Effect of short- and long-range scattering in the conductivity of graphene: Boltzmann approach vs tight-binding calculations

TL;DR

This study compares tight-binding and Boltzmann approaches to graphene conductivity, revealing significant discrepancies in the latter's predictions, especially within the Born approximation, thus questioning its applicability for experimental interpretation.

Contribution

It demonstrates the limitations of the standard Boltzmann approach within the Born approximation in accurately predicting graphene conductivity.

Findings

TB calculations agree with $\sigma o n$ dependence for both scatterer types

Standard Boltzmann approach predicts constant conductivity, which is inaccurate

Discrepancies highlight the need for beyond-Born or alternative models

Abstract

We present a comparative study of the density dependence of the conductivity of graphene sheets calculated in the tight-binding (TB) Landauer approach and on the basis of the Boltzmann theory. The TB calculations are found to give the same density dependence of the conductivity, $\sigma \sim n$, for short-range and long-range Gaussian scatterers. In the case of short-range scattering the TB calculations are in agreement with the predictions of the Boltzmann theory going beyond the Born approximation, but in qualitative and quantitative disagreement with the standard Boltzmann approach within the Born approximation, predicting $\sigma= $ const. Even for the long-range Gaussian potential in a parameter range corresponding to realistic systems the standard Boltzmann predictions are in quantitative and qualitative disagreement with the TB results. This questions the applicability of the standard Boltzmann approach within the Born approximation, commonly used for the interpretation of the results of experimental studies of the transport in graphene.