Hydrodynamic electron transport in graphene Hall-bar devices

TL;DR

This paper develops a theory for hydrodynamic electron transport in graphene Hall-bar devices, revealing how inhomogeneity and disorder influence conductivity and thermoelectric properties, especially near charge neutrality.

Contribution

It introduces a comprehensive model accounting for non-Galilean-invariant effects and inhomogeneity, providing analytic expressions for transport coefficients across different regimes.

Findings

Hydrodynamic flow strongly couples to charge transport near charge neutrality.

Effective conductivity can significantly surpass intrinsic electron liquid conductivity.

Analytic formulas describe thermoelectric coefficients from clean to disordered regimes.

Abstract

We consider hydrodynamic electron transport in the Hall-bar geometry. The theory is developed for systems with non-Galilean-invariant electron liquids. We show that inhomogeneity of the electron density induced by long-range disorder and gating leads to mixing between the hydrodynamic transport mode and transport relative to the electron liquid. For graphene systems near charge neutrality, these effects lead to strong coupling of the hydrodynamic flow to charge transport. As a result, the effective electrical conductivity of the system may significantly exceed the intrinsic conductivity of the electron liquid. We obtain analytic expressions for the thermoelectric transport coefficients of the system as a function of density in the full crossover region between clean and disorder-dominated regimes.