First Principles Calculations of Electronic Excitations in 2D Materials

Since the first reported synthesization of graphene ̣- an atomically thin carbon material - in 2004 there has been a surge of research in discovering other novel two-dimensional materials. The reason is clear: two-dimensional materials are thought to be able to lead to new fast and low-power ultra-thin electronics and high efficiency solar cells. Contrary to many other nano-materials, methods for large scale fabrication and patterning have already been demonstrated and the first real technological applications have already be showcased. Still the technology is very young and the number of well-studied 2D materials are few. However as the list of 2D materials is growing it is necessary to investigate their fundamental structural, electronic and optical properties. These are determined by the atomic and electronic structure of the materials that can quite accurately predicted by computational quantum mechanics methods.
One of these methods, Density Functional Theory (DFT), has been very successful at determining structural properties of 2D materials. It is however well-known that it less accurate when it comes to predicting the energy levels of excited states that are important in order to determine electronic transport, optical and chemical properties. On the other hand it has shown to be a great starting point for a systematic pertubation theory approach to obtain the so-called quasiparticle spectrum. In the GW approximation one considers the considers the potential from a charged excitation as if it is being screened by the electrons in the material. This method has been very successful for calculating quasiparticle energies of bulk materials but results have been more varying for 2D materials. The reason is that the 2D confined electrons are less able to screen the added charge and some of the numerical methods that are efficient for bulk systems become invalid.
In this thesis I describe the study of a set of novel 2D materials and establish their electronic and optical properties using DFT and the GW approximation while taking the reduced screening properly into account as well as taking regard to other numerical problems that have often been neglected. Secondly I show how one can efficiently take the 2D nature into account in the GW approximation and thereby make future calculations require much less computational resources.