Exactly soluble model of boundary degeneracy

TL;DR

This paper presents an exactly solvable model demonstrating boundary topological degeneracy in Abelian fractional quantum spin Hall states, which can be realized experimentally without superconductivity, using simple gating and spin-mixing.

Contribution

The authors construct and solve an exactly soluble microscopic model showing boundary degeneracy in quantum spin Hall states, expanding understanding of topological degeneracy mechanisms.

Findings

Explicit string operators for boundary degeneracy are derived.

The model suggests a feasible experimental setup for observing boundary degeneracy.

The approach does not require superconducting proximity effects.

Abstract

We investigate the topological degeneracy that can be realized in Abelian fractional quantum spin Hall states with multiply connected gapped boundaries. Such a topological degeneracy (also dubbed as "boundary degeneracy") does not require superconducting proximity effect and can be created by simply applying a depletion gate to the quantum spin Hall material and using a generic spin-mixing term (e.g., due to backscattering) to gap out the edge modes. We construct an exactly soluble microscopic model manifesting this topological degeneracy and solve it using the recently developed technique [S. Ganeshan and M. Levin, Phys. Rev. B 93, 075118 (2016)]. The corresponding string operators spanning this degeneracy are explicitly calculated. It is argued that the proposed scheme is experimentally reasonable.