Transport and subgap states in superconducting heterostructures of effective Dirac systems

This thesis deals with superconducting heterostructures of both of the aforementioned materials and examines transport phenomena as well as the formation of subgap states in such systems: In the first chapter, superconducting bilayer graphene with a chemisorbed adatom is investigated and the existence of peculiar subgab states, so-called Yu-Shiba-Rusinov states, is shown. The second chapter deals with T junction devices make out of three-dimensional (3D) TI nanowires. Together with proximity induced superconductivity in one arm and external magnetic fields, this setup allows for the occurence of crossed Andreev reflection, including perfect crossed Andreev reflection, and negative nonlocal conductances. 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 examinated in a semiclassical analysis.