General Scattering Mechanism and Transport in Graphene

TL;DR

This paper develops a semi-classical transport theory for graphene, analyzing how different scattering mechanisms affect conductivity near the Dirac point, including effects of time-varying electric and magnetic fields.

Contribution

It introduces a general scattering model with a parameter $eta$, linking scattering types to conductivity behavior in graphene.

Findings

Acoustic phonon scattering corresponds to $eta=+2$.

Long-range Coulomb scattering corresponds to $eta=+1$.

Short-range delta potential scattering corresponds to $eta=-1$.

Abstract

Using quasi-time dependent semi-classical transport theory in RTA, we obtained coupled current equations in the presence of time varying field and based on general scattering mechanism $\tau \propto \mathcal{E}^{\beta}$. We find that close to the Dirac point, the characteristic exponent $\beta = +2$ corresponds to acoustic phonon scattering. $\beta = +1$ long-range Coulomb scattering mechanism. $\beta = -1$ is short-range delta potential scattering in which the conductivity is constant of temperature. The $\beta = 0$ case is ballistic limit. In the low energy dynamics of Dirac electrons in graphene, the effect of the time-dependent electric field is to alter just the electron charge by $e \to e(1 + (\Omega \tau)^2)$ making electronic conductivity non-linear. The effect of magnetic filed is also considered.