  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, novel 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 new 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 novel
optoelectronic and quantum computing devices.
