Chaotic transport in low-dimensional superlattices

Abstract

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...

Current oscillations, switching, and hysteresis in CdSe nanorod superlattices

“…Similar effects are also expected in superlattices of lower dimensionality. 9 Usually, long tracks of CdSe QRs stacked side-by-side are spontaneously formed upon deposition of CdSe QRs on a substrate from a solution by slow solvent evaporation ͑Fig. 6͒.…”

Transport in nanoscale systems: the microcanonical versus grand-canonical picture

“…However, there may in fact be cases where solutions with the same E but different I S describe steady states of different currents at the same time t corresponding to the same voltage drop. Such instances correspond to chaotic transport and may occur in systems with intrinsic nonlinear dynamics [17].…”

Chaotic memristor

“…There is some interesting fine-structure within part of the chaotic-memristor Poincaré plot, including one sub-voltage peak at about 0.8 V, and the existence of what appears to be a tri-stable region near 1.25 V. This is typical of chaotic systems (see, e.g., Ref. [35]). …”