Disorder and topological superconductivity

Topological superconductors have the potential to be one of the simplest platforms to demonstrate topologically protected degeneracy because they are effectively non-interacting phases. Proposals such as those based on semiconductor-superconductor hybrids, topological superconductors, quantum Hall gases and iron superconductors provide a range of options to engineer such platforms. Unfortunately, despite the nominal stability of topological superconductors to weak disorder, realizing a topological phase often requires an effective one dimensional scattering rate below the induced superconducting gap. In this talk I will review how this principle restricts various platforms such as those based on semiconductor nanowires, quantum Hall systems and line Josephson junctions. I will also discuss transport experiment proposals to identify device issues from disorder and device imperfections.