Bilayer graphene with long-range scatterers: Diamagnetism and weak-field Hall effect

The diamagnetic susceptibility and the weak-field Hall conductivity are calculated for scatterers with nonzero range in bilayer graphene within a self-consistent Born approximation. The susceptibility exhibits a double-peak structure in the vicinity of zero energy. The Hall coefficient is given by the carrier concentration when the potential range is smaller or comparable to the Fermi wavelength, but becomes different when the range becomes larger than the Fermi wavelength. This deviation is not important in the case of charged impurities, but can become visible in the presence of environmental dielectric material.