Decoupled surface and bulk localization in higher order topological insulators

Three-dimensional higher-order topological insulators have both a gapped and topological bulk as well as a gapped and topological surface. It is also possible to separately tune the surface and the bulk gaps, and it's therefore a fascinating question to understand if they have separate stability conditions when subjected to various perturbations. In this talk we will discuss the effects of short-ranged quenched disorder on higher order topological insulators and show that the mobility gap of the surface can be closed separately from the bulk. While the clean limit would be described as a second order topological insulator, in the presence of finite disorder there are now gapless extended surface states. Aided by topological probes of this phase, we determine if these gapless surface states are topologically protected, and discuss the bulk topological classification. If time permits, results in two dimensions will also be discussed.