We study Density Functional Theory models for 2D materials in the 3D space. Our interest comes from the recent developments of two-dimensional materials, such as graphene and phosphorene, in the physics community. In this work, we focus on homogeneous systems. We first show that a homogeneous material can be seen as a limit of periodic systems. Next, we derive reduced models in the remaining orthogonal direction, for DFT models with and without magnetic fields. We show how the different terms of the energy are modified and we derive reduced equations in the remaining direction. We prove some properties of the ground state, such as perfect screening and precise decay estimates in the Thomas-Fermi model, and in Kohn-Sham models, we prove that the Pauli principle is replaced by a penalization term in the energy.
Idriss Mazari