Topological phases and topological surface states of three-dimensional time-reversal invariant superconductors

We study topological phases of time-reversal invariant singlet superconductors in three spatial dimensions. In these particle-hole symmetric systems the topological phases are characterized by a winding number [1], similar to the $Z_2$ invariant of the $Z_2$ topological insulators. At a two-dimensional surface the topological properties of this quantum state manifest themselves through gapless surface states, that are robust against localization from random impurities respecting the discrete symmetries of the system. We construct a tight-binding model on the diamond lattice that realizes the topologically nontrivial phase and perform numerical studies of the winding number and the surface states of this model. \\[3pt] [1] A. P. Schnyder, S. Ryu, A. Furusaki, and A. W. W. Ludwig, arXiv:0803.2786 (PRB in press).