Density-Functional Theory of Graphene Sheets

TL;DR

This paper develops a density-functional theory tailored for graphene sheets, capturing their unique electronic properties and electron-electron interactions, and demonstrates its application to impurity screening and electron-hole puddles.

Contribution

It introduces a Kohn-Sham-Dirac DFT scheme specifically designed for graphene, accounting for its unusual exchange-correlation behavior and applying it to impurity screening.

Findings

The exchange-correlation contribution increases with carrier density in graphene.

Electron-electron interactions significantly influence screening and puddle formation.

The method successfully models impurity effects consistent with experimental observations.

Abstract

We outline a Kohn-Sham-Dirac density-functional-theory (DFT) scheme for graphene sheets that treats slowly-varying inhomogeneous external potentials and electron-electron interactions on an equal footing. The theory is able to account for the the unusual property that the exchange-correlation contribution to chemical potential increases with carrier density in graphene. Consequences of this property, and advantages and disadvantages of using the DFT approach to describe it, are discussed. The approach is illustrated by solving the Kohn-Sham-Dirac equations self-consistently for a model random potential describing charged point-like impurities located close to the graphene plane. The influence of electron-electron interactions on these non-linear screening calculations is discussed at length, in the light of recent experiments reporting evidence for the presence of electron-hole puddles in nearly-neutral graphene sheets.