Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries and the fractional quantum Hall effect

Physical Review B - Condensed Matter and Materials Physics

Volumn 61, Issue 15, 2000, Pages 10267-10297

  Read, N ^a   Green, Dmitry ^a  

^a YALE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000049832     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.61.10267     Document Type: Article

References (122)

1. J. Bardeen, L.N. Cooper, and J.R. Schrieffer, Phys. Rev. 106, 162 (1957).
2. Phys. Rev.J. BardeenL.N. CooperJ.R. Schrieffer108, 1175 (1957).
3. J.R. Schrieffer, Theory of Superconductivity (Addison-Wesley, Reading, MA, 1964).
4. For a review, see, e.g., D. Vollhardt and P. Wölfle, The Superfluid Phases of Helium 3 (Taylor and Francis, London, 1990).
5. G.E. Volovik, Zh. Éksp. Teor. Fiz. 94, 123 (1988) [Sov. Phys. JETP 67, 1804 (1988)].
6. G.E. Volovik and V.M. Yakovenko, J. Phys.: Condens. Matter 1, 5263 (1989).
7. G.E. Volovik, Physica B 162, 222 (1990).
8. G.E. Volovik, Zh. Éksp. Teor. Fiz. 51, 111 (1990) [JETP Lett. 51, 125 (1990)].
9. G.E. Volovik, Zh. Éksp. Teor. Fiz. 55, 363 (1992) [JETP Lett. 55, 368 (1992)].
10. For a review, see, e.g., The Quantum Hall Effect, edited by R.E. Prange and S.M. Girvin,2nd ed. (Springer-Verlag, New York, 1990).
11. R.B. Laughlin, Phys. Rev. Lett. 50, 1395 (1983).
12. B.I. Halperin, Helv. Phys. Acta 56, 75 (1983).
13. R. Morf, N. d’Ambrunil, and B.I. Halperin, Phys. Rev. B 34, 3037 (1986).
14. F.D.M. Haldane and E.H. Rezayi, Phys. Rev. Lett. 60, 956, 1886 (E) (1988).
15. G. Moore and N. Read, Nucl. Phys. B 360, 362 (1991).
16. N. Read and G. Moore, Prog. Theor. Phys. (Kyoto) Suppl. 107, 157 (1992).
17. F.D.M. Haldane, Phys. Rev. Lett. 51, 605 (1983), and in Ref. 9.
18. S.M. Girvin and A.H. MacDonald, Phys. Rev. Lett. 58, 1252 (1987).
19. N. Read, Bull. Am. Phys. Soc. 32, 923 (1987).
20. R.B. Laughlin, Phys. Rev. Lett. 60, 2677 (1988).
21. S.C. Zhang, T.H. Hansson, and S. Kivelson, Phys. Rev. Lett. 62, 82 (1989).
22. N. Read, Phys. Rev. Lett. 62, 86 (1989).
23. J.K. Jain, Phys. Rev. Lett. 63, 199 (1989).
24. J.K. JainPhys. Rev. B 40, 8079 (1989).
25. Phys. Rev. BJ.K. Jain 41, 7653 (1990).
26. D.-H. Lee and M.P.A. Fisher, Phys. Rev. Lett. 63, 903 (1989).
27. A. Lopez and E. Fradkin, Phys. Rev. B 44, 5246 (1991).
28. B.I. Halperin, P.A. Lee, and N. Read, Phys. Rev. B 47, 7312 (1993).
29. N. Read, Semicond. Sci. Technol. 9, 1859 (1994).
30. N. Readcond-mat/9501090 (unpublished).
31. R. Shankar and G. Murthy, Phys. Rev. Lett. 79, 4437 (1997).
32. R. ShankarG. Murthycond-mat/9802244 (unpublished).
33. D.-H. Lee, Phys. Rev. Lett. 80, 4745 (1998).
34. V. Pasquier and F.D.M. Haldane, Nucl. Phys. B 516, 719 (1998).
35. N. Read, Phys. Rev. B 59, 8084 (1998).
36. R.L. Willett, J.P. Eisenstein, H.L. Stormer, D.C. Tsui, A.C. Gossard, and J.H. English, Phys. Rev. Lett. 59, 1776 (1987).
37. M. Greiter, X.-G. Wen, and F. Wilczek, Phys. Rev. Lett. 66, 3205 (1991).
38. M. GreiterX.-G. WenF. WilczekNucl. Phys. B 374, 567 (1992).
39. R. Morf, Phys. Rev. Lett. 80, 1505 (1998).
40. E.H. Rezayi and F.D.M. Haldane, cond-mat/9906137 (unpublished).
41. M. Greiter, X.-G. Wen, and F. Wilczek, Phys. Rev. B 46, 9586 (1992).
42. B.I. Halperin, Surf. Sci. 305, 1 (1994).
43. Y.W. Suen, L.W. Engel, M.B. Santos, M. Shayegan, and D.C. Tsui, Phys. Rev. Lett. 68, 1379 (1992).
44. Phys. Rev. Lett.J.P. Eisenstein, G.S. Boebinger, L.N. Pfeiffer, K.W. West, and Song He, 68, 1383 (1992).
45. S. He, X.-C. Xie, S. Das Sarma, and F.-C. Zhang, Phys. Rev. B 43, 9339 (1991).
46. Phys. Rev. BS. He, S. Das Sarma, and X.-C. Xie, 47, 4394 (1993).
47. E. Witten, Commun. Math. Phys. 121, 351 (1989).
48. X.-G. Wen, Phys. Rev. Lett. 70, 355 (1993).
49. X.-G. Wen and Y.-S. Wu, Nucl. Phys. B 419[FS], 455 (1994).
50. Nucl. Phys. BX.-G. Wen, Y.-S. Wu, and Y. Hatsugai, 422[FS], 476 (1994).
51. M. Milovanović and N. Read, Phys. Rev. B 53, 13 559 (1996).
52. C. Nayak and F. Wilczek, Nucl. Phys. B 479, 529 (1996).
53. N. Read and E. Rezayi, Phys. Rev. B 54, 16 864 (1996).
54. V. Gurarie, M. Flohr, and C. Nayak, Nucl. Phys. B 498, 513 (1998).
55. V. Gurarie and C. Nayak, Nucl. Phys. B 506, 685 (1997).
56. E. Fradkin, C. Nayak, A. Tsvelik, and F. Wilczek, Nucl. Phys. B 516, 704 (1998).
57. Nucl. Phys. BE. Fradkin, C. Nayak, and K. Schoutens, 546, 711 (1999).
58. D.C. Cabra, E. Fradkin, G.L. Rossini, and F.A. Schaposnik, cond-mat/9905192 (unpublished).
59. X.-G. Wen, Phys. Rev. B 60, 8827 (1999).
60. N. Read, Phys. Rev. Lett. 65, 1502 (1990).
61. B. Blok and X.-G. Wen, Phys. Rev. B 42, 8133 (1990).
62. Phys. Rev. BB. BlokX.-G. Wen 43, 8337 (1991).
63. P.G. de Gennes, Superconductivity of Metals and Alloys (Addison-Wesley, Reading, MA, 1989).
64. R. Oppermann, Physica A 167, 301 (1990).
65. A. Altland and M. R. Zirnbauer, Phys. Rev. B 55, 1142 (1997).
66. M.R. Zirnbauer, J. Math. Phys. 37, 4986 (1996).
67. T. Senthil, M.P.A. Fisher, L. Balents, and C. Nayak, Phys. Rev. Lett. 81, 4704 (1998).
68. R. Bundschuh, C. Cassanello, D. Serban, and M.R. Zirnbauer, Phys. Rev. B 59, 4382 (1999).
69. T. Senthil and M.P.A. Fisher, Phys. Rev. B 60, 6893 (1999).
70. V. Kagalovsky, B. Horovitz, Y. Avishai, and J.T. Chalker, Phys. Rev. Lett. 82, 3516 (1999).
71. T. Senthil, J.B. Marston, and M.P.A. Fisher, Phys. Rev. B 604245, (1999).
72. I.A. Gruzberg, A.W.W. Ludwig, and N. Read, Phys. Rev. Lett. 82, 4524 (1999).
73. R.B. Laughlin, Phys. Rev. Lett. 80, 5188 (1998).
74. J. Goryo and K. Ishikawa, Phys. Lett. A 260, 294 (1999).
75. N. Read and D. Green, Bull. Am. Phys. Soc. 44, 304 (1999).
76. P.W. Anderson, Phys. Rev. 110, 827 (1958).
77. Phys. Rev.P.W. Anderson 112, 1900 (1958).
78. F.D.M. Haldane, Phys. Rev. Lett. 55, 2095 (1985).
79. R. Jackiw and C. Rebbi, Phys. Rev. D 13, 3398 (1976).
80. C. Caroli, P.G. de Gennes, and J. Matricon, Phys. Lett. 9, 307 (1964).
81. J. Bardeen, R. Kümmel, A.E. Jacobs, and L. Tewordt, Phys. Rev. 187, 556 (1969);P.G. de Gennes, Sec. 5.2 in Ref. 50.
82. N.B. Kopnin and M.M. Salomaa, Phys. Rev. B 44, 9667 (1991).
83. X.-G. Wen and Q. Niu, Phys. Rev. B 41, 9377 (1990).
84. T.-L. Ho, Phys. Rev. Lett. 75, 1186 (1995).
85. L. Belkhir, X.-G. Wu, and J.K. Jain, Phys. Rev. B 48, 15 245 (1993).
86. M. Milovanović and N. Read, Phys. Rev. B 56, 1461 (1997).
87. D.-H. Lee and C.L. Kane, Phys. Rev. Lett. 64, 1313 (1990).
88. F.D.M. Haldane and E.H. Rezayi (unpublished).
89. D. Green, N. Read, and E. Rezayi (unpublished).
90. X.-G. Wen, Int. J. Mod. Phys. B 6, 1711 (1992).
91. F.D.M. Haldane and D.P. Arovas, Phys. Rev. B 52, 4223 (1995).
92. K. Yang, L.K. Warman, and S.M. Girvin, Phys. Rev. Lett. 70, 2641 (1993).
93. D.J. Thouless, M. Kohmoto, M.P. Nightingale, and M. Den Nijs, Phys. Rev. Lett. 49, 405 (1982).
94. J. Bellissard, A. van Elst, and H. Schulz-Baldes, J. Math. Phys. 35, 5373 (1994).
95. A.N. Redlich, Phys. Rev. Lett. 52, 18 (1984).
96. I. Affleck, J. Harvey, and E. Witten, Nucl. Phys. B 206, 413 (1982).
97. B.I. Halperin, Phys. Rev. B 25, 2185 (1982).
98. F.D.M. Haldane, Phys. Rev. Lett. 74, 2090 (1995).
99. S. Xiong, N. Read, and A.D. Stone, Phys. Rev. B 56, 3982 (1997).
100. C. Callan and J. Harvey, Nucl. Phys. B 250, 427 (1985).
101. G.E. Volovik, Pis’ma Zh. Éksp. Teor. Fiz. 66, 492 (1997)[JETP Lett. 66, 522(1997)];
102. G.E. Volovikcond-mat/9709084 (unpublished).
103. E. Witten, Commun. Math. Phys. 92, 455 (1984).
104. C.L. Kane and M.P.A. Fisher, Phys. Rev. B 55, 15 832 (1997).
105. H.W.J. Blöte, J.L. Cardy, and M.P. Nightingale, Phys. Rev. Lett. 56, 742 (1986).
106. Phys. Rev. Lett.I. Affleck, 56, 746 (1986).
107. L.G.C. Rego and G. Kirczenow, Bull. Am. Phys. Soc. 44, 212 (1999).
108. A. Belavin, A. Polyakov, and A. Zamolodchikov, Nucl. Phys. B 241, 33 (1984).
109. L. Alvarez-Gaumé and E. Witten, Nucl. Phys. B 234, 269 (1983).
110. L. Alvarez-Gaumé, S. Della Pietra, and G. Moore, Ann. Phys. (NY) 163, 288 (1985).
111. H. Verlinde, Nucl. Phys. B 337, 652 (1990).
112. F.D.M. Haldane and Y.-S. Wu, Phys. Rev. Lett. 55, 2887 (1985).
113. T. Senthil and M.P.A. Fisher, cond-mat/9906290 (unpublished).
114. T. SenthilM.P.A. FisherPhys. Rev. B 61, 9690 (2000).
115. I.A. Gruzberg, A.W.W. Ludwig, and N. Read (unpublished).
116. S. Helgason, Differential Geometry, Lie Groups, and Symmetric Spaces (Academic Press, New York, NY, 1978), Sections IV.4, V.2.
117. A.W.W. Ludwig, M.P.A. Fisher, R. Shankar, and G. Grinstein, Phys. Rev. B 50, 7526 (1994).
118. Vl.S. Dotsenko and V.S. Dotsenko, Adv. Phys. 32, 129 (1983).
119. R. Shankar, Phys. Rev. Lett. 58, 2466 (1987).
120. Phys. Rev. Lett.A.W.W. Ludwig, 61, 2388 (1988).
121. L. Kadanoff and H. Ceva, Phys. Rev. B 3, 3918 (1971).
122. A.V. Shytov, L.S. Levitov, and B.I. Halperin, Phys. Rev. Lett. 80, 141 (1998).