Hydrodynamic sound and plasmons in three dimensions

TL;DR

This paper extends hydrodynamic theory to three-dimensional metals, revealing how Coulomb interactions give mass to sound modes and relate to plasmons, with implications for understanding collective excitations in 3D electron systems.

Contribution

The work generalizes 2D hydrodynamic models to 3D, explicitly calculating sound modes and their relation to plasmons in strongly-coupled Coulomb plasmas.

Findings

Hydrodynamic and collisionless sound modes become gapped in 3D due to Coulomb interactions.

Damping rates of these modes are quadratic in momentum.

The leading-order sound mode matches the plasmon frequency in the presence of Coulomb interactions.

Abstract

In a recent paper by Lucas and Das Sarma [Physical Review B 97, 115449 (2018)], a solvable model of collective modes in 2D metals was considered in the hydrodynamic regime. In the current work, we generalize the hydrodynamic theory to 3D metals for which the calculation of sound modes in a strongly-coupled quantum Coulomb plasma can be made explicit. The specific theoretical question of interest is how the usual linearly dispersing hydrodynamic sound mode relates to the well-known gapped 3D plasmon collective mode in the presence of long-range Coulomb interaction. We show analytically that both the zero sound in the collisionless regime and the first sound in the hydrodynamic region become massive in 3D, acquiring a finite gap because of the long-range Coulomb interaction, while their damping rates become quadratic in momentum. We also discuss other types of long-range potential, where the dispersion of sound modes is modified accordingly. The general result is that the leading order hydrodynamic sound mode is always given by the leading-order plasmon frequency in the presence of long-range Coulomb interaction, but the next-to-leading-order dispersion corrections differ in hydrodynamic and colllisionless regimes.