Translation symmetry-enriched toric code insulator

TL;DR

This paper introduces a novel two-dimensional insulator with toric code topological order enriched by translation symmetry, realized through disordering a weak topological superconductor, and analyzes its anyonic excitations and symmetry properties.

Contribution

It constructs a translation symmetry-enriched toric code insulator from a coupled-wire model and provides a detailed analysis of its anyon spectrum and braiding statistics.

Findings

Identifies two types of visons with constrained motion due to fractional Josephson effect.

Shows the mutual semionic braiding statistics of visons related by translation symmetry.

Provides a band-theoretic framework for understanding fractionalization in weak topological phases.

Abstract

We introduce a two-dimensional electronic insulator that possesses a toric code topological order enriched by translation symmetry. This state can be realized from disordering a weak topological superconductor by double-vortex condensation. It is termed the toric code insulator, whose anyonic excitations consist of a charge-$e$ chargon, a neutral fermion and two types of visons. There are two types of visons because they have constrained motion as a consequence of the fractional Josephson effect of one-dimensional topological superconductor. Importantly, these two types of visons are related by a discrete translation symmetry and have a mutual semionic braiding statistics, leading to a symmetry-enrichment akin to the type in Wen's plaquette model and Kitaev's honeycomb model. We construct this state using a three-fluid coupled-wire model, and analyze the anyon spectrum and braiding statistics in detail to unveil the nature of symmetry-enrichment due to translation. We also discuss potential material realizations and present a band-theoretic understanding of the state, fitting it into a general framework for studying fractionalizaton in strongly-interacting weak topological phases.