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We study a periodically driven nanowire with Rashba-like conduction andvalence bands in the presence of a magnetic field. We identify topologicalregimes in which the system hosts zero-energy Majorana fermions. We furtherinvestigate the effect of strong electron-electron interactions that give riseto parafermion zero energy modes hosted at the nanowire ends. The first setupwe consider allows for topological phases by applying only static magneticfields without the need of superconductivity. The second setup involves bothsuperconductivity and time-dependent magnetic fields and allows one to generatetopological phases without fine-tuning of the chemical potential. Promisingcandidate materials are graphene nanoribbons due to their intrinsicparticle-hole symmetry.

Floquet Majorana and Para-Fermions in Driven Rashba Nanowires