Theory of interacting electrons on the honeycomb lattice

Physical Review B - Condensed Matter and Materials Physics

Volumn 79, Issue 8, 2009, Pages

  Herbut, Igor F ^a   Juričić, Vladimir ^a   Roy, Bitan ^a  

^a SIMON FRASER UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 62149117934     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.79.085116     Document Type: Article

References (74)

1. For reviews, see V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, Int. J. Mod. Phys. B 21, 4611 (2007) 10.1142/S0217979207038022
2. A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, Rev. Mod. Phys. 81, 109 (2009). 10.1103/RevModPhys.81.109
3. I. F. Herbut, Phys. Rev. Lett. 97, 146401 (2006). 10.1103/PhysRevLett.97. 146401
4. J. Gonzalez, F. Guinea, and M. A. H. Vozmediano, Nucl. Phys. B 424, 595 (1994) 10.1016/0550-3213(94)90410-3
5. J. Gonzales, F. Guinea, and M. A. H. Vozmediano, Phys. Rev. B 59, R2474 (1999). 10.1103/PhysRevB.59.R2474
6. O. Vafek, Phys. Rev. Lett. 98, 216401 (2007). 10.1103/PhysRevLett.98. 216401
7. I. F. Herbut, Phys. Rev. Lett. 99, 206404 (2007). 10.1103/PhysRevLett.99. 206404
8. S. Sorella and E. Tosatti, Europhys. Lett. 19, 699 (1992). 10.1209/0295-5075/19/8/007
9. L. M. Martelo, M. Dzierzawa, L. Siffert, and D. Baeriswyl, Z. Phys. B: Condens. Matter 103, 335 (1997). 10.1007/s002570050384
10. T. Paiva, R. T. Scalettar, W. Zheng, R. R. P. Singh, and J. Oitmaa, Phys. Rev. B 72, 085123 (2005). 10.1103/PhysRevB.72.085123
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) 10.1103/PhysRevLett.96.136806
12. Z. Jiang, Y. Zhang, H. L. Stormer, and P. Kim, Phys. Rev. Lett. 99, 106802 (2007). 10.1103/PhysRevLett.99.106802
13. Joseph G. Checkelsky, Lu Li, and N. P. Ong, Phys. Rev. Lett. 100, 206801 (2008) 10.1103/PhysRevLett.100.206801
14. arXiv:0808.0906 (unpublished).
15. D. V. Khveshchenko, Phys. Rev. Lett. 87, 206401 (2001) 10.1103/PhysRevLett.87.206401
16. D. V. Khveshchenko, Phys. Rev. Lett. 87, 246802 (2001). 10.1103/PhysRevLett.87.246802
17. V. P. Gusynin, V. A. Miransky, S. G. Sharapov, and I. A. Shovkovy, Phys. Rev. B 74, 195429 (2006) 10.1103/PhysRevB.74.195429
18. E. V. Gorbar, V. P. Gusynin, and V. A. Miransky, Low Temp. Phys. 34, 790 (2008). 10.1063/1.2981388
19. I. F. Herbut, Phys. Rev. B 75, 165411 (2007) 10.1103/PhysRevB.75.165411
20. I. F. Herbut, Phys. Rev. B 76, 085432 (2007) 10.1103/PhysRevB.76.085432
21. I. F. Herbut and B. Roy, Phys. Rev. B 77, 245438 (2008). 10.1103/PhysRevB.77.245438
22. J. Alicea and M. P. A. Fisher, Phys. Rev. B 74, 075422 (2006); 10.1103/PhysRevB.74.075422
23. R. L. Doretto and C. Morais-Smith, Phys. Rev. B 76, 195431 (2007). 10.1103/PhysRevB.76.195431
24. For a review, see A. K. Geim and K. S. Novoselov, Nature Mater. 6, 183 (2007). 10.1038/nmat1849
25. I. F. Herbut, V. Juričić, and O. Vafek, Phys. Rev. Lett. 100, 046403 (2008) 10.1103/PhysRevLett.100.046403
26. I. F. Herbut, V. Juričić, O. Vafek, and M. J. Case, arXiv:0809.0725 (unpublished).
27. L. Fritz, J. Schmalian, M. Muller, and S. Sachdev, Phys. Rev. B 78, 085416 (2008). 10.1103/PhysRevB.78.085416
28. By this definition the interaction that at large particle separation decays as a power law V (r) ∼1/ ra is short ranged provided that a>2.
29. Y. Takahashi, in Progress in Quantum Field Theory, edited by, H. Ezawa, and, S. Kamefuchi, (North Holland, Amsterdam, 1986).
30. For the closely related chiral symmetry of d-wave superconductors, see I. F. Herbut, Phys. Rev. B 66, 094504 (2002) 10.1103/PhysRevB.66.094504
31. I. F. Herbut, Phys. Rev. Lett. 88, 047006 (2002) 10.1103/PhysRevLett.88. 047006
32. I. F. Herbut, Phys. Rev. Lett. 94, 237001 (2005) 10.1103/PhysRevLett.94. 237001
33. D. J. Lee and I. F. Herbut, Phys. Rev. B 66, 094512 (2002) 10.1103/PhysRevB.66.094512
34. B. H. Seradjeh and I. F. Herbut, Phys. Rev. B 66, 184507 (2002) 10.1103/PhysRevB.66.184507
35. Z. Tesanovic, O. Vafek, and M. Franz, Phys. Rev. B 65, 180511 (R) (2002) 10.1103/PhysRevB.65.180511
36. M. Franz, T. Pereg-Barnea, D. E. Sheehy, and Z. Teanović, Phys. Rev. B 68, 024508 (2003) 10.1103/PhysRevB.68.024508
37. I. O. Thomas and S. Hands, Phys. Rev. B 75, 134516 (2007). 10.1103/PhysRevB.75.134516
38. At the critical point at a finite Coulomb interaction in two dimensions z is always unity, see I. F. Herbut, Phys. Rev. Lett. 87, 137004 (2001). 10.1103/PhysRevLett.87.137004
39. F. D. M. Haldane, Phys. Rev. Lett. 61, 2015 (1988). 10.1103/PhysRevLett. 61.2015
40. G. W. Semenoff, Phys. Rev. Lett. 53, 2449 (1984). 10.1103/PhysRevLett.53. 2449
41. C.-Y. Hou, C. Chamon, and C. Mudry, Phys. Rev. Lett. 98, 186809 (2007). 10.1103/PhysRevLett.98.186809
42. I. Herbut, A Modern Approach to Critical Phenomena (Cambridge University Press, Cambridge, 2007).
43. W. F. Brinkman and T. M. Rice, Phys. Rev. B 2, 4302 (1970). 10.1103/PhysRevB.2.4302
44. Y. Hasegawa, R. Konno, H. Nakano, and M. Kohmoto, Phys. Rev. B 74, 033413 (2006). 10.1103/PhysRevB.74.033413
45. I. F. Herbut, Phys. Rev. B 78, 205433 (2008). 10.1103/PhysRevB.78.205433
46. Dj. Muicki and B. Milić, Matematicke Osnove Teorijske Fizike, (Univerzitet u Beogradu, Beograd, 1984), Sec. 5.3 (in Serbian).
47. Here we treat the frequency integrals in the loops analogously to momentum integrals. For an alternative, see Ref., for example.
48. K. Kaveh and I. F. Herbut, Phys. Rev. B 71, 184519 (2005). 10.1103/PhysRevB.71.184519
49. A. M. Vasil'ev, S. E. Derkachov, N. A. Kilev, and A. S. Stepanenko, Teor. Mat. Fiz. 92, 486 (1992)
50. A. M. Vasil'ev, S. E. Derkachov, N. A. Kilev, and A. S. Stepanenko, Teor. Mat. Fiz. 97, 364 (1993).
51. J. A. Gracey, Int. J. Mod. Phys. A 9, 727 (1994). 10.1142/ S0217751X94000340
52. L. Kärkkäinen, L. Lacaze, P. Lacock, and B. Petersson, Nucl. Phys. B 415, 781 (1994) 10.1016/0550-3213(94)90309-3
53. L. Kärkkäinen, L. Lacaze, P. Lacock, and B. Petersson, Nucl. Phys. B 438, 650 (E) (1995). 10.1016/0550-3213(95)00055-W
54. L. Rosa, P. Vitale, and C. Wetterich, Phys. Rev. Lett. 86, 958 (2001) 10.1103/PhysRevLett.86.958
55. F. Hofling, C. Nowak, and C. Wetterich, Phys. Rev. B 66, 205111 (2002). 10.1103/PhysRevB.66.205111
56. S. Christofi, S. Hands, and C. Strouthos, Phys. Rev. D 75, 101701 (R) (2007) and references therein. 10.1103/PhysRevD.75.101701
57. Y. Nambu and G. Jona-Lasinio, Phys. Rev. 122, 345 (1961). 10.1103/PhysRev.122.345
58. In the purely bosonic Φ4 theories, the O (3) symmetry is currently believed not to emerge at the critical point out of Z2 ×O (2), in three dimensions. The critical behavior is governed by the "biconal" fixed point, which however, appears to be extremely close the O (3) -symmetric point in the coupling space. See P. Calabrese, A. Pelissetto, and E. Vicari, Phys. Rev. B 67, 054505 (2003). 10.1103/PhysRevB.67.054505
59. The terms allowed in the atomic limit are already contained in the terms S2 and V12.
60. See, nevertheless, Ref. for numerical results on Thirring models with more than one Dirac fermion.
61. S. Raghu, Xiao-Liang Qi, C. Honerkamp, and S.-C. Zhang, Phys. Rev. Lett. 100, 156401 (2008). 10.1103/PhysRevLett.100.156401
62. I. L. Aleiner, D. E. Kharzeev, and A. M. Tsvelik, Phys. Rev. B 76, 195415 (2007). 10.1103/PhysRevB.76.195415
63. D. T. Son, Phys. Rev. B 75, 235423 (2007) 10.1103/PhysRevB.75.235423
64. J. E. Drut and D. T. Son, Phys. Rev. B 77, 075115 (2008). 10.1103/PhysRevB.77.075115
65. E. V. Gorbar, V. P. Gusynin, V. A. Miransky, and I. A. Shovkovy, Phys. Rev. B 66, 045108 (2002). 10.1103/PhysRevB.66.045108
66. D. V. Khveshchenko and H. Leal, Nucl. Phys. B 687, 323 (2004). 10.1016/j.nuclphysb.2004.03.020
67. J. E. Drut and T. A. Lahde, Phys. Rev. Lett. 102, 026802 (2009). 10.1103/PhysRevLett.102.026802
68. S. Hands and C. Strouthos, Phys. Rev. B 78, 165423 (2008). 10.1103/PhysRevB.78.165423
69. O. Vafek and M. J. Case, Phys. Rev. B 77, 033410 (2008). 10.1103/PhysRevB.77.033410
70. See Ref. and the problem 8.10 in Ref..
71. I. F. Herbut and Z. Teanović, Phys. Rev. Lett. 76, 4588 (1996) 10.1103/PhysRevLett.76.4588
72. I. F. Herbut and Z. Teanović, Phys. Rev. Lett. 78, 980 (1997) 10.1103/PhysRevLett.78.980
73. I. F. Herbut, J. Phys. A 30, 423 (1997). 10.1088/0305-4470/30/2/010
74. For spinless fermions considered here, both insulators break the discrete Ising symmetry, so there are no Nambu-Goldstone bosons.