Matt Foster, Rice University

Topological quantum materials systems exhibit "protected" boundary modes with unusual properties--the quantum Hall effect and topological insulators being the archetypal examples. Topological superconductors (TSCs) could enable a robust form of topological quantum computation; despite progress, ongoing experiments in synthetic platforms (such as semiconductor wire networks) have yet to furnish unambiguous signatures of topology. I will discuss the hunt for an alternative: bulk solid-state TSCs These can host gapless "Majorana fluids" at the sample boundary, which should provide a host of falsifiable experimental signatures. I will give a broadbrush overview of TSCs, starting with a basic introduction to superconductivity and topology. Then I'll discuss boundary-mediated electromagnetic signatures (Meissner effect, topological anomalous skin effect) which could be used to efficiently screen material candidates. If there is any remaining time, I will describe how even weak disorder transfigures all boundary wave functions in a TSC into quantum fractals, of the type observed in the Hofstadter butterfly, and how this "spectrum-wide criticality" might actually play a key role in a non-topological system of perennial interest: the high-Tc cuprates.