Phonon-assisted damping of plasmons in three- and two-dimensional metals

TL;DR

This paper studies how lattice vibrations affect plasmon behavior in 2D and 3D metals, revealing broadening, decay, and dispersion features due to phonon coupling, with implications for interpreting electron-energy loss spectra.

Contribution

It provides a detailed numerical analysis of phonon effects on plasmons in simple metals using many-body perturbation theory, highlighting new spectral features and decay mechanisms.

Findings

Phonon coupling broadens plasmon spectral signatures.

Plasmons decay on sub-picosecond timescales due to phonons.

A kink in 2D plasmon dispersion indicates plasmon-phonon scattering onset.

Abstract

We investigate the effects of crystal lattice vibrations on the dispersion of plasmons. The loss function of the homogeneous electron gas (HEG) in two and three dimensions is evaluated numerically in presence of electronic coupling to an optical phonon mode. Our calculations are based on many-body perturbation theory for the dielectric function as formulated by the Hedin-Baym equations in the Fan-Migdal approximation. The coupling to phonons broadens the spectral signatures of plasmons in the electron-energy loss spectrum (EELS) and it induces the decay of plasmons on timescales shorter than 1 ps. Our results further reveal the formation of a kink in the plasmon dispersion of the 2D HEG, which marks the onset of plasmon-phonon scattering. Overall, these features constitute a fingerprint of plasmon-phonon coupling in the EELS of simple metals. It is shown that these effects may be accounted for by resorting to a simplified treatment of the electron-phonon interaction which is amenable to first-principles calculations.