Phonon-mediated Hydrodynamic Transport in a Weyl Semimetal

TL;DR

This paper investigates the possibility of hydrodynamic electron transport in Weyl semimetals driven by phonon-mediated interactions, analyzing conductivities and temperature-dependent behaviors to identify conditions favoring hydrodynamics.

Contribution

It provides a microscopic analysis of phonon-mediated hydrodynamic transport in Weyl semimetals, including effects of impurities and real phonons, and identifies a temperature window where hydrodynamic behavior emerges.

Findings

Virtual phonons mimic real phonons above T_BG

Lorenz ratio is modified by Fermi surface geometry

T^2 dependence of resistivity below T_BG

Abstract

We analyze from a microscopic point of view the feasibility of a hydrodynamic regime in a type-I Weyl semimetal driven by electron-electron interactions mediated by virtual phonons. Considering also the effects of of impurities and the absorption/emission of real phonons, the electric and thermal conductivities are derived. At temperatures $T$ above the Bloch-Gr\"uneisen temperature $T_\textrm{BG}$, virtual phonons behave similarly to real phonons, but the Lorenz ratio is modified by a constant prefactor dependent on the Fermi surface geometry. For temperatures below $T_\textrm{BG}$, processes that do not conserve chirality induce a $T^2$ dependence in the electric resistivity, opening a window where momentum-conserving interactions dominate transport signatures. We quantitatively discuss this hydrodynamic window and put it into context with recent experimental literature on the subject.