Random-matrix theory and stroboscopic models of topological insulators and superconductors

Abstract

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 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.