Electron optics in ballistic graphene

This thesis is centered on the experimental observation of electron-optics phenomena in graphene. In Chapter 2, graphene is introduced and the ability to form p-n junctions, with particular regard to electron optics experiments, is discussed. Since ballistic transport is crucial for this subject, the question “when is graphene
clean?” is posed in Chapter 3, where different characterization methods are compared and linked to devices of this thesis. The experimental part begins with a description of the fabrication methods in Chapter 4, which is ‘spiced’ with information about complex device structures, superconducting contacts and the use of
CVD-grown graphene. Chapter 5 describes an interference experiment over a distance of 2 μm, where we used p-n junctions to tune and manipulate ballistic Fabry-Pérot resonances. The peculiar angular dependence of the transmission allows to filter out large propagation
angles. Thus, the p-n interface can be used to form coherent planar waves, i.e. it acts in this case similar to an optical polarization filter. This filtering effect is crucial for the high visibility of Fabry-Pérot resonances we achieved in p-n and p-n-p devices.
A perpendicular magnetic can be viewed as a lense which bends and focuses electrons. Along a p-n interface, this leads to trajectories that curve back and forth. Such trajectories are called snake states and they give rise to magneto-conductance oscillations. In terms of optics, these oscillations occur since the focal point of the
magnetic lense can be either on the left- or on the right side of the p-n cavity. We demonstrate the observation of snake states in Chapter 6.
Furthermore, the p-n interface can be viewed as a mirror that is reflective or semitransparent, depending on the angle of incidence. By using such mirrors it is possible to create channels for electrons that are described in a similar way to optical waveguides. However, the refraction can be tuned dynamically and p-n interfaces can be exploited to create additional confinement. We use this to guide electrons in an electrostatic channel in Chapter 7 where we observe signatures of quasi 1-dimensional transport.
The thesis is complemented in Chapter 8 with a device that allows to explore the properties of a tilted p-n interface that acts as a beam-splitter.