Chaos in resonant-tunneling superlattices

Bulashenko, O. M.; Bonilla, L. L.

doi:10.1103/physrevb.52.7849

Cited by 90 publications

(98 citation statements)

References 18 publications

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“…[5][6][7] Due to the presence of the NDV, the vertical transport in the SL's exhibits nonlinear properties, which result in such phenomena as domain formation, 8 multistability, 9 and selfsustained oscillations. 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.…”

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confidence: 99%

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: Introductionmentioning

confidence: 99%

Multifractal dimension of chaotic attractors in a driven semiconductor superlattice

et al. 1999

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“…However, contrary to the latter case, the domain walls move across a larger number of units in the superlattice the lower the dimensionality, due to the different spatial distribution of the electric-field across the array in the three cases. Chaotic transport in GaAs/AlAs superlattices has been theoretically predicted 1 and experimentally demonstrated 2 a few years ago. It was found that, when the main charge transport mechanism is sequential resonant tunneling between adjacent quantum wells, undamped time-dependent oscillations of the current appear.…”

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“…3 Such oscillations are due to the motion and recycling of electric field and charge domain walls in the superlattice. 1 Due to the presence of such natural oscillations, spatiotemporal chaos can be induced by a suitable external oscillating field. 1,4 In recent years, new type of nanostructures, like, e.g., nanotubes, molecular or atomic wires ͑often globally referred to as quantum wires͒, have received considerable attention in view of their possible use as components in future electronic applications.…”

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“…1 Due to the presence of such natural oscillations, spatiotemporal chaos can be induced by a suitable external oscillating field. 1,4 In recent years, new type of nanostructures, like, e.g., nanotubes, molecular or atomic wires ͑often globally referred to as quantum wires͒, have received considerable attention in view of their possible use as components in future electronic applications. 5 While much of the research has focused so far on the new transport issues that arise in single quantum wires, less work has been devoted to the study of transport properties of arrays of quantum wires.…”

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Chaotic transport in low-dimensional superlattices

2003

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We predict that in arrays of quantum dots ͑0D superlattice͒ and arrays of one-dimensional quantum wires ͑1D superlattice͒ chaotic transport should be observed in the presence of an ac field and for a wide range of physical parameters, like the external dc bias, contact charge, doping levels, and disorder in the array. Timedependent current oscillations set in the array due to the formation of electric domain walls when sequential resonant tunneling is the main transport mechanism between adjacent units. Such oscillations can then be forced into spatiotemporal chaos. A similar phenomenon has been predicted and demonstrated for solid-state superlattices. However, contrary to the latter case, the domain walls move across a larger number of units in the superlattice the lower the dimensionality, due to the different spatial distribution of the electric-field across the array in the three cases. Chaotic transport in GaAs/AlAs superlattices has been theoretically predicted 1 and experimentally demonstrated 2 a few years ago. It was found that, when the main charge transport mechanism is sequential resonant tunneling between adjacent quantum wells, undamped time-dependent oscillations of the current appear. 3 Such oscillations are due to the motion and recycling of electric field and charge domain walls in the superlattice. 1 Due to the presence of such natural oscillations, spatiotemporal chaos can be induced by a suitable external oscillating field. 1,4 In recent years, new type of nanostructures, like, e.g., nanotubes, molecular or atomic wires ͑often globally referred to as quantum wires͒, have received considerable attention in view of their possible use as components in future electronic applications. 5 While much of the research has focused so far on the new transport issues that arise in single quantum wires, less work has been devoted to the study of transport properties of arrays of quantum wires. The latter systems constitute a natural step towards integration of nanoscale components into functional devices. Since such systems represent an extension of the well-known concept of two-dimensional ͑2D͒ solid-state superlattices 6 and sequential resonant tunneling can be the main transport mechanism in such structures, it is natural to ask if ͑i͒ natural oscillations can be observed in superlattices with even lower dimansionality, and, consequently, ͑ii͒ such oscillations can be forced into spatiotemporal chaos by an appropriate oscillating field.In this paper, we show that the answer to both questions is positive. In particular, we examine arrays of quantum dots ͑0D superlattice͒ and arrays of one-dimensional quantum wires ͑1D superlattice͒. By array of quantum wires we mean either a finite series of zero dimensional ͑0D͒ structures ͓see Fig. 1͑a͔͒ or a series of one dimensional ͑1D͒ structures ͓Fig. 1͑b͔͒ between two bulk electrodes. The 0D superlattice can be made of, for instance, a series of weakly coupled molecules, 7 or a series of nanowire units, 8 and the 1D superlattice a series of, say, nanotubes. 5 We...

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“…by the application of a bias voltage or by the variation of the doping densities in the wells or in the contacts. The strong non linear transport that results from the Coulomb interaction in these systems presents a rich variety of new physical phenomena: multistability and electric field domains formation [1-3], self sustained oscillations [4], bifurcation to chaos [5], etc. In particular, the current flowing through a weakly coupled doped semiconductor superlattice presents a complicated sawtooth structure with unstable regions of negative differential conductance and multistable regions.…”

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Magnetic field induced charge instabilities in weakly coupled superlattices

Aguado

Platero

1998

Physica B: Condensed Matter

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Using a time dependent selfconsistent model for vertical sequential tunneling, we study the appearance of charge instabilities that lead to the formation of electric field domains in a weakly coupled doped superlattice in the presence of high magnetic fields parallel to the transport direction. The interplay between the high non linearity of the system -coming from the Coulomb interaction-and the inter-Landau-level scattering at the domain walls (regions of charge accumulation inside the superlattice) gives rise to new unstable negative differential conductance regions and extra stable branches in the sawtooth-like I-V curves.PACS numbers: 73.40. Gk, 72.15.Gd Weakly coupled doped semiconductor superlattices are an example of non linear systems in which all intrinsic properties related to high non linearity such as multistability, spatio-temporal chaos, etc, can be externally modified : e.g. by the application of a bias voltage or by the variation of the doping densities in the wells or in the contacts. The strong non linear transport that results from the Coulomb interaction in these systems presents a rich variety of new physical phenomena: multistability and electric field domains formation [1-3], self sustained oscillations [4], bifurcation to chaos [5], etc. In particular, the current flowing through a weakly coupled doped semiconductor superlattice presents a complicated sawtooth structure with unstable regions of negative differential conductance and multistable regions. This structure of branches comes from the charge instabilities that appear due to the motion of the domain wall (acummulation layer) from one well to another. This motion, which is due to resonant tunneling between adjacent subbands, leads to the formation of electric field domains. In this Letter we study theoretically for the first time this phenomenon in the presence of high magnetic fields parallel to the transport direction. New physical questions that were not relevant in the absence of magnetic fields can be raised. In particular, what happens to the charge instabilities in the presence of the new energy scale in the problem,hω c ? Resonant tunneling through double barriers [6-10] and superlattices [11] in the presence of high magnetic fields has been widely studied. Also, dynamical instabilities and bifurcations to chaos induced by a magnetic field in a double barrier resonant tunneling diode have been recently predicted [12]. It is well known that the application of a magnetic field perpendicular to a two dimensional electron gas produces the formation of Landau levels. For ideal samples, the tunneling through the heterostructure conserves the Landau level index. However, due to interface roughness, impurity scattering, or phonon scattering, these conservation rules are relaxed and inter Landau level transitions take place [6][7][8][9][10]. Recent magnetotransport experiments on weakly coupled doped semiconductor superlattices performed by Schmidt et al. [13] show new unstable regions of negative differential conductance and e...

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Chaos in resonant-tunneling superlattices

Cited by 90 publications

References 18 publications

Multifractal dimension of chaotic attractors in a driven semiconductor superlattice

Multifractal dimension of chaotic attractors in a driven semiconductor superlattice

Chaotic transport in low-dimensional superlattices

Magnetic field induced charge instabilities in weakly coupled superlattices

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