting from the dynamics considered in this section is unity, and therefore, this term is absent here.
-
More general Hamiltonians with two bands can have a sublattice- independent energy shift but determinant of evolution operators resulting from the dynamics considered in this section is unity, and therefore, this term is absent here.
-
-
-
-
38
-
-
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
-
39
-
-
78650830064
-
-
Chern number above λc′ is again ±1.
-
Chern number above λ c ′ is again ± 1.
-
-
-
-
40
-
-
78650836099
-
-
1 also occur for such edges as well.
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1 also occur for such edges as well.
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