Screening of a hypercritical charge in graphene

TL;DR

This paper investigates how a large external charge is screened in graphene, revealing a transition from a 3/2 power decay to Coulomb law outside a hypercritical core, with implications for understanding charge interactions.

Contribution

It introduces a model for screening of hypercritical charges in graphene, showing a transition in decay behavior and the formation of a hypercritical core.

Findings

Decay of potential follows 3/2 power law initially

Potential transitions to Coulomb law outside the core

Core radius scales with external charge

Abstract

Screening of a large external charge in graphene is studied. The charge is assumed to be displaced away or smeared over a finite region of the graphene plane. The initial decay of the screened potential with distance is shown to follow the 3/2 power. It gradually changes to the Coulomb law outside of a hypercritical core whose radius is proportional to the external charge.