Cumulant Methods in the Theory of Multiphonon Absorption

  • Bernard Bendow
  • Stanford P. Yukon
Part of the Optical Physics and Engineering book series (OPEG)


Recent studies suggest that multiphonon absorption in covalent solids is substantially influenced by contributions due to nonlinear electric moments. We demonstrate that the dielectric response in the latter case may be formulated in terms of a cumulant series involving lattice displacement correlators, which avoids the usual perturbative expansions of the moment and anharmonic potential in powers of displacements, and thus accounts for various classes of phonon processes to infinite order. To assess the utility of the method we compare results obtained by truncating the cumulant series with exact ones, calculated for a single-particle model. For parameters characteristic of typical binary semiconductors, the harmonic approximation to the cumulant yields poor results. On the other hand, the use of anharmonic correlators is shown to provide good agreement with exact behavior after several terms in the cumulant have been included. Overall, the results suggest that cumulant methods are highly promising for calculating multi-phonon absorption coefficients.


Harmonic Approximation Infinite Order Anharmonic Potential Cumulant Method Phonon Process 
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  1. 1.
    S. C. Ying, B. Bendow and S. P. Yukon, in “Physics of Semiconductors,” M. Pilkuhn, ed. ( Tuebner, Stuttgart, 1974 );Google Scholar
  2. B. Bendow, S. P. Yukon and S. C. Ying, Phys. Rev. B10, 2286 (1974).ADSGoogle Scholar
  3. 2.
    D. L. Mills and A. A. Maradudin, Phys. Rev. B10, 1713 (1974).ADSGoogle Scholar
  4. 3.
    M. Sparks, Phys. Rev. B10, 2581 (1974).ADSGoogle Scholar
  5. 4.
    R. Hellwarth and M. Mangir, Phys. Rev. B10, 1635 (1974).ADSGoogle Scholar
  6. 5.
    B. Bendow, S. C. Ying and S. P. Yukon, Phys. Rev. B8, 1679 (1973);ADSGoogle Scholar
  7. B. Bendow, Phys. Rev. B8, 5821 (1973).ADSGoogle Scholar
  8. 6.
    M. Sparks and L. J. Sham, Phys. Rev. B8, 3037 (1973).ADSGoogle Scholar
  9. 7.
    T. C. McGill, R. W. Hellwarth, M. Mangir and H. V. Winston, J. Phys. Chem. Sol. 34, 2105 (1973).ADSCrossRefGoogle Scholar
  10. 8.
    D. L. Mills and A. A. Maradudin, Phys. Rev. B8, 1617 (1973).ADSGoogle Scholar
  11. 9.
    H. B. Rosenstock, J. Appl. Phys. 44, 4473 (1973);ADSCrossRefGoogle Scholar
  12. H. B. Rosenstock, Phys. Rev. B9, 1973 (1974).ADSGoogle Scholar
  13. 10.
    K. V. Namjoshi and S. S. Mitra, Phys. Rev. B9, 815 (1974).ADSGoogle Scholar
  14. 11.
    C. Flytzanis, Phys. Rev. Lett. 29, 772 (1973);ADSCrossRefGoogle Scholar
  15. C. Flytzanis, Phys. Rev. B6, 1264 (1972).ADSGoogle Scholar
  16. 12.
    A. A. Maradudin et al, “Theory of Lattice Dynamics in the Harmonic Approximation”, ( Academic, NY, 1971 ).Google Scholar
  17. 13.
    A. A. Maradudin, in “Solid State Physics”, F. Seitz and D. Turnbull, eds. (Academic, NY, 1966), Vols. 18 and 19Google Scholar
  18. 14.
    B. Szigeti, Proc. Roy. Soc. (London) A258, 377 (1960).MathSciNetADSGoogle Scholar
  19. 15.
    P. C. Kwok, in “Solid State Physics”, op. cit., Ref. 13, Vol. 20.Google Scholar
  20. 16.
    B. Bendow, P. D. Gianino, Y. F. Tsay and S. S. Mitra, Applied Optics 13, 2382 (1974).ADSCrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1975

Authors and Affiliations

  • Bernard Bendow
    • 1
  • Stanford P. Yukon
    • 2
    • 3
  1. 1.Solid State Sciences LaboratoryAir Force Cambridge Research Laboratories (AFSC)Hanscom AFBUSA
  2. 2.Parke Mathematical Labs.CarlisleUSA
  3. 3.Dept of PhysicsBrandeis UniversityWalthamUSA

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