-
2
-
-
0037122294
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.89.256601
-
Y. Asada, K. Slevin, and T. Ohtsuki, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.89.256601 89, 256601 (2002)
-
(2002)
Phys. Rev. Lett.
, vol.89
, pp. 256601
-
-
Asada, Y.1
Slevin, K.2
Ohtsuki, T.3
-
3
-
-
45849156033
-
-
PRBMDO 0163-1829 10.1103/PhysRevB.70.035115
-
Y. Asada, K. Slevin, and T. Ohtsuki, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.70.035115 70, 035115 (2004).
-
(2004)
Phys. Rev. B
, vol.70
, pp. 035115
-
-
Asada, Y.1
Slevin, K.2
Ohtsuki, T.3
-
4
-
-
34147212281
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.98.156802
-
H. Obuse, A. R. Subramaniam, A. Furusaki, I. A. Gruzberg, and A. W. W. Ludwig, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.156802 98, 156802 (2007).
-
(2007)
Phys. Rev. Lett.
, vol.98
, pp. 156802
-
-
Obuse, H.1
Subramaniam, A.R.2
Furusaki, A.3
Gruzberg, I.A.4
Ludwig, A.W.W.5
-
5
-
-
33846442443
-
-
PRBMDO 0163-1829 10.1103/PhysRevB.75.041303
-
A. Mildenberger and F. Evers, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.75.041303 75, 041303 (R) (2007).
-
(2007)
Phys. Rev. B
, vol.75
, pp. 041303
-
-
Mildenberger, A.1
Evers, F.2
-
6
-
-
28844477210
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.95.146802
-
C. L. Kane and E. J. Mele, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.146802 95, 146802 (2005)
-
(2005)
Phys. Rev. Lett.
, vol.95
, pp. 146802
-
-
Kane, C.L.1
Mele, E.J.2
-
7
-
-
28844477796
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.95.226801
-
C. L. Kane and E. J. Mele, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.226801 95, 226801 (2005).
-
(2005)
Phys. Rev. Lett.
, vol.95
, pp. 226801
-
-
Kane, C.L.1
Mele, E.J.2
-
8
-
-
33644917486
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.96.106802
-
B. A. Bernevig and S.-C. Zhang, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.106802 96, 106802 (2006).
-
(2006)
Phys. Rev. Lett.
, vol.96
, pp. 106802
-
-
Bernevig, B.A.1
Zhang, S.-C.2
-
9
-
-
33845708953
-
-
SCIEAS 0036-8075 10.1126/science.1133734
-
B. A. Bernevig, T. L. Hughes, and S.-C. Zhang, Science SCIEAS 0036-8075 10.1126/science.1133734 314, 1757 (2006).
-
(2006)
Science
, vol.314
, pp. 1757
-
-
Bernevig, B.A.1
Hughes, T.L.2
Zhang, S.-C.3
-
10
-
-
38949129028
-
-
SCIEAS 0036-8075 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 SCIEAS 0036-8075 10.1126/science.1148047 318, 766 (2007).
-
(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
-
11
-
-
33644910778
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.96.106401
-
C. Wu, B. A. Bernevig, and S.-C. Zhang, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.106401 96, 106401 (2006).
-
(2006)
Phys. Rev. Lett.
, vol.96
, pp. 106401
-
-
Wu, C.1
Bernevig, B.A.2
Zhang, S.-C.3
-
12
-
-
33144489555
-
-
PRBMDO 0163-1829 10.1103/PhysRevB.73.045322
-
C. Xu and J. E. Moore, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.73. 045322 73, 045322 (2006).
-
(2006)
Phys. Rev. B
, vol.73
, pp. 045322
-
-
Xu, C.1
Moore, J.E.2
-
13
-
-
33847015684
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.98.076802
-
M. Onoda, Y. Avishai, and N. Nagaosa, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.076802 98, 076802 (2007).
-
(2007)
Phys. Rev. Lett.
, vol.98
, pp. 076802
-
-
Onoda, M.1
Avishai, Y.2
Nagaosa, N.3
-
14
-
-
34547585386
-
-
PRBMDO 0163-1829 10.1103/PhysRevB.76.075301
-
H. Obuse, A. Furusaki, S. Ryu, and C. Mudry, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.76.075301 76, 075301 (2007).
-
(2007)
Phys. Rev. B
, vol.76
, pp. 075301
-
-
Obuse, H.1
Furusaki, A.2
Ryu, S.3
Mudry, C.4
-
15
-
-
33645325128
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.96.126802
-
A. R. Subramaniam, I. A. Gruzberg, A. W. W. Ludwig, F. Evers, A. Mildenberger, and A. D. Mirlin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.126802 96, 126802 (2006).
-
(2006)
Phys. Rev. Lett.
, vol.96
, pp. 126802
-
-
Subramaniam, A.R.1
Gruzberg, I.A.2
Ludwig, A.W.W.3
Evers, F.4
Mildenberger, A.5
Mirlin, A.D.6
-
16
-
-
51349100139
-
-
A similar analysis can be done in the opposite limit of X→0, for which the topological nature of the insulating state can be deduced by considering the limit of small θ (>0). This effectively amounts to the interchange of the nodes and S and S′. (Taking the small- θ limit is justified by the phase diagram in Fig. 11 of Ref..) By doing so, the conclusion as to whether a helical edge state is present on upper/lower boundaries is reversed compared to the conclusion for the X→∞ limit.
-
A similar analysis can be done in the opposite limit of X→0, for which the topological nature of the insulating state can be deduced by considering the limit of small θ (>0). This effectively amounts to the interchange of the nodes and S and S′. (Taking the small- θ limit is justified by the phase diagram in Fig. 11 of Ref..) By doing so, the conclusion as to whether a helical edge state is present on upper/lower boundaries is reversed compared to the conclusion for the X→∞ limit.
-
-
-
-
17
-
-
0012861668
-
-
JPSOAW 0022-3719 10.1088/0022-3719/21/14/008
-
J. T. Chalker and P. D. Coddington, J. Phys. C JPSOAW 0022-3719 10.1088/0022-3719/21/14/008 21, 2665 (1988).
-
(1988)
J. Phys. C
, vol.21
, pp. 2665
-
-
Chalker, J.T.1
Coddington, P.D.2
-
18
-
-
51349142064
-
-
Lyapunov exponents are twofold degenerate due to the Kramers degeneracy in the geometries of Figs. 3 3, for which the transfer matrices are 4M×4M matrices.
-
Lyapunov exponents are twofold degenerate due to the Kramers degeneracy in the geometries of Figs. 3 3, for which the transfer matrices are 4M×4M matrices.
-
-
-
-
20
-
-
4243641159
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.69.1584
-
M. R. Zirnbauer, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett. 69.1584 69, 1584 (1992).
-
(1992)
Phys. Rev. Lett.
, vol.69
, pp. 1584
-
-
Zirnbauer, M.R.1
-
21
-
-
21144432194
-
-
JUPSAU 0031-9015 10.1143/JPSJ.73.9
-
Y. Takane, J. Phys. Soc. Jpn. JUPSAU 0031-9015 10.1143/JPSJ.73.9 73, 9 (2004)
-
(2004)
J. Phys. Soc. Jpn.
, vol.73
, pp. 9
-
-
Takane, Y.1
-
22
-
-
20144385792
-
-
JUPSAU 0031-9015 10.1143/JPSJ.73.1430
-
Y. Takane, J. Phys. Soc. Jpn. JUPSAU 0031-9015 10.1143/JPSJ.73.1430 73, 1430 (2004)
-
(2004)
J. Phys. Soc. Jpn.
, vol.73
, pp. 1430
-
-
Takane, Y.1
-
23
-
-
20144369931
-
-
JUPSAU 0031-9015 10.1143/JPSJ.73.2366
-
Y. Takane, J. Phys. Soc. Jpn. JUPSAU 0031-9015 10.1143/JPSJ.73.2366 73, 2366 (2004).
-
(2004)
J. Phys. Soc. Jpn.
, vol.73
, pp. 2366
-
-
Takane, Y.1
-
24
-
-
0000977044
-
-
JPHAC5 0305-4470 10.1088/0305-4470/17/7/003
-
J. L. Cardy, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/17/7/003 17, L385 (1984).
-
(1984)
J. Phys. a
, vol.17
, pp. 385
-
-
Cardy, J.L.1
-
25
-
-
0000505034
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.82.382
-
K. Slevin and T. Ohtsuki, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.82.382 82, 382 (1999).
-
(1999)
Phys. Rev. Lett.
, vol.82
, pp. 382
-
-
Slevin, K.1
Ohtsuki, T.2
-
26
-
-
84956227885
-
-
EULEEJ 0295-5075 10.1209/0295-5075/32/3/007
-
R. Klesse and M. Metzler, Europhys. Lett. EULEEJ 0295-5075 10.1209/0295-5075/32/3/007 32, 229 (1995).
-
(1995)
Europhys. Lett.
, vol.32
, pp. 229
-
-
Klesse, R.1
Metzler, M.2
-
27
-
-
0000087599
-
-
IJPBEV 0217-9792 10.1142/S021797929400049X
-
M. Janssen, Int. J. Mod. Phys. B IJPBEV 0217-9792 10.1142/ S021797929400049X 8, 943 (1994)
-
(1994)
Int. J. Mod. Phys. B
, vol.8
, pp. 943
-
-
Janssen, M.1
-
28
-
-
0032016706
-
-
PRPLCM 0370-1573 10.1016/S0370-1573(97)00050-1
-
M. Janssen, Phys. Rep. PRPLCM 0370-1573 10.1016/S0370-1573(97)00050-1 295, 1 (1998).
-
(1998)
Phys. Rep.
, vol.295
, pp. 1
-
-
Janssen, M.1
-
29
-
-
34047171350
-
-
PRBMDO 0163-1829 10.1103/PhysRevB.75.094204
-
A. Mildenberger, A. R. Subramaniam, R. Narayanan, F. Evers, I. A. Gruzberg, and A. D. Mirlin, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.75. 094204 75, 094204 (2007).
-
(2007)
Phys. Rev. B
, vol.75
, pp. 094204
-
-
Mildenberger, A.1
Subramaniam, A.R.2
Narayanan, R.3
Evers, F.4
Gruzberg, I.A.5
Mirlin, A.D.6
-
30
-
-
51349145015
-
-
arXiv:0804.2334, Phys. Rev. Lett. (to be published).
-
F. Evers, A. Mildenberger, and A. D. Mirlin, arXiv:0804.2334, Phys. Rev. Lett. (to be published).
-
-
-
Evers, F.1
Mildenberger, A.2
Mirlin, A.D.3
-
31
-
-
51349132971
-
-
arXiv:0804.2409, Phys. Rev. Lett. (to be published).
-
H. Obuse, A. R. Subramaniam, A. Furusaki, I. A. Gruzberg, and A. W. W. Ludwig, arXiv:0804.2409, Phys. Rev. Lett. (to be published).
-
-
-
Obuse, H.1
Subramaniam, A.R.2
Furusaki, A.3
Gruzberg, I.A.4
Ludwig, A.W.W.5
-
33
-
-
0030572056
-
-
NUPBBO 0550-3213 10.1016/0550-3213(96)00128-9
-
C. Mudry, C. Chamon, and X.-G. Wen, Nucl. Phys. B NUPBBO 0550-3213 10.1016/0550-3213(96)00128-9 466, 383 (1996).
-
(1996)
Nucl. Phys. B
, vol.466
, pp. 383
-
-
Mudry, C.1
Chamon, C.2
Wen, X.-G.3
-
34
-
-
4243640910
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.77.4194
-
C. C. Chamon, C. Mudry, and X.-G. Wen, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.77.4194 77, 4194 (1996).
-
(1996)
Phys. Rev. Lett.
, vol.77
, pp. 4194
-
-
Chamon, C.C.1
Mudry, C.2
Wen, X.-G.3
-
35
-
-
0037301760
-
-
PRBMDO 0163-1829 10.1103/PhysRevB.67.064202
-
C. Mudry, S. Ryu, and A. Furusaki, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.67.064202 67, 064202 (2003).
-
(2003)
Phys. Rev. B
, vol.67
, pp. 064202
-
-
Mudry, C.1
Ryu, S.2
Furusaki, A.3
-
36
-
-
0034664558
-
-
PRBMDO 0163-1829 10.1103/PhysRevB.62.7920
-
A. D. Mirlin and F. Evers, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.62.7920 62, 7920 (2000).
-
(2000)
Phys. Rev. B
, vol.62
, pp. 7920
-
-
Mirlin, A.D.1
Evers, F.2
-
37
-
-
33746620967
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.97.046803
-
A. D. Mirlin, Y. V. Fyodorov, A. Mildenberger, and F. Evers, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.046803 97, 046803 (2006).
-
(2006)
Phys. Rev. Lett.
, vol.97
, pp. 046803
-
-
Mirlin, A.D.1
Fyodorov, Y.V.2
Mildenberger, A.3
Evers, F.4
-
38
-
-
0000849166
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.66.247
-
B. Duplantier and A. W. W. Ludwig, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.66.247 66, 247 (1991).
-
(1991)
Phys. Rev. Lett.
, vol.66
, pp. 247
-
-
Duplantier, B.1
Ludwig, A.W.W.2
-
39
-
-
0036971048
-
-
JUPSAU 0031-9015 10.1143/JPSJ.71.2753
-
T. Ando and H. Suzuura, J. Phys. Soc. Jpn. JUPSAU 0031-9015 10.1143/JPSJ.71.2753 71, 2753 (2002).
-
(2002)
J. Phys. Soc. Jpn.
, vol.71
, pp. 2753
-
-
Ando, T.1
Suzuura, H.2
-
40
-
-
6644222165
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.86.2094
-
R. Klesse and M. R. Zirnbauer, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86.2094 86, 2094 (2001).
-
(2001)
Phys. Rev. Lett.
, vol.86
, pp. 2094
-
-
Klesse, R.1
Zirnbauer, M.R.2
-
41
-
-
24544453124
-
-
NUPBBO 0550-3213 10.1016/0550-3213(89)90521-X
-
J. L. Cardy, Nucl. Phys. B NUPBBO 0550-3213 10.1016/0550-3213(89)90521-X 324, 581 (1989).
-
(1989)
Nucl. Phys. B
, vol.324
, pp. 581
-
-
Cardy, J.L.1
|