Transport in finite graphene samples

TL;DR

This paper investigates how finite size and random gaps affect electrical conductivity in graphene, revealing size-dependent behaviors and a critical gap threshold for conduction.

Contribution

It introduces a Dirac fermion-based model with a generalized Drude approach to analyze transport in finite graphene with random gaps, highlighting size and gap effects.

Findings

Conductivity remains constant at zero average gap.

Conductivity decreases with increasing sample size for nonzero average gaps.

Infinite sample conductivity depends on the gap being below a critical value.

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..