Elementary Excitations

  • Tapash Chakraborty
  • Pekka Pietiläinen
Part of the Springer Series in Solid-State Sciences book series (SSSOL, volume 85)

Abstract

One important result of Laughlin’s theory was the observation that the elementary charged excitations in a stable state v = 1/m are the quasiparticles and quasiholes with fractional electron charge of ±e/m. If one electron is added to the system, it amounts to adding m elementary excitations and hence, the discontinuity in slope of the energy curve can be written as
$$ {\left. {\frac{{\partial E}} {{\partial {N_e}}}} \right|_{v + }} - {\left. {\frac{{\partial E}} {{\partial {N_e}}}} \right|_{v - }} = m\left( {{{\tilde \varepsilon }_p} + {{\tilde \varepsilon }_h}} \right) = m{E_g} $$
(3.1)
where E g is the energy required to create one quasiparticle (with energy ε̃ p) and one quasihole (with energy ε̃ h) well separated from each other. The pinning of the density to v = 1/3 suggests that there will be no low frequency phonon-type of excitations at long wavelengths.

Keywords

Vortex Microwave Recombination Hexagonal GaAs 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 3.1
    R. B. Laughlin: Phys. Rev. Lett. 50, 1395 (1983)ADSCrossRefGoogle Scholar
  2. 3.2
    R. B. Laughlin: Surf. Sci. 142, 163 (1984)ADSCrossRefGoogle Scholar
  3. 3.3
    B. I. Halperin: Helv. Phys. Acta 56, 75 (1983)Google Scholar
  4. 3.4
    R. Morf, B. I. Halperin: Phys. Rev. B33, 2221 (1986)ADSGoogle Scholar
  5. 3.5
    H. Fertig, B. I. Halperin: Phys. Rev. B36, 6302 (1987)ADSGoogle Scholar
  6. 3.6
    B. I. Halperin: Surf. Sci. 170, 115 (1986)ADSCrossRefGoogle Scholar
  7. 3.7
    Tapash Chakraborty: Phys. Rev. B31, 4026 (1985)ADSGoogle Scholar
  8. 3.8
    Tapash Chakraborty: Phys. Rev. B34, 2926 (1986)ADSGoogle Scholar
  9. 3.9
    J. M. Caillol, D. Levesque, J. J. Weis, J. P. Hansen: J. Stat. Phys. 28, 325 (1982)ADSCrossRefGoogle Scholar
  10. 3.10
    Yu. A. Bychkov, E. I. Rashba: JETP 63, 200 (1986)Google Scholar
  11. 3.11
    S. Kawaji, J. Wakabayashi, J. Yoshino, H. Sakaki: J. Phys. Soc. Jpn. 53, 1915 (1984)ADSCrossRefGoogle Scholar
  12. 3.12
    D. Yoshioka, B. I. Haiperin, P. A. Lee: Phys. Rev. Lett. 50, 1219 (1983)ADSCrossRefGoogle Scholar
  13. 3.13
    D. Yoshioka: J. Phys. Soc. Jpn. 53, 3740 (1984)ADSCrossRefGoogle Scholar
  14. 3.14
    Tapash Chakraborty, P. Pietiläinen, F. C. Zhang: Phys. Rev. Lett. 57, 130 (1986)CrossRefGoogle Scholar
  15. 3.15
    Tapash Chakraborty, P. Pietiläinen: Phys. Scr. T14, 58 (1986)ADSCrossRefGoogle Scholar
  16. 3.16
    F. C. Zhang, S. Das Sarma: Phys. Rev. B33, 2903 (1986)Google Scholar
  17. 3.17
    F. D. M. Haldane, E. H. Rezayi: Phys. Rev. Lett. 54, 237 (1985)ADSCrossRefGoogle Scholar
  18. 3.18
    G. Fano, F. Ortolani, E. Colombo: Phys. Rev. B34, 2670 (1986)ADSGoogle Scholar
  19. 3.19
    R. Morf, B. I. Haiperin: Z. Phys. B68, 391 (1987)ADSCrossRefGoogle Scholar
  20. 3.20
    A. H. MacDonald, S. M. Girvin: Phys. Rev. B33, 4414 (1986)ADSGoogle Scholar
  21. 3.21
    A. H. MacDonald, S. M. Girvin: Phys. Rev. B34, 5639 (1986)ADSGoogle Scholar
  22. 3.22
    B. Tausendfreund, K. von Klitzing: Surf. Sci. 142, 220 (1984)ADSCrossRefGoogle Scholar
  23. 3.23
    A. M. Chang, M. A. Paalanen, D. C. Tsui, H. L. Störmer, J. C. Hwang: Phys. Rev. B28, 6133 (1983)ADSGoogle Scholar
  24. 3.24
    I. V. Kukushkin, V. B. Timofeev, P. A. Cheremnykh: JETP Lett. 41, 321 (1985)ADSGoogle Scholar
  25. 3.25
    I. V. Kukushkin, V. B. Timofeev: JETP 62, 976 (1985)Google Scholar
  26. 3.26
    G. S. Boebinger, A. M. Chang, H. L. Störmer, D. C. Tsui: Phys. Rev. Lett. 55, 1606 (1985)ADSCrossRefGoogle Scholar
  27. 3.27
    G. S. Boebinger, A. M. Chang, H. L. Störmer, D. C. Tsui, J. C. M. Hwang, A. Cho, C. Tu, G. Weimann: Surf. Sci. 170, 129 (1986)ADSCrossRefGoogle Scholar
  28. 3.28
    J. Wakabayashi, S. Kawaji, J. Yoshino, H. Sakaki: J. Phys. Soc. Jpn. 55, 1319 (1986)ADSCrossRefGoogle Scholar
  29. 3.29
    G. E. Ebert, K. von Klitzing, J. C. Maan, G. Remenyi, C. Probst, G. Weimann, W. Schlapp: J. Phys. C17, L775 (1984)ADSGoogle Scholar
  30. 3.30
    V. M. Pudalov, S. G. Semenchinskii: JETP Lett. 39, 170 (1984)ADSGoogle Scholar
  31. 3.31
    G. S. Boebinger, H. L. Störmer, D. C. Tsui, A. M. Chang, J. C. M. Hwang, A. Y. Cho, C. W. Tu, G. Weimann: Phys. Rev. B36, 7919 (1987)ADSGoogle Scholar
  32. 3.32
    A. H. MacDonald, K. L. Liu, S. M. Girvin, P. M. Platzman: Phys. Rev. B33, 4014 (1986)ADSGoogle Scholar
  33. 3.33
    A. Gold: Europhys. Lett. 1, 241, 479(E), (1986)ADSCrossRefGoogle Scholar
  34. 3.34
    R. B. Laughlin, M. L. Cohen, J. M. Kosterlitz, H. Levine, S. B. Libby, A. M. M. Pruisken: Phys. Rev. B32, 1311 (1985)ADSGoogle Scholar
  35. 3.35
    R. B. Laughlin: Surf. Sci. 170, 167 (1986)ADSCrossRefGoogle Scholar
  36. 3.36
    I. V. Kukushkin, V. B. Timofeev: Surf. Sci. 196, 196 (1988)ADSCrossRefGoogle Scholar
  37. 3.37
    E. Mendez: Surf. Sci. 170, 561 (1986)ADSCrossRefGoogle Scholar
  38. 3.38
    Y. Guldner, M. Voos, J. P. Vieren, J. P. Hirtz, M. Heiblum: Phys. Rev. B36, 1266 (1987)ADSGoogle Scholar
  39. 3.39
    R. J. Haug, K. von Klitzing, R. J. Nicholas, J. C. Maan, G. Weimann: Phys. Rev. B 36, 4528 (1987);ADSCrossRefGoogle Scholar
  40. 3.39a
    R. J. Haug: Dissertation, Max-Planck-Institut, Stuttgart (1988)Google Scholar
  41. 3.40
    R. B. Laughlin: In Proceedings of the 17 th Int. Conf. on the Physics of Semiconductors, ed. by D. J. Chadi, W. A. Harrison (Springer, New York, Berlin, Heidelberg 1985) p. 255Google Scholar
  42. 3.41
    F. D. M. Haldane: Phys. Rev. Lett. 51, 605 (1983)MathSciNetADSCrossRefGoogle Scholar
  43. 3.42
    B. I. Halperin: Phys. Rev. Lett. 52, 1583, 2390(E) (1984)ADSCrossRefGoogle Scholar
  44. 3.43
    R. B. Laughlin: In The Quantum Fall Effect, ed. by R. E. Prange, S. M. Girvin (Springer, New York, Berlin, Heidelberg 1987) p. 233Google Scholar
  45. 3.44
    F. D. M. Haldane: In The Quantum Hall Effect, ed. by R. E. Prange, S. M. Girvin (Springer, New York, Berlin, Heidelberg 1987) p. 303Google Scholar
  46. 3.45
    F. C. Zhang: Phys. Rev. B34, 5598 (1986)ADSGoogle Scholar
  47. 3.46
    D. Arovas, J. R. Schrieffer, F. Wilczek, Phys. Rev. Lett. 53, 722 (1984)ADSCrossRefGoogle Scholar
  48. 3.47
    A. H. MacDonald, G. C. Aers, M. W. C. Dharma-wardana: Phys. Rev. B31, 5529 (1985)ADSGoogle Scholar
  49. 3.48
    D. Yoshioka, P. A. Lee: Phys. Rev. B27, 4986 (1983)ADSGoogle Scholar
  50. 3.49
    A. H. MacDonald: Phys. Rev. B30, 4392 (1984)ADSGoogle Scholar
  51. 3.50
    A. H. MacDonald, D. B. Murray: Phys. Rev. B32, 2707 (1985)ADSGoogle Scholar
  52. 3.51
    F. C. Zhang, Tapash Chakraborty: Phys. Rev. B34, 7076 (1986)ADSGoogle Scholar
  53. 3.52
    R. Morf, N. d’Ambrumenil, B. I. Halperin: Phys. Rev. B34, 3037 (1986)ADSGoogle Scholar
  54. 3.53
    H. L. Störmer, A. M. Chang, D. C. Tsui, J. C. M. Hwang, A. C. Gossard, W. Wiegmann: Phys. Rev. Lett. 50, 1953 (1983)ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • Tapash Chakraborty
    • 1
  • Pekka Pietiläinen
    • 2
  1. 1.Max-Planck-Institut für FestkörperforschungStuttgart 80Fed. Rep. of Germany
  2. 2.Department of Theoretical PhysicsUniversity of OuluOulu 57Finland

Personalised recommendations