Boltzmann transport and residual conductivity in bilayer graphene

TL;DR

This paper uses a Drude-Boltzmann model to analyze bilayer graphene's transport properties, revealing that Coulomb impurities dominate scattering and lead to a linear conductivity at high densities and a residual plateau at low densities.

Contribution

It provides a theoretical framework for understanding bilayer graphene conductivity, highlighting the role of overscreened Coulomb impurities and deriving analytic expressions for conductivity.

Findings

Conductivity is linear in carrier density at high densities.

Residual conductivity plateau exists at low densities.

Analytic formulas for conductivity based on impurity density.

Abstract

A Drude-Boltzmann theory is used to calculate the transport properties of bilayer graphene. We find that for typical carrier densities accessible in graphene experiments, the dominant scattering mechanism is overscreened Coulomb impurities that behave like short-range scatterers. We anticipate that the conductivity $\sigma(n)$ is linear in $n$ at high density and has a plateau at low density corresponding to a residual density of $n^* = \sqrt{n_{\rm imp} {\tilde n}}$, where ${\tilde n}$ is a constant which we estimate using a self-consistent Thomas-Fermi screening approximation to be ${\tilde n} \approx 0.01 ~q_{\rm TF}^2 \approx 140 \times 10^{10} {\rm cm}^{-2}$. Analytic results are derived for the conductivity as a function of the charged impurity density. We also comment on the temperature dependence of the bilayer conductivity.