Renormalization group approach to chiral symmetry breaking in graphene

Abstract

We investigate the development of a gapped phase in the field theory of Dirac fermions in graphene with long-range Coulomb interaction. In the large-$N$ approximation, we show that the chiral symmetry is only broken below a critical number of two-component Dirac fermions ${N}_{c}=32/{\ensuremath{\pi}}^{2}$, that is exactly half the value found in quantum electrodynamics in $2+1$ dimensions. Adopting otherwise a ladder approximation, we give evidence of the existence of a critical coupling at which the anomalous dimension of the order parameter of the transition diverges. This result is consistent with the observation that chiral symmetry breaking may be driven by the long-range Coulomb interaction in the Dirac field theory, despite the divergent scaling of the Fermi velocity in the low-energy limit.