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

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 $Z\alpha \gg 1$ 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 $Z{\alpha }^2\ll 1$ is found to reside outside the cluster. The strong-screening regime $Z{\alpha }^2\gg 1$ 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.

8 pages, 1 figure, minor changes, version to be published in Phys. Rev. B

References in corpus (4)

• The electronic properties of graphene
• Vacuum Polarization and Screening of Supercritical Impurities in Graphene
• Nonlinear screening of charge impurities in graphene
• Screening of a hypercritical charge in graphene