Abstract:

Topological phases of matter have attracted considerable attention recently. Following the discovery of topological insulators, it has been proposed that a close cousin called "topological superconductors" can also exist. However, concrete examples of such exotic superconductors are still lacking. In this talk, we provide a simple criterion to identify this topological phase in odd-parity, centrosymmetric superconductors. Next, we apply the theory to the very recently discovered superconductor Cu_xBi_2Se_3. This material is particularly interesting because it is, to the best of our knowledge, the first example of a superconductor with a 3D Dirac-like band structure by strong spin-orbit coupling. We classify all possible superconducting phases of this material, and identify one of them which is topologically non-trivial. By solving a phenomenological model, we find that this phase is realized in a significant part of the phase diagram. We also suggest experiments which can unambiguously identify this phase.