Effects of spin symmetry breaking in topological insulators

Topological insulators are one of the most thoroughly investigated systems in condensed matter physics over the last years. In these systems, a prominent role is inevitably taken by time-reversal symmetry, which leads to Kramers theorem and symmetry protected edge states. However, Kramers theorem does not imply that the spin-z component is a good quantum number. This thesis sheds light on several phenomena that appear in topological insulators without this spin conservation, for example in the context of generic helical liquids. A topological insulator strip is examined which allows for forward- and backscattering between the edge states. This results in a measurable effect on the conductance. Furthermore, interfaces between edge-state regions with induced superconductivity, strong interactions and broken spin conservation are analyzed. Calculations using Luttinger liquid theory reveal parafermions at these interfaces. Finally, disorder in the Kane-Mele model in combination with Rashba spin-orbit coupling is studied. It is found that disorder can lead to a topological phase, the topological Anderson insulator, even though the clean system is a trivial insulator.