Transport and subgap states in superconducting heterostructures of effective Dirac systems

In recent years, effective Dirac systems have received a lot of attention in solid state physics. These are systems whose dispersion can effectively be described by a Dirac cone, the most prominent examples being graphene and topological insulators (TIs). These systems exhibit intriguing phenomena---for example, TIs can host perfectly transmitted modes or, in conjunction with superconductors, Majorana zero modes.This work deals with superconducting heterostructures of both of the aforementioned materials and examines transport phenomena as well as the formation of sub-gap states in such systems: In the first chapter, superconducting bilayer graphene with a chemisorbed adatom is investigated and the existence of peculiar sub-gap states, so-called Yu-Shiba-Rusinov states, is shown. The second chapter deals with T junction devices made out of three-dimensional (3D) TI nanowires.Together with proximity induced superconductivity in one arm and external magnetic fields, this setup allows for the occurrence of crossed Andreev reflection, including perfect crossed Andreev reflection, and negative nonlocal conductance. In the third chapter, Josephson junctions of 3D TI nanowires are investigated. The origin of unusual, experimentally observed supercurrent oscillations in dependence of a parallel magnetic field is examined in a semiclassical analysis.