Electronic Structure of Novel Two-dimensional Materials and Graphene Heterostructures

Today a well-equipped library of two-dimensional materials can be synthesized or exfoliated, ranging from insulating hexagonal boron nitride, to semi-metallic graphene, and metallic as well as superconducting transition metal dichalcogenides and many others. Due to strong intra-layer covalent bondings, but weak inter-layer Van-der-Waals interactions, these layered materials can be stacked in a Lego-like fashion to artificial heterostructures which do not occur in nature. Thereby, these novel systems offer the possibility to combine specific properties of each of its constituents to tailor the heterostructure's properties on demand which might allow for completely new device classes. In fact, these kind of systems are already constructed and studied in labs around the world. In order to guide these efforts, we need an in-depth understanding of these complex heterostructures starting with its smallest components, namely the different two-dimensional materials and their mutual interactions. To this end, we study electronic and optical properties of novel two-dimensional materials in this thesis. In more detail, we here aim to investigate functionalized graphene, graphene heterostructures and doped or optically excited molybdenum disulfide (MoS$_2$) monolayers for which we combine \abinitio based models with many-body or multi-scale approaches. The first part is devoted to functionalized graphene and is subdivided into the investigation of disorder-induced optical effects of fluorographene and into a detailed study of the Coulomb interaction in graphene heterostructures in form of multilayer graphene, intercalated graphite and few-layer graphene within a dielectric environment. In the case of fluorographene we use a multi-scale approach to study the effects of realistic disorder patterns to the optical conductivity. Thereby, we provide important insights into the role of non-perfect fluorination of graphene. Regarding the graphene heterostructures we present a novel approach to easily and reliably derive Coulomb-interaction matrix elements in these structures. This method is used to study the robustness of bilayer graphene's ground state to changes in its dielectric surrounding. In the second part of the thesis we study a variety of many-body effects that arise in doped and optically excited MoS$_2$ monolayers. Once again, by deriving simplified yet accurate models from first-principles we are able to investigate many-body excitations like plasmons or excitons as well as many-body instabilities like superconductivity or charge-density wave phases. Regarding the latter, we are able to extend the electron-doping phase diagram of MoS$_2$ by the formation of a charge-density-wave phase and reveal its potential coexistence with the superconducting state. In the field of many-body excitations we study in detail excitonic line shifts upon optical excitations and we precisely describe different types of plasmonic excitations under electron or hole doping in MoS$_2$. Finally, we make use of the fundamental properties of the many-body interactions in layered materials in order to externally induce heterojunctions within homogeneous semiconducting monolayers by non-local manipulations of the Coulomb interaction.