Semiclassical 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 $\rho_{xx}$ and Hall resistivity $\rho_{xy}$ as a function of field for such a system, using the effective-medium approximation. The conductivity tensors of the individual puddles are calculated using a standard Boltzmann approach suitable for the band structure of graphene near the Dirac points. The resulting resistivity saturates, provided that the area fractions $f_n$ and $1 - f_n$ of n and p type puddles are slightly unequal, and agrees with experiments if the relaxation time is weakly field-dependent. The Hall resistivity $\rho_{xy}$ found to change sign at $f_n = 1/2$.