Electron-phonon hydrodynamics

TL;DR

This paper develops a comprehensive hydrodynamic theory for isotropic electron-phonon systems, revealing multiple temperature regimes with unique thermodynamic and transport properties, applicable to various quantum materials.

Contribution

It introduces a novel theoretical framework describing electron-phonon hydrodynamics across different temperature regimes, including predictions of observable signatures.

Findings

Identification of seven distinct temperature regimes with unique properties

Predictions of signatures in transport coefficients and viscosity

Relevance to materials like WTe2, WP2, and PtSn4

Abstract

We develop the theory of hydrodynamics of an isotropic Fermi liquid of electrons coupled to isotropic acoustic phonons, assuming that umklapp processes may be neglected. At low temperatures, the fluid is approximately Galilean invariant; at high temperatures, the fluid is nearly relativistic; at intermediate temperatures, there are seven additional temperature regimes with unconventional thermodynamic properties and hydrodynamic transport coefficients in a three-dimensional system. We predict qualitative signatures of electron-phonon fluids in incoherent transport coefficients, shear and Hall viscosity, and plasmon dispersion relations. Our theory may be relevant for numerous quantum materials where strong electron-phonon scattering has been proposed to underlie a hydrodynamic regime, including $\mathrm{WTe}_2$, $\mathrm{WP}_2$, and $\mathrm{PtSn}_4$.