Electronic viscosity from first principles: link to conductivity, GW theory, and Fermi surfaces

Electronic transport is governed by momentum-relaxing electron collisions (with phonons, impurities, and sample boundaries) and momentum-conserving electron–electron (e–e) collisions. First-principles studies have so far largely targeted conductivity limited by momentum-relaxing mechanisms. In this talk, we show a first-principles theory of transport in the hydrodynamic regime, where e-e scattering is the dominant mechanism and electrons behave similar to a viscous fluid. We derive and solve the Boltzmann transport equation for two scenarios: i) applied electric field, which provides the conductivity limited by e-e scattering, and ii) applied drift-velocity gradient, which enables first-principles calculations of the electron viscosity. The similarities between these two cases enable a unified treatment of electron conductivity and viscosity in the hydrodynamic regime. We also discuss a link between this framework and GW theory. Our treatment generalizes kinetic-gas results to realistic band structures and noncircular Fermi surfaces, and identifies an experimentally accessible inertial "mass" governing momentum diffusion. We study graphene and selected 2D monolayers, obtaining viscosity tensors and relevant crossovers between limiting mechanisms. This approach paves the way for quantitative predictions of electron transport in the hydrodynamic regime.