Theory of anomalous quantum Hall effects in graphene

Physical Review B - Condensed Matter and Materials Physics

Volumn 77, Issue 19, 2008, Pages

  Ostrovsky, P M ^a,b   Gornyi, I V ^a,d   Mirlin, A D ^a,c,e  

^a KARLSRUHE INSTITUTE OF TECHNOLOGY   (Germany)

^b LANDAU INSTITUTE FOR THEORETICAL PHYSICS   (Russian Federation)

^c UNIVERSITY OF KARLSRUHE   (Germany)

^d IOFFE INSTITUTE   (Russian Federation)

^e PETERSBURG NUCLEAR PHYSICS INSTITUTE   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 44349152957     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.77.195430     Document Type: Article

References (75)

1. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science SCIEAS 0036-8075 10.1126/science.1102896 306, 666 (2004).
2. A. K. Geim and K. S. Novoselov, Nat. Mater. NMAACR 1476-1122 10.1038/nmat1849 6, 183 (2007).
3. A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, arXiv:0709.1163, Rev. Mod. Phys. RMPHAT 0034-6861 (to be published).
4. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, Nature (London) NATUAS 0028-0836 10.1038/nature04233 438, 197 (2005);
5. K. S. Novoselov, E. McCann, S. V. Morozov, V. I. Falko, M. I. Katsnelson, U. Zeitler, D. Jiang, F. Schedin, and A. K. Geim, Nat. Phys. ZZZZZZ 1745-2473 2, 177 (2006).
6. Y. Zhang, Y.-W. Tan, H. L. Stormer, and P. Kim, Nature (London) NATUAS 0028-0836 10.1038/nature04235 438, 201 (2005);
7. Y. Zhang, Z. Jiang, J. P. Small, M. S. Purewal, Y.-W. Tan, M. Fazlollahi, J. D. Chudow, J. A. Jaszczak, H. L. Stormer, and P. Kim, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.136806 96, 136806 (2006).
8. Z. Jiang, Y. Zhang, H. L. Stormer, and P. Kim, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.106802 99, 106802 (2007).
9. K. S. Novoselov, Z. Jiang, Y. Zhang, S. V. Morozov, H. L. Stormer, U. Zeitler, J. C. Maan, G. S. Boebinger, P. Kim, and A. K. Geim, Science SCIEAS 0036-8075 10.1126/science.1137201 315, 1379 (2007).
10. D. A. Abanin, K. S. Novoselov, U. Zeitler, P. A. Lee, A. K. Geim, and L. S. Levitov, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.196806 98, 196806 (2007).
11. K. v. Klitzing, G. Dorda, and M. Pepper, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.45.494 45, 494 (1980).
12. The Quantum Hall Effect, edited by, R. E. Prange, and, S. M. Girvin, (Springer, New York, 1987).
13. V. P. Gusynin and S. G. Sharapov, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.146801 95, 146801 (2005).
14. Y. Zheng and T. Ando, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.65. 245420 65, 245420 (2002).
15. N. M. R. Peres, F. Guinea, and A. H. Castro Neto, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.73.125411 73, 125411 (2006).
16. T. Ando, A. B. Fowler, and F. Stern, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.54.437 54, 437 (1982).
17. D. E. Khmel'nitskii, Helv. Phys. Acta HPACAK 0018-0238 65, 164 (1992).
18. 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 (1994).
19. F. D. M. Haldane, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett. 61.2015 61, 2015 (1988).
20. D. E. Khmelnitskii, Phys. Lett. PYLAAG 0375-9601 10.1016/0375-9601(84) 90314-1 106A, 182 (1984).
21. R. B. Laughlin, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.23.5632 23, R5632 (1981).
22. B. I. Halperin, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.25.2185 25, 2185 (1982).
23. B. Huckestein, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.67.357 67, 357 (1995).
24. F. Evers and A. D. Mirlin, arXiv:0707.4378, Rev. Mod. Phys. RMPHAT 0034-6861 (to be published).
25. I. L. Aleiner and K. B. Efetov, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.236801 97, 236801 (2006).
26. A. Altland, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97. 236802 97, 236802 (2006).
27. A. M. M. Pruisken, Nucl. Phys. B NUPBBO 0550-3213 10.1016/0550-3213(84) 90101-9 235, 277 (1984);
28. The Quantum Hall Effect (Ref.), p. 117.
29. P. M. Ostrovsky, I. V. Gornyi, and A. D. Mirlin, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.74.235443 74, 235443 (2006).
30. P. M. Ostrovsky, I. V. Gornyi, and A. D. Mirlin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.256801 98, 256801 (2007).
31. A. A. Nersesyan, A. M. Tsvelik, and F. Wenger, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.72.2628 72, 2628 (1994);
32. A. A. Nersesyan, A. M. Tsvelik, and F. Wenger, Nucl. Phys. B NUPBBO 0550-3213 10.1016/0550-3213(95)00002-A 438, 561 (1995);
33. A. M. Tsvelik, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.51.9449 51, 9449 (1995).
34. M. Bocquet, D. Serban, and M. R. Zirnbauer, Nucl. Phys. B NUPBBO 0550-3213 10.1016/S0550-3213(00)00208-X 578, 628 (2000);
35. A. Altland, B. D. Simons, and M. R. Zirnbauer, Phys. Rep. PRPLCM 0370-1573 10.1016/S0370-1573(01)00065-5 359, 283 (2002).
36. I. F. Herbut, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.75.165411 75, 165411 (2007).
37. E. V. Gorbar, V. P. Gusynin, and V. A. Miransky, arXiv:0710.3527 (unpublished).
38. M. Koshino and T. Ando, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.75.033412 75, 033412 (2007).
39. D. N. Sheng, L. Sheng, and Z. Y. Weng, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.73.233406 73, 233406 (2006).
40. P. Goswami, X. Jia, and S. Chakravarty, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.76.205408 76, 205408 (2007).
41. E. McCann, K. Kechedzhi, V. I. Fal'ko, H. Suzuura, T. Ando, and B. L. Altshuler, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.146805 97, 146805 (2006).
42. K. B. Efetov, Supersymmetry in Disorder and Chaos (Cambridge University Press, Cambridge, 1996).
43. S. Ryu, C. Mudry, H. Obuse, and A. Furusaki, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.116601 99, 116601 (2007).
44. D. E. Khmelnitskii, JETP Lett. JTPLA2 0021-3640 38, 552 (1984).
45. Y. Huo, R. E. Hetzel, and R. N. Bhatt, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.70.481 70, 481 (1993);
46. B. M. Gammel and W. Brenig, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.73.3286 73, 3286 (1994);
47. Z. Wang, B. Jovanović, and D.-H. Lee, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.77.4426 77, 4426 (1996);
48. S. Cho and M. P. A. Fisher, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.55.1637 55, 1637 (1997);
49. L. Schweitzer and P. Markoš, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.256805 95, 256805 (2005).
50. Z. Wang, M. P. A. Fisher, S. M. Girvin, and J. T. Chalker, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.61.8326 61, 8326 (2000).
51. A. M. M. Pruisken and I. S. Burmistrov, Ann. Phys. (N.Y.) APNYA6 0003-4916 10.1016/j.aop.2004.08.009 316, 285 (2005).
52. L. W. Engel, D. Shahar, C. Kurdak, and D. C. Tsui, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.71.2638 71, 2638 (1993).
53. D. K. K. Lee and J. T. Chalker, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.72.1510 72, 1510 (1994).
54. K. Nomura and A. H. MacDonald, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.256602 96, 256602 (2006).
55. L. Sheng, D. N. Sheng, F. D. M. Haldane, and L. Balents, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.196802 99, 196802 (2007).
56. K. Yang, S. Das Sarma, and A. H. MacDonald, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.74.075423 74, 075423 (2006).
57. P. M. Ostrovsky, I. V. Gornyi, and A. D. Mirlin, Eur. Phys. J. Spec. Top. ZZZZZZ 1951-6355 148, 63 (2007).
58. F. V. Tikhonenko, D. W. Horsell, R. V. Gorbachev, and A. K. Savchenko, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.100.056802 100, 056802 (2008).
59. T. Ando, J. Phys. Soc. Jpn. JUPSAU 0031-9015 10.1143/JPSJ.75.074716 75, 074716 (2006).
60. Y.-W. Tan, Y. Zhang, H. L. Stormer, and P. Kim, Eur. Phys. J. Spec. Top. ZZZZZZ 1951-6355 148, 15 (2007).
61. M. I. Katsnelson and A. K. Geim, Philos. Trans. R. Soc. London, Ser. A PTRMAD 0962-8428 10.1098/rsta.2007.2157 366, 195 (2008).
62. D. V. Khveshchenko, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.75. 241406 75, 241406 (R) (2007).
63. S. Hikami, M. Shirai, and F. Wegner, Nucl. Phys. B NUPBBO 0550-3213 10.1016/0550-3213(93)90373-W 408, 415 (1993).
64. Y. Aharonov and A. Casher, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.19.2461 19, 2461 (1979).
65. M. F. Atiyah and I. M. Singer, Ann. Math. ANMAAH 0003-486X 87, 485 (1968);
66. M. F. Atiyah and I. M. Singer, Ann. Math. ANMAAH 0003-486X 10.2307/1970717 87, 546 (1968);
67. M. F. Atiyah and I. M. Singer, Ann. Math. ANMAAH 0003-486X 10.2307/1970756 93, 119 (1971);
68. M. F. Atiyah and I. M. Singer, Ann. Math. ANMAAH 0003-486X 98, 139 (1971).
69. J.-S. Caux, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.81.4196 81, 4196 (1998).
70. A. J. M. Giesbers, U. Zeitler, M. I. Katsnelson, L. A. Ponomarenko, T. M. G. Mohiuddin, and J. C. Maan, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.206803 99, 206803 (2007).
71. E. McCann and V. I. Fal'ko, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.086805 96, 086805 (2006).
72. N. H. Shon and T. Ando, J. Phys. Soc. Jpn. JUPSAU 0031-9015 10.1143/JPSJ.67.2421 67, 2421 (1998).
73. F. Wegner, Z. Phys. B: Condens. Matter ZPCMDN 0722-3277 10.1007/BF01319209 51, 279 (1983);
74. E. Brezin, D. J. Gross, and C. Itzykson, Nucl. Phys. B NUPBBO 0550-3213 10.1016/0550-3213(84)90146-9 235, 24 (1984).
75. K. Fujikawa, Phys. Rev. D PRVDAQ 0556-2821 10.1103/PhysRevD.21.2848 21, 2848 (1980).