Renormalization group approach to chiral symmetry breaking in graphene

TL;DR

This paper uses a renormalization group approach to analyze chiral symmetry breaking in graphene, revealing a critical number of fermion flavors and a critical coupling where symmetry breaking occurs due to Coulomb interactions.

Contribution

It provides a theoretical analysis of chiral symmetry breaking in graphene using renormalization group methods, identifying critical parameters and the role of Coulomb interactions.

Findings

Chiral symmetry is broken only below a critical fermion number N_c = 32/π^2.

A critical coupling exists where the order parameter's anomalous dimension diverges.

Chiral symmetry breaking can be driven by Coulomb interactions despite Fermi velocity divergence.

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 $N_c = 32/\pi^2$, 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.