Anomalously large conductance fluctuations in weakly disordered graphene

TL;DR

This study numerically investigates conductance fluctuations in graphene, revealing that smooth potential variations cause unusually large fluctuations due to the honeycomb lattice's unique backscattering properties.

Contribution

It demonstrates that weak disorder with smooth potential landscapes leads to enhanced conductance fluctuations in graphene, highlighting the role of lattice structure in mesoscopic phenomena.

Findings

Universal conductance fluctuation values for strong disorder

Enhanced fluctuations for smooth potential landscapes

No enhancement when potential varies on atomic scale

Abstract

We have studied numerically the mesoscopic fluctuations of the conductance of a graphene strip (width W large compared to length L), in an ensemble of samples with different realizations of the random electrostatic potential landscape. For strong disorder (potential fluctuations comparable to the hopping energy), the variance of the conductance approaches the value predicted by the Altshuler-Lee-Stone theory of universal conductance fluctuations. For weaker disorder the variance is greatly enhanced if the potential is smooth on the scale of the atomic separation. There is no enhancement if the potential varies on the atomic scale, indicating that the absence of backscattering on the honeycomb lattice is at the origin of the anomalously large fluctuations.