Superconductivity at Low Density and its Relation to Superconductivity in Topological Materials
Topological superconductors are one of the most exotic states predicted for electronic matter. Recently a new family of superconductors, which appear to be promising candidates of these exotic states, have been discovered in material with topological band structures. The organizing idea is doping a topological insulator or semimetal with the hope that it will become superconducting and that the topological properties of the band structure will somehow follow into the superconducting state. This concept is working surprisingly well. Notable examples are the doped TI, Bi2Se3, and the half-Heusler semi metals (such as YPtBi). However, a major challenge for superconductivity in topological materials is that it must emerge in a system with low density, as topology is only important at in this limit (close to band touchings). Thus, a key to understanding superconductivity in these materials is to understand how can superconductivity emerge in a system with low carrier concentration. In this talk i will touch upon three such mechanisms with application to materials such as YPtBi and elemental bismuth. I will discuss mechansisms to get non-trivial pairing based on strong spin-orbit coupling.