Pulsating flow and boundary layers in viscous electronic hydrodynamics

Abstract

Motivated by experiments on a hydrodynamic regime in electron transport, we study the effect of an oscillating electric field in such a setting. We consider a long two-dimensional channel of width $L$, whose geometrical simplicity allows an analytical study as well as hopefully permitting experimental realisation. The response depends on viscosity $\nu$, driving frequency, $\omega$ and ohmic heating coefficient $\gamma$ via the dimensionless complex variable $\frac{L^2}{\nu }(i\omega +\gamma )=i\Omega +\Sigma$. While at small $\Omega$, we recover the static solution, a new regime appears at large $\Omega$ with the emergence of a boundary layer. This includes a splitting of the location of maximal flow velocity from the centre towards the edges of the boundary layer, an an increasingly reactive nature of the response, with the phase shift of the response varying across the channel. The scaling of the total optical conductance with $L$ differs between the two regimes, while its frequency dependence resembles a Drude form throughout, even in the complete absence of ohmic heating, against which, at the same time, our results are stable. Current estimates for transport coefficients in graphene and delafossites suggest that the boundary layer regime should be experimentally accessible.

5 pages, 3 figures, the title has been changed, the manuscript has been substantially modified and references updated

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• Non-local hydrodynamic transport and collective excitations in Dirac fluids
• Skin effect as a probe of transport regimes in Weyl semimetals
• Strongly coupled electron fluids in the Poiseuille regime
• Micromagnets dramatically enhance effects of viscous hydrodynamic flow in two-dimensional electron fluid
• Giant Hall effect in the ballistic transport of two-dimensional electrons
• Hall viscosity and hydrodynamic inverse Nernst effect in graphene
• Rotational viscosity in spin resonance of hydrodynamic electrons
• Spin imaging of Poiseuille flow of viscous electronic fluid
• Universal superdiffusive modes in charged two dimensional liquids
• Ballistic flow of two-dimensional electrons in a magnetic field
• Stray magnetic field and stability of time-dependent viscous electron flow
• Phase Transitions and Conductivties of Floquet Fluids
• Viscoelastic response and anisotropic hydrodynamics in Weyl semimetals
• Quantum Heat Under the Microscope: A Perspective on Cryogenic Scanning Thermal Microscopy
• Tomographic collective modes in a magnetic field
• Ballistic-to-hydrodynamic transition and collective modes for two-dimensional electron systems in magnetic field
• Hydrodynamic electrons in Graphene: a viscous boundary-layer description