Physics in graphene & quantum rings : from mesoscopic device fabrication to measurement in high magnetic fields

New materials often lead to spectacular discoveries. A prominenent example is graphene, a single layer of carbon atoms arranged in a honeycomb lattice. This one atom thick carbon sheet has a high crystal quality and remarkable electronic properties. The charge carriers in graphene behave as massless relativistic particles enabling the study of quantum electrodynamics in a 'pencil trace'. In this thesis we look at the electronic properties of graphene in high magnetic fields. The quantum Hall effect observed in this two-dimensional (2D) system displays plateaus at half-integer values, in contrast to the integer quantum Hall effect in conventional 2D systems, and remains visible up to room temperature. This last observation is not only of major importance for the understanding of quantum phenomena but it also paves the way for high temperature applications of quantum physics in solid state materials, such as the high temperature quantum resistance metrology shown in this thesis. To fundamentally understand the origin of the half-integer quantum Hall effect we look at its temperature dependence and experimentally map out the underlying Landau level structure. The zeroth Landau level appears to be energetically very sharp compared to broad higher Landau levels and it splits into two levels at very low temperatures. Scaling experiments on the plateau-plateau transitions show details on the delocalization of charge carriers in the Landau level tails. Besides new materials, also new device geometries in existing materials can lead to new physics. We use local anodic oxidation with an atomic force microscope to create quantum rings in AlGaAs-heterostructures. In the quantum limit, at high magnetic fields, these rings show a new type of quantum oscillations which are shown to be related to the flux-quantized, discrete electronic size of the ring leading to a corresponding modulation of its two-point conductance