Lectures on Localization

  • D. J. Thouless


In almost all problems in solid state physics disorder plays some part. For a perfect solid we can discuss Bloch waves for the electrons and the normal modes that give phonons, and that is sufficient for a discussion of equilibrium thermal properties, for the cyclotron resonance and oscillatory behavior in a magnetic field that show the structure of the Fermi surface. However, disorder is essential in any discussion of electrical or thermal conductivity, and without disorder thermal equilibrium would never be established. In the usual theory of metals the disorder acts as a small perturbation on the ideal system, causing transitions between electron eigenstates and broadening energy levels. Much of transport theory is based on the idea that such transitions occur independently of one another.


Localize State Wave Packet Fermi Surface Inelastic Scattering Extended State 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    P.W. Anderson, Phys. Rev., 109, 1492 (1958).CrossRefGoogle Scholar
  2. 2.
    N.F. Mott, J. Non-cryst. Solids, 1, 1 (1968).CrossRefGoogle Scholar
  3. 3.
    N.F. Mott and E.A. Davis, ‘Electronic Processes in Non-Crystalline Materials’ (Clarendon Press, Oxford, 2nd ed. 1979 ).Google Scholar
  4. 4.
    D.J. Thouless, Phys. Reports, 13C, 94 (1974).Google Scholar
  5. 5.
    D.J. Thouless, in ‘Ill-Condensed Matter’, ed. R. Balian, R. Maynard and G. Toulouse ( North-Holland, Amsterdam, 1979 ), pp. 1–62.Google Scholar
  6. 6.
    F.J. Wegner, Phys. Rev., B19, 783 (1979).CrossRefGoogle Scholar
  7. 7.
    R. Abou-Chacra, P.W. Anderson and D.J. Thouless, J. Phys., C6, 1734 (1973).Google Scholar
  8. 8.
    S. Yoshino and M. Okazaki, J. Phys. Soc. Japan, 43, 415 (1977).CrossRefGoogle Scholar
  9. 9.
    D.C. Licciardello and D.J. Thouless, J. Phys., C11, 925 (1977).Google Scholar
  10. 10.
    W. Götze, P. Prelovsek and P. Wölfle, Solid St. Commun., 30, 369 (1979).CrossRefGoogle Scholar
  11. 11.
    E. Abrahams, P.W. Anderson, D.C. Licciardello and T.V. Rama-krishnan, Phys. Rev. Letters, 42, 673 (1979).CrossRefGoogle Scholar
  12. 12.
    N.F. Mott and W.D. Twose, Adv. Phys., 10, 107 (1960).CrossRefGoogle Scholar
  13. 13.
    R. Landauer, Phil. Mag., 21, 863 (1970).CrossRefGoogle Scholar
  14. 14.
    P.W. Anderson, D.J. Thouless, E. Abrahams and D.S. Fisher, Phys. Rev. B, to be published.Google Scholar
  15. 15.
    K. Ishii, Supp. Progr. Theor. Phys., 53, 77 (1977).Google Scholar
  16. 16.
    A.A. Abrikosov and I.A. Ryzhkin, Adv. Phys., 27, 147 (1978).CrossRefGoogle Scholar
  17. 17.
    G. Czycholl and B. Kramer, Solid St. Commun., 32, 945 (1979).CrossRefGoogle Scholar
  18. 18.
    S. Kirkpatrick and D.J. Thouless, preprint.Google Scholar
  19. 19.
    P.A. Lee, Phys. Rev. Letters, 42, 1492 (1979).CrossRefGoogle Scholar
  20. 20.
    J. Stein and V. Krey, Z. Physik, B37, 13 (1980).Google Scholar
  21. 21.
    P.B. Allen, preprint.Google Scholar
  22. 22.
    R. Haydock, preprint.Google Scholar
  23. 23.
    D.J. Thouless, Phys. Rev. Letters, 39, 1167 (1977);CrossRefGoogle Scholar
  24. D.J. Thouless, J. Non-cryst. Solids, 3, 35 (1980);Google Scholar
  25. D.J. Thouless, Solid St. Commun., to be published.Google Scholar
  26. 24.
    N. Giordano, W. Gilson and D.E. Prober, Phys. Rev. Letters, 43, 725 (1979).CrossRefGoogle Scholar
  27. 25.
    N. Giordano, to be published.Google Scholar
  28. 26.
    P. Chaudhari and H.-U. Habermeier, Phys. Rev. Letters, 44, 40 (1980);CrossRefGoogle Scholar
  29. P. Chaudhari and H.-U. Habermeier, Solid St. Commun., to be published.Google Scholar
  30. 27.
    P. Chaudhari, private communication.Google Scholar
  31. 28.
    C.J. Adkins, S. Pollitt and M. Pepper, J. Physique Colloq., 37, C4, 343 (1976).Google Scholar
  32. 29.
    R.C. Dynes, J.P. Garno and J.M. Rowell, Phys. Rev. Letters, 40, 479 (1978).CrossRefGoogle Scholar
  33. 30.
    G.J. Dolan and D.D. Osheroff, Phys. Rev. Letters, 43, 721 (1979).CrossRefGoogle Scholar
  34. 31.
    D.J. Bishop, D.C. Tsui and R.C. Dynes, Phys. Rev. Letters, 44, 1153 (1980).CrossRefGoogle Scholar
  35. 32.
    R.G. Wheeler and K.M. Cham, Private communication.Google Scholar
  36. 33.
    G. Deutscher, B. Bandyopadhyay, T. Chui, P. Lindenfeld, W.L. McLean and T. Worthington, Phys. Rev. Letters, 44, 1150 (1980).CrossRefGoogle Scholar
  37. 34.
    B.L. Altshuler, A.G. Aronov and P.A. Lee, Phys. Rev. Letters, 44, 1288 (1980).CrossRefGoogle Scholar
  38. 35.
    N.F. Mott, M. Pepper, S. Pollitt, R.H. Wallis and C.J. Adkins, Proc. Roy. Soc., A345, 169 (1975).CrossRefGoogle Scholar
  39. 36.
    A.F. Ioffe and A.R. Regel, Progr. Semiconductors, 4, 237 (1960).Google Scholar
  40. 37.
    Y. Imry, Phys. Rev. Letters, 44, 469 (1980).CrossRefGoogle Scholar
  41. 38.
    B.W. Dodson, W.L. McMillan, J.M. Mochel and R.C. Dynes, Bull. Am. Phys. Soc., 25, 338 (1980).Google Scholar
  42. 39.
    G. Parisi, J. Phys. C, to be published.Google Scholar
  43. 40.
    R. Opperman and F.J. Wegner, Z. Physik, B34, 327 (1979);Google Scholar
  44. F.J. Wegner, Z. Physik, B35, 783 (1979)Google Scholar
  45. 41.
    D.E. Khmelnitzkii, preprint.Google Scholar
  46. 42.
    A. Houghton, A. Jevicki, R. Kenway and A. Pruisken, preprint.Google Scholar
  47. 43.
    M. Sayer, R. Chen, R. Fletcher and A. Mansingh, J. Phys., C8, 2059 (1975).Google Scholar
  48. 44.
    M.L. Knotek, Solid St. Commun., 17, 1431 (1975).Google Scholar

Copyright information

© Plenum Press, New York 1983

Authors and Affiliations

  • D. J. Thouless
    • 1
  1. 1.Becton CenterYale UniversityNew HavenUSA

Personalised recommendations