Alternating currents and shear waves in viscous electronics

Abstract

Strong interaction among charge carriers can make them move like viscous fluid. Here we explore alternating current (AC) effects in viscous electronics. In the Ohmic case, incompressible current distribution in a sample adjusts fast to a time-dependent voltage on the electrodes, while in the viscous case, momentum diffusion makes for retardation and for the possibility of propagating slow shear waves. We focus on specific geometries that showcase interesting aspects of such waves: current parallel to a one-dimensional defect and current applied across a long strip. We find that the phase velocity of the wave propagating along the strip respectively increases/decreases with the frequency for no-slip/no-stress boundary conditions. This is so because when the frequency or strip width goes to zero (alternatively, viscosity go to infinity), the wavelength of the current pattern tends to infinity in the no-stress case and to a finite value in a general case. We also show that for DC current across a strip with no-stress boundary, there only one pair of vortices, while there is an infinite vortex chain for all other types of boundary conditions.

10 pages

References in corpus (5)

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• Slow imbalance relaxation and thermoelectric transport in graphene
• Electromagnetic properties of viscous charged fluids
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• Nonlocal conductivity, continued fractions and current vortices in electron fluids
• Dipole excitation of collective modes in viscous two-dimensional electron systems
• Rotational viscosity in spin resonance of hydrodynamic electrons
• Spin imaging of Poiseuille flow of viscous electronic fluid
• Selective damping of plasmons in coupled two-dimensional systems by Coulomb drag
• Exact theory of edge diffraction and launching of transverse electric plasmons at two-dimensional junctions
• Ballistic-to-hydrodynamic transition and collective modes for two-dimensional electron systems in magnetic field
• Tomographic collective modes in a magnetic field