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Coulomb Interaction in Finite-Width Quantum Rings

  • Benjamin BaxevanisEmail author
  • Daniela Pfannkuche
Chapter
Part of the NanoScience and Technology book series (NANO)

Abstract

Due to the particular confinement and reduced dimensionality of quantum rings, Coulomb interaction plays an important role for their electronic structure. In this chapter, we discuss the dependency of the ground state of an idealized quantum ring contained a small number of interacting electrons on geometric parameters like ring radius, radial confinement and eccentricity. The ring geometry affects both the charge distribution and the spin configuration in a quantum ring. Numerically exact results obtained from path-integral quantum Monte Carlo demonstrate the strong connection between the structure and the total spin of the ground state emerging from the interplay between confinement and Coulomb interaction.

References

  1. 1.
    P. Singha Deo, P. Koskinen, M. Koskinen, M. Manninen, Europhys. Lett. 63(6), 846–852 (2003) ADSCrossRefGoogle Scholar
  2. 2.
    M. Szelag, M. Szopa, J. Phys. Conf. Ser. 104, 012006–012014 (2008) CrossRefGoogle Scholar
  3. 3.
    Y.V. Pershin, C. Piermarocchi, Phys. Rev. B 72(12), 125348 (2005) ADSCrossRefGoogle Scholar
  4. 4.
    N. Yang, J.-L. Zhu, Z. Dai, J. Phys. Condens. Matter 20(29), 295202–295213 (2008) CrossRefGoogle Scholar
  5. 5.
    T. Chakraborty, P. Pietiläinen, Phys. Rev. B 52, 1932–1935 (1995) ADSCrossRefGoogle Scholar
  6. 6.
    K. Niemelä, P. Pietiläinen, P. Hyvönen, T. Chakraborty, Europhys. Lett. 36(7), 533–538 (1996) ADSCrossRefGoogle Scholar
  7. 7.
    F. Pederiva, A. Emperador, E. Lipparini, Phys. Rev. B 66(16), 165314 (2002) ADSCrossRefGoogle Scholar
  8. 8.
    P. Borrmann, J. Harting, Phys. Rev. Lett. 86(14), 3120–3123 (2001) ADSCrossRefGoogle Scholar
  9. 9.
    V.M. Fomin (ed.), J. Nanoelectron. Optoelectron. 6(1) (2011) Google Scholar
  10. 10.
    Y. Saiga, D.S. Hirashima, J. Usukura, Phys. Rev. B 75(4), 045343–045354 (2007) ADSCrossRefGoogle Scholar
  11. 11.
    P. Koskinen, M. Koskinen, M. Manninen, Eur. Phys. J. B 28(4), 483–489 (2002) ADSCrossRefGoogle Scholar
  12. 12.
    L.A. Lavenere-Wanderley, A. Bruno-Alfonso, A. Latge, J. Phys. Condens. Matter 14(2), 259–270 (2002) ADSCrossRefGoogle Scholar
  13. 13.
    D. Gridin, A.T.I. Adamou, R.V. Craster, Phys. Rev. B 69(15), 155317 (2004) ADSCrossRefGoogle Scholar
  14. 14.
    A. Lorke, J.R. Luyken, A.O. Govorov, J.P. Kotthaus, J.M. Garcia, P.M. Petroff, Phys. Rev. Lett. 84(10), 2223–2226 (2000) ADSCrossRefGoogle Scholar
  15. 15.
    D.M. Ceperley, Rev. Mod. Phys. 67(2), 279–355 (1995) ADSCrossRefGoogle Scholar
  16. 16.
    B. Baxevanis, D. Pfannkuche, J. Nanoelectron. Optoelectron. 6(1), 76–80 (2011) CrossRefGoogle Scholar
  17. 17.
    M. Takahashi, M. Imada, J. Phys. Soc. Jpn. 53(3), 963–974 (1984) ADSCrossRefGoogle Scholar
  18. 18.
    R. Egger, W. Häusler, C.H. Mak, H. Grabert, Phys. Rev. Lett. 83(2), 462 (1999) ADSCrossRefGoogle Scholar
  19. 19.
    R. Pauncz, The Construction of Spin Eigenfunctions: An Exercise Book (Kluwer Academic/Plenum, New York, 2001) Google Scholar
  20. 20.
    A.P. Lyubartsev, P.N. Vorontsov-Velyaminov, Phys. Rev. A 48(6), 4075–4083 (1993) ADSCrossRefGoogle Scholar
  21. 21.
    M. Hamermesh, Group Theory and Its Application to Physical Problems (Dover, New York, 1989) Google Scholar
  22. 22.
    L. Wendler, V.M. Fomin, A.V. Chaplik, A.O. Govorov, Z. Phys. B, Condens. Matter 100, 211–221 (1996) ADSCrossRefGoogle Scholar
  23. 23.
    E. Wigner, Phys. Rev. 46(11), 1002–1011 (1934) ADSCrossRefGoogle Scholar
  24. 24.
    M. Koskinen, M. Manninen, B. Mottelson, S.M. Reimann, Phys. Rev. B 63(20), 205323 (2001) ADSCrossRefGoogle Scholar
  25. 25.
    P. Hawrylak, D. Pfannkuche, Phys. Rev. Lett. 70(4), 485–488 (1993) ADSCrossRefGoogle Scholar
  26. 26.
    P.A. Maksym, Phys. Rev. B 53(16), 10871–10886 (1996) ADSCrossRefGoogle Scholar
  27. 27.
    P.A. Maksym, Physica B, Condens. Matter 184(1–4), 385–393 (1993) ADSCrossRefGoogle Scholar
  28. 28.
    R. Courant, D. Hilbert, Methods of Mathematical Physics, vol. I (Interscience, New York, 1953) Google Scholar
  29. 29.
    C. Herring, Phys. Rev. B 11(5), 2056–2061 (1975) ADSCrossRefGoogle Scholar
  30. 30.
    M. Aizenman, E.H. Lieb, Phys. Rev. Lett. 65(12), 1470–1473 (1990) ADSCrossRefGoogle Scholar
  31. 31.
    E.H. Lieb, D. Mattis, J. Math. Phys. 3(4), 749–751 (1962) ADSCrossRefzbMATHGoogle Scholar
  32. 32.
    J. Planelles, F. Rajadell, J.I. Climente, Nanotechnology 18(37), 375402–375413 (2007) CrossRefGoogle Scholar
  33. 33.
    A. Bruno-Alfonso, A. Latgé, Phys. Rev. B 77(20), 205303 (2008) ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.I. Institute for Theoretical PhysicsUniversity of HamburgHamburgGermany

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