Relaxation of charge in monolayer graphene: fast non-linear diffusion vs Coulomb effects

TL;DR

This paper investigates charge relaxation in monolayer graphene, revealing a regime dominated by non-linear diffusion with superdiffusive behavior and unique interface phenomena due to poor screening and zero-point motion effects.

Contribution

It introduces a novel non-linear diffusion model for charge relaxation in graphene, highlighting the dominance of zero-point motion over Coulomb interactions in certain regimes.

Findings

Charge relaxation follows a non-linear diffusion equation with diverging diffusion coefficient.

Superdiffusive relaxation regimes are observed.

Finite extinction times for periodic charge profiles are identified.

Abstract

Pristine monolayer graphene exhibits very poor screening because the density of states vanishes at the Dirac point. As a result, charge relaxation is controlled by the effects of zero-point motion (rather than by the Coulomb interaction) over a wide range of parameters. Combined with the fact that graphene possesses finite intrinsic conductivity, this leads to a regime of relaxation described by a non-linear diffusion equation with a diffusion coefficient that diverges at zero charge density. Some consequences of this fast diffusion are self-similar superdiffusive regimes of relaxation, the development of a charge depleted region at the interface between electron- and hole-rich regions, and finite extinction times for periodic charge profiles.