Abstract
The weak-field Hall conductivity is calculated in graphene containing scatterers with long-range potential within a self-consistent Born approximation. In the clean limit, the diagonal conductivity and the Hall conductivity are shown to agree with the Boltzmann results. Explicit numerical calculations are performed for scatterers with a Gaussian potential with the range d, showing that the Hall conductivity as well as the density of states and the diagonal conductivity becomes universal when the energy is scaled by 1/d. For more realistic charged impurities, the singularity appearing in the Hall coefficient near the charge neutrality point is shown to be sensitive to environmental dielectric material.
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