Quasiperiodic time dependent current in driven superlattices: distorted Poincare maps and strange attractors

Intriguing routes to chaos have been experimentally observed in semiconductor superlattices driven by an ac field. In this work, we analyze theoretically the time-dependent current in ac-driven superlattices. Experiments have shown that the current is quasiperiodic and its Poincar\'e maps are distorted and twisted for certain values of the ac intensity, at fixed dc voltage. This marks the appearance of very complex attractors and routes to chaos as the ac signal amplitude increases. We show that discrete well-to-well motions of domain walls during spiky high-frequency self-oscillations of the current play a crucial role in the origin of the experimentally observed distorted maps.