Nonlocal conductivity, continued fractions and current vortices in electron fluids

TL;DR

This paper develops a framework linking microscopic scattering mechanisms to macroscopic vorticity in electron fluids, revealing how nonlocal conductivity influences vortex behavior across different transport regimes.

Contribution

It introduces a wavenumber-dependent conductivity model that connects microscopic scattering to macroscopic vortices in electron fluids, bridging ballistic and hydrodynamic phases.

Findings

Vorticity values are similar in ballistic and hydrodynamic regimes.

Ballistic vortical flows are much more resistant to momentum relaxation.

The model provides a diagnostic tool for the microscopic origin of vorticity.

Abstract

Vortices in electron fluids are a key indicator of electron hydrodynamics. However, a comprehensive framework linking macroscopic vorticity measurements with microscopic interactions and scattering mechanisms has been lacking. We employ wavenumber-dependent conductivity $\sigma(k)$ incorporating realistic microscopic scattering processes, aiming to clarify the relationship between nonlocal response and vortices across ballistic and hydrodynamic phases. Vorticity is found to take similar values in both phases but feature very different sensitivity to momentum-relaxing scattering, with ballistic vortical flows being orders-of-magnitude more resilient than the hydrodynamic ones. This behavior can serve as a simple diagnostic of the microscopic origin of vorticity in electron fluids.