Lattice Model of a Three-Dimensional Topological Singlet Superconductor with Time-Reversal Symmetry

Abstract

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 $\nu =\pm 2$. Disorder corresponds to a (nonlocalizing) random SU(2) gauge potential for the surface Dirac fermions, leading to a power-law density of states $\rho (ϵ)\sim {ϵ}^{1/7}$. The bulk effective field theory is proposed to be the ($3+1$)-dimensional SU(2) Yang-Mills theory with a theta term at $\theta =\pi$.