We develop an Effective Medium Theory to study the electrical transport properties of disordered graphene. The theory includes non-linear screening and exchange-correlation effects allowing us to consider experimentally relevant strengths of the Coulomb interaction. Assuming random Coulomb impurities, we calculate the electrical conductivity as a function of gate voltage describing quantitatively the full cross-over from the fluctuations dominated regime around the Dirac point to the large doping regime at high gate voltages. We find that the conductivity at the Dirac point is strongly affected by exchange correlation effects.
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