Magnetic catalysis and quantum Hall ferromagnetism in weakly coupled graphene
 Gordon W. Semenoff,
 Fei Zhou
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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.
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 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