Lattice model of a three-dimensional topological singlet superconductor with time-reversal symmetry

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 ν. At the surface the topological properties of this quantum state manifest themselves through the presence of ν 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 ν=±2. Disorder corresponds to a (nonlocalizing) random SU(2) gauge potential for the surface Dirac fermions, leading to a power-law density of states ρ ∼ 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 θ=π.