Beyond Ohm's law -- Bernoulli effect and streaming in electron hydrodynamics

TL;DR

This paper proposes experiments to detect nonlinear hydrodynamic effects in electron flow within 2D materials, using phenomena like Bernoulli effect and streaming, to distinguish true hydrodynamic behavior from impurity scattering.

Contribution

It introduces novel experimental approaches leveraging nonlinear Navier-Stokes effects to identify electron hydrodynamics in graphene-based devices.

Findings

Feasible experimental parameters for observing Bernoulli effect, streaming, and turbulence.

Hydrodynamic signatures are detectable within current graphene device capabilities.

Nonlinear effects can differentiate hydrodynamic flow from impurity scattering.

Abstract

Recent observations of non-local transport in ultraclean 2D materials raised the tantalizing possibility of accessing hydrodynamic correlated transport of many-electron state. However, it has been pointed out that non-local transport can also arise from impurity scattering rather than interaction. At the crux of the ambiguity is the focus on linear effects, i.e. Ohm's law, which cannot easily differentiate among different modes of transport. Here we propose experiments that can reveal rich hydrodynamic features in the system by tapping into the non-linearity of the Navier-Stokes equation. Three experiments we propose will each manifest unique phenomenon well-known in classical fluids: the Bernoulli effect, Eckart streaming, and Rayleigh streaming. Analysis of known parameters confirms that the proposed experiments are feasible and the hydrodynamic signatures are within reach of graphene-based devices. Experimental realization of any one of the three phenomena will provide a stepping stone to formulating and exploring the notions of nonlinear electron fluid dynamics with an eye to celebrated examples from classical non-laminar flows, e.g. pattern formation and turbulence.