Angular Superdiffusion and Directional Memory in Two-Dimensional Electron Fluids

Abstract

We demonstrate that 2D Fermi liquids can support peculiar excitations that are not subject to Landau's $T^2$ dissipation. The long-lived excitations relax through correlated angular dynamics involving "lock-step" angular displacements along the Fermi surface occurring in collinear two-particle collisions, a surprising behavior that is unique to 2D systems. We develop a microscopic picture of the non-Brownian random walk, describing the angular dynamics as anomalous diffusion ("superdiffusion") on the Fermi surface. Strongly-correlated dynamics with directional memory, mediated by novel undamped excitations, dominates at moderately long times, pushing the onset of conventional hydrodynamics to abnormally large timescales. This exotic behavior can be directly probed by momentum-resolved tunneling techniques.