Boundary condition and geometry engineering in electronic hydrodynamics

Abstract

We analyze the role of boundary geometry in viscous electronic hydrodynamics. We address the twin questions of how boundary geometry impacts flow profiles, and how one can engineer boundary conditions -- in particular the effective slip parameter -- to manipulate the flow in a controlled way. We first propose a micropatterned geometry involving finned barriers, for which we show by an explicit solution that one can obtain effectively no-slip boundary conditions regardless of the detailed microscopic nature of the channel surface. Next we analyse the role of mesoscopic boundary curvature on the effective slip length, in particular its impact on the Gurzhi effect. Finally we investigate a hydrodynamic flow through a circular junction, providing a solution, which suggests an experimental set-up for determining the slip parameter. We find that its transport properties differ qualitatively from the case of ballistic conduction, and thus presents a promising setting for distinguishing the two.

9 pages, 15 figures, 5 appendices

References in corpus (17)

• Negative local resistance caused by viscous electron backflow in graphene
• Observation of the Dirac fluid and the breakdown of the Wiedemann-Franz law in graphene
• Evidence for hydrodynamic electron flow in PdCoO${}_2$
• Superballistic flow of viscous electron fluid through graphene constrictions
• Hydrodynamics of electrons in graphene
• Hydrodynamic electron flow in high-mobility wires
• Measuring Hall Viscosity of Graphene's Electron Fluid
• Higher-Than-Ballistic Conduction of Viscous Electron Flows
• The properties of ultrapure delafossite metals
• Non-local transport and the Hall viscosity of 2D hydrodynamic electron liquids
• The boundary conditions of viscous electron flow
• Hydrodynamic approach to electronic transport in graphene
• A Corbino disk viscometer for 2D quantum electron liquids
• Magnetohydrodynamics in graphene: shear and Hall viscosities
• Pulsating flow and boundary layers in viscous electronic hydrodynamics
• A magnetic resonance in high-frequency viscosity of two-dimensional electrons
• Alternating currents and shear waves in viscous electronics

Cited by in corpus (17)

• Hydrodynamic approach to two-dimensional electron systems
• Electronic hydrodynamics in graphene
• Transport properties of strongly coupled electron-phonon liquids
• Imaging the breaking of electrostatic dams in graphene for ballistic and viscous fluids
• Viscometry of electron fluids from symmetry
• Non-local hydrodynamic transport and collective excitations in Dirac fluids
• Vorticity of viscous electronic flow in graphene
• Evidence for local spots of viscous electron flow in graphene at moderate mobility
• Skin effect as a probe of transport regimes in Weyl semimetals
• Functional dependence of the Hall viscosity-induced transverse voltage in two-dimensional Fermi liquids
• Geometric engineering of viscous magnetotransport in a two-dimensional electron system
• Micromagnets dramatically enhance effects of viscous hydrodynamic flow in two-dimensional electron fluid
• Obstacle-Induced Gurzhi Effect and Hydrodynamic Electron Flow in Two-Dimensional Systems
• Stray magnetic field and stability of time-dependent viscous electron flow
• Multipolar Fermi Surface Deformations in Sr${}_2$RuO${}_4$ Probed by Resistivity and Sound Attenuation: A Window into Electron Viscosity and the Collision Operator
• Tunable viscous layers in Corbino geometry using density junctions
• Stokes flow in an electronic fluid with odd viscosity