Two or More Impurities; Disordered Systems

  • Eleftherios N. Economou
Part of the Springer Series in Solid-State Sciences book series (SSSOL, volume 7)

Abstract

In this chapter we examine first a system consisting of two “impurities” embedded in a periodic tight binding hamiltonian (TBH). The total t-matrix associated with the two impurities is not simply the sum of t-matrices of each impurity but includes infinitely many terms which correspond physically to multiple scattering events. A diagrammatic representation of this fact is shown in Fig.7.1, where the propagation from site i to site j [described by G(i,j)] is decomposed to unperturbed propagations [described by G (n,n’)] and scattering events (described by the t-matrices T l , T m ) from the impurity sites l and m.

Keywords

Nickel 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 7.1
    P. Lloyd: J. Phys. C2, 1717 (1969)ADSGoogle Scholar
  2. 7.2
    R.J. Elliott, J.A. Krumhansl, P.L. Leath: Rev. Mod. Phys. 46, 465 (1974)ADSCrossRefMathSciNetGoogle Scholar
  3. 7.3
    J. Hubbard: Proc. Roy. Soc. Lond. A281, 401 (1964)ADSCrossRefGoogle Scholar
  4. 7.4
    P. Soven: Phys. Rev. 156, 809 (1967)ADSCrossRefGoogle Scholar
  5. 7.5
    D.W. Taylor: Phys. Rev. 156, 1017 (1967)ADSCrossRefGoogle Scholar
  6. 7.6
    K.F. Freed, M.H. Cohen: Phys. Rev. S3, 3400 (1971)ADSCrossRefGoogle Scholar
  7. 7.7
    C.T. White, E.N. Economou: Phys. Rev. B15, 3742 (1977)ADSCrossRefGoogle Scholar
  8. 7.8
    B.G. Nickel, W.H. Butler: Phys. Rev. Lett. 30, 373 (1973)ADSCrossRefGoogle Scholar
  9. 7.9
    H. Schmidt: Phys. Rev. 105, 425 (1957)ADSMATHCrossRefMathSciNetGoogle Scholar
  10. 7.10
    B. Velicky: Phys. Rev. 184, 614 (1969)ADSCrossRefGoogle Scholar
  11. 7.11
    E.N. Economou, C. Papatriantafillou: Phys. Rev. Lett. 32, 1130 (1974);ADSCrossRefGoogle Scholar
  12. C. Papatriantafillou, E.N. Economou, T.P. Eggarter: Phys. Rev. B13, 910 (1976);ADSGoogle Scholar
  13. C. Papatriantafillou, E.N. Economou: Phys. Rev. B13, 920 (1976)ADSCrossRefGoogle Scholar
  14. 7.12
    P.W. Anderson: Phys. Rev. 109, 1492 (1958)ADSCrossRefGoogle Scholar
  15. 7.13
    D.J. Thouless: Phys. Rep. 13C, 94 (1974)ADSCrossRefGoogle Scholar
  16. 7.14
    D.C. Licciardello, E.N. Economou: B11, 3697 (1975)Google Scholar
  17. 7.15
    See, e.g., N.F. Mott, E.A. Davis: Eleotronio Processes in Bon-Crystalline Materials (Oxford University Press, London 1971)Google Scholar
  18. 7.16
    See, e.g., J.T. Edwards, D.J. Thouless: J. Phys. C5, 807 (1972);ADSGoogle Scholar
  19. 7.16a
    K. Schönhammer, W. Brenig: Phys. Lett. A42, 447 (1973);CrossRefGoogle Scholar
  20. D. Weaire, A.R. Williams:J. Phys. C10, 1239 (1977)ADSGoogle Scholar
  21. 7.17
    See, e.g., D.C. Licciardello, D.J. Thouless: Phys. Rev. Lett. 35, 1475 (1975);ADSCrossRefGoogle Scholar
  22. 7.17a
    F.J. Wegner: Z. Phys. B25, 327 (1976)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1979

Authors and Affiliations

  • Eleftherios N. Economou
    • 1
  1. 1.Department of PhysicsUniversity of VirginiaCharlottesvilleUSA

Personalised recommendations