Conductivity and scattering in graphene bilayers: numerically exact results vs. Boltzmann approach

TL;DR

This paper compares analytical Boltzmann-based conductivity calculations for bilayer graphene with exact numerical results, revealing the scattering regime and mechanisms, and aligning theory with experimental observations.

Contribution

It provides a detailed comparison between Boltzmann and numerical methods for graphene bilayer conductivity, establishing the validity range of the Born approximation.

Findings

Both short- and long-range scattering cause linear conductivity dependence in the quantum regime.

Experimental data suggests BLG is in the quantum scattering regime with Fermi wavelength exceeding impurity range.

Bilayer and single-layer graphene share similar scattering mechanisms.

Abstract

We derive analytical expressions for the conductivity of bilayer graphene (BLG) using the Boltzmann approach within the the Born approximation for a model of Gaussian disorders describing both short- and long-range impurity scattering. The range of validity of the Born approximation is established by comparing the analytical results to exact tight-binding numerical calculations. A comparison of the obtained density dependencies of the conductivity with experimental data shows that the BLG samples investigated experimentally so far are in the quantum scattering regime where the Fermi wavelength exceeds the effective impurity range. In this regime both short- and long-range scattering lead to the same linear density dependence of the conductivity. Our calculations imply that bilayer and single layer graphene have the same scattering mechanisms. We also provide an upper limit for the effective, density dependent spatial extension of the scatterers present in the experiments.