Quantum aspects of “hydrodynamic” transport from weak electron-impurity scattering

Recent experimental observations of apparently hydrodynamic electronic transport have generated much excitement. However, theoretical understanding of the observed non-local transport (whirlpool) effects and parabolic current profiles has remained at the level of a phenomenological analogy with classical fluids. A more microscopic account of genuinely hydrodynamic electronic transport is difficult because such behavior requires strong interactions to diffuse momentum. Here, we show that the non-local conductivity effects can indeed occur for fermion systems in the presence of disorder. By explicit calculation of the conductivity at finite wavevector σ(q) for selected weakly disordered free fermion systems, we propose experimental strategies for demonstrating distinctive quantum effects in non-local transport at odds with the expectations of classical kinetic theory. Our results imply that the observation of whirlpools or other "hydrodynamic" effects does not guarantee the dominance of electron-electron scattering over electron-impurity scattering.