Numerical Investigation of the Fractional Quantum Hall Effect

  • Daijiro Yoshioka
Part of the Recent Progress in Many-Body Theories book series (RPMT, volume 1)

Abstract

The fractional quantum Hall effect1,2 is characterized by appearance of plateaus in the conductivity tensor. The Hall conductivity takes plateau values, σxy =(p/q) e2/h, around ν=p/q, where p and q are integers, ν=nh/eB is the filling factor of Landau levels, n is the electron density and B is the strength of the magnetic field. At the same time the longitudinal conductivity σxx becomes very small. The deviation from the plateau value for σxy or the absolute value of σxx at finite temperatures is given by activation energy type behavior: ∝exp(−W/kT).2,3

Keywords

Corn Ethod Haldane 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    D.C. Tsui, H.L. Starmer, and A.C. Gossard, Phys. Rev. Lett.. 48:1559 (1982).CrossRefGoogle Scholar
  2. 2.
    A.M. Chang, Chap.6, in “The Quantum Hall Effect,” R.E. Prange and S.M. Girvin eds., Springer-Verlag, New York (1987).Google Scholar
  3. 3.
    J. Wakabayashi, S. Kawaji, J. Yoshino, and H. Sakaki, J. Phys. Soc. Jpn. 55:1319 (1986).CrossRefGoogle Scholar
  4. 4.
    D. Yoshioka, B.I. Halperin, and P.A. Lee, Phys. Rev. Lett. 50:1219 (1983).CrossRefGoogle Scholar
  5. 5.
    D. Yoshioka, Phys. Rev. B29:6833 (1984).Google Scholar
  6. 6.
    F.D.M. Haldane and E.H. Rezayi, Phys. Rev. Lett. 54:237 (1985).CrossRefGoogle Scholar
  7. 7.
    G. Fano, F. Ortolani, and E. Colombo, Phys. Rev. B34:2670 (1986).Google Scholar
  8. 8.
    F.D.M. Haldane, Chap.8 in “The Quantum Hall Effect,” R.E. Prange and S.M. Girvin eds., Springer-Verlag, New York (1987).Google Scholar
  9. 9.
    R.B. Laughlin, Phys. Rev. Lett. 50:1395 (1983).CrossRefGoogle Scholar
  10. 10.
    F.D.M. Haldane, Phys. Rev. Lett. 51:605 (1983).CrossRefGoogle Scholar
  11. 11.
    S.M. Girvin, A.H. MacDonald, and P.M. Platzman, Phys. Rev. Lett. 54:581 (1985).CrossRefGoogle Scholar
  12. 12.
    R. Morf and B.I. Halperin, Phys. Rev. B33:2221 (1986).Google Scholar
  13. 13.
    S.M. Girvin, Chap.9, in “The Fractional Quantum Hall Effect,” R.E. Prange and S.M. Girvin eds., Springer-Verlag, New York (1987).Google Scholar
  14. 14.
    E.P. Wigner, Phys. Rev. 40:749 (1932).CrossRefGoogle Scholar
  15. 15.
    H. Fukuyama, P.M. Platzman, and P.W. Anderson, Phys. Rev. B19:5211 (1979).Google Scholar
  16. 16.
    J.G. Bednorz and K.A. Müller, Z. Phys. B64:188 (1986).Google Scholar
  17. 17.
    M.K. Wu, J.R. Ashburn, C.J. Torng, P.H. Hor, R.L. Meng, L. Gao, Z.J. Huang, Y.Q. Wang, and C.W. Chu, Phys. Rev. Lett. 58:908 (1987).CrossRefGoogle Scholar
  18. 18.
    D. Yoshioka, J. Phys. Soc. Jpn. 55:885 (1986).CrossRefGoogle Scholar
  19. 19.
    F.C. Zhang and S. Das Sarma, Phys. Rev. B33:2903 (1986).Google Scholar
  20. 20.
    F.D.M. Haldane, Phys. Rev. Lett. 55:2095 (1985).CrossRefGoogle Scholar
  21. 21.
    F.D.M. Haldane and E.H. Rezayi, Phys. Rev. B31:2529 (1985).Google Scholar
  22. 22.
    D. Yoshioka, J. Phys. Soc. Jpn. 53:3740 (1984).CrossRefGoogle Scholar
  23. 23.
    R. Morf and B.I. Halperin, private communication.Google Scholar
  24. 24.
    C. Kallin and B.I. Halperin, Phys. Rev. B30:5655 (1984).Google Scholar
  25. 25.
    R.B. Laughlin, Physica 126B:254 (1984).Google Scholar
  26. 26.
    P. Pietiläinen and T. Chakraborty, private communication.Google Scholar
  27. 27.
    A.H. MacDonald, H.C.A. Oji, and S.M. Girvin, Phys. Rev. Lett. 55:2208 (1985).CrossRefGoogle Scholar
  28. 28.
    C. Kallin and B.I. Halperin, Phys. Rev. B31:3635 (1985).Google Scholar
  29. 29.
    Z. Schlesinger, S.J. Allen, J.C.M. Hwang, P.M. Platzman, and N. Tzoar, Phys. Rev. B30:435 (1984).Google Scholar
  30. 30.
    Z. Schlesinger, S.J. Allen, J.C.M. Hwang, and H. Le, in “Proc. 17th Int. Conf. Physics Semiconductors,” D.J. Chadi and W.A. Harrison eds., Springer-Verlag, New York (1985) p.291.Google Scholar
  31. 31.
    G.L.J.A. Rikken, H.W. Myron, P. Wyder, G. Weimann, W. Schlapp, R.E. Horstman, and J. Wolter, J. Phys. C18: L175 (1985).Google Scholar
  32. 32.
    R. Lassing, W. Seidenbusch, E. Gornik, and G. Weiman, in “Proc. 18th Int. Conf. Physics Semiconductors,” O. Engstrom ed., World Scientific, Singapore (1987) p539.Google Scholar
  33. 33.
    Z. Schlesinger, W.I. Wang and A.H. MacDonald, Phys. Rev. Lett. 58:73 (1987).CrossRefGoogle Scholar
  34. 34.
    A.H. MacDonald and G.C. Aers, Phys. Rev. B29:5976 (1984).Google Scholar
  35. 35.
    D. Yoshioka, Prog. Theor. Phys. Suppl. No.84:97 (1985).CrossRefGoogle Scholar
  36. 36.
    F.C. Zhang, V.Z. Vulovic, Y. Guo, and S. Das Sarma, Phys. Rev. B32:6920 (1985).Google Scholar
  37. 37.
    E.H. Rezayi and F.D.M. Haldane, Phys. Rev. B32:6924 (1985).Google Scholar
  38. 38.
    D. Yoshioka, J. Phys. Soc. Jpn. 56:1301 (1987).CrossRefGoogle Scholar
  39. 39.
    D. Yoshioka, XVIII International Conference on Low Temperature Physics, Kyoto 1987.Google Scholar
  40. 40.
    J. Wakabayashi, S. Sudou, S. Kawaji, K. Hirakawa, and H. Sakaki, private Communication.Google Scholar

Copyright information

© Plenum Press, New York 1988

Authors and Affiliations

  • Daijiro Yoshioka
    • 1
  1. 1.College of General EducationKyushu UniversityFukuokaJapan

Personalised recommendations