Stokes paradox in electronic Fermi liquids

TL;DR

This paper explores the Stokes paradox in two-dimensional electron Fermi liquids, showing how it affects electrical resistance and depends on quasiparticle dynamics, with implications for current experiments.

Contribution

It demonstrates how the classical Stokes paradox influences resistance in 2D Fermi liquids and identifies observable regimes of diffusive, hydrodynamic, and ballistic behaviors.

Findings

Resistance can be significantly larger than Ohmic predictions.

The paradox's effects depend on quasiparticle dynamics.

Multiple transport regimes are observable in experiments.

Abstract

The Stokes paradox is the statement that in a viscous two dimensional fluid, the "linear response" problem of fluid flow around an obstacle is ill-posed. We present a simple consequence of this paradox in the hydrodynamic regime of a Fermi liquid of electrons in two-dimensional metals. Using hydrodynamics and kinetic theory, we estimate the contribution of a single cylindrical obstacle to the global electrical resistance of a material, within linear response. Momentum relaxation, present in any realistic electron liquid, resolves the classical paradox. Nonetheless, this paradox imprints itself in the resistance, which can be parametrically larger than predicted by Ohmic transport theory. We find a remarkably rich set of behaviors, depending on whether or not the quasiparticle dynamics in the Fermi liquid should be treated as diffusive, hydrodynamic or ballistic on the length scale of the obstacle. We argue that all three types of behavior are observable in present day experiments.