Dirac Fermions in Graphene Nanostructures

In recent years, the ability to fabricate and investigate graphenebased nanostructures has been increasing constantly. In addition, great progress has been made towards reaching the coherent ballistic transport regime in graphene systems. These developments call for a generic theoretical description and analysis of the electronic properties of ballistic graphene nanostructures, in particular in view of effects related to the system boundaries. In this thesis we provide an analytical theory of edge effects on the spectral density of states and the quantum transport properties of these systems, extending semiclassical approaches to the case of graphene. It is shown that the characteristics of the system edges have strong impact on spectrum and conductance. Numerical tightbinding simulations support these analytical predictions. Finally, numerical studies of graphene nanoribbons are presented, which show that edge scattering can have important consequences on quantum interference effects also in weakly disordered systems.