Electronic Transport in Disordered Bilayer and Trilayer Graphene

TL;DR

This study uses numerical simulations to analyze how various disorders affect electronic transport in bilayer and trilayer graphene, revealing consistent minimum conductivity and the conditions for conductivity plateaus.

Contribution

It provides a comprehensive numerical analysis of disorder effects on transport in multilayer graphene, highlighting the role of impurity types and stacking sequences.

Findings

Minimum conductivity is approximately 2e^2/h per layer at neutrality point.

Conductivity depends on disorder strength and stacking sequence.

Conductivity plateau occurs only with resonant impurities or vacancies.

Abstract

We present a detailed numerical study of the electronic transport properties of bilayer and trilayer graphene within a framework of single-electron tight-binding model. Various types of disorder are considered, such as resonant (hydrogen) impurities, vacancies, short- or long-range Gaussian random potentials, and Gaussian random nearest neighbor hopping. The algorithms are based on the numerical solution of the time-dependent Schr \"{o}dinger equation and applied to calculate the density of states and conductivities (via the Kubo formula) of large samples containing millions of atoms. In the cases under consideration, far enough from the neutrality point, depending on the strength of disorders and the stacking sequence, a linear or sublinear electron-density dependent conductivity is found. The minimum conductivity $\sigma_{\min}\approx 2e^{2}/h$ (per layer) at the charge neutrality point is the same for bilayer and trilayer graphene, independent of the type of the impurities, but the plateau of minimum conductivity around the neutrality point is only observed in the presence of resonant impurities or vacancies, originating from the formation of the impurity band.