- Access by Xinjiang University
Study of localization in Anderson's model for random lattices
Phys. Rev. B 11, 3697 – Published 15 May, 1975
DOI: https://doi.org/10.1103/PhysRevB.11.3697
Abstract
Various approaches to the problem of localization within Anderson's model for random lattices are examined. A new approximate criterion based on the Economou-Cohen approximation is developed. Results are presented and compared for several real lattices and for various probability distributions of the site energies. The new criterion is shown to be remarkably successful.
References (46)
- N. F. Mott and E. A. Davis, Electronic Processes in Non-Crystalline Materials (Oxford U. P., London, 1971)
- E. N. Economou, New Developments in Semiconductors, edited by P. R. Wallace, R. Harris, and M. J. Zuckermann (Noordhoff, Leyden, 1973) E. N. Economou, M. H. Cohen, K. Freed, and S. Kirkpatrick, in Amorphous and Liquid Semiconductors, edited by J. Tauc (Plenum, New York, 1974) E. N. Economou, in The Proceedings of the New Delhi Winter School 1972 (unpublished) D. J. Thouless, Phys. Rep. 13C, 94 (1974)
- P. W. Anderson, Comments Solid State Phys. 2, 193 (1970)
- P. W. Anderson, Phys. Rev. 109, 1492 (1958)
- J. M. Ziman, J. Phys. C 2, 1230 (1969)
- D. J. Thouless, J. Phys. C 3, 1559 (1970)
- M. Kikuchi, J. Phys. Soc. Jpn. 29, 296 (1970)
- E. N. Economou and Morrel H. Cohen, Phys. Rev. Lett. 25, 1445 (1970) Phys. Rev. B 5, 2931 (1972)
- D. J. Thouless, J. Non-Cryst. Solids 8-10, 461 (1972)
- D. C. Herbert and R. Jones, J. Phys. C 4, 1145 (1971)
- T. Lukes, J. Non-Cryst. Solids 8-10, 470 (1972)
- M. A. Ball, J. Phys. C 4, 1747 (1971) N. Kumar and R. R. Subramanian, 7, 1817 (1974)
- R. Haydock and A. Mookerjee, J. Phys. C 7, 3001 (1974)
- S. F. Edwards, in New Developments in Semiconductors, edited by P. R. Wallace, R. Harris, and M. J. Zuckermann (Noordhoff, Leyden, 1973), p. 249
- K. F. Freed, Phys. Rev. B 5, 4802 (1972)
- R. Abou-Chacra, P. W. Anderson, and D. J. Thouless, J. Phys. C 6, 1734 (1973)
- A. R. Bishop, Philos. Mag. 27, 651 (1973) ibid.27, 1489 (1973) J. Phys. C 6, 2089 (1973) report, 1974 (unpublished)
- D. C. Licciardello and E. N. Economou, Solid State Commun 15, 969 (1974)
- N. F. Mott, Phys. Rev. Lett. 31, 466 (1973)
- J. T. Edwards and D. J. Thouless, J. Phys. C 5, 807 (1972)
- K. Schönhammer and W. Brenig, Phys. Lett. A 42, 447 (1973) private communication
- E. N. Economou, S. Kirpatrick, M. H. Cohen, and T. P. Eggarter, Phys. Rev. Lett. 25, 250 (1970)
- S. R. Broadbent and J. M. Hammersley, Proc. Camb. Philos. Soc. 53, 629 (1957)
- V. K. S. Shante and S. Kirkpatrick, Adv. Phys. 30, 325 (1971)
- B. J. Last and D. J. Thouless, J. Phys. C 7, 699 (1974)
- E. Feenberg, Phys. Rev. 74, 206 (1948)
- K. M. Watson, Phys. Rev. 105, 1388 (1957)
- R. Abou-Chacra and D. J. Thouless, J. Phys. C 7, 65 (1974)
- A. Mookerjee, J. Phys. C 7, 4069 (1974)
- E. N. Economou and Morrel H. Cohen, Phys. Rev. B 4, 396 (1971)
- P. W. Anderson, Proc. Natl. Acad. Sci. USA 69, 1097 (1972)
- R. A. Abram and S. F. Edwards, J. Phys. C 5, 1183 (1972) ibid.5, 1196 (1972)
- B. Velicky, S. Kirkpatrick, and H. Ehrenreich, Phys. Rev. 175, 747 (1968)
- R. J. Elliott, J. A. Krumhansl, and P. L. Leath, Rev. Mod. Phys. 46, 437 (1974)
- P. Soven, Phys. Rev. 156, 809 (1967) D. W. Taylor, 156, 1017 (1967)
Omitted endnote
- D. C. Licciardello and E. N. Economou, Solid State Commun. 12, 1275 (1973)
- K. Schönhammer, Phys. Lett. A 36, 181 (1971)
Omitted endnote
- K. E. Khor and P. V. Smith, J. Phys. C 4, 2029 (1971) ibid.4, 2041 (1971)
- A. Mookerjee, Ph. D. thesis (Cambridge University, 1972) (unpublished)
- E. N. Economou, Phys. Rev. Lett. 28, 1206 (1972)
- D. C. Licciardello, E. N. Economou, and C. Papatriantaphillou, Amorphous Magnetism, edited by H. O. Hooper and A. M. de Graaf (Plenum, New York, 1973), p. 387
- F. Brouers, J. Phys. C 1, 1 (1971) ibid.1773 (1971)
- N. Kumar, J. Heinrichs, and A. A. Kumar (unpublished)
- A. R. Bishop, Phys. Lett. A 49, 5 (1974)