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Interactions of charge carriers with lattice vibrations, or phonons, play a critical role in unconventional electronic transport of metals and semimetals. Recent observations of phonon-mediated collective electron flow in bulk semimetals, termed electron hydrodynamics, present new opportunities in the search for strong electron-electron interactions in high carrier density materials. Here we present the general transport signatures of such a second-order scattering mechanism, along with analytical limits at the Eliashberg level of theory. We study electronic transport, using $ab$ $initio$ calculations, in finite-size channels of semimetallic ZrSiS and TaAs$_2$ with and without topological band crossings, respectively. The order of magnitude separation between momentum-relaxing and momentum-conserving scattering length-scales across a wide temperature range make both of them promising candidates for further experimental observation of electron hydrodynamics. More generally, our calculations show that the hydrodynamic transport regime can be realized in a much broader class of anisotropic metals and does not, to first order, rely on the topological nature of the bands. Finally, we discuss general design principles guiding future search for hydrodynamic candidates, based on the analytical formulation and our $ab$ $initio$ predictions. We find that systems with strong electron-phonon interactions, reduced electronic phase space, and suppressed phonon-phonon scattering at temperatures of interest are likely to feature hydrodynamic electron transport. We predict that layered and/or anisotropic semimetals composed of half-filled $d$-shells and light group V/VI elements with lower crystal symmetry are ideal candidates to observe hydrodynamic phenomena in future.
We present a new framework for computing low frequency transport properties of strongly correlated, ergodic systems. Our main assumption is that, when a thermalizing diffusive system is driven at frequency $omega$, domains of size $xi simsqrt{D/omega
Details are presented of an efficient formalism for calculating transmission and reflection matrices from first principles in layered materials. Within the framework of spin density functional theory and using tight-binding muffin-tin orbitals, scatt
We develop the theory of hydrodynamic electron transport in a long-range disorder potential for conductors in which the underlying electron liquid lacks Galilean invariance. For weak disorder, we express the transport coefficients of the system in te
Nonequilibrium electron dynamics in solids is an important subject from both fundamental and technological points of view. The recent development of laser technology has enabled us to study ultrafast electron dynamics in the time domain. First-princi
We derive the system of hydrodynamic equations governing the collective motion of massless fermions in graphene. The obtained equations demonstrate the lack of Galilean- and Lorentz invariance, and contain a variety of nonlinear terms due to quasi-re