Electric Transport Theory of Dirac Fermions in Graphene

TL;DR

This paper develops a theoretical framework for understanding electric transport in graphene with finite-range impurity scatterings, revealing differences from short-range impurity models and providing conductivity predictions that align qualitatively with experiments.

Contribution

It introduces a self-consistent Born approximation approach for Dirac fermions with finite-range impurities, deriving coupled integral equations for current correlations and calculating conductivity.

Findings

Conductivity varies linearly with carrier concentration at zero temperature.

Minimum conductivity at zero doping exceeds previous theoretical estimates.

Room temperature conductivity behavior is similar to zero temperature, with slight increases in minimum conductivity.

Abstract

Using the self-consistent Born approximation to the Dirac fermions under finite-range impurity scatterings, we show that the current-current correlation function is determined by four-coupled integral equations. This is very different from the case for impurities with short-range potentials. As a test of the present approach, we calculate the electric conductivity in graphene for charged impurities with screened Coulomb potentials. The obtained conductivity at zero temperature varies linearly with the carrier concentration, and the minimum conductivity at zero doping is larger than the existing theoretical predictions, but still smaller than that of the experimental measurement. The overall behavior of the conductivity obtained by the present calculation at room temperature is similar to that at zero temperature except the minimum conductivity is slightly larger.