Universal scaling of current fluctuations in disordered graphene

TL;DR

This paper investigates the universal scaling behavior of current fluctuations in disordered graphene, revealing that all current cumulants scale identically with system parameters and identifying universal Fano factor values for different disorder types.

Contribution

It provides analytical and numerical evidence for universal scaling of current cumulants and Fano factors in disordered graphene, extending understanding of transport statistics in such systems.

Findings

All current cumulants scale identically with system parameters in large systems.

Universal Fano factor values are identified: 0.243 for 1D disorder and 0.295 for 2D disorder.

Conductivity grows as rac12;L in 1D and Log L in 2D with system length L.

Abstract

We analyze the full transport statistics of graphene with smooth disorder at low dopings. First we consider the case of 1D disorder for which the transmission probability distribution is given analytically in terms of the graphene-specific mean free path. All current cumulants are shown to scale with system parameters (doping, size, disorder strength and correlation length) in an identical fashion for large enough systems. In the case of 2D disorder, numerical evidence is given for the same kind of identical scaling of all current cumulants, so that the ratio of any two such cumulants is universal. Specific universal values are given for the Fano factor, which is smaller than the pseudodiffusive value of ballistic graphene (F=1/3) both for 1D (F=0.243) and 2D (F=0.295) disorder. On the other hand, conductivity in wide samples is shown to grow without saturation as \sqrt{L} and Log L with system length L in the 1D and 2D cases respectively.