Geometry-Induced Skin Effect in Electron Hydrodynamics

TL;DR

This paper reveals a geometry-induced skin effect in hydrodynamic electron flows in ultra-clean 2D materials, where obstacles enhance local current suppression, providing a hydrodynamic explanation for observed edge current profiles.

Contribution

It introduces a simple Brinkman equation framework showing geometric effects on electron hydrodynamics, independent of ballistic dynamics, and interprets experimental flow patterns in graphene.

Findings

Obstacles cause local current enhancement and suppression far from edges.

Hydrodynamic flow patterns match recent experimental observations.

Geometry significantly influences electron flow in hydrodynamic regimes.

Abstract

In ultra-clean 2d materials electron viscosity is as important as Ohmic dissipation and electron transport exhibits hydrodynamic features. Using a simple framework of Brinkman equations we find that hydrodynamic electron flows exhibit a geometric skin effect: sharp obstacles locally enhance the current suppressing it far from the edges where the flow is unobstructed. This effect arises within hydrodynamic transport with finite momentum relaxation and does not rely on ballistic dynamics. Our results provide a natural hydrodynamic interpretation of edge-enhanced and double-bump current profiles observed in constricted geometries. By comparing with recent scanning NV magnetometry experiments on gated graphene, we demonstrate that such flow patterns are consistent with viscous hydrodynamics shaped by geometry, clarifying the role of geometric effects in the interpretation of electronic flow experiments.