Transport in finite graphene samples

Abstract

We study the DC transport of finite graphene samples with random gap. Using Dirac fermions to describe the low-energy physics near the Dirac point, we employ a generalized Drude form for the conductivity. The latter is constant for a vanishing average gap but always decreases with increasing sample size for a nonzero average gap. The asymptotic conductivity of the infinite sample is either nonzero if the average gap is smaller than a critical value or zero otherwise. Our results are in agreement with recent numerical calculations of Bardarson et al..