Lattice gauge theory model for graphene

Abstract

The effects of the electromagnetic (em) 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 em 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 em interactions among electrons facilitate the spontaneous distortion of the lattice and the opening of a gap.