Computational Studies of Two-Dimensional Materials and Heterostructures

Since the exfoliation of graphene in 2004, 2D materials have offered an intriguing playground for researchers to study new quantum mechanical effects at the quantum scale in materials. Due to the atomically thin nature of 2D materials these structures exhibit a very low dielectric screening which leads to strong light-matter interaction and pronounced many-body effects. It has in recent years become possible to not only isolate single monolayers of 2D sheets, but also to stack the monolayers into so-called van der Waals heterostructures (vdWHs) which, as the name suggests, are layered monolayers only weakly interacting through the van der Waals force. The possibility to seamlessly freely stack and rotate the individual monolayers in vdWHs relative to each other in the lab, makes accurate ab-initio calculations unable to describe such multilayer systems and effective models are needed to calculate the electronic and optical properties of vdWHs. In this thesis, entitled Computational Studies of Two-Dimensional Materials and Heterostructures, computational methods and models have been applied, developed, and implemented into the electronic structure code GPAW to overcome the computational difficulties when performing ab-initio calculations of vdWHs. The Bethe-Salpeter Equation (BSE) has been implemented with the previously developed Quantum Electrostatic Heterostructure (QEH) model to efficiently calculate exciton binding energies and absorption spectra for multilayer vdWHs and is found to accurately calculate the redshift of intralayer exciton energies in vdWHs. A feature shown not to be accurately described by the already existing Mott-Wannier equation. An appealing feature of the BSE-QEH implementation is that the computational requirement scales linearly with the number of layers in the vdWH. The fact that excitonic states have previously been described accurately by the Mott-Wannier model shows the hydrogen-like nature of the exciton state. In this thesis it is shown that this picture is not complete in the ...