Anomalous Quasiparticle Symmetries and Non-Abelian Defects on Symmetrically Gapped Surfaces of Weak Topological Insulators

TL;DR

This paper demonstrates that the surfaces of weak topological insulators can be symmetrically gapped to host Abelian topological order, with dislocations forming non-Abelian defects trapping parafermion zero modes, revealing novel symmetry and defect phenomena.

Contribution

It introduces a mechanism for gapping weak topological insulator surfaces with symmetry-preserving interactions and uncovers non-Abelian defects associated with dislocations.

Findings

Boundaries can be gapped with Abelian order while preserving symmetry.

Symmetries act non-trivially on quasiparticles, changing anyon types.

Dislocations trap non-Abelian parafermion zero modes.

Abstract

We show that boundaries of 3D weak topological insulators can become gapped by strong interactions while preserving all symmetries, leading to Abelian surface topological order. The anomalous nature of the weak topological insulators manifests itself in a non-trivial action of symmetries on the quasiparticles; most strikingly, translations change the anyon types in a manner impossible in strictly 2D systems with the same symmetry. As a further consequence, screw dislocations form non-Abelian defects that trap $\mathbb{Z}_4$ parafermion zero modes.