Density functional theory of graphene sheets

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 equal footing. The theory is able to account for the unusual property that the exchange-correlation contribution to chemical potential increases with carrier density in graphene. The 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 pointlike impurities located close to the graphene plane. The influence of electron-electron interactions on these nonlinear screening calculations is discussed at length in light of recent experiments reporting evidence for the presence of electron-hole puddles in nearly neutral graphene sheets.