Parafermion chain with $2\pi/k$ Floquet edge modes

TL;DR

This paper investigates $ ext{Z}_3$ parafermion chains under periodic driving, revealing new Floquet edge modes at nontrivial quasienergies, mapping their phase diagram, and demonstrating robustness to disorder, thus extending understanding beyond Majorana systems.

Contribution

It introduces the existence of $2 ext{pi}/3$ Floquet edge modes in driven $ ext{Z}_3$ parafermion chains and explores their phase diagram and robustness, advancing the study of strongly interacting topological phases.

Findings

Discovery of $2 ext{pi}/3$ Floquet edge modes in $ ext{Z}_3$ chains.

Phase diagram mapping of these modes in parameter space.

Robustness of modes to weak disorder.

Abstract

We study parafermion chains with $\mathbb{Z}_k$ symmetry subject to a periodic binary drive. We focus on the case $k=3$. We find that the chains support different Floquet edge modes at nontrivial quasienergies, distinct from those for the static system. We map out the corresponding phase diagram by a combination of analytics and numerics, and provide the location of $2\pi/3$ modes in parameter space. We also show that the modes are robust to weak disorder. While the previously studied $\mathbb{Z}_2$-invariant Majorana systems posesses a transparent weakly interacting case where the existence of a $\pi$-Majorana mode is manifest, our intrinsically strongly interacting generalization demonstrates that the existence of such a limit is not necessary.