Thomas-Fermi theory of out-of-plane charge screening in graphene

Document Type

Article

Publication Date

7-31-2024

Abstract

This paper provides a variational treatment of the effect of external charges on the free charges in an infinite free-standing graphene sheet within the Thomas-Fermi theory. We establish existence, uniqueness and regularity of the energy minimizers corresponding to the free charge densities that screen the effect of an external electrostatic potential at the neutrality point. For the potential due to one or several off-layer point charges, we also prove positivity and a precise universal asymptotic decay rate for the screening charge density, as well as an exact charge cancellation by the graphene sheet. We also treat a simpler case of the non-zero background charge density and establish similar results in that case.

Identifier

85201412136 (Scopus)

Publication Title

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

External Full Text Location

https://doi.org/10.1098/rspa.2023.0570

e-ISSN

14712946

ISSN

13645021

Issue

2294

Volume

480

Grant

DMS-1614948

Fund Ref

Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni

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