Ground state properties of graphene in Hartree-Fock theory

TL;DR

This paper investigates the ground state properties of graphene using non-perturbative Hartree-Fock theory, revealing a divergent Fermi velocity and analyzing effects of defects and external fields.

Contribution

It provides a non-perturbative analysis of graphene's ground state, including the divergence of Fermi velocity and effects of local defects within Hartree-Fock approximation.

Findings

Fermi velocity diverges logarithmically at zero momentum

Existence of ground state with local defects proven

Linear response to electric field characterized

Abstract

We study the Hartree-Fock approximation of graphene in infinite volume, with instantaneous Coulomb interactions. First we construct its translation-invariant ground state and we recover the well-known fact that, due to the exchange term, the effective Fermi velocity is logarithmically divergent at zero momentum. In a second step we prove the existence of a ground state in the presence of local defects and we discuss some properties of the linear response to an external electric field. All our results are non perturbative.