Statistics of random voltage fluctuations and the low-density residual conductivity of graphene

TL;DR

This paper derives an analytic, non-Gaussian distribution for voltage fluctuations caused by charged impurities near a graphene sheet, explaining residual conductivity at zero gate voltage through disorder-induced electron and hole puddles.

Contribution

It provides a new analytic expression for voltage fluctuation distribution and links it to residual conductivity and puddle formation in graphene.

Findings

Voltage fluctuations are non-Gaussian.

Disorder-induced puddles cause finite residual conductivity.

Estimated size of electron and hole puddles.

Abstract

We consider a graphene sheet in the vicinity of a substrate, which contains charged impurities. An analytic expression for the probability distribution function of voltage fluctuations due to the charged impurities is derived. The distribution function is shown to be non-Gaussian. The voltage fluctuations lead to the appearance of randomly distributed density inhomogeneities in the graphene plane. We argue that these disorder-induced density fluctuations produce a finite conductivity even at a zero gate voltage in accordance with recent experimental observations. We estimate the width of the minimal conductivity plateau and the typical size of the electron and hole puddles. The existence of inhomogeneous random puddles of electrons and holes should be a generic feature of all graphene layers at low gate voltages due to the invariable presence of charged impurities in the substrate.