Advertisement

Electronic States in Two-Dimensional Random Systems in the Presence of a Strong Magnetic Field

  • B. Kramer
  • Y. Ono
  • T. Ohtsuki
Conference paper
Part of the Springer Series in Solid-State Sciences book series (SSSOL, volume 87)

Abstract

We discuss the status of the theory of localisation in two dimensions in the presence of a strong perpendicular magnetic field. The model potentials which have been used are described. The importance of the various length scales in the problem is pointed out. A summary of the currently available definitions of localisation is given. The results for the localisation length, the inverse participation number of the states, and their shape, obtained so far are summarised.

Keywords

Critical Exponent Critical Behavior Localisation Length Equipotential Line Landau Model 
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.
    K. von Klitzing, G. Dorda and M. Pepper, Phys. Rev. Letters 45 494 (1980)CrossRefGoogle Scholar
  2. 2.
    H. Aoki, Rep. Progr. Phys. 50 655 (1987)CrossRefGoogle Scholar
  3. 3.
    B. Kramer, preprint, to be published in Procs. 5th Int. Winterschool on New Dev. Sol. St.Phys., Mautemdorf Austria, (1988)Google Scholar
  4. 4.
    B. Kramer, Y. Ono and T. Ohtsuki, Surface. Sci. 196 127 (1988)CrossRefGoogle Scholar
  5. 5.
    T. Ando, A. B. Fowler and F. Stern, Rev. Mod. Phys. 54 437 (1982)CrossRefGoogle Scholar
  6. 6.
    T. Ando and H. Aoki, Phys. Rev. Letters 54 832 (1985); J. Phys. Soc Japan 54 2238 (1985)CrossRefGoogle Scholar
  7. 7.
    J. M. Luttinger, Phys. Rev. 84 814 (1951)CrossRefGoogle Scholar
  8. 8.
    D. R. Hofstadter, Phys. Rev. B14 2239 (1976)CrossRefGoogle Scholar
  9. 9.
    G. H. Wannier, G. M. Obermair, and R. Ray, phys. stat. sol. (b) 93 337 (1979)Google Scholar
  10. 10.
    L. Schweitzer, B. Kramer, and A. MacKinnon, J. Phys. C17 4111 (1984)Google Scholar
  11. 11.
    A. MacKinnon, B. Kramer, and L. Schweitzer, Proc. LTTPIM Suppl. (PTB-PG-1) 314 (PTB Braunschweig 1984 )Google Scholar
  12. 12.
    A. MacKinnon, B. Kramer, Lecture Notes in Physics 177 74 (1983)CrossRefGoogle Scholar
  13. 13.
    H. Aoki, J. Phys. C18 L67 (1985); Procs. LTTPIM Suppl. (PTB-PG-1) 302 (PTB Braunschweig 1984 )Google Scholar
  14. 14.
    P. G. Harper, Proc. Phys. Soc. London A68 874 (1955)CrossRefGoogle Scholar
  15. 15.
    A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw Hill New York) 1984 )Google Scholar
  16. 16.
    Y. Ono, J. Phys. Soc. Japan 512055, 3544 (1982); 52 2492 (1983); Suppl. 247; 53 2342 (1984)Google Scholar
  17. 17.
    S. Hikami and E. Brezin, J. Physique 46 2021 (1985)CrossRefGoogle Scholar
  18. 18.
    H. Levine, S. B. Libby and A. M. M. Pruisken, Nucl. Phys. B240[FS 12] 30, 40, and 57 (1984)Google Scholar
  19. 19.
    A. M. M Pruisken, Nucl. Phys. B235 [FS 11] 277 (1984)CrossRefGoogle Scholar
  20. 20.
    H. A. Weidenmüller, Nucl. Phys. B290 [FS20] 87 (1987)CrossRefGoogle Scholar
  21. 21.
    Masaru Tsukada, J. Phys. Soc. Japan 41 1466 (1976)CrossRefGoogle Scholar
  22. 22.
    S. V. Iordansky, Sol. St. Commun. 43 1 (1982)CrossRefGoogle Scholar
  23. 23.
    R. F. Kazarinov and Serge Luryi, Phys. Rev. B25 7626 (1982)CrossRefGoogle Scholar
  24. 24.
    Y. Ono, J. Phys. Soc. Japan 51, 237 (1982)CrossRefGoogle Scholar
  25. 25.
    S. A. Trugman, Phys. Rev. B27 7539 (1983)CrossRefGoogle Scholar
  26. 26.
    S. Luryi and R. F. Kazarinov, Phys. Rev. B27 1386 (1983)CrossRefGoogle Scholar
  27. 27.
    S. M. Apenko and Yu. E. Lozovik, preprint 196, Acad. Sci (Moscow 1984 )Google Scholar
  28. 28.
    J. T. Chalker, P. D. Coddington, J. Phys. C21 2665 (1988)Google Scholar
  29. 29.
    E. Abrahams, P. W. Anderson, D. C. Licciardello, T. V. Ramakrishnan, Phys. Rev. Letters 42 673 (1979)CrossRefGoogle Scholar
  30. 30.
    F. J. Wegner, Z. Phys. 25 327 (1976)Google Scholar
  31. 31.
    F. J. Wegner,Springer Ser. Sol. St. Sci. 6199 (1985)Google Scholar
  32. 32.
    A. MacKinnon and B. Kramer, Phys. Rev. Letters 47 1546 (1981)CrossRefGoogle Scholar
  33. 33.
    A. MacKinnon and B. Kramer, Z. Phys. B53 1 (1983)CrossRefGoogle Scholar
  34. 34.
    J. Sajeev, M. J. Stephen, Phys. Rev. B28 6358 (198Google Scholar
  35. 35.
    R. Johnston and B. Kramer, Z. Phys. 63 273 (1986)CrossRefGoogle Scholar
  36. 36.
    T. Ando, Prog. Theor. Phys. Suppl. 84 69 (1985)CrossRefGoogle Scholar
  37. 37.
    D. J. Thouless, Phys. Rep. 13 93 (1974)CrossRefGoogle Scholar
  38. 38.
    B. Kramer M. Schreiber, Lecture Notes in Physics 268 351 (1987)CrossRefGoogle Scholar
  39. 39.
    P. Dean, Rev. Mod. Phys. 44 127 (1972)CrossRefGoogle Scholar
  40. 40.
    A. MacKinnon, Z. Phys. B59 385 (1985)CrossRefGoogle Scholar
  41. 41.
    B. Kramer, M. Schreiber, to be publishedGoogle Scholar
  42. 42.
    J. T. Edwards, D. J. Thouless, J. Phys. C5 807 (1972)Google Scholar
  43. 43.
    H. Kühl, PHD Thesis, unpublished (Universität zu Köln 1980 )Google Scholar
  44. 44.
    D. C. Licciardello, D. J. Thouless, J. Phys. C8 4157 (1975); J. Phys. C11 925 (1978)Google Scholar
  45. 45.
    H. Aoki, J. Phys. C15 L1227 (1982); Lecture Notes in Physics 177 11 (1983); J. Phys. C16 1893 (1983); C18 1885 (1984)Google Scholar
  46. 46.
    J. Bell, P. Dean, Disc. Faraday Soc. 50 55 (1970)CrossRefGoogle Scholar
  47. 47.
    F. Wegner, Z. Phys. B36 209 (1980)Google Scholar
  48. 48.
    Y. Ono, Progr. Theor. Phys. (Suppl.) 84 138 (1985)CrossRefGoogle Scholar
  49. 49.
    S. Hikami, Phys. Rev. B29 3726 (1984); Progr. Theor. Phys. 72 722 (1984)CrossRefGoogle Scholar
  50. 50.
    S. Hikami, Progr. Theor. Phys. 76 1210 (1986)CrossRefGoogle Scholar
  51. 51.
    S. Hikami, E. Brezin, Surf. Sci 170 262 (1986)CrossRefGoogle Scholar
  52. 52.
    R. R. P. Singh, S. Chakravarty, Nucl. Phys. B265 [FS15] 265 (1986)CrossRefGoogle Scholar
  53. 53.
    T. Ando, J. Phys. Soc. Japan 521740 (1983); 53 3101, 3126 (1984)Google Scholar
  54. 54.
    T. Ando,Springer Ser. Sol. St. Sci. 39 176 (1982);71 2 (1987); Surf. Sci 196 120 (1988); Springer Procs. in Phys. 28 252 (1988)Google Scholar
  55. 55.
    H. Aoki, Surf. Sci. 196 107 (1988)CrossRefGoogle Scholar
  56. 56.
    H. Aoki, T. Ando, Springer Ser. Sol. St. Sci. 7145 (1987)CrossRefGoogle Scholar
  57. 57.
    B. Kramer, A. MacKinnon, Teubner Texte zur Physik 3 157 (Leipzig 1984 )Google Scholar
  58. 58.
    H. Aoki, J. Phys. C161205 (1983); J. Phys. C17 1875 (1984); Phys. Rev. B33 7310 (1986)Google Scholar
  59. 59.
    G. C. Aers, A. H. MacDonald, J. Phys. C17 5491 (1984)Google Scholar
  60. 60.
    A. MacKinnon, this volumeGoogle Scholar
  61. 61.
    M. Schreiber, B. Kramer, A. MacKinnon, Phys. Scripta, to be published (1988)Google Scholar
  62. 62.
    D. E. Khmel’nitskii, JETP Lett. 38 552 (1983)Google Scholar
  63. 63.
    I. Affleck, Nucl. Phys. B265 [FS15] 409 (1986)CrossRefGoogle Scholar
  64. 64.
    H. Aoki, T. Ando, Surf. Sci. 170 249 (1986)CrossRefGoogle Scholar
  65. 65.
    H. Kunz, and B. Soulliard, J. Physique Lett. 43 L39 (1982)CrossRefGoogle Scholar
  66. 66.
    M. R. Zinnbauer, Nucl. Phys. B235 [FS15] 375 (1986)CrossRefGoogle Scholar
  67. 67.
    T. Ohtsuki, Y. Ono, to be publishedGoogle Scholar
  68. 68.
    H.P. Wei, this volumeGoogle Scholar
  69. 69.
    H.P. Wei, D.C. Tsui, A.M.M. Pruisken, Phys. Rev. B33 1488 (1986)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin, Heidelberg 1989

Authors and Affiliations

  • B. Kramer
    • 1
  • Y. Ono
    • 2
  • T. Ohtsuki
    • 3
  1. 1.Physikalisch-Technische BundesanstaltBraunschweigFed. Rep. of Germany
  2. 2.Toho UniversityFunabashi-shi, Chiba, 274Japan
  3. 3.University of TokyoBunkyo-ku, Tokyo 113Japan

Personalised recommendations