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

We revisit the issue of plasmon damping due to electron-electron interaction. The plasmon linewidth can be related to the imaginary part of the charge susceptibility or, equivalently, to the real part of the optical conductivity, Reσ(q,ω). Approaching the problem first via a standard semiclassical Boltzmann equation, we show that Reσ(q,ω) of a two-dimensional (2D) electron gas scales as q2T2/ω4 for ω≪T, which agrees with the results of Principi et al. [Phys. Rev. B 88, 195405 (2013)1098-012110.1103/PhysRevB.88.195405] and Sharma et al. [Phys. Rev. B 104, 045142 (2021)2469-995010.1103/PhysRevB.104.045142] but disagrees with that of Mishchenko et al. [Phys. Rev. B 69, 195302 (2004)1098-012110.1103/PhysRevB.69.195302], according to which Reσ(q,ω)∝q2T2/ω2. To resolve this disagreement, we rederive Reσ(q,ω) using the original method of Mishchenko et al. for an arbitrary ratio ω/T and show that while the last term is, indeed, present, it is subleading to the q2T2/ω4 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 Reσ(q,ω) for a three-dimensional electron gas and doped monolayer graphene. We find that, all other parameters being equal, finite temperature has the strongest effect on the plasmon linewidth in graphene, where it scales as T4lnT for ω≪T.