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 distrib ution and long-range hopping couplings are obtained. Total collapse of the quasi-energy spectrum is found to take place at suitably chosen field param eters, which leads to the transition between localization and delocalizatio n. Moreover, this localization/delocalization behaviour persists even if lo ng-range hoppings are taken into account. The transport property of the sys tem is also investigated where the signatures of the transition between loc alization and delocalization as well as fractional Wannier-Stark ladders ar e manifested.