Abstract
A nonlocal dynamic coherent-potential approximation is formulated as a further development of the dynamic coherent-potential method. The nonlocal dynamic coherent-potential approximation is an efficient method of determining the one-exciton Green’s function in a model with the Hamiltonian in the strong-coupling approximation, where a spectrum of optical phonons is assumed, and the exciton-phonon interaction operator is linear or quadratic in the phonon operators. A system of recursion equations is derived, from which the coherent potential is found as a function of the energy E and the wave vector k. An analytical expression is derived for the one-exciton Green’s function in the case of narrow (in comparison with the phonon energy) exciton bands and exciton-phonon interaction linear in the phonon operators. For broader exciton bands and more complex exciton-phonon interaction the system of equations determining the coherent potential represents a recursion algorithm, which can be effectively implemented by numerical means.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. A. Abrikosov, L. P. Gor’kov, and I. E. Dzyaloshinskii, Methods of Quantum Field Theory in Statistical Physics (Prentice-Hall, Englewood Cliffs, New Jersey 1963) [Russian original, Fizmatgiz, Moscow, 1962].
L. D. Lee and D. Pines, Phys. Rev. 88, 960 (1952).
Yu. A. Firsov, in Polarons edited by Yu. A. Firsov [in Russian], Moscow (1975), p. 205.
Y. B. Levinson and E. I. Rashba, Rep. Prog. Phys. 36, 1499 (1973).
P. Soven, Phys. Rev. 156, 809 (1967).
D. W. Taylor, Phys. Rev. 156, 1017 (1967).
V. Velicky, S. Kirkpatrick, and H. Ehrenreich, Phys. Rev. 175, 747 (1968).
Y. Rangette, Y. Yanase, and J. Kübler, Solid State Commun. 12, 171 (1973).
K. Kubo, J. Phys. Soc. Jpn. 36, 32 (1974).
H. Sumi, J. Phys. Soc. Jpn. 36, 770 (1974).
H. Sumi, J. Phys. Soc. Jpn. 38, 825 (1975).
H. Sumi, J. Chem. Phys. 67, 2943 (1977).
V. Čápek and V. Špička, Czech. J. Phys. B 34, 115 (1984).
S. Abe, J. Phys. Soc. Jpn. 57, 4029 (1988).
S. Abe, J. Phys. Soc. Jpn. 57, 4036 (1988).
S. Abe, J. Lumin. 45, 272 (1990).
S. Abe, Rev. Solid State Sci. 4, 191 (1990).
Y. Tokura and T. Koda, Solid State Commun. 40, 299 (1981).
Y. Wada, Y. Tokura, and T. Koda, J. Chem. Phys. 86, 3009 (1987).
N. F. Berk, D. J. Shazeer, and R. A. Tahir-Kheli, Phys. Rev. B 8, 2496 (1973).
S. V. Tyablikov, Zh. Éksp. Teor. Fiz. 23, 381 (1952).
É. I. Rashba, Opt. Spektrosk. 3, 568 (1957).
Y. Toyozawa, Prog. Theor. Phys. 26, 29 (1961).
R. Silbey, Ann. Rev. Phys. Chem. 27, 203 (1976).
J. Singh and A. Matsui, Phys. Rev. B 36, 6094 (1986).
T. Holstein, Ann. Phys. (N.Y.) 8, 325 (1959).
J. Ranninger, Phys. Rev. B 48, 13 166 (1993).
Y. J. Takada, J. Phys. Chem. Solids 54, 1779 (1993).
W. Gautschi, in Handbook of Mathematical Functions, edited by M. Abramowitz and I. A. Stegun (Dover, New York, 1964), p. 295.
Author information
Authors and Affiliations
Additional information
Fiz. Tverd. Tela (St. Petersburg) 39, 1560–1563 (September 1997)
Rights and permissions
About this article
Cite this article
Izvekov, S.V. Excitonic polaron in the molecular crystal model: Nonlocal dynamic coherent-potential approximation. Phys. Solid State 39, 1383–1388 (1997). https://doi.org/10.1134/1.1130084
Received:
Issue Date:
DOI: https://doi.org/10.1134/1.1130084