Conductance fluctuation and shot noise in disordered graphene systems, a perturbation expansion approach

TL;DR

This paper introduces a perturbation expansion method based on CPA to efficiently calculate conductance fluctuation and shot noise in disordered graphene, showing good agreement with brute-force methods at low disorder and doping levels.

Contribution

The authors develop a CPA-based expansion approach that accurately predicts transport properties in disordered graphene without extensive computation, especially at low disorder and doping concentrations.

Findings

Method agrees with brute-force results for low disorder and doping levels.

Accurate for disorder strength up to 0.4t for conductance fluctuation.

Applicable to both graphene and square lattice systems.

Abstract

We report the investigation of conductance fluctuation and shot noise in disordered graphene systems with two kinds of disorder, Anderson type impurities and random dopants. To avoid the brute-force calculation which is time consuming and impractical at low doping concentration, we develop an expansion method based on the coherent potential approximation (CPA) to calculate the average of four Green's functions and the results are obtained by truncating the expansion up to 6th order in terms of "single-site-T-matrix". Since our expansion is with respect to "single-site-T-matrix" instead of disorder strength $W$, good result can be obtained at 6th order for finite $W$. We benchmark our results against brute-force method on disordered graphene systems as well as the two dimensional square lattice model systems for both Anderson disorder and the random doping. The results show that in the regime where the disorder strength $W$ is small or the doping concentration is low, our results agree well with the results obtained from the brute-force method. Specifically, for the graphene system with Anderson impurities, our results for conductance fluctuation show good agreement for $W$ up to $0.4t$, where $t$ is the hopping energy. While for average shot noise, the results are good for $W$ up to $0.2t$. When the graphene system is doped with low concentration 1%, the conductance fluctuation and shot noise agrees with brute-force results for large $W$ which is comparable to the hopping energy $t$. At large doping concentration 10%, good agreement can be reached for conductance fluctuation and shot noise for $W$ up to $0.4t$. We have also tested our formalism on square lattice with similar results. Our formalism can be easily combined with linear muffin-tin orbital first-principles transport calculations for light doping nano-scaled systems, making prediction on variability of nano-devices.