Bulk and shear viscosities of the 2D electron liquid in a doped graphene sheet

Abstract

Hydrodynamic flow occurs in an electron liquid when the mean free path for electron-electron collisions is the shortest length scale in the problem. In this regime, transport is described by the Navier-Stokes equation, which contains two fundamental parameters, the bulk and shear viscosities. In this Article we present extensive results for these transport coefficients in the case of the two-dimensional massless Dirac fermion liquid in a doped graphene sheet. Our approach relies on microscopic calculations of the viscosities up to second order in the strength of electron-electron interactions and in the high-frequency limit, where perturbation theory is applicable. We then use simple interpolation formulae that allow to reach the low-frequency hydrodynamic regime where perturbation theory is no longer directly applicable. The key ingredient for the interpolation formulae is the "viscosity transport time" ${\tau }_{\mathrm{v}}$, which we calculate in this Article. The transverse nature of the excitations contributing to ${\tau }_{\mathrm{v}}$ leads to the suppression of scattering events with small momentum transfer, which are inherently longitudinal. Therefore, contrary to the quasiparticle lifetime, which goes as $-1/[T^2\ln (T/T_{\mathrm{F}})]$, in the low temperature limit we find ${\tau }_{\mathrm{v}}\sim 1/T^2$.

27 pages, 6 figures, 5 appendices

References in corpus (16)

• The electronic properties of graphene
• Dielectric function, screening, and plasmons in 2D graphene
• Dynamical polarization of graphene at finite doping
• Highly confined low-loss plasmons in graphene-boron nitride heterostructures
• Negative local resistance caused by viscous electron backflow in graphene
• The Role of Electron-electron Interactions in Graphene ARPES Spectra
• Non-local transport and the hydrodynamic shear viscosity in graphene
• Drude weight, plasmon dispersion, and a.c. conductivity in doped graphene sheets
• Hydrodynamics in graphene: Linear-response transport
• Linear response of doped graphene sheets to vector potentials
• Plasmon losses due to electron-phonon scattering: the case of graphene encapsulated in hexagonal Boron Nitride
• f-Sum Rule and Unconventional Spectral Weight Transfer in Graphene
• Finite temperature inelastic mean free path and quasiparticle lifetime in graphene
• Hydrodynamic Model for Conductivity in Graphene
• Electrical plasmon detection in graphene waveguides
• The intrinsic charge and spin conductivities of doped graphene in the Fermi-Liquid regime

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