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Chaotic electron diffusion through stochastic webs enhances current flow in superlattices


Understanding how complex systems respond to change is of fundamental importance in the natural sciences. There is particular interest in systems whose classical newtonian motion becomes chaotic1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22 as an applied perturbation grows. The transition to chaos usually occurs by the gradual destruction of stable orbits in parameter space, in accordance with the Kolmogorov–Arnold–Moser (KAM) theorem1,2,3,6,7,8,9—a cornerstone of nonlinear dynamics that explains, for example, gaps in the asteroid belt2. By contrast, ‘non-KAM’ chaos switches on and off abruptly at critical values of the perturbation frequency6,7,8,9. This type of dynamics has wide-ranging implications in the theory of plasma physics10, tokamak fusion11, turbulence6,7,12, ion traps13, and quasicrystals6,8. Here we realize non-KAM chaos experimentally by exploiting the quantum properties of electrons in the periodic potential of a semiconductor superlattice22,23,24,25,26,27 with an applied voltage and magnetic field. The onset of chaos at discrete voltages is observed as a large increase in the current flow due to the creation of unbound electron orbits, which propagate through intricate web patterns6,7,8,9,10,12,13,14,15,16 in phase space. Non-KAM chaos therefore provides a mechanism for controlling the electrical conductivity of a condensed matter device: its extreme sensitivity could find applications in quantum electronics and photonics.

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Figure 1: Properties of the SL.
Figure 2: Resonant enhancement of current.
Figure 3: Electron trajectories and wavefunctions.
Figure 4: Classical and quantum phase space structure.


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This work was supported by the EPSRC, The Royal Society, CONACyT, and INSA. S.B. is funded by an EU Marie Curie Fellowship and is grateful for support from the Institute of Physics, Wrocław University of Technology, Poland. We are grateful to R. Airey for processing our samples.

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Fromhold, T., Patanè, A., Bujkiewicz, S. et al. Chaotic electron diffusion through stochastic webs enhances current flow in superlattices. Nature 428, 726–730 (2004).

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