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
This thesis deals with characterizing topological phases as well as the transitions between them, focusing on transport properties and the effects of disorder. In Chapters 2 and 3 we derived... Show moreThis thesis deals with characterizing topological phases as well as the transitions between them, focusing on transport properties and the effects of disorder. In Chapters 2 and 3 we derived scattering matrix expressions for the topological invariants of systems. This approach is oftentimes numerically easier to evaluate than Hamiltonian expressions. In Chapter 4 we predict novel transport features of the quantum Hall plateau transition, and efficiently estimate the associated critical exponent. In Chapter 5 we examine the universal properties of phase transitions in two-dimensional helical topological superconductors. We compute the critical exponents characterizing the divergence of the localization length, as well as the critical conductance. In Chapter 6, we model a one-dimensional topological superconductor in a bottom-up fashion, as an array of coupled quantum dots. We show how to tune this system deep within the non-trivial phase, with well localized Majorana bound states at its ends. In Chapter 7, we find a new class of disordered topological insulators protected not by an exact symmetry, but by an average symmetry of the disordered ensemble. This greatly increases the range of non-trivial phases, as every topological phase transition gives rise to infinitely many higher-dimensional topological phases 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
This thesis addresses a variety of systems in which the diffusion is anomalous, mainly motivated by recent experimental developments. The main topics discussed are: * We look at the consequences... Show moreThis thesis addresses a variety of systems in which the diffusion is anomalous, mainly motivated by recent experimental developments. The main topics discussed are: * We look at the consequences that subdiffusion on fractals has for shot noise. * The effects correlations have on superdiffusion in one dimension are examined. * We develop and demonstrate the usefulness of a method to simulate the anomalous diffusion of Dirac fermions in a computer. * A spin precession experiment in topological insulators is proposed and analyzed. * We present the mechanism for the conversion of an ordinary insulator into a topological insulator by disorder which was reported in the literature, on the basis of computer simulations, but had remained unexplained. Show less
