Density Functional Theory for two-dimensional homogeneous materials

TL;DR

This paper extends density functional theory models to homogeneous 2D materials, deriving reduced equations and analyzing properties like screening, decay, and well-posedness in various models.

Contribution

It introduces and analyzes reduced DFT models for translationally invariant 2D systems, including proofs of perfect screening and well-posedness.

Findings

Proves perfect screening in the Thomas-Fermi model.

Provides decay estimates for electronic density.

Establishes well-posedness of the reduced Hartree-Fock model.

Abstract

We study Density Functional Theory models for systems which are translationally invariant in some directions, such as a homogeneous 2-d slab in the 3-d space. We show how the different terms of the energy are modified and we derive reduced equations in the remaining directions. In the Thomas-Fermi model, we prove that there is perfect screening, and provide decay estimates for the electronic density away from the slab. In Kohn-Sham models, we prove that the Pauli principle is replaced by a penalization term in the energy. In the reduced Hartree-Fock model in particular, we prove that the resulting model is well-posed, and provide some properties for the minimizer.