Toward theory of quantum Hall effect in graphene

Fizika Nizkikh Temperatur (Kharkov)

Volumn 34, Issue 10, 2008, Pages 1007-1011

  Gorbar, E V ^a   Gusynin, V P ^a   Miransky, V A ^a,b  

^a BOGOLYUBOV INSTITUTE FOR THEORETICAL PHYSICS   (Ukraine)

^b UNIVERSITY OF WESTERN ONTARIO   (Canada)

Author keywords

Dirac quasiparticle; Graphene; Quantum Hall effect

Indexed keywords

DYNAMICS; ELECTRIC CURRENTS; GALLIUM ALLOYS; GALVANOMAGNETIC EFFECTS; HALL EFFECT; MAGNETIC FIELD MEASUREMENT; MAGNETIC FIELDS; MAGNETIC MATERIALS; SOUND REPRODUCTION;

DIRAC QUASIPARTICLE; DIRAC QUASIPARTICLES; GAP EQUATIONS; GAPLESS EDGE; GRAPHENE; MAGNETIC CATALYSIS; ORDER PARAMETERS; QUANTUM HALL; QUANTUM HALL EFFECT; STRONG MAGNETIC FIELDS;

MAGNETIC FIELD EFFECTS;

EID: 53449100338     PISSN: 01326414     EISSN: 18160328     Source Type: Journal    
DOI: None     Document Type: Article

References (47)

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 306, 666 (2004).
2. 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 438, 197 (2005).
3. Y. Zhang, Y.-W. Tan, H.L. Störmer, and P. Kim, Nature 438, 201 (2005).
4. Y. Zheng and T. Ando, Phys. Rev. B65, 245420 (2002).
5. V.P. Gusynin and S.G. Sharapov, Phys. Rev. Lett. 95, 146801 (2005);
6. Phys. Rev. B73, 245411 (2006).
7. N.M.R. Peres, F. Guinea, and A.H. Castro Neto, Phys. Rev. B73, 125411 (2006).
8. G.W. Semenoff, Phys. Rev. Lett. 53, 2449 (1984).
9. F.D.M. Haldane, Phys. Rev. Lett. 61, 2015 (1988).
10. I.A. Luk'yanchuk and Y. Kopelevich, Phys. Rev. Lett. 93, 166402 (2004).
11. 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. 96, 136806 (2006).
12. Z. Jiang, Y. Zhang, H.L. Stormer, and P. Kim, Phys. Rev. Lett. 99, 106802 (2007).
13. K. Nomura and A.H. MacDonald, Phys. Rev. Lett. 96, 256602 (2006);
14. K. Yang, S. Das Sarma, and A.H. MacDonald, Phys. Rev. B74, 075423 (2006).
15. M.O. Goerbig, R. Moessner, and B. Doucot, Phys. Rev. B74, 161407(R) (2006).
16. J. Alicea and M.P.A. Fisher, Phys. Rev. B74, 075422 (2006).
17. L. Sheng, D.N. Sheng, F.D.M. Haldane, and Leon Balents, Phys. Rev. Lett. 99, 196802 (2007).
18. D.A. Abanin, P.A. Lee, and L.S Levitov, Phys. Rev. Lett. 96, 176803 (2006).
19. V.P. Gusynin, V.A. Miransky, S.G. Sharapov, and I.A. Shovkovy, Phys. Rev. B74, 195429 (2006); arXiv:condmat/0612488.
20. I.F. Herbut, Phys. Rev. Lett. 97, 146401 (2006);
21. Phys. Rev. B75, 165411 (2007);
22. ibid. 76, 085432 (2007).
23. J.-N. Fuchs and P. Lederer, Phys. Rev. Lett. 98, 016803 (2007).
24. M. Ezawa, J. Phys. Soc. Jpn. 76, 094701 (2007);
25. Physica E40, 269 (2007).
26. K. Yang, Solid State Commun. 143, 27 (2007).
27. D.P. Arovas, A, Karlhelde, and D. Lilliehook, Phys. Rev. B59, 13147 (1999);
28. Z.F. Ezawa and K. Hasebe, Phys. Rev. B65, 075311 (2002).
29. V.P. Gusynin, V.A. Miransky, and I.A. Shovkovy, Phys. Rev. Lett. 73, 3499 (1994);
30. Nucl. Phys. B462, 249 (1996).
31. D.V. Khveshchenko, Phys. Rev. Lett. 87, 206401 (2001);
32. ibid. 87, 246802 (2001).
33. E.V. Gorbar, V.P. Gusynin, V.A. Miransky, and I.A. Shovkovy, Phys. Rev. B66, 045108 (2002).
34. 3.
35. V.A. Miransky, Dynamical Symmetry Breaking in Quantum Field Theories, World Scientific, Singapore (1993).
36. 0 = 0. [M.I. Katsnelson, Phys. Rev. B74, 201401(R) (2006);
37. B. Wunsch, T. Stauber, F. Sols, and F. Guinea, New J. Phys. 8, 318 (2007).]
38. F, we expect that the present approximation is qualitatively reliable even near the Dirac point.
39. V.P. Gusynin, S.G. Sharapov, and J.P. Carbotte, Int. J. Mod. Phys. B21, 4611 (2007).
40. This relation can be easily obtained in the formalism of the effective action for composite operators developed in J.M. Luttinger and J.D. Ward, Phys. Rev. 118, 1417 (1960);
41. G. Baym, Phys. Rev. 127, 1391 (1962);
42. J.M. Cornwall, R. Jackiw, and E. Tomboulis, Phys. Rev. D10, 2428 (1974).
43. In dynamics in a magnetic field at zero temperature, there is no one-to-one correspondence between electron density and chemical potential. As a result, different values of the latter may correspond to the same physics, as it takes place for this solution.
44. This expression for Δ̃ is valid only for λ < 1: in a supercritical regime, with λ > 1, a dynamical Dirac mass (gap) is generated even with no magnetic field. Experiments [2,3] clearly show that the subcritical regime, with λ < 1, takes place in graphene.
45. D.A. Abanin, K.S. Novoselov, U. Zeitler, P.A. Lee, A.K. Geim, and L.S. Levitov, Phys. Rev. Lett. 98, 196806 (2007).
46. J.G. Checkelsky, L. Li, and N.P. Ong, Phys. Rev. Lett. 100, 206801 (2008).
47. A.J.M. Giesbers, U. Zeitler, M.I. Katsnelson, L.A. Ponomarenko, T.M.G. Mohiuddin, and J.C. Maan, Phys. Rev. Lett. 99, 206803 (2007).