Zeitschrift für Physik B Condensed Matter

, Volume 35, Issue 3, pp 207–210 | Cite as

The mobility edge problem: Continuous symmetry and a conjecture

  • Franz Wegner
Article

Abstract

An apparently overlooked symmetry of the disordered electron problem is derived. It yields the well-known Ward-identity connecting the one- and two-particle Green's function. This symmetry and the apparent shortrange behaviour of the averaged one-particle Green's function are used to conjecture that the critical behaviour near the mobility edge coincides with that of interacting matrices which have two different eigenvalues of multiplicity zero (due to replicas). As a consequence the exponents of the d.c. conductivity is expected to approach 1 for real matrices and 1/2 for complex matrices as the dimensionality of the system approaches two from above. In two dimensions no metallic conductivity is expected.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Nitzan, A., Freed, K.H., Cohen, M.H.: Phys. Rev. B15, 4476 (1977) compare also: Ma, S.K.: unpublished note (1972) Edwards, S.F.: Phys. C8, 1660 (1975) Thouless, D.J.: J. Phys. C8, 1803 (1975)Google Scholar
  2. 2.
    Aharony, A., Imry, Y.: J. Phys. C10, L487 (1977)Google Scholar
  3. 3.
    Velicky, B.: Phys. Rev.184, 614 (1969)Google Scholar
  4. 4.
    Brézin, E., Hikami, S., Zinn-Justin, J.: to be publishedGoogle Scholar
  5. 5.
    Oppermann, R., Wegner, F.: Z. Physik B34, 327 (1979)Google Scholar
  6. 6.
    Schuster, H.G.: Z. Physik B31, 99 (1978)Google Scholar
  7. 7.
    Wegner, F.: Z. Physik25, 327 (1976)Google Scholar
  8. 8.
    Götze, W., Prelovsek, P., Wölfle, P.: Solid State Communications30, 369 (1979)Google Scholar
  9. 9.
    Abrahams, E., Anderson, P.W., Licciardello, D.C., Ramakrishnan, T.V.: Phys. Rev. Lett.42, 673 (1979)Google Scholar

Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • Franz Wegner
    • 1
  1. 1.Institut für Theoretische PhysikUniversität HeidelbergHeidelberg 1Federal Republic of Germany

Personalised recommendations