-
1
-
-
84968282200
-
-
PRPLCM 0370-1573 10.1016/0370-1573(80)90130-1
-
T. Eguchi, P. B. Gilkey, and A. J. Hanson, Phys. Rep. PRPLCM 0370-1573 10.1016/0370-1573(80)90130-1 66, 213 (1980).
-
(1980)
Phys. Rep.
, vol.66
, pp. 213
-
-
Eguchi, T.1
Gilkey, P.B.2
Hanson, A.J.3
-
2
-
-
0004012649
-
-
edited by S. B. Treiman, R. Jackiw, B. Zumino, and E. Witten (World Scientific, Singapore
-
Current Algebra and Anomaly, edited by, S. B. Treiman,,, R. Jackiw,,, B. Zumino,, and, E. Witten, (World Scientific, Singapore 1985).
-
(1985)
Current Algebra and Anomaly
-
-
-
3
-
-
3442881546
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.53.2449
-
G. W. Semenoff, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.53. 2449 53, 2449 (1984).
-
(1984)
Phys. Rev. Lett.
, vol.53
, pp. 2449
-
-
Semenoff, G.W.1
-
4
-
-
0000783193
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.61.2015
-
F. D. M. Haldane, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett. 61.2015 61, 2015 (1987).
-
(1987)
Phys. Rev. Lett.
, vol.61
, pp. 2015
-
-
Haldane, F.D.M.1
-
5
-
-
3342931760
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.71.1887
-
P. A. Lee, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.71.1887 71, 1887 (1993).
-
(1993)
Phys. Rev. Lett.
, vol.71
, pp. 1887
-
-
Lee, P.A.1
-
7
-
-
0000463250
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.63.907
-
Y. Hasegawa, P. Lederer, T. M. Rice, and P. B. Wiegmann, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.63.907 63, 907 (1989).
-
(1989)
Phys. Rev. Lett.
, vol.63
, pp. 907
-
-
Hasegawa, Y.1
Lederer, P.2
Rice, T.M.3
Wiegmann, P.B.4
-
8
-
-
35949009606
-
-
PRBMDO 0163-1829 10.1103/PhysRevB.39.11413
-
X. G. Wen, F. Wilczek, and A. Zee, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.39.11413 39, 11413 (1989).
-
(1989)
Phys. Rev. B
, vol.39
, pp. 11413
-
-
Wen, X.G.1
Wilczek, F.2
Zee, A.3
-
9
-
-
0000608158
-
-
NUPBBO 0550-3213 10.1016/0550-3213(85)90272-X
-
M. P. A. Fisher and E. Fradkin, Nucl. Phys. B NUPBBO 0550-3213 10.1016/0550-3213(85)90272-X 251, 457 (1984).
-
(1984)
Nucl. Phys. B
, vol.251
, pp. 457
-
-
Fisher, M.P.A.1
Fradkin, E.2
-
10
-
-
0034261268
-
-
PRBMDO 0163-1829 10.1103/PhysRevB.62.R6065
-
K. Ohgushi, S. Murakami, and N. Nagaosa, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.62.R6065 62, R6065 (2000).
-
(2000)
Phys. Rev. B
, vol.62
, pp. 6065
-
-
Ohgushi, K.1
Murakami, S.2
Nagaosa, N.3
-
11
-
-
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
-
12
-
-
0001106242
-
-
PRBMDO 0163-1829 10.1103/PhysRevB.50.7526
-
A. W. W. Ludwig, M. P. A. Fisher, R. Shankar, and G. Grinstein, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.50.7526 50, 7526 (1993).
-
(1993)
Phys. Rev. B
, vol.50
, pp. 7526
-
-
Ludwig, A.W.W.1
Fisher, M.P.A.2
Shankar, R.3
Grinstein, G.4
-
13
-
-
0001615308
-
-
PRBMDO 0163-1829 10.1103/PhysRevB.42.8282
-
Y. Hatsugai and M. Kohmoto, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.42.8282 42, 8282 (1990).
-
(1990)
Phys. Rev. B
, vol.42
, pp. 8282
-
-
Hatsugai, Y.1
Kohmoto, M.2
-
14
-
-
0000807850
-
-
Landau levels in honeycomb lattice, including the E=0 level, were first obtained by PHRVAO 0031-899X 10.1103/PhysRev.104.666
-
Landau levels in honeycomb lattice, including the E=0 level, were first obtained by J. W. McClure, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.104.666 104, 666 (1956).
-
(1956)
Phys. Rev.
, vol.104
, pp. 666
-
-
McClure, J.W.1
-
15
-
-
0037098490
-
-
PRBMDO 0163-1829 10.1103/PhysRevB.65.245420
-
Y. Zheng and T. Ando, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.65. 245420 65, 245420 (2002).
-
(2002)
Phys. Rev. B
, vol.65
, pp. 245420
-
-
Zheng, Y.1
Ando, T.2
-
16
-
-
28844482338
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.95.146801
-
V. P. Gusynin and S. G. Sharapov, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.146801 95, 146801 (2005).
-
(2005)
Phys. Rev. Lett.
, vol.95
, pp. 146801
-
-
Gusynin, V.P.1
Sharapov, S.G.2
-
17
-
-
33645752733
-
-
ZZZZZZ 1745-2473
-
K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. J. Kutsnelson, I. V. Grigovieva, S. V. Dubonos, and A. A. Firsov, Nat. Phys. ZZZZZZ 1745-2473 2, 177 (2006).
-
(2006)
Nat. Phys.
, vol.2
, pp. 177
-
-
Novoselov, K.S.1
Geim, A.K.2
Morozov, S.V.3
Jiang, D.4
Kutsnelson, M.J.5
Grigovieva, I.V.6
Dubonos, S.V.7
Firsov, A.A.8
-
19
-
-
27744534165
-
-
NATUAS 0028-0836 10.1038/nature04233
-
K. S. Novoselov, E. McCann, S. V. Morozov, V. I. Fal'ko, M. I. Katsnelson, V. Zeitler, D. Jiang, F. Schedin, and A. K. Geim, Nature (London) NATUAS 0028-0836 10.1038/nature04233 438, 197 (2005).
-
(2005)
Nature (London)
, vol.438
, pp. 197
-
-
Novoselov, K.S.1
McCann, E.2
Morozov, S.V.3
Fal'Ko, V.I.4
Katsnelson, M.I.5
Zeitler, V.6
Jiang, D.7
Schedin, F.8
Geim, A.K.9
-
20
-
-
27744475163
-
-
NATUAS 0028-0836 10.1038/nature04235
-
Y. Zhang, Y.-W. Tan, H. L. Stormer, and P. Kim, Nature (London) NATUAS 0028-0836 10.1038/nature04235 438, 201 (2005).
-
(2005)
Nature (London)
, vol.438
, pp. 201
-
-
Zhang, Y.1
Tan, Y.-W.2
Stormer, H.L.3
Kim, P.4
-
21
-
-
24344434159
-
-
JUPSAU 0031-9015 10.1143/JPSJ.74.777
-
T. Ando, J. Phys. Soc. Jpn. JUPSAU 0031-9015 10.1143/JPSJ.74.777 74, 777 (2005).
-
(2005)
J. Phys. Soc. Jpn.
, vol.74
, pp. 777
-
-
Ando, T.1
-
22
-
-
0030492538
-
-
JUPSAU 0031-9015 10.1143/JPSJ.65.1920
-
M. Fujita, K. Wakabayashi, K. Nakada, and K. Kusakabe, J. Phys. Soc. Jpn. JUPSAU 0031-9015 10.1143/JPSJ.65.1920 65, 1920 (1996).
-
(1996)
J. Phys. Soc. Jpn.
, vol.65
, pp. 1920
-
-
Fujita, M.1
Wakabayashi, K.2
Nakada, K.3
Kusakabe, K.4
-
23
-
-
0000703370
-
-
PRBMDO 0163-1829 10.1103/PhysRevB.59.8271
-
K. Wakabayashi, M. Fujita, H. Ajiki, and M. Sigrist, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.59.8271 59, 8271 (1999).
-
(1999)
Phys. Rev. B
, vol.59
, pp. 8271
-
-
Wakabayashi, K.1
Fujita, M.2
Ajiki, H.3
Sigrist, M.4
-
25
-
-
0001345770
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.51.2167
-
B. Simon, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.51.2167 51, 2167 (1983).
-
(1983)
Phys. Rev. Lett.
, vol.51
, pp. 2167
-
-
Simon, B.1
-
26
-
-
0000413493
-
-
PRBMDO 0163-1829 10.1103/PhysRevB.40.7387
-
X. G. Wen, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.40.7387 40, 7387 (1989).
-
(1989)
Phys. Rev. B
, vol.40
, pp. 7387
-
-
Wen, X.G.1
-
27
-
-
0003468178
-
-
edited by A. Shapere and F. Wilczek (World Scientific, Singapore
-
Geometric Phases in Physics, edited by, A. Shapere, and, F. Wilczek, (World Scientific, Singapore, 1989).
-
(1989)
Geometric Phases in Physics
-
-
-
28
-
-
20444366206
-
-
JUPSAU 0031-9015 10.1143/JPSJ.73.2604
-
Y. Hatsugai, J. Phys. Soc. Jpn. JUPSAU 0031-9015 10.1143/JPSJ.73.2604 73, 2604 (2004).
-
(2004)
J. Phys. Soc. Jpn.
, vol.73
, pp. 2604
-
-
Hatsugai, Y.1
-
29
-
-
20444428732
-
-
JUPSAU 0031-9015 10.1143/JPSJ.74.1374
-
Y. Hatsugai, J. Phys. Soc. Jpn. JUPSAU 0031-9015 10.1143/JPSJ.74.1374 74, 1374 (2004).
-
(2004)
J. Phys. Soc. Jpn.
, vol.74
, pp. 1374
-
-
Hatsugai, Y.1
-
30
-
-
0000840903
-
-
PRBMDO 0163-1829 10.1103/PhysRevB.23.5632
-
R. B. Laughlin, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.23.5632 23, 5632 (1981).
-
(1981)
Phys. Rev. B
, vol.23
, pp. 5632
-
-
Laughlin, R.B.1
-
31
-
-
23544435097
-
-
PRBMDO 0163-1829 10.1103/PhysRevB.25.2185
-
B. I. Halperin, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.25.2185 25, 2185 (1982).
-
(1982)
Phys. Rev. B
, vol.25
, pp. 2185
-
-
Halperin, B.I.1
-
32
-
-
0001295828
-
-
PRBMDO 0163-1829 10.1103/PhysRevB.48.11851
-
Y. Hatsugai, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.48.11851 48, 11851 (1993).
-
(1993)
Phys. Rev. B
, vol.48
, pp. 11851
-
-
Hatsugai, Y.1
-
33
-
-
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
-
34
-
-
0000921531
-
-
PYLBAJ 0370-2693 10.1016/0370-2693(82)90728-6
-
E. Witten, Phys. Lett. PYLBAJ 0370-2693 10.1016/0370-2693(82)90728-6 117B, 324 (1982).
-
(1982)
Phys. Lett.
, vol.117
, pp. 324
-
-
Witten, E.1
-
35
-
-
0000268290
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.51.2077
-
A. J. Niemi and G. W. Semenoff, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.51.2077 51, 2077 (1983).
-
(1983)
Phys. Rev. Lett.
, vol.51
, pp. 2077
-
-
Niemi, A.J.1
Semenoff, G.W.2
-
36
-
-
45849155239
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.89.077002
-
S. Ryu and Y. Hatsugai, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.89.077002 89, 077002 (2002).
-
(2002)
Phys. Rev. Lett.
, vol.89
, pp. 077002
-
-
Ryu, S.1
Hatsugai, Y.2
-
37
-
-
33751012817
-
-
Δ delineates a circle centered at C0 =1+ ei k2 with a radius r= 1+2 (t′ t)cos k2 + (t′ t) 2 in the complex Δ plane when k1 is varied from 0 to 2π. By examining C0 and r, we can show that we have a Dirac (linear) dispersion when the circle goes through the origin, which occurs for -3≤ t′ t≤1.
-
Δ delineates a circle centered at C0 =1+ ei k2 with a radius r= 1+2 (t′ t)cos k2 + (t′ t) 2 in the complex Δ plane when k1 is varied from 0 to 2π. By examining C0 and r, we can show that we have a Dirac (linear) dispersion when the circle goes through the origin, which occurs for -3≤ t′ t≤1.
-
-
-
-
38
-
-
0001032458
-
-
PLRBAQ 0556-2805 10.1103/PhysRevB.14.2239
-
D. R. Hofstadter, Phys. Rev. B PLRBAQ 0556-2805 10.1103/PhysRevB.14.2239 14, 2239 (1976).
-
(1976)
Phys. Rev. B
, vol.14
, pp. 2239
-
-
Hofstadter, D.R.1
-
39
-
-
0037850925
-
-
PHYCE6 0921-4534
-
S. Ryu and Y. Hatsugai, Physica C PHYCE6 0921-4534 388-389, 90 (2003).
-
(2003)
Physica C
, vol.388-389
, pp. 90
-
-
Ryu, S.1
Hatsugai, Y.2
-
40
-
-
33745505316
-
-
PRBMDO 0163-1829 10.1103/PhysRevB.73.233406
-
D. N. Sheng, L. Sheng, and Z. Y. Weng, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.73.233406 73, 233406 (2006).
-
(2006)
Phys. Rev. B
, vol.73
, pp. 233406
-
-
Sheng, D.N.1
Sheng, L.2
Weng, Z.Y.3
-
41
-
-
33751003928
-
-
cond-mat/0604433;
-
Topological QHE numbers when the transfer energies along three directions in the honeycomb lattice are varied including the isotropic case have recently been discussed by Y. Hasegawa, R. Konno, H. Nakano, and M. Kohmoto, cond-mat/0604433;
-
-
-
Hasegawa, Y.1
Konno, R.2
Nakano, H.3
Kohmoto, M.4
-
43
-
-
33751009472
-
-
A fermion doubling in honeycomb lattice in zero total flux was discussed in.
-
A fermion doubling in honeycomb lattice in zero total flux was discussed in.
-
-
-
-
44
-
-
0022114032
-
-
JOPQAG 0302-0738
-
R. Rammal, J. Phys. (Paris) JOPQAG 0302-0738 46, 1345 (1985).
-
(1985)
J. Phys. (Paris)
, vol.46
, pp. 1345
-
-
Rammal, R.1
-
45
-
-
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
-
46
-
-
33646635283
-
-
APNYA6 0003-4916 10.1016/0003-4916(85)90148-4
-
M. Kohmoto, Ann. Phys. (N.Y.) APNYA6 0003-4916 10.1016/0003-4916(85) 90148-4 160, 355 (1985).
-
(1985)
Ann. Phys. (N.Y.)
, vol.160
, pp. 355
-
-
Kohmoto, M.1
-
47
-
-
0019582156
-
-
SSCOA4 0038-1098 10.1016/0038-1098(81)90021-1
-
H. Aoki and T. Ando, Solid State Commun. SSCOA4 0038-1098 10.1016/0038-1098(81)90021-1 38, 1079 (1981).
-
(1981)
Solid State Commun.
, vol.38
, pp. 1079
-
-
Aoki, H.1
Ando, T.2
-
50
-
-
0010134338
-
-
CMPHAY 0010-3616 10.1007/BF02029132
-
M. Lüscher, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/BF02029132 85, 39 (1982).
-
(1982)
Commun. Math. Phys.
, vol.85
, pp. 39
-
-
Lüscher, M.1
-
51
-
-
0000968658
-
-
APNYA6 0003-4916 10.1016/0003-4916(85)90086-7
-
A. Phillips, Ann. Phys. (N.Y.) APNYA6 0003-4916 10.1016/0003-4916(85) 90086-7 161, 399 (1985).
-
(1985)
Ann. Phys. (N.Y.)
, vol.161
, pp. 399
-
-
Phillips, A.1
-
52
-
-
0001010770
-
-
CMPHAY 0010-3616 10.1007/BF01211167
-
A. Phillips and D. Stone, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/BF01211167 103, 599 (1986).
-
(1986)
Commun. Math. Phys.
, vol.103
, pp. 599
-
-
Phillips, A.1
Stone, D.2
-
54
-
-
0033545139
-
-
NUPBBO 0550-3213 10.1016/S0550-3213(98)00680-4
-
M. Lüscher, Nucl. Phys. B NUPBBO 0550-3213 10.1016/S0550-3213(98) 00680-4 538, 515 (1999).
-
(1999)
Nucl. Phys. B
, vol.538
, pp. 515
-
-
Lüscher, M.1
-
56
-
-
0038471908
-
-
JCOMEL 0953-8984 10.1088/0953-8984/9/12/003
-
Y. Hatsugai, J. Phys.: Condens. Matter JCOMEL 0953-8984 10.1088/0953-8984/9/12/003 9, 2507 (1997).
-
(1997)
J. Phys.: Condens. Matter
, vol.9
, pp. 2507
-
-
Hatsugai, Y.1
-
58
-
-
0026820664
-
-
SUSCAS 0039-6028 10.1016/0039-6028(92)90323-X
-
H. Aoki, Surf. Sci. SUSCAS 0039-6028 10.1016/0039-6028(92)90323-X 263, 137 (1992).
-
(1992)
Surf. Sci.
, vol.263
, pp. 137
-
-
Aoki, H.1
|