Graphene resistivity in diffusive limit due to scalar and vector potential electron-phonon scattering

TL;DR

This paper analytically and numerically investigates how scalar and vector potential electron-phonon interactions influence graphene resistivity in the diffusive limit, considering screening effects, disorder, and temperature dependencies.

Contribution

It provides analytical expressions and numerical analysis of electron-phonon scattering effects on graphene resistivity, including screening and disorder influences, in the diffusive regime.

Findings

Resistivity behavior matches analytical limits in clean and strong impurity cases.

Screening modifies the temperature dependence of resistivity.

Disorder suppresses VP coupling but enhances DP coupling.

Abstract

We calculate the contribution of unscreened and screened scalar and vector potential electron acoustic phonon coupling to resistivity in disordered graphene through Keldysh Greens function method within the diffusive limit. We obtain analytical results in the asymptotic limits of clean and strong impurities for both DP and VP coupling, which is in observed to be in good agreement with the resistivity behavior in these limits. We find that the complete numerical results approach the analytical result in the extreme limits, but give different temperature dependencies in between these limits. The graphene resistivity has been investigated as functions of temperature, mean free path and carrier density. We also evaluated the screened behavior in the Thomas Fermi and Random phase approximation dielectric function and obtained the temperature power exponents. We find that in the absence of screening when the electronic disorder is less than the critical disoeder limit, the two coupling mechanisms are affected differently and the relaxation rate associated with the VP coupling is suppressed by disorder as compared to the DP coupling, and the DP coupling is enhanced by disorder.