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arXiv:cond-mat/0509090 · Physical Review B

Effective electron-phonon coupling and polaronic transition in the presence of strong correlation

Paolo Barone, Roberto Raimondi, Massimo Capone, Claudio Castellani

Published Feb 28, 2006• 15 citations
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Abstract

We study the Hubbard-Holstein model using slave-boson mean-field and a variational Lang-Firsov transformation. We identify weak and strong $e$-ph coupling solutions, whose stability depends both on the bare $e$-ph coupling and on the correlation strength. At mean field level the evolution from weak to strong electron-phonon coupling occurs via a first-order polaronic transition if the adiabatic parameter is below a critical value. In the strongly correlated regime and in the adiabatic limit, the region in which the weak-coupling solution is stable is sizeably enlarged with respect to the weakly correlated system and the Mott metal-insulator transition is found to be robust with respect to $e$-ph interaction.

DOI
10.1103/physrevb.73.085120

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We study the Hubbard-Holstein model using slave-boson mean-field and a variational Lang-Firsov transformation. We identify weak and strong eee-ph coupling solutions, whose stability depends both on the bare eee-ph coupling and on the correlation strength. At mean field level the evolution from weak to strong electron-phonon coupling occurs via a first-order polaronic transition if the adiabatic parameter is below a critical value. In the strongly correlated regime and in the adiabatic limit, the region in which the weak-coupling solution is stable is sizeably enlarged with respect to the weakly correlated system and the Mott metal-insulator transition is found to be robust with respect to eee-ph interaction.
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.
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.
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.
The role of the electron-phonon interaction in the Holstein-Hubbard model is investigated in the metallic phase close to the Mott transition and in the insulating Mott phase. The model is studied by means of a variational slave boson technique. At half-filling, mean-field static quantities are in good agreement with the results obtained by numerical techniques. By taking into account Gaussian fluctuations, an analytic expression of the spectral density is derived in the Mott insulating phase showing that an increase of the electron-phonon coupling leads to a sensitive reduction of the Mott gap through a reduced effective repulsion. The relation of the results with recent experimental observations in strongly correlated systems is discussed.
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.
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