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We study topological phases of time-reversal invariant singlet superconductors in three spatial dimensions. In these systems the topological phases are characterized by an even-numbered winding number nu. At the surface the topological properties of this quantum state manifest themselves through the presence of nu flavors of gapless Dirac fermion surface states, which are robust against localization from random impurities. We construct a lattice tight-binding model that realizes a topologically nontrivial phase, in which nu=+/-2. Disorder corresponds to a (nonlocalizing) random SU (2) gauge potential for the surface Dirac fermions, leading to a power-law density of states rho () approximately ;1/7. The bulk effective field theory is proposed to be the (3+1) -dimensional SU (2) Yang-Mills theory with a theta term at theta=pi.
Schnyder et al. (Fri,) studied this question.