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 presence of a dielectric substrate, where the system enters a substrate-dominated screening regime. This new dielectric screening regime of exciton physics is explored, where the exciton series becomes underbound rather than overbound as in the usual 2D excitonic hydrogen model.

Furtheremore, To help the scientific community in the calculation of electronic and optical properties of vdWHs, an efficient scheme has been developed to calculate the interlayer hybridisation and charge transfer in large vdWHs. The method corrects the (possibly) wrong description of the interlayer hybridisation offered by non-self-consistent state-of-the-art ab-initio methods such as the G0W0 approximation.

By combining the developed methods with ab-initio calculations we benchmark to what accuracy exciton energies can be calculated in comparison to experimental measurements in vdWHs by explicitly calculating the effect of twist-angle and substrate effects on the exciton energies. Furthermore we show that the inherent non-locality of the dielectric screening in 2D can be used to accurately control quasi-particle energies in semiconductors by placing the 2D semiconductor on a gated graphene layer.

A direct example of the potential in using vdWHs for applications such as photodetectors, pnjunctions, solar cells, or single-photon emission devices is shown by proving the existence of a vdWH with strong low-energy exciton states as a low-energy infrared photodetector. In the final chapter is presented a thorough study of the properties of the new class of 2D Janus monolayers.

This class of 2D monolayers exhibit an intrinsic out-of-plane dipole moment and it is shown how both the electronic and optical properties of vdWHs can be accurately manipulated and controlled by use of this class of structures. Finally, a new paradigm of materials science is introduced, by proving the existence of and examining self-intercalated bilayers: 2D bilayers with self-intercalated single-atoms.

It is shown that the self-intercalation process in fact leads to stable self-intercalated structures, for a large set of host bilayers and that the self-intercalation significantly alters the electronic properties and magnetic phase of the bilayer.