Space charge and screening of a supercritical impurity cluster in monolayer graphene

TL;DR

This paper revisits the Thomas-Fermi screening theory in monolayer graphene, analyzing how supercritical impurity clusters are screened, revealing a transition from external to internal charge localization as the screening parameter varies.

Contribution

It provides a detailed analysis of screening behavior in graphene for supercritical impurity clusters using the Thomas-Fermi approach, highlighting the transition between weak and strong screening regimes.

Findings

In the weak-screening regime, most charge resides outside the impurity cluster.

In the strong-screening regime, charge is mostly inside the cluster, nearly neutralizing the impurity.

A transition layer appears near the cluster's edge in the strong-screening regime.

Abstract

Coulomb impurity of charge $Ze$ is known to destabilize the ground state of undoped graphene with respect to creation of screening space charge if $Z$ exceeds a critical value of $1/2\alpha$ set by material's fine structure constant $\alpha$. Recent experimental advances made it possible to explore this transition in a controlled manner by tuning $Z$ across the critical point. Combined with relatively large value of $\alpha$ this opens a possibility to study graphene's screening response to a supercritical impurity $Z\alpha\gg1$ when the screening charge is large, and the Thomas-Fermi analysis, that we revisit, is adequate. The character of screening in this regime is controlled by the dimensionless screening parameter $Z\alpha^{2}$. Specifically, for circular impurity cluster most of the screening charge in the weak-screening regime $Z\alpha^{2}\ll1$ is found to reside outside the cluster. The strong-screening regime $Z\alpha^{2}\gg1$ provides a realization of the Thomson atom: most of the screening charge is inside the cluster nearly perfectly neutralizing the source charge with the exception of a transition layer near cluster's edge where the rest of the space charge is localized.