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Chaos current

Researchers at the University of Nottingham in the UK report "non-KAM chaos" in semiconductor superlattices (Nature, April 15, 2004). Large increases in current flow are seen at discreet voltages. This is interpreted as being due to the creation of unbound electron orbits that propagate through intricate web patterns in phase space. The scientists say that this provides a mechanism for controlling conductivity that could result in extremely sensitive quantum electronic and photonic devices.
Researchers at the University of Nottingham in the UK report "non-KAM chaos" in semiconductor superlattices (Nature, April 15, 2004). Large increases in current flow are seen at discreet voltages. This is interpreted as being due to the creation of unbound electron orbits that propagate through intricate web patterns in phase space. The scientists say that this provides a mechanism for controlling conductivity that could result in extremely sensitive quantum electronic and photonic devices.

KAM chaos refers to the sort of instability that occurs according to the Kolmogorov-Arnold-Moser theorem in classical mechanics – pertubation of stable periodic systems leads to stable regions surrounded by instability (KAM tori). As the perturbation increases the stable regions shrink. KAM theory has been used to explain gaps in the asteroid belt as being due to unstable orbits. The transition to chaos is a gradual process.

By contrast, non-KAM chaos switches on and off abruptly at critical perturbations. Non-KAM theory has application in plasma physics, turbulence, ion traps and quasi-crystals.

In the Nottingham experiment, the superlattice consisted of alternate layers of different compound semiconductor material. The basic unit of the superlattice consisted of 3.5nm of GaAs, a 0.3nm monolayer of InAs, another 3.5nm GaAs layer and 1nm of AlAs. The monolayer at the centre of the quantum well lowers the energy of the first miniband to make it easier to inject electrons into the structure and reduces Zener tunnelling between minibands. An 11Tesla magnetic field was applied at a range of tilt angles to the superlattice axis. Applying a voltage across the superlattice initially resulted in a monotonic increase in current. However, strong resonant peaks in differential conductance were seen above a threshold voltage of around 250mV for tilt angles between 10degrees and 55degress.

The system is related to an extensively studied theoretical non-KAM system – a harmonic oscillator driven by a monochromatic plane wave. The authors say that the system has never before been realised in a quantum system that can be explored experimentally.

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