Surfaces and slabs of fractional topological insulator heterostructures

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

Figure 1

Summary of the QP and gauge flux content in FTI slabs. A pair of ${\mathrm{Pf}}^{*}$ FTI slabs are merged into a fractional Chern FTI slab $\mathcal{F}$ by gluing the two TR symmetric $\mathcal{T}-{\mathrm{Pf}}^{*}$ surfaces. Directed bold lines on the front surface are chiral edge modes of the ${\mathrm{Pf}}^{*}$ and $\mathcal{F}$ FTI slabs.