Quantum aspects of hydrodynamic transport from weak electron-impurity scattering

Abstract

Recent experimental observations of apparently hydrodynamic electronic\ntransport have generated much excitement. However, the understanding of the\nobserved non-local transport (whirlpool) effects and parabolic\n(Poiseuille-like) current profiles has largely been motivated by a\nphenomenological analogy to classical fluids. This is due to difficulty in\nincorporating strong correlations in quantum mechanical calculation of\ntransport, which has been the primary angle for interpreting the apparently\nhydrodynamic transport. Here we demonstrate that even free fermion systems, in\nthe presence of (inevitable) disorder, exhibit non-local conductivity effects\nsuch as those observed in experiment because of the fermionic system's\nlong-range entangled nature. On the basis of explicit calculations of the\nconductivity at finite wavevector, $\\sigma({\\bf q})$, for selected weakly\ndisordered free fermion systems, we propose experimental strategies for\ndemonstrating distinctive quantum effects in non-local transport at odds with\nthe expectations of classical kinetic theory. Our results imply that the\nobservation of whirlpools or other "hydrodynamic" effects does not guarantee\nthe dominance of electron-electron scattering over electron-impurity\nscattering.\n