A self-consistent theory for graphene transport

doi:10.1073/pnas.0704772104

A self-consistent theory for graphene transport

Condensed Matter Theory Center, Department of Physics, University of Maryland, College Park, MD 20742-4111

Edited by Ellen D. Williams, University of Maryland, College Park, MD, and approved October 1, 2007 (received for review May 23, 2007)

Abstract

We demonstrate theoretically that most of the observed transport properties of graphene sheets at zero magnetic field can be explained by scattering from charged impurities. We find that, contrary to common perception, these properties are not universal but depend on the concentration of charged impurities n _imp. For dirty samples (250 × 10¹⁰ cm⁻² < n _imp < 400 × 10¹⁰ cm⁻²), the value of the minimum conductivity at low carrier density is indeed 4e ²/h in agreement with early experiments, with weak dependence on impurity concentration. For cleaner samples, we predict that the minimum conductivity depends strongly on n _imp, increasing to 8e ²/h for n _imp ≈ 20 × 10¹⁰ cm⁻². A clear strategy to improve graphene mobility is to eliminate charged impurities or use a substrate with a larger dielectric constant.

Footnotes

^†To whom correspondence should be addressed. E-mail: adam1{at}umd.edu
Author contributions: S.A., E.H.H., V.M.G., and S.D.S. designed research; S.A., E.H.H., V.M.G., and S.D.S. performed research; and S.A. and S.D.S. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
Abbreviations:

MOSFET,

metal oxide-semiconductor-field effect transistor;

RPA,

random phase approximation.