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

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.

6 pages, 4 figures

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• Fermionic Lieb-Schultz-Mattis Theorems and Weak Symmetry-Protected Phases
• Pairing in Luttinger Liquids and Quantum Hall States
• Coupled-wire constructions: a Luttinger liquid approach to topology
• Bulk characterization of topological crystalline insulators: stability under interactions and relations to symmetry enriched U(1) quantum spin liquids
• Quantum Hall hierarchy from coupled wires
• Microscopic Theory of Surface Topological Order for Topological Crystalline Superconductors
• Bosonic Analogue of Dirac Composite Fermi Liquid
• Space group constraints on weak indices in topological insulators
• Coupled Wire Model of Z4 Orbifold Quantum Hall States
• Classification and surface anomaly of glide symmetry protected topological phases in three dimensions
• Translation symmetry-enriched toric code insulator
• Gapping fragile topological bands by interactions
• Quantum spin liquids bootstrapped from Ising criticality in Rydberg arrays