Amorphous topological insulators in theory and experiment

A central goal of contemporary material science is to find new, robust, and universal phenomena that can be technologically useful. Topological phases of matter are one of the most robust phases of matter, and host such potential. However, these phases are often predicted using crystal symmetries, although topological phases don't rely on them to exist. By doing so seem forced to exclude all amorphous materials, which are ubiquitous in technology and can display properties that surpass those of crystals. In this talk I will review how topological phases have been recently shown to emerge in non-crystalline systems, notably in amorphous systems, both in experiment and theory. I will present a way to define symmetry indicators for amorphous topology, and discuss signatures of amorphous topological phases in amorphous bismuth selenide. At the end, I will touch upon the many remaining open questions that remain unanswered, with the aim of sparking discussion.