2015/06/19 by Alessandro Principi, Giovanni Vignale, Matteo Carrega +1 · 4 citations
Materials Science · Physics and Astronomy · #Condensed matter physics #Electron #Graphene #Graphene research and applications #Massless particle #Momentum transfer #Physics #Quantum and electron transport phenomena #Quantum mechanics #Quasiparticle #Scattering #Superconductivity #Topological Materials and Phenomena #cond-mat.mes-hall
paper · pdf · doi:10.1103/physrevb.93.125410
published as Phys. Rev. B 93, 125410 (2016) · 27 pages, 6 figures, 5 appendices
arxiv created 2015/06/19 · openalex publication_date 2016/03/07 · arxiv updated 2016/03/08 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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 paper, 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 formulas that allow to reach the low-frequency hydrodynamic regime where perturbation theory is no longer directly applicable. The key ingredient for the interpolation formulas is the ``viscosity transport time'' \ensuremathτv, which we calculate in this paper. The transverse nature of the excitations contributing to \ensuremathτv leads to the suppression of scattering events with small momentum transfer, which are inherently longitudinal. Therefore, contrary to the quasiparticle lifetime, which goes as \ensuremath-1/[T2ln(T/TF)], in the low-temperature limit we find \ensuremathτv\ensuremath∼1/T2.