Thomas-Fermi Screening in Graphene

TL;DR

This paper investigates the static in-plane screening of a charge in graphene using a Thomas-Fermi approach, providing exact and approximate solutions and revising earlier conclusions about screening behavior.

Contribution

It introduces a self-consistent real-space Thomas-Fermi method for graphene screening and offers new insights into the potential tail dependence on carrier density.

Findings

Screened potential exhibits a tail influenced by free carrier density.

Exact and approximate solutions for the screening potential are provided.

Revised understanding of Thomas-Fermi screening in graphene.

Abstract

The in-plane static screening of the field originated by a charge placed in a graphene sheet is investigated. A self-consistent field equation in the real space domain is obtained by using a suitable Thomas-Fermi procedure. Exact and approximated (for qualitative considerations) solutions are presented. In the case of a charged sheet, the screened potential presents a tail dependent on the free carrier density whose importance is connected with the local features of the impurity system. Early conclusions about Thomas-Fermi screening in graphene are revised.