Quantum aspects of "hydrodynamic" transport from weak electron-impurity scattering

TL;DR

This paper shows that free fermion systems with disorder can exhibit non-local transport effects similar to hydrodynamic behavior, challenging the classical interpretation that such effects imply dominant electron-electron interactions.

Contribution

The study provides explicit calculations of non-local conductivity in disordered free fermion systems, highlighting quantum effects that mimic hydrodynamic transport phenomena.

Findings

Disordered free fermion systems exhibit non-local conductivity effects.

Quantum effects can produce whirlpool-like transport without strong electron-electron interactions.

Experimental strategies are proposed to distinguish quantum from classical hydrodynamic effects.

Abstract

Recent experimental observations of apparently hydrodynamic electronic transport have generated much excitement. However, the understanding of the observed non-local transport (whirlpool) effects and parabolic (Poiseuille-like) current profiles has largely been motivated by a phenomenological analogy to classical fluids. This is due to difficulty in incorporating strong correlations in quantum mechanical calculation of transport, which has been the primary angle for interpreting the apparently hydrodynamic transport. Here we demonstrate that even free fermion systems, in the presence of (inevitable) disorder, exhibit non-local conductivity effects such as those observed in experiment because of the fermionic system's long-range entangled nature. On the basis of explicit calculations of the conductivity at finite wavevector, $\sigma({\bf q})$, for selected weakly disordered free fermion systems, we propose experimental strategies for demonstrating distinctive quantum effects in non-local transport at odds with the expectations of classical kinetic theory. Our results imply that the observation of whirlpools or other "hydrodynamic" effects does not guarantee the dominance of electron-electron scattering over electron-impurity scattering.