Influence of higher harmonics on Poincaré maps derived from current self-oscillations in a semiconductor superlattice

Luo, Kun; Grahn, H. T.; Teitsworth, Stephen W.

doi:10.1103/physrevb.58.12613

Cited by 13 publications

(15 citation statements)

References 10 publications

(10 reference statements)

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“…For quasiperiodicity, the Poincaré map should be a smooth loop. 17 Consequently, it is expected that a quasiperiodic attractor is one dimensional, i.e., D q is equal to one for all values of q. However, the D q curves for the quasiperiodic attractors in our experiments ͑between V ac ϭ1 and 37 mV͒ do not exhibit a horizontal line as shown for 9 and 34 mV in Fig.…”

Section: Characterization Of Attractorscontrasting

confidence: 40%

Multifractal dimension of chaotic attractors in a driven semiconductor superlattice

et al. 1999

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The multifractal dimension of chaotic attractors has been studied in a weakly coupled superlattice driven by an incommensurate sinusoidal voltage as a function of the driving voltage amplitude. The derived multifractal dimension for the observed bifurcation sequence shows different characteristics for chaotic, quasiperiodic, and frequency-locked attractors. In the chaotic regime, strange attractors are observed. Even in the quasiperiodic regime, attractors with a certain degree of strangeness may exist. From the observed multifractal dimensions, the deterministic nature of the chaotic oscillations is clearly identified. ͓S0163-1829͑99͒03032-5͔

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Section: Characterization Of Attractorscontrasting

confidence: 40%

Multifractal dimension of chaotic attractors in a driven semiconductor superlattice

et al. 1999

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“…In n-doped weakly coupled superlattices, multistability due to domain formation has been much studied both theoretically and experimentally, [141,142,143,144,145,146]. When the doping in the wells is reduced, self-sustained current oscillations [147,148,149,150,151] and chaos [152,153,154,155,156] due to domain dynamics are possible. As we have discussed previously, Coulomb interaction in heterostructures with large area wells is a small effect compared with the energy difference between noninteracting eigenstates of the structure.…”

Section: Weakly-coupled Superlattices As a Paradigm Of A Nonlinear Dymentioning

confidence: 99%

“…43(c), is much more complicated than in the previous case, showing three well defined distorted loops. Since loops in the Poincaré map are due to combination of strong enough signals of different frequencies [155], the greater strength of the high-frequency spikes gives rise to the additional loop structure and higher harmonic content ( Fig. 43(b)).…”

Section: Eqs (148-151)mentioning

confidence: 99%

Photon-assisted transport in semiconductor nanostructures

2004

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In this review we focus on electronic transport through semiconductor nanostructures which are driven by ac fields. Along the review we describe the available experimental information on different nanostructures, like resonant tunneling diodes, superlattices or quantum dots, together with the theoretical tools needed to describe the observed features. These theoretical tools such as, for instance, the Floquet formalism, the non-equilibrium Green's function technique or the density matrix technique, are suitable for tackling with photon-assisted transport problems where the interplay of different aspects like nonequilibrium, nonlinearity, quantum confinement or electron-electron interactions gives rise to many intriguing new phenomena. Along the review we give many examples which demonstrate the possibility of using appropriate ac fields to control/manipulate coherent quantum states in semiconductor nanostructures.

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“…When the ac frequency is incommensurate with the natural frequency of the SL, intriguing routes to chaos giving rise to complicated Poincaré maps have been observed. 24 In that case, the ac frequency is of the order of tens of MHz and it results in an adiabatic modulation of the SL electrostatic drops.…”

Section: Introductionmentioning

confidence: 99%

Dynamical instability of electric-field domains in ac-driven superlattices

2003

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We analyze theoretically the dynamical transport through a weakly coupled semiconductor superlattice, under an ac potential with frequencies in the THz regime, by means of a general model for time-dependent sequential tunneling within a nonequilibrium-Green's-function framework. Highly doped superlattices present, under certain conditions, the formation of electric-field domains at a static dc voltage bias. We find that the THz signal drives the system from a stationary current toward an oscillatory time dependence as the ac intensity increases. However, the current oscillates periodically in the MHz regime, reflecting an ac-induced motion and recycling of traveling domain walls. Finally, we predict that on further increasing the intensity of the ac potential, the tunneling current undergoes a transition from a periodically time-dependent state to a stationary one in which a homogeneous electric-field distribution builds up along the sample.

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Influence of higher harmonics on Poincaré maps derived from current self-oscillations in a semiconductor superlattice

Cited by 13 publications

References 10 publications

Multifractal dimension of chaotic attractors in a driven semiconductor superlattice

Multifractal dimension of chaotic attractors in a driven semiconductor superlattice

Photon-assisted transport in semiconductor nanostructures

Dynamical instability of electric-field domains in ac-driven superlattices

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