Graphene pn junction

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-Perot 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-Perot 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.

Klein tunneling in graphene under substrate electric field

Terahertz plasmons and magnetoplasmons propagating along electrically and chemically doped graphene p-n junctions are investigated. It is shown that such junctions support non-reciprocal magnetoplasmonic modes which get concentrated at the middle of the junction in one direction and split away from the middle of the junction in the other direction under the application of an external static magnetic field. This phenomenon follows from the combined effects of circular birefringence and carrier density non-uniformity. It can be exploited for the realization of plasmonic isolators.

We show how a superconducting region (S) sandwiched between two normal leads\n(N), in the presence of barriers, can act as a lens for propagating electron\nand hole waves by virtue of the so- called crossed Andreev reflection (CAR).\nThe CAR process which is equivalent to the Cooper pair splitting into the two N\nelectrodes provides a unique possibility of constructing entangled electrons in\nsolid state systems. When electrons are locally injected from an N lead, due to\nthe CAR and normal reflection of quasiparticles by the insulating barriers at\nthe interfaces, sequences of electron and hole focuses are established inside\nanother N electrode. This behavior originates from the change of momentum\nduring electron-hole conversion beside the successive normal reflections of\nelectrons and holes due to the barriers. The focusing phenomena studied here is\nfundamentally different from the electron focusing in other systems like\ngraphene pn junctions. In particular due to the electron-hole symmetry of\nsuperconducting state, the focusing of electrons and holes are robust against\nthermal excitations. Furthermore the effect of superconducting layer width, the\ninjection point position, and barriers strength is investigated on the focusing\nbehavior of the junction. Very intriguingly, it is shown that by varying the\nbarriers strength, one can separately control the density of electrons or holes\nat the focuses.\n