Parafermionic wires at the interface of chiral topological states

TL;DR

This paper investigates gapped interfaces between chiral topological states, revealing they support parafermionic excitations and behave as topological anyon Andreev reflectors, thus acting as topological parafermionic wires.

Contribution

It demonstrates that gapped interfaces between distinct chiral topological phases host parafermionic zero modes and act as topological anyon reflectors, introducing a new class of topological interfaces.

Findings

Gapped interfaces support parafermion zero modes.

Interfaces act as topological anyon Andreev reflectors.

Different topological orders can be connected via topological gapped interfaces.

Abstract

We explore a scenario where local interactions form one-dimensional gapped interfaces between a pair of distinct chiral two-dimensional topological states - referred to as phases 1 and 2 - such that each gapped region terminates at a domain wall separating the chiral gapless edge states of these phases. We show that this type of T-junction supports point-like fractionalized excitations obeying parafermion statistics, thus implying that the one-dimensional gapped interface forms an effective topological parafermionic wire possessing a non-trivial ground state degeneracy. The physical properties of the anyon condensate that gives rise to the gapped interface are investigated. Remarkably, this condensate causes the gapped interface to behave as a type of anyon "Andreev reflector" in the bulk, whereby anyons from one phase, upon hitting the interface, can be transformed into a combination of reflected anyons and outgoing anyons from the other phase. Thus, we conclude that while different topological orders can be connected via gapped interfaces, the interfaces are themselves topological.