  An intense laser field in the high-frequency regime drives carriers in
graphene nanoribbons (GNRs) out of equilibrium and creates
topologically-protected edge states. Using Floquet theory on driven GNRs, we
calculate the time evolution of local excitations of these edge states and show
that they exhibit a robust dynamics also in the presence of very localized
lattice defects (atomic vacancies), which is characteristic of topologically
non-trivial behavior. We show how it is possible to control them by a modulated
electrostatic potential: They can be fully transmitted on the same edge,
reflected on the opposite one, or can be split between the two edges, in
analogy with Hall edge states, making them promising candidates for
flying-qubit architectures.
