Conformal maps of viscous electron flow in the Gurzhi crossover

TL;DR

This paper analyzes how geometric constrictions influence viscous electron flow using conformal mapping, revealing potential experimental tests and discussing complex physics like the Gurzhi effect and nonlocality in hydrodynamic regimes.

Contribution

It provides analytical solutions for potential distribution in viscous electron flow through constrictions and explores the physics of the Gurzhi effect with implications for experiments.

Findings

Potential profiles can be tested experimentally with scanning tunneling potentiometry.

The Gurzhi effect enhances conductivity in viscous flow under certain conditions.

Nonlocal effects and inhomogeneous current profiles are significant in the hydrodynamic regime.

Abstract

We investigate the impact of geometric constriction on the viscous flow of electron liquid through quantum point contacts. We provide analysis on the electric potential distribution given the setup of a slit configuration and use the method of conformal mapping to obtain analytical results. The potential profile can be tested and contrasted experimentally with the scanning tunneling potentiometry technique. We discuss intricate physics that underlies the Gurzhi effect, i.e., the enhancement of conductivity in the viscous flow, and compare results for different boundary conditions. In addition, we calculate the temperature dependence of the momentum relaxation time as a result of impurity assisted quasiballistic interference effects and discuss various correlational corrections that lead to the violation of Matthiessen's rule in the hydrodynamic regime. We caution that spatially inhomogeneous profiles of current in the Gurzhi crossover between Ohmic and Stokes flows might also appear in the nonhydrodynamic limit where nonlocality plays an important role. This conclusion is corroborated by calculation of dispersive conductivity in the weakly impure limit.