Hall viscosity and hydrodynamic inverse Nernst effect in graphene

TL;DR

This paper investigates how Hall viscosity influences hydrodynamic electron transport in graphene, revealing complex magnetic field-dependent behaviors and potential experimental signatures in the inverse Nernst effect.

Contribution

It introduces a detailed analysis of the interplay between Hall viscous and Lorentz forces in graphene's hydrodynamics, highlighting non-linear effects and the dominance of Hall viscosity in the inverse Nernst signal.

Findings

Non-linear magnetic field dependence of Hall and inverse Nernst signals.

Cancellation points at critical magnetic field values.

Suppression of Lorenz ratio due to finite channel width.

Abstract

Motivated by Hall viscosity measurements in graphene sheets, we study hydrodynamic transport of electrons in a channel of finite width in external electric and magnetic fields. We consider electric charge densities varying from close to the Dirac point up to the Fermi liquid regime. We find two competing contributions to the hydrodynamic Hall and inverse Nernst signals that originate from the Hall viscous and Lorentz forces. This competition leads to a non-linear dependence of the full signals on the magnetic field and even a cancellation at different critical field values for both signals. In particular, the hydrodynamic inverse Nernst signal in the Fermi liquid regime is dominated by the Hall viscous contribution. We further show that a finite channel width leads to a suppression of the Lorenz ratio, while the magnetic field enhances this ratio. All of these effects are predicted in parameter regimes accessible in experiments.