Advertisement

The Anderson Transition and the Nonlinear σ-Model

  • F. J. Wegner
Part of the Springer Series in Solid-State Sciences book series (SSSOL, volume 39)

Abstract

A particle (e.g. an electron) moving in a random one-particle tight-binding potential
$$H = \sum\limits_{r,{r^1}} {{v_{r,{r^1}}}\left| {r > < {r^1}} \right|}$$
(1)
may have localized and extended eigenstates depending on the energy of the particle. The energy Ec which separates the localized states from the extended states is called the mobility edge. Extended states can carry a direct current whereas localized states are bound to a certain region and can move only with the assistance of other mechanisms (e.g. by phonon-assisted hopping). Thus the residual d.c. conductivity is expected to vanish for Fermi energies E in the region of localized states, and to be nonzero for E in the region of the extended states.

Keywords

Extended State Mobility Edge Symplectic Case Anderson Transition Symmetry Breaking Term 
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.
    F. J. Wegner in International Summer School “Recent Advances in Statistical Mechanics”, Brasov (1979) 63Google Scholar
  2. 2.
    D. J. Thouless, p.5, E. Abrahams, p.9, F. Wegner, p.15, Phys. Reports 67 (1980)Google Scholar
  3. 3.
    S. K. Ma, unpublished (1972)Google Scholar
  4. S. F. Edwards, J. Physics C8 (1975) 1660ADSGoogle Scholar
  5. A. Nitzan, K. H. Freed, M. H. Cohen, Phys. Rev. B15 (1977) 4476CrossRefADSGoogle Scholar
  6. 4.
    D. J. Thouless, J. Phys. C8 (1975) 1803ADSGoogle Scholar
  7. 5.
    F. J. Wegner, Z. Phys. B25 (1976) 327Google Scholar
  8. 6.
    A. Aharony, Y. Imry, J. Physics C10 (1977) L487ADSGoogle Scholar
  9. 7.
    F. J. Wegner, Phys. Rev. B19 (1979) 783ADSGoogle Scholar
  10. 8.
    L. Schäfer, F. Wegner, Z. Phys. B38 (1980) 113CrossRefADSGoogle Scholar
  11. 9.
    A. B. Harris, T. C. Lubensky, Sol. St. Comm. 34 (1980) 343CrossRefADSGoogle Scholar
  12. 10.
    F. Wegner, Z. Phys. B35 (1979) 207ADSGoogle Scholar
  13. 11.
    E. Brézin, S. Hikami, J. Zinn-Justin, Nucl. Phys. 6165 (1980) 528CrossRefADSGoogle Scholar
  14. 12.
    S. Hikami, Progr. Theor. Phys. 64 (1980) 1466CrossRefMATHADSMathSciNetGoogle Scholar
  15. 13.
    S. Hikami, A. I. Larkin, Y. Nagaoka, Prog. Theor. Phys. 63 (1980) 707CrossRefADSGoogle Scholar
  16. 14.
    R. Oppermann, K. Jüngling, Phys. Lett. 76A (1980) 449ADSGoogle Scholar
  17. 15.
    K. Jüngling, R. Oppermann, Z. Phys. B38 (1980) 93CrossRefADSGoogle Scholar
  18. 16.
    E. Abrahams, P. W. Anderson, D. C. Licciardello, T. V. Ramakrishnan, Phys. Rev. Lett. 42 (1979) 673CrossRefADSGoogle Scholar
  19. 17.
    R. Oppermann, F. Wegner, Z. Phys. B34 (1979) 327ADSGoogle Scholar
  20. 18.
    L. P. Gorkov, A. I. Larkin, D. E. Khmelnitzkii, Pis. Zh. Eksp. Teor. Fiz. 30 (1979) 248Google Scholar
  21. L. P. Gorkov, A. I. Larkin, D. E. Khmelnitzkii, JETP Lett. 30 (1979) 228ADSGoogle Scholar
  22. 19.
    F. Wegner, Z. Phys. B36 (1980) 209ADSGoogle Scholar
  23. 20.
    F. Wegner, to be publishedGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1982

Authors and Affiliations

  • F. J. Wegner
    • 1
  1. 1.Institut für Theoretische PhysikRuprecht-Karls-UniversitätHeidelbergFed. Rep. of Germany

Personalised recommendations