Non-Abelian order in s-wave superconductors: Phases and quantum transitions*

Non-Abelian topological superconductivity has been predicted to occur in s-wave superconductors with a sizable spin-orbit (SO) coupling. As is now well known, such a system can be used for topological quantum computation. When an external Zeeman splitting crosses a critical value, the system passes from a regular, non-topological, superconducting phase to a topological one. On the other hand, in the absence of SO coupling this critical value corresponds to the Zeeman splitting above which the system loses its s-wave superconductivity. We are thus led to the paradoxical conclusion that the topological superconducting phase appears in a parameter regime at which the system actually is non- superconducting in the absence of SO coupling. In this work we resolve this paradox.