Advertisement

Dipole at ν = 1

  • V. Pasquier
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 550)

Abstract

I consider the problem of Bosonic particles interacting repulsively in a strong magnetic field at the filling factor ν = 1. We project the system in the lowest Landau level and map the dynamics into an interacting Fermion system. We study the resulting Hamiltonian in the Hartree-Fock approximation in the case of a δ repulsive potential. The physical picture which emerges is in agreement with the proposal of N. Read that the composite Fermions behave as a gas of dipoles. We argue that the consequence of this is that the composite Fermions interact with screened short range interactions.We develop a Landau theory which we also expect to describe the physical ν = 1/2 Fermionic state. The form factor, the effective mass and the conductivity are analyzed in this model 1.

Keywords

Form Factor Fermi Surface Landau Level Fermi Liquid Fermi Momentum 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    R.B. Laughlin, Phys. Rev. Lett.50, 1395 (1983).CrossRefADSGoogle Scholar
  2. 2.
    J.K. Jain, Phys. Rev. Lett. 63, 199 (1989).CrossRefADSGoogle Scholar
  3. 3.
    R.L. Willet, M.A. Paalanen, R.R. Ruel, K.W. West, L.N. Pfeiffer and D.J. Bishop, Phys. Rev. Lett. 54, 112 (1990).CrossRefADSGoogle Scholar
  4. 4.
    B.A. Halperin, P.A. Lee and N. Read, Phys. Rev. B47, 7312 (1993).ADSGoogle Scholar
  5. 5.
    N. Read, Semicon. Sci. Tech. 9, 1859 (1994).CrossRefADSGoogle Scholar
  6. 6.
    N. Read, Phys. Rev. Lett. 62, 86 (1989).CrossRefADSGoogle Scholar
  7. 7.
    G. Baskaran, Physica B212, 320 (1995).ADSGoogle Scholar
  8. 8.
    H.J. Kwon, A. Houghton and J.B. Marston, Phys. Rev. Lett. 73, 284 (1994).CrossRefADSGoogle Scholar
  9. 9.
    Y.B. Kim, W.G. Wen, P.A. Lee and A. Furusaki, Phys. Rev. B50, 17917 (1994).ADSGoogle Scholar
  10. 10.
    B.L. Altshuler, L.B. Ioffe and A.J. Millis, Phys. Rev. B50, 14084 (1994).Google Scholar
  11. 11.
    C. Nayak and F. Wilczed, Nucl. Phys. B417, 359 (1994).CrossRefADSGoogle Scholar
  12. 12.
    D.C. Tsui, H. Störmer and A. Gossard, Phys. Rev. Lett. 48, 1559 (1982).CrossRefADSGoogle Scholar
  13. 13.
    E.H. Rezayi and N. Read, Phys. Rev. Lett. 72, 900 (1994).CrossRefADSGoogle Scholar
  14. 14.
    C. Kallin and B. Halperin, Phys. Rev. B30, 5655 (1984).ADSGoogle Scholar
  15. 15.
    I.V. Lerner and Yu.E. Lozovik, Zh. Eksp. Theor. Fiz 78, 1167 (1978) [Sov. Phys. JETP51, 588 (1980)].Google Scholar
  16. 16.
    L.P. Gor’kov and I.E. Dzyoloshinskii, Sov. Phys. JETP26, 449 (1968).ADSGoogle Scholar
  17. 17.
    S.M. Girvin, A.H. MacDonald and P.M. Platzman, Phys. Rev. B33, 2481(1986).ADSGoogle Scholar
  18. 18.
    F.D.M. Haldane, Private communication.Google Scholar
  19. 19.
    F. Dyson, Phys. Rev. 102, 1217 (1956).zbMATHCrossRefADSMathSciNetGoogle Scholar
  20. 20.
    D. Mumford “Tata Lectures on Theta” Birkhäuser (1983).Google Scholar
  21. 21.
    K. Moon, H. Mori, Kun Yang, S.M. Girvin, A.H. MacDonald, L. Zheng, D. Yoshioka and shou-Cheng Zhang, Phys. Rev. B51, 5138 (1995).ADSGoogle Scholar
  22. 22.
    D. Pines and P. Nozières “The Theory of Quantum Liquids” Vol.1, W.A. Benjamin, Inc. (1966).Google Scholar
  23. 23.
    M. Greiter, X.G. Wen and F. Wilczek, Phys. Rev. Lett. 66, 3205 (1991).CrossRefADSGoogle Scholar
  24. 24.
    R. Shankar and G. Murthy, Phys. Rev. Lett. 79, 4437 (1997).CrossRefADSGoogle Scholar
  25. 25.
    V. Pasquier and F.D.M. Haldane, Nucl. Phys. B51, 719 (1998).CrossRefADSMathSciNetGoogle Scholar
  26. 26.
    N. Read, Phys. Rev. B58, 16262 (1998).ADSGoogle Scholar
  27. 27.
    D.H. Lee, Phys. Rev. Lett. 80, 4745 (1998).CrossRefADSGoogle Scholar
  28. 28.
    A. Stern, B.I. Halperin, F. von Oppen, S. Simon, cond-mat/9812135.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • V. Pasquier
    • 1
  1. 1.CEA/SaclayOrme des MerisiersGif-sur-Yvette CedexFRANCE

Personalised recommendations