Chemically modified and nanostructured graphene

After its experimental discovery in 2004, graphene has been the topic of intense research. Its extraordinary linear dispersion relation in the vicinity of the Fermi surface allows the study of relativistic quantum mechanics in a condensed-matter context. The gapless spectrum is beneficial in, for instance, optical applications as the optical absorption is nearly constant in the visible spectrum. In transistor applications, however, the absence of a gap leads to poor on-off ratios. Thus, inducing a gap is of interest for applications, and both quantum confinement as well as chemical modification can be used to achieve this goal. In this thesis, the electronic properties of modified graphene systems are studied using density-functional theory and lattice models. Additionally, a novel lattice density-functional theory approach is introduced. The chemical modification of graphene using chlorine and hydrogen is addressed considering also its chemical environment, a silicon dioxide substrate and a gaseous atmosphere treated using ab initio thermodynamics. Electronic states in finite metal-deposited graphene nanostructures with gaps induced by quantum confinement are studied together with experimental measurements. Finally, the prospect of superconductivity in rhombohedral graphite is addressed by studying flat bands in rhombohedral graphene multilayers. The results add to the understanding of the electronic properties of graphene in complex environments. We clarify the effect of the substrate in hydrogen adsorption on graphene and provide a suggestion to prepare graphene nanoribbons using chlorine to unzip carbon nanotubes. We aid in the interpretation of recent scanning tunneling microscopy experiments on metal-deposited finite graphene nanostructures, as well as provide reference data for the detection of end states in graphene ribbons.