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Abstract

We study parafermion chains with Zk symmetry subject to a periodic binary drive, focusing 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 2π/3 modes in parameter space. We also show that the modes are robust to weak disorder. While the previously studied Z2-invariant Majorana systems possess a transparent weakly interacting limit where the existence of a π-Majorana mode is manifest, our intrinsically strongly interacting generalization demonstrates that the existence of such a limit is not necessary.