Surfaces and Slabs of Fractional Topological Insulator Heterostructures

Fractional topological insulators (FTI) are electronic topological phases in $(3+1)$ dimensions enriched by time reversal (TR) and charge $U(1)$ conservation symmetries. We focus on the simplest series of fermionic FTI, whose bulk quasiparticles consist of deconfined partons that carry fractional electric charges in integral units of $e^\ast=e/(2n+1)$ and couple to a discrete $\mathbb{Z}_{2n+1}$ 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.