Topological defects in symmetry-protected topological phases

The phenomena associated with topological defects have had an enormous impact in condensed matter physics for more than 50 years. Beginning with an understanding of topological defects in ordered phases, the field is now sharply focused on defects in topological phases of matter. In this review, we cover aspects of defects in conventional ordered media, bound states on defects in strong topological insulators (TIs) and topological superconductors (TSCs), and bound states on defects in crystalline topological phases protected by spatial symmetries. As a unifying theme, we present the structure of many types of index theorems that relate the existence of topological bound states to the bulk topology of the host phase of matter and the topological charge of the relevant defects.