A self-consistent theory for graphene transport

TL;DR

This paper presents a self-consistent theoretical model explaining graphene's transport properties at zero magnetic field primarily through charged impurity scattering, highlighting the impurity concentration's impact on conductivity.

Contribution

It introduces a theory that accounts for impurity concentration dependence in graphene transport, challenging the notion of universal conductivity values.

Findings

Minimum conductivity is about 4 e^2/h in dirty samples.

Cleaner samples show increased minimum conductivity up to 8 e^2/h.

Reducing charged impurities can significantly improve graphene mobility.

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 $n_{\rm imp}$. For dirty samples ($250 \times 10^{10} {\rm cm}^{-2} < n_{\rm imp} < 400 \times 10^{10} {\rm cm}^{-2}$), the value of the minimum conductivity at low carrier density is indeed $4 e^2/h$ in agreement with early experiments, with weak dependence on impurity concentration. For cleaner samples, we predict that the minimum conductivity depends strongly on $n_{\rm imp}$, increasing to $8 e^2/h$ for $n_{\rm imp} \sim 20 \times 10^{10}{\rm cm}^{-2}$. A clear strategy to improve graphene mobility is to eliminate charged impurities or use a substrate with a larger dielectric constant.