Two-dimensional hydrodynamic electron flow through periodic and random potentials

TL;DR

This paper investigates how two-dimensional hydrodynamic electron flow in smooth potentials results in unique temperature-dependent resistivity behaviors, revealing new mechanisms for linear and non-linear resistivity in different potential landscapes.

Contribution

It introduces a hydrodynamic framework for electron flow through periodic and random potentials, explaining linear-in-T resistivity and a T^{10/3} growth in resistivity.

Findings

Hydrodynamic flow causes linear-in-T resistivity in periodic potentials.

Resistivity in random potentials grows as T^{10/3}.

Flow channels follow percolating equipotential contours.

Abstract

We study the hydrodynamic flow of electrons through a smooth potential energy landscape in two dimensions, for which the electrical current is concentrated along thin channels that follow percolating equipotential contours. The width of these channels, and hence the electrical resistance, is determined by a competition between viscous and thermoelectric forces. For the case of periodic (moir\'{e}) potentials, we find that hydrodynamic flow provides a new route to linear-in-$T$ resistivity. We calculate the associated prefactors for potentials with $C_3$ and $C_4$ symmetry. On the other hand, for a random potential the resistivity has qualitatively different behavior because equipotential paths become increasingly tortuous as their width is reduced. This effect leads to a resistivity that grows with temperature as $T^{10/3}$.