Transverse voltage in anisotropic hydrodynamic conductors

TL;DR

This paper proposes using transverse voltage measurements at zero magnetic field to distinguish hydrodynamic electronic flow from ballistic flow in anisotropic conductors, revealing unique signatures of viscous behavior.

Contribution

It introduces a method based on transverse voltage to diagnose hydrodynamic flow, accounting for anisotropic Fermi surfaces and boundary effects, which was not previously explored.

Findings

Transverse voltage is sensitive to anisotropic Fermiology and boundary scattering.

A sign change in transverse voltage indicates crossover from ballistic to hydrodynamic regimes.

Channel-size dependence of transverse voltage serves as a hallmark of viscous electronic flow.

Abstract

Weak momentum dissipation in ultra-clean metals gives rise to novel non-Ohmic current flow, including ballistic and hydrodynamic regimes. Recently, hydrodynamic flow has attracted intense interest because it presents a valuable window into the electronic correlations and the longest lived collective modes of quantum materials. However, diagnosing viscous flow is difficult as the macroscopic observables of ballistic and hydrodynamic transport such as the average current distribution can be deceptively similar, even if their respective microscopics deviate notably. Based on kinetic Boltzmann theory, here we propose to address this issue via the transverse channel voltage at zero magnetic field, which can efficiently detect hydrodynamic flow in a number of materials. To this end, we show that the transverse voltage is sensitive to the interplay between anisotropic fermiology and boundary scattering, resulting in a non-trivial behavior in narrow channels along crystalline low-symmetry directions. We discuss several materials where the channel-size dependent stress of the quantum fluid leads to a characteristic sign change of the transverse voltage as a new hallmark of the cross-over from the ballistic to the hydrodynamic regime.