Abstract
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.
