# Freely flowing currents and electric field expulsion in viscous electronics

## TL;DR

This paper explores how viscous electronic fluids exhibit electric field expulsion and freely flowing currents due to nonlocal current-field relations, revealing unique boundary behaviors and geometric dependencies.

## Contribution

It introduces the concept of electric field expulsion in viscous electronics, deriving boundary conditions and analyzing flow and potential distribution in this new hydrodynamic regime.

## Key findings

- Electric field can be expelled from viscous electronic flows.
- Boundary jumps in electric potential occur at current-injecting electrodes.
- Field expulsion depends on electrode geometry and breaks conformal invariance.

## Abstract

Electronic fluids bring into hydrodynamics a new setting: equipotential flow sources embedded inside the fluid. Here we show that nonlocal relation between current and electric field due to momentum-conserving inter-particle collisions leads to a total or partial field expulsion from such flows. That results in freely flowing currents in the bulk and boundary jump in electric potential at current-injecting electrodes. We derive the appropriate boundary conditions, analyze current distribution in free flows, discuss how the field expulsion depends upon geometry of the electrode, and link the phenomenon to breakdown of conformal invariance.