Stokes paradox in electronic Fermi liquids

Abstract

The Stokes paradox is the statement that in a viscous two dimensional fluid, the "linear response" problem of fluid flow around an obstacle is ill-posed. We present a simple consequence of this paradox in the hydrodynamic regime of a Fermi liquid of electrons in two-dimensional metals. Using hydrodynamics and kinetic theory, we estimate the contribution of a single cylindrical obstacle to the global electrical resistance of a material, within linear response. Momentum relaxation, present in any realistic electron liquid, resolves the classical paradox. Nonetheless, this paradox imprints itself in the resistance, which can be parametrically larger than predicted by Ohmic transport theory. We find a remarkably rich set of behaviors, depending on whether or not the quasiparticle dynamics in the Fermi liquid should be treated as diffusive, hydrodynamic or ballistic on the length scale of the obstacle. We argue that all three types of behavior are observable in present day experiments.

23+3 pages, 7+1 figures. v2: published version with expanded introduction

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• Controlling electron-phonon interactions in graphene at ultra high carrier densities
• Acoustic phonon scattering limited carrier mobility in 2D extrinsic graphene
• Theory of the Nernst effect near quantum phase transitions in condensed matter, and in dyonic black holes
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Cited by in corpus (11)

• Hydrodynamics of electrons in graphene
• Hydrodynamic approach to two-dimensional electron systems
• Observation of current whirlpools in graphene at room temperature
• Kinetic theory of transport for inhomogeneous electron fluids
• Stokes flow around an obstacle in viscous two-dimensional electron liquid
• Manifestations of classical size effect and electronic viscosity in the magnetoresistance of narrow two-dimensional conductors: Theory and experiment
• Viscous magnetotransport and Gurzhi effect in bilayer electron system
• Linking boundary conditions for kinetic and hydrodynamic description of fermion gas
• Two-dimensional electron hydrodynamics in a random array of impenetrable obstacles: Magnetoresistivity, Hall viscosity, and the Landauer dipole
• Geometric engineering of viscous magnetotransport in a two-dimensional electron system
• Magnetohydrodynamics and electro-electron interaction of massless Dirac fermions