Optical conductivity and damping of plasmons due to electron-electron interaction

TL;DR

This paper investigates how electron-electron interactions affect plasmon damping in 2D and 3D electron gases and graphene, clarifying previous disagreements and deriving temperature-dependent scaling laws for plasmon linewidths.

Contribution

The study re-derives the optical conductivity related to plasmon damping, resolving discrepancies in previous results and extending analysis to 3D gases and graphene with new temperature scaling laws.

Findings

Re-derivation confirms the $q^2T^2/\omega^4$ scaling for 2D electron gas.

Finite temperature effects are strongest in graphene, with linewidth scaling as $T^4\ln T$.

Discrepancy with previous work is resolved by showing the subleading term is negligible.

Abstract

We re-visit the issue of plasmon damping due to electron-electron interaction. The plasmon linewidth can related to the imaginary part of the charge susceptibility or, equivalently, to the real part of the optical conductivity, $\mathrm{Re}\sigma(q,\omega)$. Approaching the problem first via a standard semi-classical Boltzmann equation, we show that $\mathrm{Re}\sigma(q,\omega)$ of two-dimensional (2D) electron gas scales as $q^2T^2/\omega^4$ for $\omega\ll T$, which agrees with the results of Refs. [1] and [2] but disagrees with that of Ref. [3], according to which $\mathrm{Re}\sigma(q,\omega) \propto q^2T^2/\omega^2$. To resolve this disagreement, we re-derive $\mathrm{Re}\sigma(q,\omega)$ using the original method of Ref. {mishchenko:2004} for an arbitrary ratio $\omega/T$ and show that, while the last term is, indeed, present, it is subleading to the $q^2T^2/\omega^4$ term. We give a physical interpretation of both leading and subleading contributions in terms of the shear and bulk viscosities of an electron liquid, respectively. We also calculate $\mathrm{Re}\sigma(q,\omega)$ for a three-dimensional (3D) electron gas and doped monolayer graphene. We find that, with all other parameters being equal, finite temperature has the strongest effect on the plasmon linewidth in graphene, where it scales as $T^4\ln T$ for $\omega\ll T$.