Determination of the interactions in confined macroscopic Wigner islands: theory and experiments

  • P. Galatola
  • G. CoupierEmail author
  • M. Saint Jean
  • J.-B. Fournier
  • C. Guthmann
Solid and Condensed State Physics


Macroscopic Wigner islands present an interesting complementary approach to explore the properties of two-dimensional confined particles systems. In this work, we characterize theoretically and experimentally the interaction between their basic components, viz., conducting spheres lying on the bottom electrode of a plane condenser. We show that the interaction energy can be approximately described by a decaying exponential as well as by a modified Bessel function of the second kind. In particular, this implies that the interactions in this system, whose characteristics are easily controllable, are the same as those between vortices in type-II superconductors.


41.20.Cv Electrostatics; Poisson and Laplace equations, boundary-value problems 68.65.-k Low-dimensional, mesoscopic, and nanoscale systems: structure and nonelectronic properties 


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  1. Y. Hata, J. Suzuki, I. Kakeya, K. Kadowaki, A. Odawara, A. Nagata, S. Nakayama, K. Chinone, Physica C 388, 719 (2003) CrossRefADSGoogle Scholar
  2. A. Kanda, B.J. Baelus, F.M. Peeters, K. Kadowaki, Y. Ootuka, Phys. Rev. Lett. 93, 257002 (2004) CrossRefADSGoogle Scholar
  3. I.V. Grigorieva, W. Escoffier, J. Richardson, L.Y. Vinnikov, S. Dubonos, V. Oboznov, Phys. Rev. Lett. 96, 077005 (2006) CrossRefADSGoogle Scholar
  4. Other related systems are, for instance, colloids, electrons in quantum dots, vortices in superfluid \(^4\mbox{He}\), electron dimples on a liquid helium surface, trapped cooled ions or vortices in a Bose-Einstein condensate Google Scholar
  5. G. Coupier, M. Saint Jean, C. Guthmann, Phys. Rev. E 73, 031112 (2006) CrossRefADSGoogle Scholar
  6. G. Coupier, C. Guthmann, Y. Noat, M. Saint Jean, Phys. Rev. E 71, 046105 (2005) CrossRefADSGoogle Scholar
  7. M. Saint Jean, C. Even, C. Guthmann, Europhys. Lett. 55, 45 (2001) CrossRefGoogle Scholar
  8. M. Saint Jean, C. Guthmann, J. Phys.: Condens. Matter 14, 13653 (2002) CrossRefADSGoogle Scholar
  9. L.J. Campbell, R.M. Ziff, Phys. Rev. B 20, 1886 (1979) CrossRefADSGoogle Scholar
  10. V.M. Bedanov, F.M. Peeters, Phys. Rev. B 49, 2667 (1994) CrossRefADSGoogle Scholar
  11. Y.J. Lai, L.I, Phys. Rev. E 60, 4743 (1999) CrossRefADSGoogle Scholar
  12. M. Saint Jean, C. Guthmann, G. Coupier, Eur. Phys. J. B 39, 61 (2004) ADSGoogle Scholar
  13. C. Meyers, M. Daumens, Phys. Rev. B 62, 9762 (2000) CrossRefADSGoogle Scholar
  14. Private communication Google Scholar
  15. P.G. de Gennes, Superconductivity of metals and alloys (W.A. Benjamin, 1966) Google Scholar
  16. M. Abramowitz, I.A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Table (Dover Publications, New York, 1970) Google Scholar
  17. L. Landau, E. Lifchitz, Théorie des champs (Mir, Moscou, 1989), p. 133 Google Scholar
  18. E. Durand, Electrostatique (Masson, Paris, 1964) Google Scholar
  19. J. Mathews, R.L. Walker, Mathematical methods of physics (Addison-Wesley, Reading, MA, 1970) Google Scholar
  20. P.E. Gill, W. Murray, M.H. Wright, Practical optimization (Academic Press, New York, 1981) Google Scholar
  21. H.A. Kramers, Physica 7, 284 (1940) zbMATHMathSciNetCrossRefGoogle Scholar

Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2006

Authors and Affiliations

  • P. Galatola
    • 1
  • G. Coupier
    • 2
    Email author
  • M. Saint Jean
    • 2
  • J.-B. Fournier
    • 3
    • 1
  • C. Guthmann
    • 2
  1. 1.Laboratoire Matière et Systèmes Complexes, UMR 7057 CNRS & Université Paris 7 – 2 place JussieuParis Cedex 05France
  2. 2.Laboratoire Matière et Systèmes Complexes, UMR 7057 CNRS & Université Paris 7 – 140 rue de LourmelParisFrance
  3. 3.Laboratoire de Physico-Chimie Théorique, UMR 7083 CNRS – ESPCIParis Cedex 05France

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