# Surfaces and Slabs of Fractional Topological Insulator Heterostructures

## TL;DR

This paper investigates the surface states and topological order of fractional topological insulator heterostructures, revealing new phases and edge theories in these complex quantum systems.

## Contribution

It introduces novel surface states and topological orders for fractional topological insulators, expanding understanding of their boundary phenomena and quasiparticle excitations.

## Key findings

- Identification of symmetry-preserving and breaking surface states.
- Derivation of topological order for FTI slabs.
- Characterization of edge conformal field theories.

## Abstract

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.