Chiral symmetry breaking in graphene

Physica Scripta

Volumn , Issue T146, 2012, Pages

  Semenoff, Gordon W ^a  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

ANTIFERROMAGNETICS; CHIRAL SYMMETRY; MOTT INSULATORS; SPIN DEGENERACY; STRONG-COUPLING EXPANSION; SUB-LATTICES; SUBLATTICE SYMMETRY; SYMMETRY-BREAKING;

ANTIFERROMAGNETISM; COULOMB INTERACTIONS; GROUND STATE; HAMILTONIANS;

GRAPHENE;

EID: 84858202595     PISSN: 00318949     EISSN: 14024896     Source Type: Journal    
DOI: 10.1088/0031-8949/2012/T146/014016     Document Type: Article

References (75)

1. Semenoff G W 1984 Condensed matter simulation of a three-dimensional anomaly Phys. Rev. Lett. 53 2449
2. Deser S, Jackiw R and Templeton S 1982 Topologically massive gauge theories Ann. Phys. 140 372
3. Deser S, Jackiw R and Templeton S 1982 Topologically massive gauge theories Ann. Phys. 185 406 (erratum)
4. Deser S, Jackiw R and Templeton S 1988 Ann. Phys. 185 406
5. Deser S, Jackiw R and Templeton S 2000 Ann. Phys. 281 409
6. Deser S, Jackiw R and Templeton S 1982 Three-dimensional massive gauge theories Phys. Rev. Lett. 48 975
7. Niemi A J and Semenoff G W 1983 Axial anomaly induced fermion fractionization and effective gauge theory actions in odd dimensional space-times Phys. Rev. Lett. 51 2077
8. Redlich A N 1984 Parity violation and gauge noninvariance of the effective gauge field action in three-dimensions Phys. Rev. D 29 2366-74
9. Redlich A N 1984 Gauge noninvariance and parity violation of three-dimensional fermions Phys. Rev. Lett. 52
10. Jackiw R 1984 Fractional charge and zero modes for planar systems in a magnetic field Phys. Rev. D 29 2375
11. Paranjape M B and Semenoff G W 1983 Spectral asymmetry, trace identities and the fractional fermion number of magnetic monopoles Phys. Lett. B 132 369
12. Niemi A J and Semenoff G W 1984 Spectral asymmetry on an open space Phys. Rev. D 30 809
13. Niemi A J and Semenoff G W 1986 Index theorems on open infinite manifolds Nucl. Phys. B 269 131
14. Niemi A J and Semenoff G W 1986 Fermion number fractionization in quantum field theory Phys. Rep. 135 99
15. Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y, Dubonos S V, Grigorieva I V, Firsov A A and Novoselov K S 2004 Electric field effect in atomically thin carbon films Science 306 666
16. Novoselov K S, Geim A K, Morozov S V, Jiang D, Katsnelson M I, Grigorieva I V, Dubonos S V and Firsov A A 2005 Two-dimensional gas of massless Dirac fermions in graphene Nature 438 197
17. Zhang Y B, Tan Y W, Stormer H L and Kim P 2005 Experimental observation of the quantum Hall effect and Berry's phase in graphene Nature 438 201
18. Gusynin V P and Sharapov S G 2005 Unconventional integer quantum Hall effect in graphene Phys. Rev. Lett. 95 146801
19. Peres N M R, Guinea F and Castro Neto A H 2006 Electronic properties of disordered two-dimensional carbon Phys. Rev. B 73 125411 (arXiv:cond-mat/ 0506575)
20. 2 topological order and the quantum spin Hall effect Phys. Rev. Lett. 95 146802
21. Bernevig B A, Hughes T L and Zhang S-C 2006 Quantum spin Hall effect and topological phase transition in HgTe quantum wells Science 314 1757-61 (Pubitemid 44969083)
22. Fu L and Kane C L 2007 Topological insulators with inversion symmetry Phys. Rev. B 76 045302
23. Murakami S 2007 Phase transition between the quantum spin Hall and insulator phases in 3D: emergence of a topological gapless phase New J. Phys. 9 356-6
24. Jackiw R and Templeton S 1981 How super-renormalizable interactions cure their infrared divergences Phys. Rev. D 23 2291
25. Pisarski R D 1984 Chiral symmetry breaking in three-dimensional electrodynamics Phys. Rev. D 29 2423
26. Appelquist T W, Bowick M J, Karabali D and Wijewardhana LCR 1986 Spontaneous chiral symmetry breaking in three-dimensional QED Phys. Rev. D 33 3704
27. Appelquist T, Nash D and Wijewardhana L C R 1988 Critical behavior in ( 2+1)-dimensional QED Phys. Rev. Lett. 60 2575
28. Semenoff G W and Wijewardhana L C R 1989 Dynamical mass generation in 3D four-fermion theory Phys. Rev. Lett. 63 2633
29. Kocic A, Hands S, Kogut J B and Dagotto E 1990 The equation of state and critical exponents in quenched strongly coupled QED Nucl. Phys. B 347 217
30. Semenoff G W and Wijewardhana L C R 1992 Dynamical violation of parity and chiral symmetry in three-dimensional four-Fermi theory Phys. Rev. D 45 1342
31. Appelquist T and Wijewardhana L C R 2004 Phase structure of non-compact QED3 and the Abelian Higgs model Quantum Theory and Symmetries ed P C Argyres, T J Hodges, F Mansouri, J J Scanio, P Suranyi and L C R Wijewardhana (Singapore: World Scientific) pp177-191 (arXiv:hep-ph/0403250)
32. Armour W, Hands S and Strouthos C 2010 Monte Carlo simulation of the semimetal-insulator phase transition in monolayer graphene Phys. Rev. B 81 125105 (arXiv:0910.5646)
33. Armour W, Hands S and Strouthos C 2009 Lattice simulations near the semimetal-insulator phase transition of graphene arXiv:0908.0118
34. Hands S and Strouthos C 2009 Quantum phase transition in a graphene model J. Phys.: Conf. Ser. 150 042191 (arXiv:0808.2720)
35. Hands S and Strouthos C 2008 Quantum critical behaviour in a graphene-like model Phys. Rev. B 78 165423 (arXiv:0806.4877)
36. Drut J E and Lahde T A 2009 Critical exponents of the semimetal-insulator transition in graphene: a Monte Carlo study Phys. Rev. B 79 241405 (arXiv:0905.1320)
37. Drut J E, Lahde T A and Suoranta L 2010 First-order chiral transition in the compact lattice theory of graphene and the case for improved actions arXiv:1002.1273
38. Drut J E and Lahde T A 2009 Lattice field theory simulations of graphene arXiv:0901.0584
39. Drut J E and Lahde T A 2008 Is graphene in vacuum an insulator? arXiv:0807.0834
40. Drut J E, Lahde T A and Tolo E 2010 Signatures of a gap in the conductivity of graphene arXiv:1005.5089
41. Drut J E, Lahde T A and Tolo E 2010 Graphene: from materials science to particle physics (Plenary talk) 28th Int. Symp. on Lattice Field Theory (14-19 June 2010) (arXiv:1011.0643)
42. Araki Y 2011 Chiral symmetry breaking in monolayer graphene by strong coupling expansion of compact and non-compact U(1) lattice gauge theories Ann. Phys. 326 1408-24
43. Herbut I F 2006 Interactions and phase transitions on graphene's honeycomb lattice Phys. Rev. Lett. 97 146401 (arXiv:cond-mat/0606195)
44. Herbut I F, Juricic V and Vafek O 2009 Relativistic Mott criticality in graphene Phys. Rev. B 80 075432
45. Gonzalez J, Guinea F and Vozmediano M A H 1994 Non-Fermi liquid behaviour of electrons in the half-filled honeycomb lattice Nucl. Phys. B 424 595
46. Gonzalez J, Guinea F and Vozmediano M A H 1999 Marginal Fermi-liquid behavior from two-dimensional Coulomb interaction Phys. Rev. B 59 R2474
47. Gorbar E V, Gusynin V P and Miransky V A 2001 Dynamical chiral symmetry breaking on a brane in reduced QED Phys. Rev. D 64 105028
48. Gorbar E V, Gusynin V P, Miransky V A and Shovkovy I A 2002 Magnetic field driven metal-insulator phase transition in planar systems Phys. Rev. B 66 045108
49. Sheehy D E and Schmalian J 2007 Quantum critical scaling in graphene Phys. Rev. Lett. 99 226803
50. Vafek O and Case M J 2008 Renormalization group approach to two-dimensional Coulomb interacting Dirac fermions with random gauge potential Phys. Rev. B 77 033410
51. Herbut I F, Juricic V and Vafek O 2008 Coulomb interaction, ripples and the minimal conductivity of graphene Phys. Rev. Lett. 100 046403
52. Juricic V, Herbut I F and Semenoff G W 2009 Coulomb interaction at the metal-insulator critical point in graphene Phys. Rev. B 80 081405
53. Herbut I F, Juricic V and Vafek O 2010 Conductivity of interacting massless Dirac particles in graphene: collisionless regime Phys. Rev. B 82 235402
54. de Juan F, Grushin A G and Vozmediano M A H 2010 Renormalization of Coulomb interaction in graphene: computing observable quantities Phys. Rev. B 82 125409 (arXiv:1002.3111)
55. Kotov V N, Uchoa B and Castro Neto A H 2008 Electron-electron interactions in the vacuum polarization of graphene Phys. Rev. B 78 035119
56. Son D T 2007 Quantum critical point in graphene approached in the limit of infinitely strong Coulomb interaction arXiv:cond-mat/0701501
57. Biswas R R, Sachdev S and Son D T 2007 Coulomb impurity in graphene arXiv:0706.3907
58. Drut J E and Son D T 2008 Renormalization group flow of quartic perturbations in graphene: strong coupling and large-N limits Phys. Rev. B 77 075115 (arXiv:0710.1315)
59. Kotov V N, Uchoa B and Castro Neto A H 2009 1/N expansion in correlated graphene Phys. Rev. B 80 165424
60. Gusynin V P, Miransky V A and Shovkovy I A 1994 Catalysis of dynamical flavor symmetry breaking by a magnetic field in ( 2+1)-dimensions Phys. Rev. Lett. 73 3499-502 (Pubitemid 24977936)
61. Khveshchenko D V 2001 Magnetic-field-induced insulating behavior in highly oriented pyrolitic graphite Phys. Rev. Lett. 87 206401 (arXiv:cond-mat/0106261)
62. Gorbar E V, Gusynin V P, Miransky V A and Shovkovy I A 2002 Magnetic field driven metal insulator phase transition in planar systems Phys. Rev. B 66 045108 (arXiv:cond-mat/0202422)
63. Gorbar E V, Gusynin V P, Miransky V A and Shovkovy I A 2011 Coulomb interaction and magnetic catalysis in the quantum Hall effect in graphene arXiv:1105.1360
64. Semenoff G W and Zhou F 2011 Magnetic catalysis and quantum Hall ferromagnetism in weakly coupled graphene J. High Energy Phys. JHEP1107(2011)037 (arXiv:1104.4714)
65. Kutasov D, Lin J and Parnachev A 2011 Conformal phase transitions at weak and strong coupling arXiv:1107.2324
66. Davis J L, Omid H and Semenoff G W 2011 Holographic fermionic fixed points in d=3 arXiv:1107.4397
67. Wehling T O, Sasioglu E, Friedrich C, Lichtenstein A, Katsnelson M I and Blugel S 2011 Strength of effective coulomb interactions in graphene and graphite Phys. Rev. Lett. 106 236805
68. Jackiw R and Pi S-Y 2007 Chiral gauge theory for graphene Phys. Rev. Lett. 98 266402
69. Chamon C, Hou C Y, Jackiw R, Mudry C, Pi S Y and Schnyder A P 2007 Irrational versus rational charge and statistics in two-dimensional quantum systems arXiv:0707.0293
70. Chamon C, Hou C Y, Jackiw R, Mudry C, Pi S Y and Semenoff G 2007 Electron fractionalization for two-dimensional Dirac fermions arXiv:0712.2439
71. Sorella S and Tosatti E 1992 Semi-metal-insulator transition of the Hubbard model in the honeycomb lattice Europhys. Lett. 19 699
72. Paiva T, Scalettar R T, Zheng W, Singh R R P and Oitmaa J 2005 Ground state and finite temperature signatures of quantum criticality in the half-filled Hubbard model on a honeycomb lattice Phys. Rev. B 72 085123
73. Meng Z Y, Lang T C, Wessel S, Assaad F F and Muramatsu A 2010 Quantum spin-liquid emerging in two-dimensional correlated Dirac fermions Nature 464 847
74. Wu W, Chen Y-H, Tao H-S, Tong N-H and Liu M-M 2010 Interacting Dirac fermions on honeycomb lattice Phys. Rev. B 82 245102
75. Wang G, Goerbig M O, Miniatura C and Grémaud B 2011 Emergent spin liquids in the Hubbard model on the anisotropic honeycomb lattice Europhys. Lett. 95 47013