Boundary conditions of viscous electron flow

Egor I. Kiselev and Jörg Schmalian
Phys. Rev. B 99, 035430 – Published 22 January 2019

Abstract

The sensitivity of charge, heat, or momentum transport to the sample geometry is a hallmark of viscous electron flow. Therefore hydrodynamic electronics requires a detailed understanding of electron flow in finite geometries. The solution of the corresponding generalized Navier-Stokes equations depends sensitively on the nature of boundary conditions. The latter can be characterized by a slip length ζ with extreme cases being no-slip ζ0 and no-stress ζ conditions. We develop a kinetic theory that determines the temperature dependent slip length at a rough interface for Dirac liquids, e.g., graphene, and for Fermi liquids. For strongly disordered edges that scatter electrons in a fully diffuse way, we find that the slip length is of the order of the momentum conserving mean free path lee that determines the electron viscosity. For boundaries with nearly specular scattering, ζ is parametrically large compared to lee. Since for all quantum fluids lee diverges as T0, the ultimate low-temperature flow is always in the no-stress regime. Only at intermediate T and for sufficiently large sample sizes can the slip lengths be short enough such that no-slip conditions are appropriate. We discuss numerical examples for several experimentally investigated systems. To identify hydrodynamic flow governed by no-stress boundary conditions, we propose the transport through an infinitely long strip containing an impenetrable circular obstacle.

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  • Received 13 June 2018
  • Revised 12 October 2018

DOI:https://doi.org/10.1103/PhysRevB.99.035430

©2019 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Egor I. Kiselev1 and Jörg Schmalian1,2

  • 1Institut für Theorie der Kondensierten Materie, Karlsruher Institut für Technologie, 76131 Karlsruhe, Germany
  • 2Institut für Festkörperphysik, Karlsruher Institut für Technologie, 76131 Karlsruhe, Germany

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Issue

Vol. 99, Iss. 3 — 15 January 2019

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