Model for the magnetoresistance and Hall coefficient of inhomogeneous graphene

We show that when bulk graphene breaks into n-type and p-type puddles, the in-plane resistivity becomes strongly field dependent in the presence of a perpendicular magnetic field even if homogeneous graphene has a field-independent resistivity. We calculate the longitudinal resistivity xx and Hall resistivity xy as a function of field for this system using the effective-medium approximation. The conductivity tensors of the individual puddles are calculated using a Boltzmann approach suitable for the band structure of graphene near the Dirac points. The resulting resistivity agrees well with experiment provided that the relaxation time is weakly field dependent. The calculated Hall resistivity has the sign of the carriers in the puddles occupying the greater area of the composite and vanishes when there are equal areas of nand p-type puddles.