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 ${\mathrm{PtSn}}_4$.

24+10 pages, 4 figures. v2: published version

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Cited by in corpus (30)

• Hydrodynamic approach to two-dimensional electron systems
• Colloquium: Hydrodynamics and holography of charge density wave phases
• Extrinsic phonon thermal Hall transport from Hall viscosity
• Evidence of a coupled electron-phonon liquid in NbGe${}_2$
• Phonon drag thermal Hall effect in metallic strontium titanate
• Hydrodynamics of charged two-dimensional Dirac systems I: thermo-electric transport
• A unified theory of second sound in two dimensional materials
• Anisotropic phonon-mediated electronic transport in chiral Weyl semimetals
• Hydrodynamic effective field theories with discrete rotational symmetry
• Formation of an electron-phonon bi-fluid in bulk antimony
• Hydrodynamics with triangular point group
• Fingerprints of quantum criticality in locally resolved transport
• Nonlinear density waves on graphene electron fluids
• Shear viscosity expression for a graphene system in relaxation time approximation
• Phonon hydrodynamics in bulk insulators and semi-metals
• Phonon-mediated Hydrodynamic Transport in a Weyl Semimetal
• Hydrodynamics of the electronic Fermi liquid: a pedagogical overview
• Phonon renormalization and Pomeranchuk instability in the Holstein model
• 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
• Distinguishing viscous, ballistic, and diffusive current flows in anisotropic metals
• Lorenz ratios of diagonal and Hall conductivities in a Dirac electron liquid
• Wiedemann-Franz law violation domain for graphene and nonrelativistic systems
• 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
• Tuning transport in solid-state Bose-Fermi mixtures by Feshbach resonances
• 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
• Plasmon-sound hybridization in ionic crystals