Vacuum Polarization and Screening of Supercritical Impurities in Graphene

TL;DR

This paper investigates how charge impurities in graphene are screened by vacuum polarization, revealing a critical charge threshold and power-law screening behavior for supercritical impurities, with observable standing wave oscillations.

Contribution

It provides an exact solution for vacuum polarization in graphene's Dirac model, highlighting the transition from no perturbation to power-law screening at supercritical impurity charges.

Findings

No density perturbation below critical charge.

Power-law polarization distribution for supercritical charge.

Standing wave oscillations in local density of states.

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 certain critical value no density perturbation is found away from the impurity, in agreement with the linear response theory result. For 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 appear and become prominent in the supercritical regime.