Universal superdiffusive modes in charged two dimensional liquids

TL;DR

This paper reveals that in two-dimensional charged liquids, charge diffusion is inherently superdiffusive, governed by a plasmon mode, with magnetic fields influencing the diffusion process, relevant to electrons in solids and plasmas.

Contribution

It introduces the concept of superdiffusive charge transport in 2D Coulomb liquids and analyzes the effects of magnetic fields on these collective modes.

Findings

Charge relaxation is governed by an overdamped superdiffusive plasmon mode.

Particles follow Levy flight trajectories indicating superdiffusion.

Magnetic fields slow down the superdiffusive charge transport.

Abstract

Using a hydrodynamic approach, we show that charge diffusion in two dimensional Coulomb interacting liquids with broken momentum conservation is intrinsically anomalous. The charge relaxation is governed by an overdamped, superdiffusive plasmon mode. We demonstrate that the diffusing particles follow L\'evy flight trajectories, and study the hydrodynamic collective modes under the influence of magnetic fields. The latter are shown to slow down the superdiffusive process. The results are argued to be relevant to electron liquids in solids, as well as plasmas.