Transport regimes in surface disordered graphene sheets

TL;DR

This study explores how surface disorder affects the conductance scaling in graphene sheets, revealing size-dependent behaviors and the influence of disorder and magnetic fields on electronic transport.

Contribution

It provides a detailed analysis of conductance scaling laws in disordered graphene, highlighting the effects of size, disorder, and magnetic fields on transport properties.

Findings

Conductance remains constant for fixed W/L ratio as size increases.

Disorder reduces exponential decay of conductance with length.

Conductance increases linearly with width W due to contact states.

Abstract

We investigate the size scaling of the conductance of surface disordered graphene sheets of width W and length L. Metallic leads are attached to the sample ends across its width. At E ~ 0, the conductance scales with the system size as follows: i) For constant W/L, it remains constant as size is increased, at a value which depends almost lineally on that ratio; this scaling allows the definition of a conductivity value that results similar to the experimental one. ii) For fixed width, the conductance decreases exponentially with length L, both for ordered and disordered samples. Disorder reduces the exponential decay, leading to a higher conductance. iii) For constant length, conductance increases linearly with width W, a result that is exclusively due to the tails of the states of the metallic wide contact. iv) The average conductance does not show an appreciable dependence on magnetic field. Away from E = 0, the conductance shows the behavior expected in two-dimensional systems with surface disorder, i.e., ballistic transport.