title: Vacuum polarization and screening of supercritical impurities in graphene.
abstract: Screening of charge impurities in graphene is analyzed using the exact solution for vacuum polarization obtained from the massless Dirac-Kepler problem. For the impurity charge below a certain critical value, no density perturbation is found away from the impurity, in agreement with perturbation theory. For the supercritical charge, however, the polarization distribution is shown to have a power law profile, leading to screening of the excess charge at large distances. The Dirac-Kepler scattering states give rise to standing wave oscillations in the local density of states which are prominent in the supercritical regime.
authors.affiliation: Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA.
authors.forename: A V
authors.initials: AV
authors.lastname: Shytov
authors.forename: M I
authors.initials: MI
authors.lastname: Katsnelson
authors.forename: L S
authors.initials: LS
authors.lastname: Levitov