Effects of a random gauge field on the conductivity of graphene sheets with disordered ripples

Abstract

We study the effect of disordered ripples on the conductivity of monolayer graphene flakes. We calculate the relaxation times and the Boltzmann conductivities associated with two mechanisms. First, we study the conductivity correction due to an external in-plane magnetic field ${B}_{\ensuremath{\parallel}}$. Due to the irregular local curvature found in graphene sheets deposited over a substrate, ${B}_{\ensuremath{\parallel}}$ can be mapped into an effective random magnetic field perpendicular to the graphene surface. Second, we study the electron momentum relaxation due to intrinsic pseudomagnetic fields originated from deformations and strain. We find that the competition between these mechanisms gives rise to a strong anisotropy in the conductivity tensor. This result provides a new strategy to quantitatively infer the strength of pseudomagnetic fields in rippled graphene flakes.