Chiral Symmetry Breaking in Graphene

TL;DR

This paper investigates whether Coulomb interactions can induce chiral symmetry breaking in un-doped graphene, proposing a strong coupling approach and analyzing the potential for an antiferromagnetic Mott insulator ground state.

Contribution

It introduces a strong coupling expansion method to analyze Coulomb interactions in graphene and suggests the ground state could be an antiferromagnetic Mott insulator.

Findings

Coulomb interaction is subcritical and unlikely to cause symmetry breaking in graphene.

The ground state may be an antiferromagnetic Mott insulator.

Without spin degeneracy, weak Coulomb interactions could open a gap.

Abstract

The question of whether the Coulomb interaction is strong enough to break the sublattice symmetry of un-doped graphene is discussed. We formulate a strong coupling expansion where the ground state of the Coulomb Hamiltonian is found exactly and the kinetic hopping Hamiltonian is treated as a perturbation. We argue that many of the properties of the resulting system would be shared by graphene with a Hubbard model interaction. In particular, the best candidate sublattice symmetry breaking ground state is an antiferromagnetic Mott insulator. We discuss the results of some numerical simulations which indicate that the Coulomb interaction is indeed subcritical. We also point out the curious fact that, if the electron did not have spin degeneracy, the tendency to break chiral symmetry would be much greater and even relatively weak Coulomb interactions would likely gap the spectrum.