Majorana modes in time-reversal invariant s-wave topological superconductors

We present a time-reversal invariant $s$-wave superconductor supporting Majorana edge modes. The multi-band character of the model together with spin-orbit coupling are key to realizing such a topological superconductor. We characterize the topological phase diagram by using a partial Chern number sum, and show that the latter is physically related to the parity of the fermion number of the time-reversal invariant modes. By taking the self-consistency constraint on the $s$-wave pairing gap into account, we also establish the possibility of a direct topological superconductor-to-topological insulator quantum phase transition.