Parafermionic Wires at the Interface of Chiral Topological States

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 pointlike fractionalized excitations obeying parafermion statistics, thus implying that the one-dimensional gapped interface forms an effective topological parafermionic wire possessing a nontrivial 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.

Figure 1

(a) An array of phases 1 (blue) and 2 (brown) showing the gapped interfaces along the $x$ direction (green). Each gapped interface constitutes an AC that acts as an anyon Andreev reflector whereby certain quasiparticles of phase 1 are transformed into quasiparticles of phase 2 (and vice versa) as they cross the interface; and quasiparticles can be reflected into different quasiparticle types. (b) Original chiral gapless edge states of the two phases. (c) Parafermion zero modes (black dots) are located at the $T$ junctions where the end points of the gapped interface define a domain wall between the chiral gapless edge modes of phases 1 and 2.