Chiral symmetry of graphene and strong coupling lattice gauge theory

TL;DR

This paper models electrons in graphene using lattice gauge theories, showing that strong coupling leads to an insulating state with dynamical gap formation and excitonic modes, drawing parallels to chiral symmetry breaking in gauge theories.

Contribution

It introduces a lattice gauge theory approach to graphene, demonstrating dynamical gap formation and excitonic modes, and compares compact and non-compact formulations at strong coupling.

Findings

Graphene modeled as a U(1) lattice gauge theory exhibits insulator behavior at strong coupling.

Dynamical gap formation analogous to chiral symmetry breaking is observed.

A pseudo-Nambu--Goldstone mode obeying a Gell-Mann--Oakes--Renner type relation is identified.

Abstract

We model the electrons on a monolayer graphene in terms of the compact and non-compact U(1) lattice gauge theories. The system is analyzed by the strong coupling expansion and is shown to be an insulator due to dynamical gap formation in/around the strong coupling limit. This is similar to the spontaneous chiral symmetry breaking in strong coupling gauge theories. The results from the compact and non-compact formulations are compared up to the next-to-leading order of the strong coupling expansion. Excitonic modes and their dispersion relations in the insulating phase are also investigated: it is found that there arises a pseudo-Nambu--Goldstone mode obeying the Gell-Mann--Oakes--Renner type formula.