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

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.

8 pages, 5 figures + 6 pages of appendices

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• Corbino magnetoresistance in neutral graphene
• Current Noise of Hydrodynamic Electrons
• Hawking radiation from acoustic black holes in hydrodynamic flow of electrons
• Shear viscosity expression for a graphene system in relaxation time approximation
• Hydrodynamics of the electronic Fermi liquid: a pedagogical overview
• Two-dimensional hydrodynamic electron flow through periodic and random potentials
• Orbital Inverse Faraday and Cotton-Mouton Effects in Hall Fluids
• Wiedemann-Franz law violation domain for graphene and nonrelativistic systems
• Resolving the Corbino Shockley-Ramo Paradox for Hydrodynamic Current Noise
• Graphene is neither Relativistic nor Non-Relativistic case: Thermodynamics Aspects
• Tunable viscous layers in Corbino geometry using density junctions
• Electron Hydrodynamics and Bernoulli Effect in Venturi-Shaped 2D Systems