Z4 parafermionic edge modes in an interacting periodically driven topological superconductor

I theoretically present a means to generate Z₄ parafermion edge modes without fractional quantum Hall systems or complicated interactions. My proposal only requires a few simple ingredients, i.e., p-wave superconductivity, magnetic field, fermionic Hubbard interaction, and periodic driving, all of which are compatible with current technology. I further show that the obtained parafermions, which can be analytically derived at special parameter values, have no static counterpart and arise from the interplay between an interaction effect and periodic driving. Strong numerical evidence suggests that these exotic quasiparticles are robust against variations in parameter values and spatial disorder. My construction not only serves as an excellent starting point for topological quantum computing beyond Majorana fermions, but also provides an intuitive mechanism of nonequilibrium quantum many-body phases.