We have theoretically studied chaotic dynamics of ballistic electrons in GaAs-based quantum dot miniband superlattices under the influence of an intense terahertz electromagnetic radiation, using the balance equations coupling the self-consistent field equation. The electron motion that incorporates the influence of the selfconsistent field within the miniband superlattices produces a cooperative nonlinear oscillatory mode, which can lead to complicated chaotic dynamics with the driving amplitude, driving frequency, and the relaxation frequency of the external circuit as the controlling parameters. The temporal behaviors of the solutions of the nonlinear dynamical system are analyzed by using different methods, such as phase portrait, power spectra, first return map, and Lyapunov exponent. The two-dimensional driving amplitude-frequency phase diagrams are calculated with a realistic treatment of scattering contributions by impurity, acoustic phonon, and polaroptic phonons in order to visualize the chaotic regions in the parameter space. The dependence of chaotic regions on the superlattice parameter, lattice temperature, and external circuit condition, is extensively investigated, which provides useful guidance of controlling chaos in realistic device applications.

Phenomenological theory of tunnel emitter transit time oscillators for the terahertz rangeWe present a model calculation of hole current oscillations in doped p ϩ pp ϩ ballistic diodes using the nonparabolic balance-equation theory and a time-dependent drift-diffusion model. Such an oscillation originates from a negative effective mass ͑NEM͒ region in the hole dispersion relation. In the present balance-equation calculation, we consider the scatterings by hole-impurity, hole-acoustic phonon, hole-polar-phonon, and hole-nonpolar-phonon-hole interactions, and yield a ''N-shape'' velocity-field relation, which are quite different from the two-valley results for electrons in bulk GaAs. We provide a detailed analysis of the resulting oscillations as a function of the applied voltage, base length, base doping, and the dispersion relation. Typical frequencies for a 0.2 m structure NEM oscillator are in the terahertz range. Qualitative agreement is obtained between the present calculations and the existing Boltzmann results.

We report on a detailed theoretical study of current self-oscillations and chaotic dynamics in negative effective mass ͑NEM͒ p ϩ pp ϩ diodes driven by dc and ac electric fields with a terahertz ͑THz͒ frequency. An ''N-shaped'' velocity-field relation is yielded by using the nonparabolic balance-equation theory with a realistic treatment of carrier scatterings by impurity, acoustic phonon, and optic phonon. The dependence of the self-oscillating mode and its frequency on the dc bias, doping concentration, and lattice temperature is examined in detail. The THz-driven p ϩ pp ϩ NEM diodes can produce a cooperative nonlinear oscillatory mode which leads to very complicated chaotic dynamics with the dc bias, ac amplitude, and ac frequency as the controlling parameters. The transitions between the periodic and chaotic states are carefully studied by different chaos-detecting methods, such as phase portrait, Poincaré bifurcation diagram, power spectrum, and first return map. The resulting power spectrum bifurcation diagram displays a very complicated mosaic structure with a self-similar emergence of high-order mixing frequencies.

Articles you may be interested inOn the modeling and nonlinear dynamics of autonomous Silva-Young type chaotic oscillators with flat power spectrum Chaos 24, 043134 (2014); 10.1063/1.4903313 Phenomenological theory of tunnel emitter transit time oscillators for the terahertz rangeWe report on a theoretical investigation of power spectrum dynamics in negative-effective-mass ͑NEM͒ p ϩ pp ϩ oscillators under the influence of terahertz ͑THz͒ electromagnetic radiation. Possible types of transport states ͑periodic or chaotic͒ and transitions between them are examined with the intensity and frequency of the radiation as controlling parameters. When the driving frequency is fixed to the self-oscillating frequency times the inverse Golden ratio, the resulting power spectrum pattern displays a very complex mosaic scenario with a self-similar emergence of high-order mixing frequencies.

We have theoretically studied terahertz-driven nonlinear dynamics of a quantum-dot miniband superlattice with a realistic treatment of the scatterings by impurity, acoustic phonon, and polar optic phonons. The electron motion that incorporates the influence of the self-consistent field within the miniband superlattice produces a cooperative nonlinear oscillatory mode, which can lead to complicated chaotic dynamics with the driving amplitude, driving frequency, and the relaxation frequency of the external circuit as the controlling parameters. The two-dimensional driving amplitude−frequency phase diagrams are calculated, which distinguishes the chaotic region from the periodic region. The present result provides a useful guidance of controlling chaos in the realistic superlattice device.