# Magnetohydrodynamics in graphene: shear and Hall viscosities

## TL;DR

This paper provides a comprehensive calculation of shear and Hall viscosities in graphene, revealing how these viscosities depend on doping levels and magnetic fields, with implications for understanding hydrodynamic electron flow.

## Contribution

It introduces a unified kinetic theory and renormalization group approach to compute viscosities in graphene across various doping levels and magnetic fields.

## Key findings

- Hall viscosity vanishes at charge neutrality.
- Shear viscosity decreases with magnetic field and saturates at high fields.
- Viscosity behavior aligns with semiclassical predictions away from neutrality.

## Abstract

Viscous phenomena are the hallmark of the hydrodynamic flow exhibited by Dirac fermions in clean graphene at high enough temperatures. We report a quantitative calculation of the electronic shear and Hall viscosities in graphene based on the kinetic theory combined with the renormalization group providing a unified description at arbitrary doping levels and non-quantizing magnetic fields. At charge neutrality, the Hall viscosity vanishes, while the field-dependent shear viscosity decays from its zero-field value saturating to a nonzero value in classically strong fields. Away from charge neutrality, the field-dependent viscosity coefficients tend to agree with the semiclassical expectation.