Engineering anomalous quantum Hall plateaus and antichiral states with ac fields

We investigate the ac electric field induced quantum anomalous Hall effect in honeycomb lattices and derive the full phase diagram for arbitrary field amplitude and phase polarization. We show how to induce antichiral edge modes as well as topological phases characterized by a Chern number larger than 1 by means of suitable drivings. In particular, we find that the Chern number develops plateaus as a function of the frequency, providing a time-dependent analog to the ones in the quantum Hall effect.