  Inducing topological transitions by a time-periodic perturbation offers a
route to controlling the properties of materials. Here we show that the
adiabatic preparation of a non-trivial state involves a selective population of
edge-states, due to exponentially-small gaps preventing adiabaticity. We
illustrate this by studying graphene-like ribbons with hopping's phases of
slowly increasing amplitude, as for, e.g., a circularly polarized laser slowly
turned-on. The induced currents have large periodic oscillations, but flow
solely at the edges upon time-averaging, and can be controlled by focusing the
laser on either edge. The bulk undergoes a non-equilibrium topological
transition, as signaled by the local Chern marker introduced by Bianco & Resta
in equilibrium. The failure of the adiabatic picture in presence of intraband
resonances is discussed.
