Lattice gauge theory model for graphene

TL;DR

This paper models electron-electron interactions in graphene using lattice gauge theory, revealing that electromagnetic interactions promote lattice distortions and gap formation, with implications for understanding graphene's electronic properties.

Contribution

It introduces a lattice gauge theory approach to analyze electromagnetic effects in graphene, deriving an exact gap equation and showing interactions enhance lattice instabilities.

Findings

Electromagnetic interactions amplify responses to Kekulé and charge density wave distortions.

Strong e.m. interactions facilitate spontaneous lattice distortion and gap opening.

Derived an exact non-BCS gap equation demonstrating the role of e.m. interactions.

Abstract

The effects of the electromagnetic (e.m.) electron-electron interactions in half-filled graphene are investigated in terms of a lattice gauge theory model. By using exact Renormalization Group methods and lattice Ward Identities, we show that the e.m. interactions amplify the responses to the excitonic pairings associated to a Kekul\'e distortion and to a charge density wave. The effect of the electronic repulsion on the Peierls-Kekul\'e instability, usually neglected, is evaluated by deriving an exact non-BCS gap equation, from which we find evidence that strong e.m. interactions among electrons facilitate the spontaneous distortion of the lattice and the opening of a gap.