Supercritical Coulomb Impurities in Gapped Graphene

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.

Revised and extended version

References in corpus (14)

• Two-Dimensional Gas of Massless Dirac Fermions in Graphene
• Substrate-induced band gap opening in epitaxial graphene
• Charged Impurity Scattering in Graphene
• A self-consistent theory for graphene transport
• Epitaxial graphene
• Quantum transport of massless Dirac fermions in graphene
• Graphene: new bridge between condensed matter physics and quantum electrodynamics
• The Coulomb impurity problem in graphene
• Elastic scattering theory and transport in graphene
• Atomic Collapse and Quasi-Rydberg States in Graphene
• Screening of a hypercritical charge in graphene
• Screening of Coulomb Impurities in Graphene
• Coulomb impurity in graphene
• Dirac electron in a Coulomb Field in 2+1 Dimensions

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