Plateau Formation by Force from Pinning Centres in the Fractional Quantum Hall Effect

  • H. Bruus
  • O. P. Hansen
  • E. B. Hansen
Conference paper
Part of the Springer Series in Solid-State Sciences book series (SSSOL, volume 87)


Consider a QHE sample containing N electrons. As the flux is increased (decreased) relative to the mid-plateau value, mNФ0, by a given number of flux quanta, the electron liquid responds by forming the same number Vυ (V α) of fractionally charged vortices (antivortices) [1,2,3]:
$$ \begin{array}{*{20}{c}} {V\upsilon = \frac{\Phi }{{{\Phi _0}}} - mN{\text{ }}}&{{\text{for }}\Phi {\text{ > }}mN{\Phi _0}} \\ {V\alpha = mN - \frac{\Phi }{{{\Phi _0}}}}&{{\text{for }}\Phi {\text{ < }}mN{\Phi _0}}\end{array} $$


Magnetic Force Force Balance Electric Force Quantum Hall Effect Vortex State 
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  1. 1.
    S.M. Girvin: chap. 10 in The Quantum Hall Effect ed. by R.E.Prange and S.M. Girvin (Springer, Berlin, Heidelberg 1987)Google Scholar
  2. 2.
    H. Bruus, O.P. Hansen, and E.B. Hansen: Jour. Phys. C 21 L375 (1988)CrossRefGoogle Scholar
  3. 3.
    H. Bruus, O.P. Hansen, and E.B. Hansen: to be published in Zeitschrift f. PhysikGoogle Scholar
  4. 4.
    R.B. Laughlin: Phys. Rev. Lett. 50 1395 (1983)CrossRefGoogle Scholar
  5. 5.
    H. Bruus, O.P. Hansen, and E.B. Hansen: Proceedings of the 19. Int. Conf. on the Physics of Semiconductors, Warsaw August 1988Google Scholar

Copyright information

© Springer-Verlag Berlin, Heidelberg 1989

Authors and Affiliations

  • H. Bruus
    • 1
  • O. P. Hansen
    • 2
  • E. B. Hansen
    • 2
  1. 1.Danish Institute of Fundamental MetrologyLyngbyDenmark
  2. 2.Physics Laboratory, H.C. Ørsted InstituteUniversity of CopenhagenCopenhagen ØDenmark

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