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Physical Review B

Strong interaction of correlated electrons with acoustical phonons using the extended Hubbard-Holstein model

V. A. Moskalenko, P. Entel, D. F. Digor

Published Aug 22, 2006• 4 citations
Publisher

Abstract

We investigate the interaction of correlated electrons with acoustical phonons using the extended Hubbard-Holstein model. The Lang-Firsov canonical transformation allows us to obtain mobile polarons for which a diagram technique and generalized Wick's theorem is used. In the strong-coupling limit of the electron-phonon interaction, and in the normal as well as in the superconducting phase, chronological thermodynamical averages of products of acoustical phonon-cloud operators can be expressed by one-cloud propagators. The pairing of electrons in the presence of acoustical phonon clouds is discussed and the critical temperature of the superconducting phase transition is determined for the special case $U<0$, where $U$ is the renormalized value of the on-site Coulomb repulsion. The renormalization is caused by the electron-phonon interaction.

DOI
10.1103/physrevb.74.075109

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We investigate the interaction of correlated electrons with acoustical phonons using the extended Hubbard-Holstein model. The Lang-Firsov canonical transformation allows us to obtain mobile polarons for which a diagram technique and generalized Wick's theorem is used. In the strong-coupling limit of the electron-phonon interaction, and in the normal as well as in the superconducting phase, chronological thermodynamical averages of products of acoustical phonon-cloud operators can be expressed by one-cloud propagators. The pairing of electrons in the presence of acoustical phonon clouds is discussed and the critical temperature of the superconducting phase transition is determined for the special case U<0U<0U<0, where UUU is the renormalized value of the on-site Coulomb repulsion. The renormalization is caused by the electron-phonon interaction.
We investigate the interaction of correlated electrons with acoustical phonons using the extended Hubbard–Holstein model. The Lang–Firsov canonical transformation allows one to obtain mobile polarons for which a new diagram technique and generalized Wick’s theorem is used. The physics of emission and absorption of the collective phonon-field mode by the polarons is discussed in detail. In the strong-coupling limit of the electron–phonon interaction, and in the normal as well as in the superconducting phase, chronological thermodynamic averages of products of acoustical phonon-cloud operators can be expressed by the products of one-cloud operator averages. While the normal one-cloud propagator has the form of a Lorentzian, the anomalous one is of Gaussian form and considerably smaller. We have established the Mott–Hubbard and superconducting phase transitions in this model.
We investigate the interaction of correlated electrons with acoustical phonons using the extended \nHubbard–Holstein model. The Lang–Firsov canonical transformation allows one to obtain \nmobile polarons for which a new diagram technique and generalized Wick’s theorem is used. The \nphysics of emission and absorption of the collective phonon-field mode by the polarons is discussed \nin detail. In the strong-coupling limit of the electron-phonon interaction, and in the normal as \nwell as in the superconducting phase, chronological thermodynamical averages of products of \nacoustical phonon-cloud operators can be expressed by the products of one-cloud operator averages. \nWhile the normal one-cloud propagator has the form of a Lorentzian, the anomalous one is of \nGaussian form and considerably smaller. We have established the Mott–Hubbard and superconducting \nphase transitions in this model.
The interaction of strongly correlated electrons with phonons in the framework of the Hubbard-Holstein model is investigated. The electron-phonon interaction is considered to be strong and is an important parameter of the model, in addition to the Coulomb repulsion of electrons and the band filling. This interaction with nondispersive optical phonons is transformed to the problem of mobile polarons using the canonical transformation of Lang and Firsov. We discuss the case where the on-site Coulomb repulsion is exactly canceled by the phonon-mediated attractive interaction. It is suggested that polarons exchanging phonon clouds can lead to polaron pairing and superconductivity. The fact that the frequency of the collective mode of phonon clouds is larger than the bare frequency then determines the superconducting transition temperature.
We investigate the interaction of strongly correlated electrons with phonons in the frame of the Hubbard-Holstein model. The electron-phonon interaction is considered to be strong and is an important parameter of the model besides the Coulomb repulsion of electrons and band filling. This interaction with the nondispersive optical phonons has been transformed to the problem of mobile polarons by using the canonical transformation of Lang and Firsov. A new diagram technique is used in order to handle the strong Coulomb repulsion of the electrons, which leads to a closed set of integral equations for the irreducible on-site many-particle Green's functions. The coupling to the phonons leads to an essential renormalization of the one- and two-particle irreducible Green's functions. It also influences the parameters which control the metal-insulator or superconducting phase transition. In addition we find a collective mode of phonon clouds which surround the polarons. The physics of the emission and absorption of this mode by the polarons has been investigated.
The Hubbard-Holstein model after canonical Lang-Firsov transformation is investigated. Two peculiarities of the model are taken into account: a) the strong electron correlations and b) the fact that the hoppings of polarons between lattice sites are accompanied by an indefinite number of phonons. A new diagram technique based on the classification of irreducible many-particle Green functions or Kubo cumulants is developed. Phonon renormalization of electronic functions is considered. A theorem about connected vacuum diagrams is established, and Dyson equation for electron Green function is obtained.