Density functional theory for homogeneous two dimensional materials with magnetic fields

TL;DR

This paper develops a reduced density functional theory model for homogeneous two-dimensional materials in magnetic fields, simplifying the 3D problem to 1D by exploiting symmetry and translation invariance, and introduces a penalization for the Pauli principle.

Contribution

It presents a novel reduction technique for DFT models in magnetic fields, removing the Pauli principle and simplifying the analysis of 2D materials.

Findings

Reduction of 3D energy functional to 1D for 2D materials in magnetic fields

Introduction of a penalization term replacing the Pauli principle

Method for minimizing over states invariant under magnetic translations

Abstract

This paper studies DFT models for homogeneous 2D materials in 3D space, under a constant perpendicular magnetic field. We show how to reduce the three--dimensional energy functional to a one--dimensional one, similarly as in our previous work. This is done by minimizing over states invariant under magnetic translations and that commute with the Landau operator. In the reduced model, the Pauli principle no longer appears. It is replaced by a penalization term in the energy.