Floquet Majorana fermions and parafermions in driven Rashba nanowires

We study a periodically driven nanowire with Rashba-like conduction and valence bands in the presence of a magnetic field. We identify topological regimes in which the noninteracting system hosts zero-energy bound states. We further investigate the effect of strong electron-electron interactions that give rise to parafermion zero energy modes hosted at the nanowire ends. The first setup we consider allows for topological phases by applying only static magnetic fields without the need of superconductivity. The second setup involves both superconductivity and time-dependent magnetic fields and supports topological phases without fine tuning of the chemical potential. Promising candidate materials are graphene nanoribbons due to their intrinsic particle-hole symmetry.