Density Functional Theory for Two-Dimensional Homogeneous Materials

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 give some properties of the minimizer.

Automated summary

In this study, Density Functional Theory models for translationally invariant systems were investigated, showing modifications to energy terms and deriving reduced equations in remaining directions. It was demonstrated that perfect screening exists in the Thomas-Fermi model, with decay estimates provided for electronic density away from the slab. The Pauli principle is replaced by a penalization term in Kohn-Sham models, and properties of the minimizer in the reduced Hartree-Fock model were elucidated.