Topological superconductors in multiple flavors: gapped and gapless in wires and 2DEGs

In this talk I will discuss new aspects of topological superconductivity I will first present a novel route to topological superconductivity in one dimension based on Josephson junctions in which two superconductors are separated by a two dimensional electron system with strong spin orbit coupling Remarkably in these systems a phase bias can induce a robust topological superconducting phase in the junction requiring no fine tuning of other parameters in contrast to the more commonly studied wire realization Moreover we identify a regime of parameters for which the system can tune itself into the topological phase via a first order phase transition In the second part of my talk I will address the question of the existence of a gapless topological superconducting phase in one dimension I will argue that in presence of time reversal symmetry this notion is well defined and show how it can be realized