# Hydrodynamic Electron Flow and Hall Viscosity

## TL;DR

This paper explores hydrodynamic electron flow in small metallic samples, focusing on how viscosity and Hall viscosity influence transport, and proposes methods for their experimental measurement.

## Contribution

It introduces a microscopic approach to measure both even and odd viscosity components in electronic systems under magnetic fields.

## Key findings

- Hydrodynamic regime dominates electron transport in small samples.
- Hall viscosity effects can be detected through specific transport measurements.
- Proposes experimental setups to measure viscosity components.

## Abstract

In metallic samples of small enough size and sufficiently strong momentum-conserving scattering, the viscosity of the electron gas can become the dominant process governing transport. In this regime, momentum is a long-lived quantity whose evolution is described by an emergent hydrodynamical theory. Furthermore, breaking time-reversal symmetry leads to the appearance of an odd component to the viscosity called the Hall viscosity, which has attracted considerable attention recently due to its quantized nature in gapped systems but still eludes experimental confirmation. Based on microscopic calculations, we discuss how to measure the effects of both the even and odd components of the viscosity using hydrodynamic electronic transport in mesoscopic samples under applied magnetic fields.