Magnetic catalysis and quantum Hall ferromagnetism in weakly coupled graphene
 Gordon W. Semenoff,
 Fei Zhou
 … show all 2 hide
Purchase on Springer.com
$39.95 / €34.95 / £29.95*
Rent the article at a discount
Rent now* Final gross prices may vary according to local VAT.
Abstract
We study the realization in a model of graphene of the phenomenon whereby the tendency of gaugefield mediated interactions to break chiral symmetry spontaneously is greatly enhanced in an external magnetic field. We prove that, in the weak coupling limit, and where the electronelectron interaction satisfies certain mild conditions, the ground state of charge neutral graphene in an external magnetic field is a quantum Hall ferromagnet which spontaneously breaks the emergent U(4) symmetry to U(2) × U(2). We argue that, due to a residual CP symmetry, the quantum Hall ferromagnet order parameter is given exactly by the leading order in perturbation theory. On the other hand, the chiral condensate which is the order parameter for chiral symmetry breaking generically obtains contributions at all orders. We compute the leading correction to the chiral condensate. We argue that the ensuing fermion spectrum resembles that of massive fermions with a vanishing U(4)valued chemical potential. We discuss the realization of parity and charge conjugation symmetries and argue that, in the context of our model, the charge neutral quantum Hall state in graphene is a bulk insulator, with vanishing longitudinal conductivity due to a charge gap and Hall conductivity vanishing due to a residual discrete particlehole symmetry.
 G.W. Semenoff, Condensed matter simulation of a threedimensional anomaly, Phys. Rev. Lett. 53 (1984) 2449 [SPIRES]. CrossRef
 K.S. Novoselov et al. , Electric field effect in atomically thin carbon films, Science 306 (2004) 666. CrossRef
 K.S. Novoselov et al., Twodimensional gas of massless Dirac fermions in graphene, Nature 438 (2005) 197 [condmat/0509330] [SPIRES]. CrossRef
 K. S. Novoselov et al., Twodimensional atomic crystals, PNAS 102 (2005) 10451. CrossRef
 A.K. Geim and K.S. Novoselov, The rise of graphene, Nat. Mater. 6 (2007) 183. CrossRef
 K.S. Novoselov, Graphene: mind the gap, Nat. Mater. 6 (2007) 720. CrossRef
 S.Y. Zhou et al. ,Substrateinduced bandgap opening in epitaxial graphene, Nat. Mater. 6 (2007) 770. CrossRef
 M.I. Katsnelson, Graphene: carbon in two dimensions, Materials Today 10 (2007) 20. CrossRef
 Y. Zhang, Y.W. Tan, H.L. Stormer and P. Kim, Experimental observation of the quantum Hall effect and Berry’s phase in graphene, Nature 438 (2005) 201. CrossRef
 V.P. Gusynin and S.G. Sharapov, Unconventional integer quantum Hall effect in graphene, Phys. Rev. Lett. 95 (2005) 146801 [condmat/0506575] [SPIRES]. CrossRef
 N.M.R. Peres, F. Guinea, A.H. Castro Neto, Electronic properties of disordered twodimensional carbon, Phys. Rev. Lett. 73 (2006) 125411 [condmat/0512091].
 D.V. Khveshchenko, Magneticfieldinduced insulating behavior in highly oriented pyrolitic graphite, Phys. Rev. Lett. 87 (2001) 206401 [SPIRES]. CrossRef
 E.V. Gorbar, V.P. Gusynin, V.A. Miransky and I.A. Shovkovy, Magnetic field driven metalinsulator phase transition in planar systems, Phys. Rev. B 66 (2002) 045108 [condmat/0202422] [SPIRES].
 I.F. Herbut, Interactions and phase transitions on graphene’s honeycomb lattice, Phys. Rev. Lett. 97 (2006) 146401 [condmat/0606195] [SPIRES]. CrossRef
 D.T. Son, critical point in graphene approached in the limit of infinitely strong Coulomb interaction, Phys. Rev. B 75 (2007) 235423 [condmat/0701501].
 J.E. Drut and D.T. Son, Renormalization group flow of quartic perturbations in graphene: Strong coupling and largeN limits, Phys. Rev. B 77 (2008) 075115 [arXiv:0710.1315] [SPIRES].
 A.H. Castro Neto, Pauling’s dreams for graphene, Physics 2 (2009) 30. CrossRef
 I.F. Herbut, V. Juricic and B. Roy, Theory of interacting electrons on the honeycomb lattice, Phys. Rev. B 79 (2009) 085116 [arXiv:0811.0610] [SPIRES].
 I.F. Herbut, V. Juricic and O. Vafek, Relativistic Mott criticality in graphene, Phys. Rev. B 80 (2009) 075432 [arXiv:0904.1019] [SPIRES].
 V. Juricic, I.F. Herbut and G.W. Semenoff, Coulomb interaction at the metalinsulator critical point in graphene, Phys. Rev. B 80 (2009) 081405 [arXiv:0906.3513] [SPIRES].
 W. Armour, S. Hands and C. Strouthos, Monte Carlo simulation of the semimetalinsulator phase transition in monolayer graphene, Phys. Rev. B 81 (2010) 125105 [arXiv:0910.5646] [SPIRES].
 W. Armour, S. Hands and C. Strouthos, Lattice simulations near the semimetalinsulator phase transition of graphene, arXiv:0908.0118 [SPIRES].
 S. Hands and C. Strouthos, Quantum phase transition in a graphene model, J. Phys. Conf. Ser. 150 (2009) 042191 [arXiv:0808.2720] [SPIRES]. CrossRef
 S. Hands and C. Strouthos, Quantum critical behaviour in a graphenelike model, Phys. Rev. B 78 (2008) 165423 [arXiv:0806.4877] [SPIRES].
 J.E. Drut and T.A. Lahde, Critical exponents of the semimetalinsulator transition in graphene: a Monte Carlo study, Phys. Rev. B 79 (2009) 241405 [arXiv:0905.1320] [SPIRES].
 J.E. Drut, T.A. Lahde and L. Suoranta, Firstorder chiral transition in the compact lattice theory of graphene and the case for improved actions, arXiv:1002.1273 [SPIRES].
 J.E. Drut and T.A. Lahde, Lattice field theory simulations of graphene, arXiv:0901.0584 [SPIRES].
 J.E. Drut and T.A. Lahde, Is graphene in vacuum an insulator?, arXiv:0807.0834 [SPIRES].
 J.E. Drut, T.A. Lahde and E. Tolo, Signatures of a gap in the conductivity of graphene, arXiv:1005.5089 [SPIRES].
 J.E. Drut, T.A. Lahde and E. Tolo, Graphene: from materials science to particle physics, PoS LATTICE2010 (2010) 006 [arXiv:1011.0643] [SPIRES].
 Y. Zhang et al., Landaulevel splitting in graphene in high magnetic fields, Phys. Rev. Lett. 96 (2006) 136806 [condmat/0602649]. CrossRef
 D.A. Abanin et al., Dissipative quantum Hall effect in graphene near the Dirac point, Phys. Rev. Lett. 98 (2007) 196806 [condmat/0702125]. CrossRef
 Z. Jiang et al., Quantum Hall states near the chargeneutral Dirac point in graphene, Phys. Rev. Lett. 99 (2007) 106802 [arXiv:0705.1102]. CrossRef
 A.J.M. Giesbers et al., QuantumHall activation gaps in graphene, Phys. Rev. Lett. 99 (2007) 206803 [arXiv:1009.5485]. CrossRef
 J.G. Checkelsky, L. Li and N.P. Ong, Zeroenergy state in graphene in a high magnetic field, Phys. Rev. Lett. 100 (2008) 206801 [arXiv:0708.1959]. CrossRef
 J.G. Checkelsky, L. Li, N.P. Ong, Divergent resistance at the Dirac point in graphene: evidence for a transition in a high magnetic field, Phys. Rev. B 79 (2009) 115434 [arXiv:0808.0906].
 L. Zhang et al., Breakdown of the N = 0 quantum Hall state in graphene: two insulating regimes, Phys. Rev. B 80 (2009) 241412 [arXiv:0904.1996].
 A.J.M. Giesbers et al., Gap opening in the zeroth Landau level of graphene, Phys. Rev. B 80 (2009) 201403(R) [arXiv:0904.0948].
 Xu Du, I. Skachko, F. Duerr, A. Luican, E.Y. Andrei, Fractional quantum Hall effect and insulating phase of Dirac electrons in graphene, Nature 462 (2009) 192. CrossRef
 K.I. Bolotin et al., Observation of the fractional quantum Hall effect in graphene, Nature 462 (2009) 196. CrossRef
 D.A. Abanin et al., Fractional quantum Hall effect in suspended graphene: transport coefficients and electron interaction strength, Phys. Rev. B 81 (2010) 115410 [arXiv:0912.1134].
 C.R. Dean et al., Multicomponent fractional quantum Hall effect in graphene, arXiv:1010.1179.
 F. Ghahari et al., Measurement of the ν = 1/3 fractional quantum Hall energy gap in suspended graphene, Phys. Rev. Lett. 106 (2011) 046801. CrossRef
 K.G. Klimenko, Threedimensional GrossNeveu model in an external magnetic field, Theor. Math. Phys. 89 (1992) 1161 [SPIRES]. CrossRef
 K.G. Klimenko, Threedimensional GrossNeveu model at nonzero temperature and in an external magnetic field, Theor. Math. Phys. 90 (1992) 1 [SPIRES]. CrossRef
 V.P. Gusynin, V.A. Miransky and I.A. Shovkovy, Catalysis of dynamical flavor symmetry breaking by a magnetic field in (2 + 1)dimensions, Phys. Rev. Lett. 73 (1994) 3499 [hepph/9405262] [SPIRES]. CrossRef
 V.P. Gusynin, V.A. Miransky and I.A. Shovkovy, Dynamical flavor symmetry breaking by a magnetic field in (2 + 1)dimensions, Phys. Rev. D 52 (1995) 4718 [hepth/9407168] [SPIRES].
 V.P. Gusynin, V.A. Miransky and I.A. Shovkovy, Dimensional reduction and catalysis of dynamical symmetry breaking by a magnetic field, Nucl. Phys. B 462 (1996) 249 [hepph/9509320] [SPIRES]. CrossRef
 V.P. Gusynin, V.A. Miransky, S.G. Sharapov and I.A. Shovkovy, Excitonic gap, phase transition and quantum Hall effect in graphene, Phys. Rev. B 74 (2006) 195429 [condmat/0605348] [SPIRES].
 I.F. Herbut, Pseudomagnetic catalysis of the timereversal symmetry breaking in graphene, Phys. Rev. B 78 (2008) 205433 [arXiv:0804.3594].
 E.V. Gorbar, V.P. Gusynin, V.A. Miransky and I.A. Shovkovy, Dynamics in the quantum Hall effect and the phase diagram of graphene, Phys. Rev. B 78 (2008) 085437 [arXiv:0806.0846] [SPIRES].
 M. Ezawa, Intrinsic Zeeman effect in graphene, J. Phys. Soc. Jpn. 76 (2007) 094701 [SPIRES]. CrossRef
 G.W. Semenoff, I.A. Shovkovy and L.C.R. Wijewardhana, Phase transition induced by a magnetic field, Mod. Phys. Lett. A 13 (1998) 1143 [hepph/9803371] [SPIRES]. CrossRef
 V.P. Gusynin, S.G. Sharapov and J.P. Carbotte, AC conductivity of graphene: from tightbinding model to 2 + 1dimensional quantum electrodynamics, Int. J. Mod. Phys. B 21 (2007) 4611 [arXiv:0706.3016] [SPIRES].
 K. Nomura, A.H. MacDonald, Quantum Hall ferromagnetism in graphene, Phys. Rev. Lett. 96 (2006) 256602 [condmat/0604113]. CrossRef
 S.M. Girvin and A.H. MacDonald, Multicomponent quantum Hall systems: the sum of their parts and more, in Perspectives in Quantum Hall Effects, S. Das Sarma and A. Pinczuk eds., John Wiley and Soons, New York U.S.A. (1997).
 K. Yang, S. Das Sarma and A.H. MacDonald, Collective modes and skyrmion excitations in graphene SU(4) quantum Hall ferromagnets, Phys. Rev. B 74 (2006) 075423.
 A.J. Niemi and G.W. Semenoff, Axial anomaly induced fermion fractionization and effective gauge theory actions in odd dimensional spacetimes, Phys. Rev. Lett. 51 (1983) 2077 [SPIRES]. CrossRef
 A.N. Redlich, Parity violation and gauge noninvariance of the effective gauge field action in threedimensions, Phys. Rev. D 29 (1984) 2366 [SPIRES].
 A.N. Redlich, Gauge noninvariance and parity nonconservation of threedimensional fermions, Phys. Rev. Lett. 52 (1984) 18 [SPIRES]. CrossRef
 C. Vafa and E. Witten, Restrictions on symmetry breaking in vectorlike gauge theories, Nucl. Phys. B 234 (1984) 173 [SPIRES]. CrossRef
 S. Ryu, C. Mudry, C.Y. Hou, C. Chamon, Masses in graphenelike twodimensional electronic systems: topological defects in order parameters and their fractional exchange statistics, Phys. Rev. B 80 (2009) 205319.
 A. Tanaka, X. Hu, Manybody spin Berry phases emerging from the πflux state: competition between antiferromagnetism and the valencebondsolid state, Phys. Rev. Lett. 95 (2005) 036402. CrossRef
 A. Tanaka, X. Hu, Effective field theory with a θvacua structure for twodimensional spin systems, Phys. Rev. B 74 (2006) 140407.
 P. Ghaemi, S. Ryu, D.H. Lee, The quantum valley Hall effect in proximityinduced superconducting graphene: an experimental window for deconfined quantum criticality, arXiv:0704.2234.
 I.F. Herbut, Zeroenergy states and fragmentation of spin in the easy plane antiferromagnet on honeycomb lattice, Phys. Rev. Lett. 99 (2007) 206404 [arXiv:0704.2234] [SPIRES]. CrossRef
 J. Gonzalez, F. Guinea and M.A.H. Vozmediano, NonFermi liquid behavior of electrons in the half filled honeycomb lattice (A Renormalization group approach), Nucl. Phys. B 424 (1994) 595 [hepth/9311105] [SPIRES]. CrossRef
 J. Gonzalez, F. Guinea and M.A.H. Vozmediano, MarginalFermiliquid behavior from twodimensional Coulomb interaction, Phys. Rev. B 59 (1999) 2474(R) [condmat/0302164].
 H. Leal and D.V. Khveshchenko, Excitonic instability in twodimensional degenerate semimetals, Nucl. Phys. B 687 (2004) 323 [condmat/0302164] [SPIRES].
 D.V. Khveshchenko, Coulombinteracting Dirac fermions in disordered graphene, Phys. Rev. B 74 (2006) 161402 [condmat/0612651].
 E.G. Mishchenko, Effect of electronelectron interactions on the conductivity of clean graphene, Phys. Rev. Lett. 98 (2007) 216801 [condmat/0604601]. CrossRef
 D.E. Sheehy, J. Schmalian, Quantum critical scaling in graphene, Phys. Rev. Lett. 99 (2007) 226803. CrossRef
 O. Vafek, M.J. Case, Renormalization group approach to twodimensional Coulomb interacting Dirac fermions with random gauge potential, Phys. Rev. B 77 (2008) 033410 [arXiv:1103.6285].
 J. Alicea, M.P.A. Fisher, Graphene integer quantum Hall effect in the ferromagnetic and paramagnetic regimes, Phys. Rev. B 74 (2006) 075422 [SPIRES].
 M. Kharitonov, Phase diagram for the ν = 0 quantum Hall state in monolayer graphene, SPIRES.
 R. Jackiw and C. Rebbi, Solitons with fermion number 1/2, Phys. Rev. D 13 (1976) 3398 [SPIRES].
 A.J. Niemi and G.W. Semenoff, Fermion number fractionization in quantum field theory, Phys. Rept. 135 (1986) 99 [SPIRES]. CrossRef
 S.R. Coleman and B.R. Hill, No more corrections to the topological mass term in QED in threedimensions, Phys. Lett. B 159 (1985) 184 [SPIRES].
 G.W. Semenoff, P. Sodano and Y.S. Wu, Renormalization of the statistics parameter in threedimensional electrodynamics, Phys. Rev. Lett. 62 (1989) 715 [SPIRES]. CrossRef
 Title
 Magnetic catalysis and quantum Hall ferromagnetism in weakly coupled graphene
 Journal

Journal of High Energy Physics
2011:37
 Online Date
 July 2011
 DOI
 10.1007/JHEP07(2011)037
 Online ISSN
 10298479
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Field Theories in Lower Dimensions
 Spontaneous Symmetry Breaking
 Industry Sectors
 Authors

 Gordon W. Semenoff ^{(1)}
 Fei Zhou ^{(1)}
 Author Affiliations

 1. Department of Physics and Astronomy, University of British Columbia, Vancouver, British Columbia, V6T 1Z1, Canada