Non-local transport and the hydrodynamic shear viscosity in graphene

TL;DR

This paper provides a theoretical framework for measuring the hydrodynamic shear viscosity of doped graphene's electron liquid using non-local resistance measurements and scanning probe techniques, advancing understanding of 2D hydrodynamic transport.

Contribution

It introduces an analytical method to extract shear viscosity from non-local resistance measurements in graphene, applicable to any 2D electron liquid in the hydrodynamic regime.

Findings

Analytical relation between non-local resistance and shear viscosity.

Proposed experimental techniques for probing hydrodynamic regime.

Applicable to high-mobility 2D materials.

Abstract

Motivated by recent experimental progress in preparing encapsulated graphene sheets with ultra-high mobilities up to room temperature, we present a theoretical study of dc transport in doped graphene in the hydrodynamic regime. By using the continuity and Navier-Stokes equations, we demonstrate analytically that measurements of non-local resistances in multi-terminal Hall bar devices can be used to extract the hydrodynamic shear viscosity of the two-dimensional (2D) electron liquid in graphene. We also discuss how to probe the viscosity-dominated hydrodynamic transport regime by scanning probe potentiometry and magnetometry. Our approach enables measurements of the viscosity of any 2D electron liquid in the hydrodynamic transport regime.