Strongly correlated confined electrons

  • W. Häusler
Part of the Advances in Solid State Physics book series (ASSP, volume 34)


A few-electron system, as realized in semiconducting quantum dots, is investigated. Numerical results for the charge density distribution in quasi onedimensional (1D) systems reveal three characteristic regimes of electron densities. At low carrier densities the ground state and the collective excitations correspond to those of a finite Wigner crystal. At intermediate densities low energy excitations involving the spin occur in 1D and 2D. They are investigated using correlated “pocket state” basis functions. For non-isotropic confining potentials and sufficiently large mean electron distances γs this method becomes exact. The ratios between the lowest energy excitation energies are determined quantitatively using group theoretical methods. They are independent of the detailed form of the electron-electron repulsion potential and of γs. The results of the pocket state apprach are compared with available numerical data. Transport through a quantum dot is investigated under Coulomb blockade conditions for weak coupling to perfect leads. A master equation approach allows to incorporate nonequilibrium properties at finite applied voltages as well as spin selection rules for the transitions between the correlated many electron states. A model for the recently discovered negative differential conductances is proposed. Asymmetries in the transport is predicted for asymmetric dot-lead coupling. Recent experimental results for in-plane magnetic fields can be described by the Zeeman-splitting of the many electron states.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    E. Wigner, Phys. Rev. 46, 1002 (1934).zbMATHCrossRefADSGoogle Scholar
  2. [2]
    D. M. Ceperley, B. J. Adler, Phys. Rev. Lett. 45, 566 (1980).CrossRefADSGoogle Scholar
  3. [3]
    K. Jauregui, W. Häusler, B. Kramer, Europhys. Lett. 24, 581 (1993).CrossRefADSGoogle Scholar
  4. [4]
    L. I. Glazman, I. M. Ruzin, B. I. Shklovskii, Phys. Rev. B 45, 8454 (1992).CrossRefADSGoogle Scholar
  5. [5]
    D. V. Averin, Yu. V. Nazarov, Phys. Rev. B 47, 9944 (1993).CrossRefADSGoogle Scholar
  6. [6]
    D. V. Averin, K. K. Likharev in: Quantum Effects in Small Disordered Systems, ed. by B. L. Altshuler, P. A. Lee, R. A. Webb (Elsevier, Amsterdam, 1991) G. Schön, A. D. Zaikin, Phys. Rep. 198, 237 (1990); H. Grabert, G. L. Ingold, M. H. Devoret, D. Esteve, H. Pothier, C. Urbina, Z. Phys. B 84, 143 (1991); A good review can be found in: H. Grabert, M. Devoret, editors, Single Charge Tunneling NATO ASI Series, Plenum Press, volume 294 (1992).Google Scholar
  7. [7]
    U. Meirav, M. A. Kastner, S. J. Wind, Phys. Rev. Lett. 65, 771 (1990).CrossRefADSGoogle Scholar
  8. [8]
    Special Issue on Single Charge Tunneling edited by H. Grabert, Z. Phys. B85, 317–468 (1991).Google Scholar
  9. [9]
    M. A. Kastner, Rev. Mod. Phys. 64, 849 (1992).CrossRefADSGoogle Scholar
  10. [10]
    A. T. Johnson, L. P. Kouwenhoven, W. de Jong, N. C. van der Vaart, C. J. P. M. Harmanns, C. T. Foxon, Phys. Rev. Lett. 69, 1592 (1992).CrossRefADSGoogle Scholar
  11. [11]
    J. Weis, R. J. Haug, K. v. Klitzing, K. Ploog, Phys. Rev. B 46, 12837 (1992).CrossRefADSGoogle Scholar
  12. [12]
    Proceedings of the Conference The Physics of Few-Electron Nanostructures, Noordwijk, Physica B 189, 1–277 (1993).Google Scholar
  13. [13]
    Ch. Sikorski, U. Merkt, Phys. Rev. Lett. 62, 2164 (1989); B. Meurer, D. Heitmann, K. Ploog, Phys. Rev. Lett. 68, 1371 (1992); R. C. Ashoori, H. L. Stormer, J. S. Weiner, L. N. Pfeiffer, S. J. Pearton, K. W. Baldwin, K. W. West, Phys. Rev. Lett. 68, 3088 (1992); R. C. Ashoori, H. L. Stormer, J. S. Weiner, L. N. Pfeiffer, K. W. Baldwin, K. W. West, Phys. Rev. Lett. 71, 613 (1993).CrossRefADSGoogle Scholar
  14. [14]
    D. Pfannkuche, R. R. Gerhards, Phys. Rev. B 44, 13132 (1991).CrossRefADSGoogle Scholar
  15. [15]
    D. V. Averin, A. N. Korotkov, Journ. of Low Temp. Phys. 80, 173 (1990). D. V. Averin, A. N. Korotkov, K. K. Likharev, Phys. Rev. B44, 6199 (1991); E. B. Foxman, P. L. McEuen, U. Meirav, N. S. Wingreen, Y. Meir, P. A. Belk, N. R. Belk, M. A. Kastner, S. J. Wind, Phys. Rev. B47, 10020 (1993).CrossRefADSGoogle Scholar
  16. [16]
    J. Weis, R. J. Haug, K. v. Klitzing, K. Ploog, Phys. Rev. Lett. 71, 4019 (1993).CrossRefADSGoogle Scholar
  17. [17]
    W. Häusler, K. Jauregui, D. Weinmann, T. Brandes, B. Kramer, Physica B 194–196, 1325 (1994)CrossRefGoogle Scholar
  18. [18]
    D. Weinmann, W. Häusler, W. Pfaff, B. Kramer, U. Weiss, to appear in Europhys. Lettrs (1994).Google Scholar
  19. [19]
    D. Weinmann, W. Häusler, B. Kramer, unpublished.Google Scholar
  20. [20]
    C. W. J. Beenakker, Phys. Rev. B 44, 1646 (1991).CrossRefADSGoogle Scholar
  21. [21]
    U. Merkt, J. Huser, M. Wagner, Phys. Rev. B 43, 7320 (1991).CrossRefADSGoogle Scholar
  22. [22]
    P. Hawrylak, D. Pfannkuche, Phys. Rev. Lett. 70, 485 (1993).CrossRefADSGoogle Scholar
  23. [23]
    G. W. Bryant, Phys. Rev. Lett. 59, 1140 (1987).CrossRefADSGoogle Scholar
  24. [24]
    W. Häusler, B. Kramer, J. Mašek, Z. Phys. B 85, 435 (1991).CrossRefADSGoogle Scholar
  25. [25]
    W. Häusler, B. Kramer, Phys. Rev. B 47, 16353 (1993).CrossRefADSGoogle Scholar
  26. [26]
    P. Maksym, Physica B 184, 385 (1993).CrossRefADSGoogle Scholar
  27. [27]
    G. Meissner, H. Namaizawa, M. Voss, Phys. Rev. B 13, 1370 (1976).CrossRefADSGoogle Scholar
  28. [28]
    D. Pfannkuche, V. Gudmundsson, P. A. Maksym, Phys. Rev. B 47, 2244 (1993).CrossRefADSGoogle Scholar
  29. [29]
    J. Mašek, unpublished.Google Scholar
  30. [30]
    E. Lieb, D. Mattis, Phys. Rev. 125, 164 (1962).zbMATHCrossRefADSGoogle Scholar
  31. [31]
    A. Hüller, D. M. Kroll, J. Chem. Phys. 63, 4495 (1975).CrossRefADSGoogle Scholar
  32. [32]
    M. Hamermesh: “Group Theory and its Applications to Physical Problems”, new edition, Dover Publications, New York (1989).Google Scholar
  33. [33]
    Bjørn Felsager: “Geometry, Priticles and fields”, Odense University Press (1981).Google Scholar
  34. [34]
    T. Inui, Y. Tanabe, Y. Onodera: “Solid State Sciences”, Springer, Berlin (1990).Google Scholar
  35. [35]
    K. Moulopoulos, N. W. Ashcroft, Phys. Rev. Lett. 69, 2555 (1992).CrossRefADSGoogle Scholar
  36. [36]
    C. Bruder, H. Schoeller, Phys. Rev. Lett. 72, 1076 (1994).CrossRefADSGoogle Scholar
  37. [37]
    J. Weis, PhD thesis, University of Stuttgart (1994).Google Scholar
  38. [38]
    N. C. van der Vaart, A. T. Johnson, L. P. Kouwenhoven, D. J. Mass, W. de Jong M. P. de Ruyter van Steveninck, A. van der Enden, C. J. P. M. Harmanns in Ref. [12].CrossRefADSGoogle Scholar
  39. [39]
    J. T. Nicholls, J. E. F. Frost, M. Pepper, D. A. Ritchie, M. P. Grimshaw, G. A. Jones, Phys. Rev. B 48, 8866 (1993).CrossRefADSGoogle Scholar
  40. [40]
    J. Weis, R. J. Haug, private communication.Google Scholar
  41. [41]
    J. J. Palacios, L. Martin-Moreno, C. Tejedor, Europhys. Lett. 23, 495 (1993).CrossRefADSGoogle Scholar
  42. [42]
    L. P. Kouwenhoven, PhD thesis, Technical University of Delft (1992).Google Scholar
  43. [43]
    R. N. Ghosh, R. H. Silsbee, Phys. Rev. B 46, 12508 (1992).CrossRefADSGoogle Scholar

Copyright information

© Friedr. Vieweg & Sohn Verlagsgesellschaft mbH 1995

Authors and Affiliations

  • W. Häusler
    • 1
  1. 1.I. Institut für Theoretische PhysikHamburgF. R. G.

Personalised recommendations