Manipulation of band electrons with a rectangular-wave electric field

We study the propagation of an electron in a superlattice under the action of a rectangular-wave electric field. Exact results for any initial distribution and long-range hopping couplings are obtained. Total collapse of the quasi-energy spectrum is found to take place at suitably chosen field parameters, which leads to the transition between localization and delocalization. Moreover, this localization/delocalization behaviour persists even if long-range hoppings are taken into account. The transport property of the system is also investigated where the signatures of the transition between localization and delocalization as well as fractional Wannier-Stark ladders are manifested.