Parafermion chain with 2π/k Floquet edge modes

We study parafermion chains with Z(k) 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 2 pi/3 modes in parameter space. We also show that the modes are robust to weak disorder. While the previously studied Z(2)-invariant Majorana systems possess a transparent weakly interacting limit 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.