# Unified description of the classical Hall viscosity

## TL;DR

This paper derives a generalized relation between Hall viscosity and transverse electric field, exploring measurement methods in different geometries, and introduces a viscous Hall angle to characterize flow regimes.

## Contribution

It provides a unified theoretical framework for understanding and measuring Hall viscosity in electron flows, extending beyond hydrodynamic definitions.

## Key findings

- Hall viscosity can be measured via local transverse electric field probes.
- In a Corbino geometry, viscous effects are due to circular flow patterns, not boundary friction.
- The viscous Hall angle remains well-defined across flow regimes.

## Abstract

In absence of time-reversal symmetry, viscous electron flow hosts a number of interesting phenomena, of which we focus here on the Hall viscosity. Taking a step beyond the hydrodynamic definition of the Hall viscosity, we derive a generalized relation between Hall viscosity and transverse electric field using a kinetic equation approach. We explore two different geometries where the Hall viscosity is accessible to measurement. For hydrodynamic flow of electrons in a narrow channel, we find that the viscosity may be measured by a local probe of the transverse electric field near the center of the channel. Ballistic flow, on the other hand, is dominated by boundary effects. In a Corbino geometry viscous effects arise not from boundary friction but from the circular flow pattern of the Hall current. In this geometry we introduce a viscous Hall angle which remains well defined throughout the crossover from ballistic to hydrodynamic flow, and captures the bulk viscous response of the fluid.