Topological aspects of the quantum Hall effect

Journal of Physics Condensed Matter

Volumn 9, Issue 12, 1997, Pages 2507-2549

  Hatsugai, Y ^a  

^a UNIVERSITY OF TOKYO   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038471908     PISSN: 09538984     EISSN: None     Source Type: Journal    
DOI: 10.1088/0953-8984/9/12/003     Document Type: Review

References (73)

1. See for example Shapere A and Wilczek F (ed) 1989 Geometric Phases in Physics (Singapore: World Scientific)
2. Dirac P A M 1931 Proc. R. Soc. A 133 60
3. Wu T T and Yang C N 1975 Phys. Rev. D 12 3845
4. Byers N and Yang C N 1961 Phys. Rev. Lett. 7 46
5. Aharonov Y and Bohm D 1959 Phys. Rev. 115 485
6. Berry M V 1984 Proc. R. Soc. A 392 45
7. von Klitzing K, Dorda G and Pepper M 1980 Phys. Rev. Lett. 45 494
8. Zak J 1964 Phys. Rev. 134 A1602 Zak J 1964 Phys. Rev. 134 A1607
9. Zak J 1964 Phys. Rev. 134 A1602 Zak J 1964 Phys. Rev. 134 A1607
10. Laughlin R B 1981 Phys. Rev. B 23 5632
11. Halperin B I 1982 Phys. Rev. B 25 2185
12. Azbel M Ya 1964 Zh. Eksp. Teor. Fiz. 46 929 (Engl. Transl. 1964 Sov. Phys.-JETP 19 634)
13. Azbel M Ya 1964 Zh. Eksp. Teor. Fiz. 46 929 (Engl. Transl. 1964 Sov. Phys.-JETP 19 634)
14. Hofstadter D R 1976 Phys. Rev. B 14 2239
15. Wannier G H 1978 Phys. Status Solidi b 88 757 Wannier G H, Obermair G M and Ray R 1979 Phys. Status Solidi b 93 337
16. Wannier G H 1978 Phys. Status Solidi b 88 757 Wannier G H, Obermair G M and Ray R 1979 Phys. Status Solidi b 93 337
17. Thouless D J, Kohmoto M, Nightingale P and den Nijs M 1982 Phys. Rev. Lett. 49 405
18. Kohmoto M 1985 Ann. Phys., NY 160 355
19. Hatsugai Y 1993 Phys. Rev. B 48 11 851
20. Hatsugai Y 1993 Phys. Rev. Lett. 71 3697
21. Hatsugai Y 1996 Quantum Coherence and Decoherence ed K Fujikawa and Y A Ono (Amsterdam: North-Holland) p 167
22. Wiegmann P B and Zabrodin A V 1994 Phys. Rev. Lett. 72 1890
23. Fadeev L D and Kashaev R M 1993 University of Helsinki Report No HU-TFT-93-63
24. Hatsugai Y, Kohmoto M and Wu Y S 1994 Phys. Rev. Lett. 73 1134
25. Jain J K 1989 Phys. Rev. Lett. 63 199
26. M Stone (ed) 1992 Quantum Hall Effect (Singapore: World Scientific)
27. Wilczek F (ed) 1990 Fractional Statistics and Anyon Superconductivity (Singapore: World Scientific)
28. Hatsugai Y 1997 in preparation
29. See Haldane F D M 1987 The Quantum Hall Effect ed R E Prange and S M Girvin (Berlin: Springer)
30. Wu Y-S, private communication
31. Hiramoto H and Kohmoto M 1992 Int. J. Mod. Phys. B 6 281
32. Hatsugai Y, Kohmoto M and Wu Y-S 1996 Phys. Rev. B 53 9697
33. Kohmoto M 1989 Phys. Rev. B 39 11 943
34. Avron J, Seiler R and Simon B 1983 Phys. Rev. Lett. 51 51
35. Niu Q, Thouless D J and Wu Y S 1985 Phys. Rev. B 31 3372
36. Chang M-C and Niu Q 1996 Phys. Rev. B 53 7010
37. Douçot B and Stamp P C E 1991 Phys. Rev. Lett. 66 2503
38. Takahashi M, Hatsugai Y and Kohmoto M 1996 J. Phys. Soc. Japan 65 529
39. Rammal R Toulouse G, Jaekel M T and Halpenn B I 1983 Phys. Rev. B 27 5142
40. Schweitzer L, Kramer B and MacKinnon A 1984 J. Phys. C: Solid State Phys. 17 4111 Johnston R, Kramer B, MacKinnon A and Schweitzer L 1986 Surf. Sci. 170 256
41. Schweitzer L, Kramer B and MacKinnon A 1984 J. Phys. C: Solid State Phys. 17 4111 Johnston R, Kramer B, MacKinnon A and Schweitzer L 1986 Surf. Sci. 170 256
42. MacDonald A H 1984 Phys. Rev. B 29 6563
43. MacDonald A H and Strěda P 1984 Phys. Rev. B 29 1616
44. Sun S N and Ralston J P 1991 Phys. Rev. B 44 13603
45. Harper P G 1955 Proc. Phys. Soc. A 68 874
46. Toda M 1981 Theory of Nonlinear Lattices (Berlin: Springer) and references therein
47. Date E and Tanaka S 1976 Prog. Theor. Phys. 55 457
48. Date E and Tanaka S 1976 Prog. Theor. Phys. Suppl. 59 107
49. Mumford D 1983 Tata Lectures on Theta I, II (Boston: Birkhäuser)
50. The theory of the non-linear lattice is applied to the problem of a one-dimensional quasi-crystal by Iguchi K 1992 J. Math. Phys. 33 3938
51. 21(∈) are simple, as shown in appendix C.
52. qk+1 in general.
53. Wen X G and Zee A 1989 Nucl. Phys. B 316 641
54. Hatsugai Y and Kohmoto M 1990 Phys. Rev. B 42 8282
55. 2 = 4, which is similar to equation (110).
56. q.
57. Charge transport is also discussed in the following references: Tešanović Z, Axel F and Halperin B I 1989 Phys. Rev B 39 8525 Kunz H 1986 Phys. Rev. Lett. 57 1095 Thouless D J 1983 Phys. Rev. B 27 6083 MacDonald A H 1983 Phys. Rev. B 28 6713
58. Charge transport is also discussed in the following references: Tešanović Z, Axel F and Halperin B I 1989 Phys. Rev B 39 8525 Kunz H 1986 Phys. Rev. Lett. 57 1095 Thouless D J 1983 Phys. Rev. B 27 6083 MacDonald A H 1983 Phys. Rev. B 28 6713
59. Charge transport is also discussed in the following references: Tešanović Z, Axel F and Halperin B I 1989 Phys. Rev B 39 8525 Kunz H 1986 Phys. Rev. Lett. 57 1095 Thouless D J 1983 Phys. Rev. B 27 6083 MacDonald A H 1983 Phys. Rev. B 28 6713
60. Charge transport is also discussed in the following references: Tešanović Z, Axel F and Halperin B I 1989 Phys. Rev B 39 8525 Kunz H 1986 Phys. Rev. Lett. 57 1095 Thouless D J 1983 Phys. Rev. B 27 6083 MacDonald A H 1983 Phys. Rev. B 28 6713
61. Widom A 1982 Phys. Lett. 90A 474
62. Strěda P 1982 J. Phys. C: Solid State Phys. 15 L717
63. These degenerate zero modes in the infinite system were investigated using topological methods by Wen and Zee [48] in detail.
64. Wen X G, Wilczek F and Zee A 1989 Phys. Rev. B 39 11 413
65. Even if we include the next-nearest-neighbour hoppings, it is still possible to reduce the problem to a one-dimensional one [49] and to define the Riemann surface of the Bloch function.
66. Hatsugai Y, Kohmoto M and Wu Y-S 1996 Phys. Rev. B 54 4896
67. Aoki H and Ando T 1981 Solid State Commun. 38 1079
68. Aoki H and Ando T 1986 Phys. Rev. Lett. 57 3093
69. Canright G S, Girvin S M and Brass A 1989 Phys. Rev. Lett. 63 2291
70. Wen X G, Dagotto E and Fradkin E 1990 Phys. Rev. B 42 6110
71. Hatsugai Y, Kohmoto M and Wu Y-S 1991 Phys. Rev. B 43 2661
72. Girvin S and MacDonald A H 1987 Phys. Rev. Lett. 58 1252
73. Thouless D J 1983 Phys. Rev. B 28 4272