Synchronization and chaos in miniband semiconductor superlattices

Abstract

Spatiotemporal synchronization and chaos in miniband semiconductor superlattices are theoretically investigated by using the time-dependent hydrodynamic balance equations. When driven by a dc and an ac bias voltages in the form of $V_{\mathrm{dc}}{+V}_{\mathrm{ac}}\sin \left(2\mathrm{}\pi f_{\mathrm{act}}\right),$ the miniband superlattice constructs a typical nonlinear dynamic system with the dc bias, ac amplitudes, and the ac frequency as the control parameters. The transitions between chaotic and periodic states of the spatiotemporal solutions are examined in detail. It is found that, in the case of large-amplitude ac signal, the solution is attracted to the period-one orbit synchronized with the ac frequency, and the current-voltage curve yielded by the time average of the synchronized solutions exhibits the microwave-radiation-induced dc current suppression. A good agreement is obtained between the calculated dc current and the recent experiment for a GaAs/AlAs miniband superlattice. When the amplitude of the ac voltage decreases the solutions become period-doubling or chaotic with a quite complex bifurcation scenario.