Quantum Hall effect in graphene: Emergent modular symmetry and the semicircle law

Physical Review B - Condensed Matter and Materials Physics

Volumn 76, Issue 11, 2007, Pages

  Burgess, C P ^a,b   Dolan, Brian P ^c,d  

^a MCMASTER UNIVERSITY   (Canada)

^b PERIMETER INSTITUTE FOR THEORETICAL PHYSICS   (Canada)

^c NATIONAL UNIVERSITY OF IRELAND   (Ireland)

^d DUBLIN INSTITUTE FOR ADVANCED STUDIES   (Ireland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34548707566     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.76.113406     Document Type: Article

References (35)

1. 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).
2. Y. Zhang, Yan-Wen Tang, H. L. Stormer, and P. Kim, Nature (London) NATUAS 0028-0836 10.1038/nature04235 438, 201 (2005).
3. A. Shapere and F. Wilczek, Nucl. Phys. B NUPBBO 0550-3213 10.1016/0550-3213(89)90016-3 320, 669 (1989).
4. C. A. Lütken and G. G. Ross, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.45.11837 45, 11837 (1992).
5. C. A. Lütken and G. G. Ross, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.48.2500 48, 2500 (1993).
6. C. A. Lütken, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/26/17/ 011 26, L811 (1993);
7. C. A. Lütken, Nucl. Phys. B NUPBBO 0550-3213 10.1016/0550-3213(93) 90667-E 396, 670 (1993);
8. C. P. Burgess and C. A. Lutken, Nucl. Phys. B NUPBBO 0550-3213 10.1016/S0550-3213(97)00318-0 500, 367 (1997);
9. C. P. Burgess and C. A. Lutken, Phys. Lett. B PYLBAJ 0370-2693 10.1016/S0370-2693(99)00239-7 451, 365 (1999).
10. D.-H. Lee, S. Kivelson, and S.-C. Zhang, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.68.2386 68, 2386 (1992);
11. S. Kivelson, D.-H. Lee, and S.-C. Zhang, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.46.2223 46, 2223 (1992).
12. J. K. Jain, S. A. Kivelson, and N. Trivedi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.64.1297 64, 1297 (1990);
13. J. K. Jain and V. J. Goldman, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.45.1255 45, 1255 (1992).
14. D. Shahar, D. C. Tsui, and M. Shayegan, Science SCIEAS 0036-8075 10.1126/science.274.5287.589 274, 589 (1996).
15. C. P. Burgess and B. P. Dolan, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.63.155309 63, 155309 (2001).
16. C. P. Burgess and B. P. Dolan, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.65.155323 65, 155323 (2002).
17. E. Witten, in From Fields to Strings, edited by, M. Shifman, (unpublished), Vol. 2, pp. 1173-1200.
18. C. P. Burgess, Rim Dib, and B. P. Dolan, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.62.15359 62, 15359 (2000).
19. B. P. Dolan, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/32/21/101 32, L243 (1999).
20. B. P. Dolan, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.62.10278 62, 10278 (2000).
21. C. F. Huang, Y. H. Chang, H. H. Cheng, Z. P. Yang, H. D. Yeh, C. H. Hsu, C.-T. Liang, D. R. Hang, and H. H. Lin, J. Phys.: Condens. Matter JCOMEL 0953-8984 10.1088/0953-8984/19/2/026205 19, 026205 (2007).
22. T. Ando, T. Nakaishi and R. Saito, J. Phys. Soc. Jpn. JUPSAU 0031-9015 10.1143/JPSJ.67.2857 67, 2857 (1998);
23. G. P. Mikitik and Y. V. Sharlai, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.82.2147 82, 2147 (1999).
24. C. Töke, P. E. Lammert, V. H. Crespi, and J. K. Jain, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.74.235417 74, 235417 (2006).
25. C. P. Burgess and B. P. Dolan, arXiv:cond-mat/0701535, Phys. Rev. B (to be published).
26. S. S. Murzin, M. Weiss, A. G. M. Jansen, and K. Eberl, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.66.233314 66, 233314 (2002);
27. S. S. Murzin, S. I. Dorozhkin, D. K. Maude, and A. G. M. Jansen, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.72.195317 72, 195317 (2005).
28. B. P. Dolan, Int. J. Mod. Phys. A IMPAEF 0217-751X 10.1142/ S0217751X06033891 21, 4807 (2006).
29. M. P. A. Fisher, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett. 65.923 65, 923 (1990).
30. D. Shahar, D. C. Tsui, M. Shayegan, E. Shimshoni, and S. L. Sondhi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.79.479 79, 479 (1997).
31. V. P. Gusynin and S. G. Sharapov, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.146801 95, 146801 (2005).
32. B. P. Dolan, Nucl. Phys. B NUPBBO 0550-3213 10.1016/S0550-3213(99)00326-0 554, 487 (1999).
33. 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).
34. J. K. Jain, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.63.199 63, 199 (1989);
35. J. K. Jain, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.41.7653 41, 7653 (1990).