  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 system hosts zero-energy Majorana fermions. 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 allows one to generate
topological phases without fine-tuning of the chemical potential. Promising
candidate materials are graphene nanoribbons due to their intrinsic
particle-hole symmetry.
