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
Burrello, M.; Fulga, I.C.; Alba, E.; Lepori, L.; Trombettoni, A. 2013
