Topological Phases in Nodeless Tetragonal Superconductors*

We compute the topological phase diagram of 2D tetragonal superconductors for the only possible nodeless pairing channels compatible with that crystal symmetry. Subject to a Zeeman field and spin-orbit coupling, we demonstrate that these superconductors show surprising topological features: non-trivial high Chern numbers, massive edge states, and zero-energy modes out of high symmetry points, even though the edge states remain topologically protected. Interestingly, one of these pairing symmetries, d+id, has been proposed to describe materials such as water-intercalated sodium cobaltates, bilayer silicene or highly doped monolayer graphene.