Advertisement

Dynamics of Localized Phonon Modes

  • M. Balkanski
Part of the Physics of Solids and Liquids book series (PSLI)

Abstract

Localized states occur in a solid when the translational invariance is lost. The most obvious case of interrupting the translational symmetry is the surface of the crystal lattice. Another case is the presence of a foreign atom in the lattice. In both cases, the force constants of the surface atoms or the foreign atom differ from that in the uniform bulk volume of the lattice and the atoms concerned have vibrations out of the perfect crystal. These vibrations are called “localized modes.”

Keywords

Force Constant Localize Mode Perfect Crystal Impurity State Phonon Dispersion 
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.
    R. F. Wallis, Phys. Rev. 105, 540 (1957).ADSCrossRefzbMATHGoogle Scholar
  2. 2.
    R. F. Wallis, Phys. Rev. 116, 302 (1959).MathSciNetADSCrossRefzbMATHGoogle Scholar
  3. 3.
    R. F. Wallis, Surf. Sci. 2, 146 (1964).ADSCrossRefGoogle Scholar
  4. 4.
    H. Kaplan, Phys. Rev. 125, 1271 (1962).ADSCrossRefGoogle Scholar
  5. 5.
    J. Hori and T. Asahi, Prog. Theor. Phys. 31, 49 (1964).ADSCrossRefGoogle Scholar
  6. 6.
    E. J. Routh, Dynamics of a System of Rigid Bodies, Dover, New York (1955).zbMATHGoogle Scholar
  7. 7.
    Lord Rayleigh, Theory of Sound, Vol. 1, Dover, New York (1955).Google Scholar
  8. 8.
    I. M. Lifshitz, Nuovo Cimento, Suppl, 3, 716 (1956).MathSciNetCrossRefGoogle Scholar
  9. 9.
    E. W. Montroll and P. B. Potts, Phys. Rev. 100, 525 (1955);MathSciNetADSCrossRefGoogle Scholar
  10. 9a.
    E. W. Montroll and P. B. Potts, Phys. Rev. 102, 72 (1956).ADSCrossRefzbMATHGoogle Scholar
  11. 10.
    R. J. Elliott, Phil. Mag. 1, 298 (1956).ADSCrossRefGoogle Scholar
  12. 11.
    R. J. Elliott, Phonons, Aberdeen Summer School Lectures, Oliver and Boyd (1965).Google Scholar
  13. 12.
    A. A. Maradudin, Rep. Prog. Phys. 28, 331 (1965).ADSCrossRefGoogle Scholar
  14. 13.
    D. W. Taylor, in: Dynamical Properties of Solids (G. K. Horton and A. A. Maradudin, eds.), Vol. 2, p. 285, North-Holland Publishing Company, Amsterdam (1965).Google Scholar
  15. 14.
    R. Kubo, J. Phys. Soc. Jpn. 12, 570 (1957).MathSciNetADSCrossRefGoogle Scholar
  16. 15.
    D. N. Zubarev, Sov. Phys. Usp. 3, 320 (1960).MathSciNetADSCrossRefGoogle Scholar
  17. 16.
    R. J. Elliott and P. G. Dawber, Proc. R. Soc. London, Ser. A 273, 222 (1963);ADSCrossRefzbMATHGoogle Scholar
  18. 16a.
    R. J. Elliott and P. G. Dawber, Proc. Phys. Soc. 81, 521 (1963);CrossRefGoogle Scholar
  19. 16b.
    M. Balkanski and W. Nazarewicz, J. Phys. Chem. Solids 27, 671 (1966);ADSCrossRefGoogle Scholar
  20. 16c.
    R. M. Chrenko, R. S. McDonald, and E. M. Pell, Phys. Rev. A 138, 1775 (1965).ADSGoogle Scholar
  21. 17.
    M. Wadner, M. A. Miller, and W. A. Spitzer, Phys. Rev. A 140, 172 (1965).ADSGoogle Scholar
  22. 18.
    P. Pfeuty, Thesis, Paris (1968).Google Scholar
  23. 19.
    M. Balkanski, R. J. Elliott, W. Nazarewicz, and P. Pfeuty, Lattice Defects in Semiconductors (R. R. Hasiguti, ed.), Tokyo (1968).Google Scholar
  24. 20.
    R. J. Elliott and P. Pfeuty, J. Phys. Chem. Solids 28, 1789 (1967).ADSCrossRefGoogle Scholar
  25. 21.
    G. Benedek and G. P. Nardelli, Phys. Rev. A 155, 100 (1967).Google Scholar
  26. 22.
    D. Strauch and J. B. Page, Int. Conf. on Localized Excitations, Irvine, Plenum Press, New York (1968).Google Scholar
  27. 23.
    P. Pfeuty, J. L. Birman, M. A. Nusimovici, and M. Balkanski, Int. Conf. on Localized Excitations, Irvine Plenum Press, New York (1968).Google Scholar
  28. 24.
    M. Balkanski, R. Beserman, and L. K. Vodopionou, Int. Conf. on Localized Excitations, Irvine, Plenum Press, New York (1968).Google Scholar
  29. 25.
    M. Balkanski and R. Beserman, Proc. Conf. Semiconductors, Moscow, Nauka, Leningrad (1968).Google Scholar
  30. 26.
    K. P. Jain, S. Nakashima, M. Jouanne, E. Amzallag, and M. Balkanski, Solid State Commun. 33, 1079 (1980).ADSCrossRefGoogle Scholar
  31. 27.
    M. A. Kanehisa, M. Balkanski, and R. J. Elliott, J. Phys. Soc. Jpn. 49, Suppl. A, 699 (1980).Google Scholar
  32. 28.
    S. M. Kogan and R. A. Suris, Zh. Eksp. Teor. Fiz. 50, 1279 (1966);Google Scholar
  33. 28a.
    S. M. Kogan and R. A. Suris, Sov. Phys. JETP 23, 850 (1966).ADSGoogle Scholar
  34. 29.
    P. J. Dean, D. D. Manchon Jr., and J. J. Hopfield, Phys. Rev. Lett. 25, 1027 (1970).ADSCrossRefGoogle Scholar
  35. 30.
    A. S. Barker Jr., Phys. Rev. B 7, 2507 (1973).MathSciNetADSCrossRefGoogle Scholar
  36. 31.
    D. C. Reynolds, C. W. Litton, and T. C. Collins, Phys. Rev. B 4, 1868 (1971).ADSCrossRefGoogle Scholar
  37. 32.
    H. Venghaus and P. J. Dean, Phys. Rev. B 21, 1596 (1980).ADSCrossRefGoogle Scholar
  38. 33.
    E. I. Rashba, Pis’ma Zh. Eksp. Teor. Fiz. 15, 577 (1972)Google Scholar
  39. 33a.
    E. I. Rashba, JETP Lett. 15, 411 (1972);ADSGoogle Scholar
  40. 33b.
    E. I. Rashba, Zh. Eksp. Teor. Fiz. 71, 319 (1976)Google Scholar
  41. 33c.
    E. I. Rashba, [Sov. Phys. JETP 40, 166 (1976)].ADSGoogle Scholar
  42. 34.
    J. Mahanty and V. V. Paranjape, Phys. Rev. B 10, 2596 (1974).ADSCrossRefGoogle Scholar
  43. 35.
    Y. B. Levinson and E. I. Rashba, Rep. Prog. Phys. 36, 1499 (1973).ADSCrossRefGoogle Scholar
  44. 36.
    M. V. Klein, in: Light Scattering in Solids (M. Cardona, ed.), p. 147, Springer-Verlag, Berlin (1975).CrossRefGoogle Scholar
  45. 37.
    W. Kohn, in Solid State Physics (F. Seitz and D. Turnbull, eds.), Vol. 5, p. 257, Academic Press, New York (1957).Google Scholar
  46. 38.
    A. Baldereschi and N. O. Lipari, Phys. Rev. B 8, 2697 (1973).ADSCrossRefGoogle Scholar
  47. 39.
    M. Kanehisa, D. Petritis, and M. Balkanski, Phys. Rev. B 31, 6469 (1985).ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1986

Authors and Affiliations

  • M. Balkanski
    • 1
  1. 1.Laboratoire de Physique des Solides associé au C.N.R.S.Université P. et M. CurieParis Cédex 05France

Personalised recommendations