Damping effects in hole-doped graphene: the relaxation-time approximation

TL;DR

This paper examines the damping effects in hole-doped graphene using a gauge-invariant response theory, demonstrating the conditions under which the relaxation-time approximation accurately describes conductivity and resistivity.

Contribution

It shows that the relaxation-time approximation can be valid for damping effects in multiband systems if local charge conservation and gauge invariance are properly incorporated, with applications to graphene.

Findings

The model predicts two maxima in energy-loss spectra: Dirac plasmons and $$ plasmons.

The relaxation-time approximation accurately describes dc resistivity and conductivity when damping is due to direct scattering.

Ballistic transport and plasmon damping require beyond relaxation-time approximation approaches.

Abstract

The dynamical conductivity of interacting multiband electronic systems derived in Ref.[1] is shown to be consistent with the general form of the Ward identity. Using the semiphenomenological form of this conductivity formula, we have demonstrated that the relaxation-time approximation can be used to describe the damping effects in weakly interacting multiband systems only if local charge conservation in the system and gauge invariance of the response theory are properly treated. Such a gauge-invariant response theory is illustrated on the common tight-binding model for conduction electrons in hole-doped graphene. The model predicts two distinctly resolved maxima in the energy-loss-function spectra. The first one corresponds to the intraband plasmons (usually called the Dirac plasmons). On the other hand, the second maximum ($\pi$ plasmon structure) is simply a consequence of the van Hove singularity in the single-electron density of states. The dc resistivity and the real part of the dynamical conductivity are found to be well described by the relaxation-time approximation, but only in the parametric space in which the damping is dominated by the direct scattering processes. The ballistic transport and the damping of Dirac plasmons are thus the questions that require abandoning the relaxation-time approximation.