Graphene as a Lattice Field Theory

TL;DR

This paper models the electronic properties of graphene using relativistic lattice field theories, exploring how strong interactions can lead to insulating states and excitonic condensates, with preliminary results on quasiparticle behavior.

Contribution

It introduces a lattice field theory approach to graphene's electronic properties, including modeling strong interactions and phase transitions without sign problems.

Findings

Strong interactions can induce an insulating state in monolayer graphene.

Interlayer bias in bilayer graphene leads to excitonic condensates disrupting the Fermi surface.

Preliminary quasiparticle dispersion results estimate Fermi momentum and energy gaps.

Abstract

We introduce effective field theories for the electronic properties of graphene in terms of relativistic fermions propagating in 2+1 dimensions, and outline how strong inter-electron interactions may be modelled by numerical simulation of a lattice field theory. For strong enough coupling an insulating state can form via condensation of particle-hole pairs, and it is demonstrated that this is a theoretical possibility for monolayer graphene. For bilayer graphene the effect of an interlayer bias voltage can be modelled by the introduction of a chemical potential (akin to isopsin chemical potential in QCD) with no accompanying sign problem; simulations reveal the presence of strong interactions among the residual degrees of freedom at the resulting Fermi surface, which is disrupted by an excitonic condensate. We also present preliminary results for the quasiparticle dispersion, which permit direct estimates of both the Fermi momentum and the induced gap.