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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.
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