Hamiltonian Chaos in Lateral Surface Superlattices

  • Theo Geisel
  • Josef Wagenhuber
Part of the NATO ASI Series book series (NSSB, volume 254)


Semiconductor physics and technology have reached a stage, where the creation of diverse artificial microstructures can be realized. High-purity Al x Ga1-x As/GaAs hetero-junctions permit a ballistic motion of charge carriers in two dimensions (2 D) with elastic mean free paths of the order of 10μm. In addition, lateral structures such as quantum dots, quantum wires, or lateral surface superlattices [1–3] (LSSL) are imposed in search of novel electronic properties for future devices. These lateral structures represent a 2D potential for the charge carriers. We demonstrate in this article that the ballistic motion of charge carriers typically exhibits chaotic behavior. At present the spatial scales of the structures are still larger (≥ a factor of 10 for LSSLs) than the Fermi wavelength. The particle dynamics can thus be described by classical approximations. We have shown some time ago that these approximations exhibit chaotic particle motions associated with 1/f-noise [4]. On the other hand, as the spatial scales will be reduced further, these systems will also become interesting objects and a testing field for studies in quantum chaos.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    R.R. Gerhardts, D. Weiss, and K. v. Klitzing, Phys. Rev. Lett. 62, 1173 (1989)ADSCrossRefGoogle Scholar
  2. [2]
    R.W. Winkler, J.P. Kotthaus, and K. Ploog, Phys. Rev. Lett. 62, 1177 (1989)ADSCrossRefGoogle Scholar
  3. [3]
    K. Ismail, W. Chu, A. Yen, D.A. Antoniadis, and H.I. Smith, Appl. Phys. Lett. 54, 460 (1989)ADSCrossRefGoogle Scholar
  4. [4]
    T. Geisel, A. Zacherl, and G. Radons, Phys. Rev. Lett. 59, 2503 (1987);ADSCrossRefMathSciNetGoogle Scholar
  5. [4a]
    T. Geisel, A. Zacherl, and G. Radons, Z. Phys. B71, 117 (1988)CrossRefMathSciNetGoogle Scholar
  6. [5]
    T. Geisel, J. Wagenhuber, P. Niebauer, and G. Obermair, Phys. Rev. Lett. 64, 1581 (1990)ADSCrossRefGoogle Scholar
  7. [6]
    D.R. Hofstadter, Phys. Rev. B14, 2239 (1976)ADSCrossRefGoogle Scholar
  8. [7]
    C.W.J. Beenakker, Phys. Rev. Lett. 62, 2020 (1989)ADSCrossRefGoogle Scholar
  9. [8]
    A. Zacherl, T. Geisel, J. Nierwetberg, and G. Radons, Phys. Lett. 114A, 317 (1986)CrossRefGoogle Scholar
  10. [9]
    see e.g., M.V. Berry, in: Topics in Nonlinear Dynamics, S. Jorna, ed., AIP Conference Proc. No. 46, p. 16, American Institute of Physics, New York, (1978)Google Scholar
  11. [10]
    R.S. MacKay, J.D. Meiss, and I.C. Percival, Physica 13D, 55 (1984)zbMATHMathSciNetGoogle Scholar
  12. [11]
    J. Wagenhuber, T. Geisel, P. Niebauer, G. Obermair, to be publishedGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • Theo Geisel
    • 1
    • 2
  • Josef Wagenhuber
    • 1
    • 2
  1. 1.Institut für Theoretische PhysikUniversität RegensburgRegensburgF. R. Germany
  2. 2.Institut für Theoretische PhysikUniversität FrankfurtFrankfurtF. R. Germany

Personalised recommendations