Advertisement

Coexistence of Localized and Extended States?

  • Scott Kirkpatrick
  • Thomas P. Eggarter
Conference paper
Part of the The IBM Research Symposia Series book series (IRSS)

Abstract

The localized electronic states of a simple model of a substitutional alloy are studied in the strong scattering or separated subband limit, using the tight-binding approximation. We observe states localized in small isolated clusters (as studied in percolation theory), and localized states decaying exponentially at large distances (as in the Anderson model), plus a class of small localized states which have not been discussed before. These last states occur at special energies in the middle of the band, yet are not physically isolated from the rest of the material, or from the extended states of the system.

Keywords

Localize State Monte Carlo Sample Extended State Localize Excita Coherent Potential Approximation 
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.
    P. Dean, Proc. Royal Soc. (London) A, 254, 507 (1960). Sharp structure in the density of states had previously been observed by R. Landauer and J. C. Helland, J. Chem. Phys. 22, 1655 (1954). For a review of Monte Carlo calculations on alloys, and description of numerical techniques, see P. Dean, Rev. Mod. Phys. 44, 127 (1972).CrossRefGoogle Scholar
  2. 2.
    N. F. Mott and W. D. Twose, Adv. in Phys. 10, 107 (1961).CrossRefGoogle Scholar
  3. 3.
    P. W. Anderson, Phys. Rev. 109, 1492 (1958).CrossRefGoogle Scholar
  4. 4.
    S. Kirkpatrick and T. P. Eggarter, to appear in Phys. Rev. B15.Google Scholar
  5. 5.
    B. Velicky, S. Kirkpatrick and H. Ehrenreich, Phys. Rev. 175, 747 (1968), and Appendix B of Phys. Rev. B1, 3250 (1970).CrossRefGoogle Scholar
  6. 6.
    V. K. S. Shante and S. Kirkpatrick, Adv. in Phys. 20, 325 (1971).CrossRefGoogle Scholar
  7. 7.
    S. Kirkpatrick, J. Non-Cryst. Solids 8, to appear as part of the proceedings, Int’l. Conf. on Liquid and Amorphous Semiconductors, Ann Arbor, Mich., 1971.Google Scholar
  8. 8.
    N. F. Mott, Adv. in Physics 16, 49 (1967).CrossRefGoogle Scholar
  9. 9.
    E. N. Economou, S. Kirkpatrick, M. H. Cohen and T. P. Eggarter, Phys. Rev. Letters 25, 520 (1970).CrossRefGoogle Scholar
  10. 10.
    W. Kohn and J. T. Olson, Proceedings of Conf. on Electronic Properties of Ordered and Disordered Solids, Menton, France, 1971 (to appear).Google Scholar
  11. 11.
    M. H. Cohen, Proceedings, Tenth Int’l. Conf. on the Physics of Semiconductors, Cambridge, Mass., (1970) p. 645.Google Scholar
  12. 12.
    H. Matsuda, Progr. Theoret. Phys. 31, 161 (1964); R. E. Borland, Proc. Phys. Soc. (London) 83, 1027 (1964).CrossRefGoogle Scholar
  13. 13.
    J. E. Gubernatis and P. L. Taylor, J. Phys. C4, L94 (1971).Google Scholar
  14. 14.
    J. Hori and K. Wada, Progr. Theoret. Phys. Suppl. 45, 36 (1970), review this work.CrossRefGoogle Scholar
  15. 15.
    J. T. Edwards and D. J. Thouless, J. Phys. C5, 807 (1972).Google Scholar
  16. 16.
    P. Soven, Phys. Rev. 156, 809 (1967).CrossRefGoogle Scholar
  17. 17.
    B. G. Nickel, Phys. Rev. B4, 4354 (1971); L. Schwartz and E. Siggia, Phys. Rev. B5, 383 (1972); and private communications.Google Scholar
  18. 18.
    G. Lucovsky, M. H. Brodsky and E. Burstein, Phys. Rev. B2, 3295 (1970).CrossRefGoogle Scholar
  19. 19.
    R. C. Zeller and R. O. Pohl, Phys. Rev. B4, 2029 (1971).CrossRefGoogle Scholar
  20. 20.
    P. W. Anderson, B. I. Halperin and C. M. Varma, Phil. Mag. 25, 1 (1972); P. Fulde and H. Wagner, Phys. Rev. Letters 27, 1280 (1971); H. B. Rosenstock, J. Non-Cryst. Solids 7, 123 (1972).CrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1973

Authors and Affiliations

  • Scott Kirkpatrick
    • 1
  • Thomas P. Eggarter
    • 2
  1. 1.IBM T. J. Watson Research CenterUSA
  2. 2.James Franck InstituteUniversity of ChicagoUSA

Personalised recommendations