Local defects are always neutral in the Thomas-Fermi-von Weisz\"acker theory of crystals

TL;DR

This paper develops a mathematical model for the electronic structure of crystals with local defects within the Thomas-Fermi-von Weizs"acker theory, demonstrating that such defects are always neutral and analyzing their properties.

Contribution

It introduces a new model for local defects in crystals under TFW theory and proves the neutrality of these defects, extending previous models to this framework.

Findings

Local defects are always neutral in TFW theory.

Charged defects cannot be modeled within this framework.

Additional properties of the ground state density are derived.

Abstract

The aim of this article is to propose a mathematical model describing the electronic structure of crystals with local defects in the framework of the Thomas-Fermi-von Weizs\"acker (TFW) theory. The approach follows the same lines as that used in {\it E. Canc\`es, A. Deleurence and M. Lewin, Commun. Math. Phys., 281 (2008), pp. 129--177} for the reduced Hartree-Fock model, and is based on thermodynamic limit arguments. We prove in particular that it is not possible to model charged defects within the TFW theory of crystals. We finally derive some additional properties of the TFW ground state electronic density of a crystal with a local defect, in the special case when the host crystal is modelled by a homogeneous medium.