The Coulomb impurity problem in graphene

Abstract

We address the problem of an unscreened Coulomb charge in graphene, and calculate the local density of states and displaced charge as a function of energy and distance from the impurity. This is done non-perturbatively in two different ways: (1) solving the problem exactly by studying numerically the tight-binding model on the lattice; (2) using the continuum description in terms of the 2D Dirac equation. We show that the Dirac equation, when properly regularized, provides a qualitative and quantitative low energy description of the problem. The lattice solution shows extra features that cannot be described by the Dirac equation, namely bound state formation and strong renormalization of the van Hove singularities.

3 Figures; minor typo corrections and minor update in Fig. 3d

References in corpus (1)

• Disorder Induced Localized States in Graphene

Cited by in corpus (10)

• Modeling disorder in graphene
• Tuning the effective fine structure constant in graphene: opposing effects of dielectric screening on short- and long-range potential scattering
• Electronic properties of bilayer and multilayer graphene
• Ground-state of graphene in the presence of random charged impurities
• Screening of a hypercritical charge in graphene
• Density-Functional Theory of Graphene Sheets
• Supercritical Coulomb Impurities in Gapped Graphene
• Screening of Coulomb Impurities in Graphene
• Polarization Charge Distribution in Gapped Graphene
• Electron-Electron Interactions in the Vacuum Polarization of Graphene