Abstract
Our study of Anderson's tight binding model for strongly disordered electronic systems is extended to a numerical treatment of thed c-conductivityσ atT=0. For 100 × 100 square lattices, 129 × 129 triangular lattices, and for diamond lattices with 27,000 sites, the behaviour ofσ is studied as a function of the Fermi energy and the disorder. The calculations are based on the exact eigenfunction representation of the Kubo formula, which is evaluated by the systematic application of recursion algorithms. Our results are in favour of Mott's original suggestion of a minimum metallic conductivityσ min, both in two and three dimensions. In two dimensions we find the universal value ofσ min=(0.11 ±0.02)e 2/ℏ.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Stein, J., Krey, U.: Z. PhysikB 34, 287 (1979), and references therein
Haydock, R., Heine, V., Kelly, M.J.: J. Phys. C: Solid St. Phys.8, 2591 (1975)
Eliott, R.J., Krumhansl, J.A., Leath, P.L.: Rev. Mod. Phys.46, 465 (1974)
Licciardello, D.C., Thouless, D.J.: J. Phys. C: Solid St. Phys.8, 4157 (1975)
Kramer, B., Weaire, D.: J. Phys. C: Solid St. Phys.11, L5 (1978)
Prelovšek, P.: Phys. Rev.B 18, 3657 (1978); Solid State Commun.31, 179 (1979)
Mott, N.F., Davis, E.: Electronic Processes in Non-Crystalline Materials. Oxford: Clarendon Press 1971
Schuster, H.G.: Z. PhysikB 31, 99 (1978)
Götze, W., Prelovšek, P., Wölfle, P.: Solid State Commun.30, 369 (1979)
Abrahams, E., Anderson, P.W., Licciardello, D.C., Ramakrishnan, T.V.: Phys. Rev. Lett.42, 673 (1979)
Oppermann, R., Wegner, F.J.: Z. PhysikB 34, 327 (1979)
Lee, P.: Phys. Rev. Lett.42, 1492 (1979)
Sherrington, D., Kirkpatrick, S.: Phys. Rev. Lett.35, 1792 (1975)
Wegner, F.J.: preprint, Heidelberg 1979
Nelson, D.R., Kosterlitz, J.M.: Phys. Rev. Lett.39, 1201 (1977)
Zittartz, J.: Z. PhysikB 31, 63, 79, 89 (1978)
Kimball, J.G.: J. Phys. C: Solid St. Phys.11, 4347 (1978)
Wagner, V., Krey, U.: Z. PhysikB 30, 367 (1978)
Krey, U.: Z. PhysikB 31, 247 (1978)
Fujiwara, T.: J. Phys. C: Solid St. Phys.10, 5035 (1977)
Wilkinson, H.J.: The Algebraic Eigenvalue Problem. Oxford: Clarendon Press 1965
Anderson, P.W., Abrahams, E., Ramakrishnan, T.V.: Phys. Rev. Lett.43, 718 (1979)
Dolan, G.J., Osheroff, D.D.: Phys. Rev. Lett.43, 721 (1979)
Anderson, P.W.: Phys. Rev.109, 1492 (1958)
Economou, E.N., Cohen, M.W.: Phys. Rev.B 5, 2391 (1972)
Yoshino, S., Okazaki, M.: J. Phys. Soc. Jap.43, 415 (1977)
Mott, N.F., Davies, E.A.: Electronic Processes in Noncrystalline Material, 2nd edition; Oxford: Clarendon Press 1979
Wegner, F.: Z. PhysikB 25, 537 (1976)
Author information
Authors and Affiliations
Additional information
Based on the thesis of J. Stein, Regensburg 1979
Rights and permissions
About this article
Cite this article
Stein, J., Krey, U. Numerical studies on the anderson localization problem. Z Physik B 37, 13–22 (1980). https://doi.org/10.1007/BF01325498
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01325498