Interplay between intrinsic and emergent topological protection on interacting helical modes

TL;DR

This paper explores how interactions affect topological protection in helical edge modes of a 2D topological insulator, revealing phases with trivial insulator behavior and enhanced topological properties with emergent symmetries.

Contribution

It demonstrates the emergence of a novel topological phase with $ ext{Z}_3$ symmetry and protected conductance due to interactions, extending understanding of topological protection beyond non-interacting systems.

Findings

Interaction induces a trivial insulator phase with zero conductance.

A new phase with $ ext{Z}_3$ parafermions and conductance $3e^2/h$ emerges.

Emergent $ ext{Z}_3$ symmetry enhances topological protection.

Abstract

The interplay between topology and interactions on the edge of a two dimensional topological insulator with time reversal symmetry is studied. We consider a simple non-interacting system of three helical channels with an inherent $\mathbb{Z}_{2}$ topological protection, and hence a zero-temperature conductance of $G=e^2/h$. We show that when interactions are added to the model, the ground state exhibits two different phases as function of the interaction parameters. One of these phases is a trivial insulator at zero temperature, as the symmetry protecting the non-interacting topological phase is spontaneously broken. In this phase, there is zero conductance $G=0$ at zero-temperature. The other phase displays enhanced topological properties, with the neutral sector described by a massive version of $\mathbb{Z}_{3}$ parafermions. In this phase, the system at low energies displays an emergent $\mathbb{Z}_3$ symmetry, which is not present in the lattice model, and has a topologically protected zero-temperature conductance of $G=3e^2/h$. This state is an example of a dynamically enhanced symmetry protected topological state.