Coulomb impurity in graphene

TL;DR

This paper investigates how electron-electron interactions affect the screening of a charged impurity in graphene, revealing a transition from localized to extended charge distributions with specific asymptotic behavior.

Contribution

It provides a detailed analysis of screening in graphene considering electron interactions, highlighting the change in charge distribution compared to non-interacting models.

Findings

Screening charge sign is opposite to impurity when interactions are ignored.

Electron interactions cause the induced charge to spread out with an r^{-2} tail.

The induced charge sign aligns with the impurity when interactions are included.

Abstract

We consider the problem of screening of an electrically charged impurity in a clean graphene sheet. When electron-electron interactions are neglected, the screening charge has a sign opposite to that of the impurity, and is localized near the impurity. Interactions between electrons smear out the induced charge density to give a large-distance tail that follows approximately, but not exactly, an r^{-2} behavior and with a sign which is the same as that of the impurity.