Engineering Dirac states in graphene: Coexisting type-I and type-II Floquet-Dirac fermions

The coupling of monochromatic light fields and solids introduces nonequilibrium Floquet states, offering opportunities to create and explore new topological phenomena. Using combined first-principles and Floquet analysis we show that one can freely engineer Floquet-Dirac fermions (FDFs) in graphene by tuning the frequency and intensity of linearly polarized light. Not only type-II FDFs are created, but they also coexist with type-I FDFs near the Fermi level. Intriguingly, topologically nontrivial edge states connecting type-I and type-II Floquet-Dirac points emerge in photodriven graphene, providing an ideal channel to realize electron transport between the two types of Dirac states. Simulating time- and angle-resolved photoelectron spectroscopy suggests that the coexisting state of type-I and type-II fermions is experimentally accessible. This work implies that a rich FDF phenomenon can be engineered in atomically thin graphene, hinting for developments of optoelectronic and quantum computing devices.