Explosive Bifurcation to Chaos in Weakly Coupled Semiconductor Superlattices

Abstract

The bifurcation scenario to chaos has been studied for vertical transport in an incommensurately driven superlattice system. With increasing driving amplitude, quasiperiodic, frequency-locked, and chaotic oscillations are identified by using Poincaré maps, which show a variety of attractors in the chaotic regime. The dimension of the attractor is abruptly increased in the transition process, i.e., the bifurcation between frequency locking and chaos is explosive. However, the bifurcation pattern depends strongly on the applied dc bias, providing clear evidence that the system is spatially inhomogeneous in the vertical direction. [S0031-9007(98)06837-9] PACS numbers: 73.50.Fq, 73.20.Dx, 73.40.Gk Spatiotemporal chaos has been studied both experimentally and theoretically in liquid and chemical systems [1], in coupled map lattices [2], as well as in solid-state systems [3][4][5][6][7]. When the investigated system is driven by an incommensurate frequency, i.e., the ratio of the natural frequency and the driving frequency is an irrational number, the transition to chaos has been predicted theoretically to occur via the following routes: either quasiperiodicity ! frequency locking ! chaos or directly from quasiperiodicity to chaos [2][3][4][5]. Both routes to chaos have been observed in a number of experiments [3][4][5].Vertical transport in weakly coupled semiconductor superlattices (SL's) is known to exhibit nonlinear phenomena such as domain formation [8-10], multistability [11], and self-sustained current oscillations [12][13][14]. It has been shown that the self-sustained current oscillations are due to a quasi-one-dimensional motion of the domain boundary in the SL direction, i.e., vertical to the SL layers [8,[12][13][14][15]. Therefore, the temporal behavior of the current oscillations is directly related to the vertical spatiotemporal motion of the domain boundary inside the SL. Theoretical studies predict the appearance of chaos in such SL systems accompanied by the breakdown of spatiotemporal coherence of the motion of the domain boundary [15]. Although driven and undriven chaos of these current oscillations have been recently observed in the frequency power spectra [16], little is known about the transition process between synchronization (frequency locking) and chaos as well as the actual type of chaotic behavior in the experimentally investigated SL system. This type of information can be obtained only from real-time measurements.In this paper, we present Poincaré maps in the presence of an external driving voltage applied parallel to the growth direction of a weakly coupled semiconductor SL. These Poincaré maps clearly indicate that the transition from frequency locking to chaos is accompanied by a loss of spatiotemporal coherence. Furthermore, the Poincaré maps reveal that a number of attractors with varying complexity exist in the chaotic regime. However, for different dc biases, completely different routes to chaos are observed. At the same time, the observed bifurcation patterns are more complicat...

High magnetic field transport and photoluminescence in doped InGaAs/InP superlattices

“…Shubnikov-de Haas spectra of the samples showed a v ery well resolved doublet structure associated with the belly and neck orbits in the E1 miniband. The quantum mobility for electrons con ned in the E1 miniband was deduced to be 970 cm 2 Vs. This represents an improvement of nearly 40 in comparison with periodically delta-doped structures.…”

Multifractal dimension of chaotic attractors in a driven semiconductor superlattice

“…The detailed information about the samples and the performed experiments can be found in Ref. 13. In this paper we will discuss the bifurcation route at the dc bias of 6.574 V, where the current self-oscillations exhibit an intrinsic fundamental frequency f 0 of 30.5 MHz.…”

“…1͑a͒ in Ref. 13, which shows the following sequence: quasiperiodicity˜synchronized chaos˜frequency locking chaos˜chaos with higher complexity. The Poincaré maps derived from real-time traces further verify this bifurcation route to chaos.…”

“…6,7,10 In this nonlinear system, chaos has also been studied theoretically 11 and experimentally. 12,13 Recently, an explosive bifurcation to chaos has been experimentally observed in the power spectra of a driven SL and unambiguously identified using Poincaré maps. 13 During the bifurcation sequence from frequency-locking to chaos, the Poincaré map expands from isolated points to connected branches, indicating that the dimension of the underlying attractors increases with increasing amplitude of the driving voltage.…”

“…12,13 Recently, an explosive bifurcation to chaos has been experimentally observed in the power spectra of a driven SL and unambiguously identified using Poincaré maps. 13 During the bifurcation sequence from frequency-locking to chaos, the Poincaré map expands from isolated points to connected branches, indicating that the dimension of the underlying attractors increases with increasing amplitude of the driving voltage. When the system enters the chaotic regime, the Poincaré map becomes more complex indicating that the attractor acquires a higher dimension.…”