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Elementary Excitations

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The Fractional Quantum Hall Effect

Part of the book series: Springer Series in Solid-State Sciences ((SSSOL,volume 85))

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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.

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References

  1. R. B. Laughlin: Phys. Rev. Lett. 50, 1395 (1983)

    Article  ADS  Google Scholar 

  2. R. B. Laughlin: Surf. Sci. 142, 163 (1984)

    Article  ADS  Google Scholar 

  3. B. I. Halperin: Helv. Phys. Acta 56, 75 (1983)

    Google Scholar 

  4. R. Morf, B. I. Halperin: Phys. Rev. B33, 2221 (1986)

    ADS  Google Scholar 

  5. H. Fertig, B. I. Halperin: Phys. Rev. B36, 6302 (1987)

    ADS  Google Scholar 

  6. B. I. Halperin: Surf. Sci. 170, 115 (1986)

    Article  ADS  Google Scholar 

  7. Tapash Chakraborty: Phys. Rev. B31, 4026 (1985)

    ADS  Google Scholar 

  8. Tapash Chakraborty: Phys. Rev. B34, 2926 (1986)

    ADS  Google Scholar 

  9. J. M. Caillol, D. Levesque, J. J. Weis, J. P. Hansen: J. Stat. Phys. 28, 325 (1982)

    Article  ADS  Google Scholar 

  10. Yu. A. Bychkov, E. I. Rashba: JETP 63, 200 (1986)

    Google Scholar 

  11. S. Kawaji, J. Wakabayashi, J. Yoshino, H. Sakaki: J. Phys. Soc. Jpn. 53, 1915 (1984)

    Article  ADS  Google Scholar 

  12. D. Yoshioka, B. I. Haiperin, P. A. Lee: Phys. Rev. Lett. 50, 1219 (1983)

    Article  ADS  Google Scholar 

  13. D. Yoshioka: J. Phys. Soc. Jpn. 53, 3740 (1984)

    Article  ADS  Google Scholar 

  14. Tapash Chakraborty, P. Pietiläinen, F. C. Zhang: Phys. Rev. Lett. 57, 130 (1986)

    Article  Google Scholar 

  15. Tapash Chakraborty, P. Pietiläinen: Phys. Scr. T14, 58 (1986)

    Article  ADS  Google Scholar 

  16. F. C. Zhang, S. Das Sarma: Phys. Rev. B33, 2903 (1986)

    Google Scholar 

  17. F. D. M. Haldane, E. H. Rezayi: Phys. Rev. Lett. 54, 237 (1985)

    Article  ADS  Google Scholar 

  18. G. Fano, F. Ortolani, E. Colombo: Phys. Rev. B34, 2670 (1986)

    ADS  Google Scholar 

  19. R. Morf, B. I. Haiperin: Z. Phys. B68, 391 (1987)

    Article  ADS  Google Scholar 

  20. A. H. MacDonald, S. M. Girvin: Phys. Rev. B33, 4414 (1986)

    ADS  Google Scholar 

  21. A. H. MacDonald, S. M. Girvin: Phys. Rev. B34, 5639 (1986)

    ADS  Google Scholar 

  22. B. Tausendfreund, K. von Klitzing: Surf. Sci. 142, 220 (1984)

    Article  ADS  Google Scholar 

  23. A. M. Chang, M. A. Paalanen, D. C. Tsui, H. L. Störmer, J. C. Hwang: Phys. Rev. B28, 6133 (1983)

    ADS  Google Scholar 

  24. I. V. Kukushkin, V. B. Timofeev, P. A. Cheremnykh: JETP Lett. 41, 321 (1985)

    ADS  Google Scholar 

  25. I. V. Kukushkin, V. B. Timofeev: JETP 62, 976 (1985)

    Google Scholar 

  26. G. S. Boebinger, A. M. Chang, H. L. Störmer, D. C. Tsui: Phys. Rev. Lett. 55, 1606 (1985)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  28. J. Wakabayashi, S. Kawaji, J. Yoshino, H. Sakaki: J. Phys. Soc. Jpn. 55, 1319 (1986)

    Article  ADS  Google Scholar 

  29. G. E. Ebert, K. von Klitzing, J. C. Maan, G. Remenyi, C. Probst, G. Weimann, W. Schlapp: J. Phys. C17, L775 (1984)

    ADS  Google Scholar 

  30. V. M. Pudalov, S. G. Semenchinskii: JETP Lett. 39, 170 (1984)

    ADS  Google Scholar 

  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)

    ADS  Google Scholar 

  32. A. H. MacDonald, K. L. Liu, S. M. Girvin, P. M. Platzman: Phys. Rev. B33, 4014 (1986)

    ADS  Google Scholar 

  33. A. Gold: Europhys. Lett. 1, 241, 479(E), (1986)

    Article  ADS  Google Scholar 

  34. R. B. Laughlin, M. L. Cohen, J. M. Kosterlitz, H. Levine, S. B. Libby, A. M. M. Pruisken: Phys. Rev. B32, 1311 (1985)

    ADS  Google Scholar 

  35. R. B. Laughlin: Surf. Sci. 170, 167 (1986)

    Article  ADS  Google Scholar 

  36. I. V. Kukushkin, V. B. Timofeev: Surf. Sci. 196, 196 (1988)

    Article  ADS  Google Scholar 

  37. E. Mendez: Surf. Sci. 170, 561 (1986)

    Article  ADS  Google Scholar 

  38. Y. Guldner, M. Voos, J. P. Vieren, J. P. Hirtz, M. Heiblum: Phys. Rev. B36, 1266 (1987)

    ADS  Google Scholar 

  39. R. J. Haug, K. von Klitzing, R. J. Nicholas, J. C. Maan, G. Weimann: Phys. Rev. B 36, 4528 (1987);

    Article  ADS  Google Scholar 

  40. R. J. Haug: Dissertation, Max-Planck-Institut, Stuttgart (1988)

    Google Scholar 

  41. 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. 255

    Google Scholar 

  42. F. D. M. Haldane: Phys. Rev. Lett. 51, 605 (1983)

    Article  MathSciNet  ADS  Google Scholar 

  43. B. I. Halperin: Phys. Rev. Lett. 52, 1583, 2390(E) (1984)

    Article  ADS  Google Scholar 

  44. R. B. Laughlin: In The Quantum Fall Effect, ed. by R. E. Prange, S. M. Girvin (Springer, New York, Berlin, Heidelberg 1987) p. 233

    Google Scholar 

  45. F. D. M. Haldane: In The Quantum Hall Effect, ed. by R. E. Prange, S. M. Girvin (Springer, New York, Berlin, Heidelberg 1987) p. 303

    Google Scholar 

  46. F. C. Zhang: Phys. Rev. B34, 5598 (1986)

    ADS  Google Scholar 

  47. D. Arovas, J. R. Schrieffer, F. Wilczek, Phys. Rev. Lett. 53, 722 (1984)

    Article  ADS  Google Scholar 

  48. A. H. MacDonald, G. C. Aers, M. W. C. Dharma-wardana: Phys. Rev. B31, 5529 (1985)

    ADS  Google Scholar 

  49. D. Yoshioka, P. A. Lee: Phys. Rev. B27, 4986 (1983)

    ADS  Google Scholar 

  50. A. H. MacDonald: Phys. Rev. B30, 4392 (1984)

    ADS  Google Scholar 

  51. A. H. MacDonald, D. B. Murray: Phys. Rev. B32, 2707 (1985)

    ADS  Google Scholar 

  52. F. C. Zhang, Tapash Chakraborty: Phys. Rev. B34, 7076 (1986)

    ADS  Google Scholar 

  53. R. Morf, N. d’Ambrumenil, B. I. Halperin: Phys. Rev. B34, 3037 (1986)

    ADS  Google Scholar 

  54. H. L. Störmer, A. M. Chang, D. C. Tsui, J. C. M. Hwang, A. C. Gossard, W. Wiegmann: Phys. Rev. Lett. 50, 1953 (1983)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Max-Planck-Institut für Festkörperforschung, Heisenbergstrasse 1, D-7000, Stuttgart 80, Fed. Rep. of Germany

    Dr. Tapash Chakraborty

  2. Department of Theoretical Physics, University of Oulu, Linnanmaa, 90570, Oulu 57, Finland

    Dr. Pekka Pietiläinen

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  1. Dr. Tapash Chakraborty
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  2. Dr. Pekka Pietiläinen
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© 1988 Springer-Verlag Berlin Heidelberg

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Chakraborty, T., Pietiläinen, P. (1988). Elementary Excitations. In: The Fractional Quantum Hall Effect. Springer Series in Solid-State Sciences, vol 85. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-97101-3_3

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  • DOI: https://doi.org/10.1007/978-3-642-97101-3_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-97103-7

  • Online ISBN: 978-3-642-97101-3

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