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.
Categories: cond-mat.stat-mech