Chiral Gap and Collective Excitations in Monolayer Graphene from Strong Coupling Expansion of Lattice Gauge Theory

TL;DR

This paper uses lattice gauge theory to analytically demonstrate that monolayer graphene exhibits a dynamically generated fermion bandgap and excitations due to chiral symmetry breaking, similar to phenomena in QCD.

Contribution

It provides an analytical framework linking chiral symmetry breaking in graphene to strong coupling lattice gauge theory, deriving a GOR-like relation for pi-excitons.

Findings

Fermion bandgap is generated via chiral symmetry breaking.

A Gell-Mann--Oakes--Renner type relation for pi-excitons is derived.

Experimental verification of the relation would confirm chiral symmetry breaking in graphene.

Abstract

Using the strong coupling expansion of the compact and non-compact U(1) lattice gauge theory for monolayer graphene, we show analytically that fermion bandgap and pseudo Nambu--Goldstone exciton (pi-exciton) are dynamically generated due to chiral symmetry breaking. The mechanism is similar to the generation of quark mass and pion excitation in quantum chromodynamics (QCD). We derive a formula for the pi-exciton analogous to the Gell-Mann--Oakes--Renner (GOR) relation in QCD. Experimental confirmation of the GOR relation on a suspended monolayer graphene would be a clear evidence of chiral symmetry breaking.