Electron-phonon hydrodynamics

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 ${\mathrm{PtSn}}_4$.

arXiv comment24+10 pages, 4 figures. v2: published version

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• Phonon hydrodynamics in bulk insulators and semi-metals
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• Hydrodynamics of the electronic Fermi liquid: a pedagogical overview
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• Purity-dependent Lorenz number, electron hydrodynamics and electron-phonon coupling in WTe${}_2$
• Theory of high-energy correlated multiphoton x-ray diffraction for synchrotron radiation sources
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• Disorder-enhanced effective masses and deviations from Matthiessen's rule in PdCoO${}_2$ thin films
• Descriptors of intrinsic hydrodynamic thermal transport: screening a phonon database in a machine learning approach
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• Graphene is neither Relativistic nor Non-Relativistic case: Thermodynamics Aspects
• Multipolar Fermi Surface Deformations in Sr${}_2$RuO${}_4$ Probed by Resistivity and Sound Attenuation: A Window into Electron Viscosity and the Collision Operator
• Thermal transport in crystals: from the quantum Dyson equation to mesoscopic phonon hydrodynamics
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