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

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.

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