Orbital-free density functional theory of out-of-plane charge screening in graphene

TL;DR

This paper develops a density functional theory model to describe how graphene responds to external charges, providing mathematical proofs of existence, uniqueness, and behavior of charge distributions.

Contribution

It introduces a new variational framework for modeling charge screening in graphene, including conditions for minimizer uniqueness and bifurcation analysis.

Findings

Existence of energy minimizers for the model.

Conditions for uniqueness of charge density profiles.

Identification of a bifurcation point for charge response.

Abstract

We propose a density functional theory of Thomas-Fermi-Dirac-von Weizs\"acker type to describe the response of a single layer of graphene resting on a dielectric substrate to a point charge or a collection of charges some distance away from the layer. We formulate a variational setting in which the proposed energy functional admits minimizers, both in the case of free graphene layers and under back-gating. We further provide conditions under which those minimizers are unique and correspond to configurations consisting of inhomogeneous density profiles of charge carrier of only one type. The associated Euler-Lagrange equation for the charge density is also obtained, and uniqueness, regularity and decay of the minimizers are proved under general conditions. In addition, a bifurcation from zero to non-zero response at a finite threshold value of the external charge is proved.