A self-consistent theory for graphene transport

Abstract

We demonstrate theoretically that most of the observed transport properties of graphene sheets at zero magnetic field can be explained by scattering from charged impurities. We find that, contrary to common perception, these properties are not universal but depend on the concentration of charged impurities n_imp. For dirty samples (250 × 10¹⁰ cm⁻² < n_imp < 400 × 10¹⁰ cm⁻²), the value of the minimum conductivity at low carrier density is indeed 4e²/h in agreement with early experiments, with weak dependence on impurity concentration. For cleaner samples, we predict that the minimum conductivity depends strongly on n_imp, increasing to 8e²/h for n_imp ≈ 20 × 10¹⁰ cm⁻². A clear strategy to improve graphene mobility is to eliminate charged impurities or use a substrate with a larger dielectric constant.