Chaotic dynamics of electric-field domains in periodically driven superlattices

Abstract

Self-sustained time-dependent current oscillations under dc voltage bias have been observed in recent experiments on n-doped semiconductor superlattices with sequential resonant tunneling. The current oscillations are caused by the motion and recycling of the domain wall separating low-and high-electric-field regions of the superlattice, as the analysis of a discrete drift model shows and experimental evidence supports. Numerical simulation shows that different nonlinear dynamical regimes of the domain wall appear when an external microwave signal is superimposed on the dc bias and its driving frequency and driving amplitude vary. On the frequency-amplitude parameter plane, there are regions of entrainment and quasiperiodicity forming Arnol'd tongues. Chaos is demonstrated to appear at the boundaries of the tongues and in the regions where they overlap. Coexistence of up to four electric-field domains randomly nucleated in space is detected under ac ϩdc driving.

Forcing of chaos in semiconductor superlattices

“…For the pure dc case (a = 0) the SL exhibits undamped time-periodic current oscillations when the doping density ν, for our set of parameters, is between 0.07 and 0.17 [8]. We fix the doping inside these values at ν=0.1 and calculate the time evolution of the current for different values of the driving frequency ω and the driving amplitude a.…”

“…Note that to identify chaotic solutions and to distinguish between different regions in Fig. 1 we calculated the largest Lyapunov exponent λ 1 [8]. For chaotic regions we found λ 1 > 0, which indicates exponential divergence of nearby trajectories.…”

THE DYNAMICS AND HYSTERESIS IN GaAs/AlGaAs HETEROSTRUCTURE UNDER THE ACTION OF ELECTRIC AND MAGNETIC FIELDS

“…[5][6][7][8] The central motivation of these studies has been the possible application of these systems in real devices. They give rise to a rich variety of interesting nonlinear effects like self-sustained current oscillations, 9,10 frequency locking and chaotic dynamics 6,11,12 when they are associated with the external electric field and magnetic field. Especially, the current oscillations and chaotic transport 13 are found in the lower dimensionality because the domain walls move across a larger number of units in the array of the quantum dots (zero-dimensional superlattice) and one-dimensional quantum wires (1D supperlatice).…”

Chaotic dynamics in quantum-dot miniband superlattices

“…10,11 Recently, by involving novel electromagnetic radiation sources and coupling techniques the effect of THz radiation field on the nonlinear current-voltage characteristics of miniband superlattices has been investigated experimentally, including multiphotonassisted resonant tunneling, 6 negative absolute resistance, 7 and Shapiro steps on dc current-voltage curve. 8 Also, it is noted that when a miniband superlattice 14,15 or a sequential resonant tunneling superlattice [16][17][18][19] is subjected to a dcϩac field the superlattice system can produce an alternative mode of operation and lead to the transition between the synchronized current oscillation and various types of deterministic spatiotemporal chaos. The bifurcation scenario to chaos for electron transport was further studied experimentally in an incommensurately driven superlattice system.…”