Enhancement of non-local exchange near isolated band-crossings in graphene

TL;DR

This paper investigates non-local exchange interactions in graphene with isolated band-crossings, highlighting how lattice effects and screening influence symmetry-breaking states and exchange effects.

Contribution

It provides a detailed analysis of non-local exchange effects in graphene near band-crossings using a tight-binding Hartree-Fock model, emphasizing the impact of lattice-scale Coulomb interactions.

Findings

Non-local exchange effects are significant near isolated band-crossings.

Lattice details of Coulomb interactions influence symmetry-breaking states.

Screening modifies the strength and character of exchange interactions.

Abstract

The physics of non-local exchange interactions in graphene sheets is studied within a $\pi$-orbital tight-binding model using a Hartree-Fock approximation and Coulomb interactions modified at short distances by lattice effects and at large distances by dielectric screening. We use this study to comment on the strong non-locality of exchange effects in systems with isolated band-crossings at energies close to the Fermi energy. We also discuss the role of lattice scale details of the effective Coulomb interaction in determining whether or not broken symmetry states appear at strong interaction strengths, and in determining the character of those states when they do appear.