Topological superconductors are a novel type of superconductors that carry Majorana particles at their boundary. These surface states are equal superpositions of electrons and holes, and hence are... Show moreTopological superconductors are a novel type of superconductors that carry Majorana particles at their boundary. These surface states are equal superpositions of electrons and holes, and hence are their own anti-particles. There has been a recent surge of theoretical and experimental effort to realize these special particles in the lab. While first observations support the theoretical predictions, fail-safe experimental evidence for Majoranas is still needed. Part of the challenge is that due to their vanishing charge they are not easily detected electrically. The topic of this thesis is the proposal and study of electrical signatures of Majoranas that are present in spite of their charge neutrality. By applying scattering and random matrix theory we first examine their generic properties. With the tool of numerical simulations we then put our predictions to test on realistic systems. Show less
Topological phases of matter are exceptional because they do not arise due to a symmetry breaking mechanism. Instead they are characterized by topological invariants -- integer numbers that are... Show moreTopological phases of matter are exceptional because they do not arise due to a symmetry breaking mechanism. Instead they are characterized by topological invariants -- integer numbers that are insensitive to small perturbations of the Hamiltonian. As a consequence they support conducting surface states that are protected against disorder and other imperfections. Furthermore, a variety of unusual transport properties arise due to the presence of topology. In this work the interplay between topology and sample imperfections is investigated with a focus on transport phenomena. Show less
The theoretical foundation for the work reported here is provided by Landauer's scattering theory of electron transport. The three main ingredients of a scattering problem are (1) a set of... Show moreThe theoretical foundation for the work reported here is provided by Landauer's scattering theory of electron transport. The three main ingredients of a scattering problem are (1) a set of reservoirs that emit and absorb particles, (2) the particles themselves, that propagate as waves between the reservoirs and (3) a scatterer that obstructs free propagation. In this thesis two classes of problems are considered. The first class results when the physical quantities characterizing the reservoirs or the scatterer are not constant in time. The second class results when wave propagation is described by the Dirac equation rather than the Schroedinger equation, as is the case in a 2D form of carbon, called graphene. Show less
