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Statistics of random voltage fluctuations and the low-density residual conductivity of graphene Victor M. Galitski, Shaffique Adam, and S. Das Sarma
 

Summary: Statistics of random voltage fluctuations and the low-density residual conductivity of graphene
Victor M. Galitski, Shaffique Adam, and S. Das Sarma
Condensed Matter Theory Center, Department of Physics, University of Maryland, College Park, Maryland 20742-4111, USA
Received 9 February 2007; revised manuscript received 12 August 2007; published 7 December 2007
We consider a graphene sheet in the vicinity of a substrate, which contains charged impurities. A general
analytic theory to describe the statistical properties of voltage fluctuations due to the long-range disorder is
developed. In particular, we derive a general expression for the probability distribution function of voltage
fluctuations, which 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 fluc-
tuations produce a finite conductivity even at a zero gate voltage in accordance with recent experimental
observations. We determine the width of the minimal conductivity plateau and the typical size of the electron
and hole puddles. We also propose a simple self-consistent approach to estimate the residual density and the
nonuniversal minimal conductivity in the low-density regime. 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.
DOI: 10.1103/PhysRevB.76.245405 PACS number s : 73.40. c, 72.10. d, 81.05.Uw
I. INTRODUCTION
Charge inhomogeneities are known to play an important
role in understanding transport properties of semiconductors.
The randomly positioned impurity ions give rise to a random

  

Source: Adam, Shaffique - Condensed Matter Theory Center, University of Maryland at College Park

 

Collections: Physics