Fractionalization and Interaction in Topological Superconductors and Insulators

We present a study of novel topological order in three dimensional (3+1D) topological superconductors and fractional topological insulators. Such topological order occurs when the surface is gapped due to the presence of many-body interactions that respect the time-reversal symmetry.

3+1D time reversal symmetric topological superconductors are characterized by gapless (massless) Majorana fermions on its surface. They are robust against any time reversal symmetric single-body perturbation weaker than the bulk energy gap. We mimic this gapless surface by coupled wire models in two spatial dimensions. We show modified models with additional time-reversal symmetric many-body interaction, that gives energy gaps to all low energy degrees of freedom. We used the embedding trick using Wess-Zumino-Witten conformal field theory to find such interacting model Hamiltonian. We show the gapped models generically carry non-trivial topological order and support \textit{anyons}. Using these anyons and their condensation process, we show the topological order has a 32-fold periodicity.

Fractional topological insulators (FTI) are electronic topological phases in 3+1D enriched by the time reversal and charge U(1) conservation symmetries. We focus on the simplest series of fermionic FTI, whose bulk quasiparticles consist of deconfined partons. Theses partons carry fractional electric charges in integral units of e*=e/(2n+1) and couple to a discrete $\mathbf{Z}_{2n+1}$ gauge theory. We propose massive symmetry preserving or breaking FTI surface states. Combining the long-ranged entangled bulk with these topological surface states, we deduce the novel topological order of quasi-(2+1) dimensional FTI slabs as well as their corresponding edge conformal field theories.