Supercritical Coulomb Impurities in Gapped Graphene

TL;DR

This paper investigates how Coulomb impurities induce charging in gapped graphene, revealing a supercritical regime where screening significantly reduces the impurity's Coulomb field at nanometer scales.

Contribution

It introduces the concept of a supercritical regime in gapped graphene and demonstrates its existence through analytical and numerical methods, extending understanding beyond massless graphene.

Findings

Critical Coulomb coupling is higher in gapped graphene.

A supercritical regime with strong screening is possible.

Numerical solutions confirm the analytical predictions.

Abstract

We study the problem of Coulomb field-induced charging of the ground state in a system of 2D massive Dirac particles (gapped graphene). As in its 3D QED counterpart, the critical Coulomb coupling is renormalized to higher values, compared to the massless case. We find that in gapped graphene a novel supercritical regime is possible, where the screening charge is comparable to the impurity charge, thus leading to suppression of the Coulomb field at nanometer scales. We corroborate this with numerical solution of the tight-binding problem in the honeycomb lattice.