Model for the magnetoresistance and Hall coefficient of inhomogeneous graphene

TL;DR

This paper models how inhomogeneous graphene with n- and p-type puddles exhibits magnetic field-dependent resistivity and Hall effect, aligning well with experimental data using an effective-medium approach.

Contribution

It introduces a model combining effective-medium approximation and Boltzmann transport to explain magnetoresistance and Hall coefficient in inhomogeneous graphene.

Findings

Resistivity becomes strongly field-dependent due to puddle inhomogeneity.

Hall resistivity sign reflects majority carriers and vanishes at equal n- and p-puddle concentrations.

Model matches experimental results when relaxation time is weakly field-dependent.

Abstract

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 homoge- neous graphene has a field-independent resistivity. We calculate the longitudinal resistivity \rho_{xx} and Hall resistivity \rho_{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 suit- able 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 majority carrier and vanishes when there are equal number of n and p type puddles.