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Springer series in solid-state sciences

Theories for Many-Electron Systems with Strong Electron—Phonon and Interelectron Coulombic Interactions

Nobuo Tsuda, Keiichirō Nasu, Atsushi Fujimori, Kiiti Siratori

Published Jan 1, 2000• 1 citation
Publisher
DOI
10.1007/978-3-662-04011-9_3

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The Hubbard model augmented by the Holstein interaction of localized electrons and optical dispersionless phonons is reduced (with the help of a canonical transformation) to a model, in which there occur jumps of polarons and scattering on “impurity” scatterers, which are accompanied by jumps and scatterings of an unlimited number of phonons. This circumstance and the fact that there is a strong on-site interaction of electrons inherent in the Hubbard model, lead to the need for the formulation of a new theory of the phenomenon and the use of a diagrammatic technique. A theory of perturbations in disorder for electrons moving in the random field of “impurity” scatterers has been developed. A collective mode of the phonon cloud surrounding a polaron has been found and the influence of the processes of scattering of this mode on the energy spectrum of both localized and delocalized polarons has been established. The motion of the delocalized polarons related to their scattering is described in the approximation of chain diagrams, in which the manyparticle irreducible Green’s functions of the polaron are ignored. The electron-energy spectrum obtained consists of four subbands.
We study effects of the Coulomb repulsion on the electron-phonon interaction (EPI) in the Holstein-Hubbard model, using the antiferromagnetic (AF) dynamical mean-field approximation. AF correlations strongly enhance EPI effects on the electron Green's function with respect to the paramagnetic correlated system, but the net effect of the Coulomb interaction is a moderate suppression of the EPI. Doping leads to additional suppression. In contrast, the Coulomb interaction strongly suppresses EPI effects on phonons, but the suppression weakens with doping.