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The European Physical Journal B

Electron correlations and quantum lattice vibrations in strongly coupled electron-phonon systems: A variational slave boson approach

U. Trapper, Holger Fehske, Martin Deeg, H. B�ttner

Published Dec 1, 1994• 26 citations
Publisher
DOI
10.1007/bf01314251

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d-wave superconductivity in a strongly correlated electron-phonon system

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The problem of phonon-mediated and phonon-free contributions to d-wave superconductivity in the two-dimensional Hubbard model has been addressed. Strong local correlations (U\ensuremath{\rightarrow}\ensuremath{\infty} limit) have been incorporated in the slave boson formulation. In order to consider electron-boson and electron-phonon coupling on equal footing, fluctuations of the auxiliary boson fields over their mean-field value have been introduced. The magnitude of effective pairing interactions derived with the help of a canonical transformation indicates that within the weak-coupling theory, phonon-mediated pairing plays a marginal role and can be dominated by a phonon-free pairing mechanism. On the other hand, in the strong-coupling limit (Eliashberg formulation), electron-phonon and electron-phonon-boson interactions can significantly enhance the superconducting transition temperature. It is also shown that Coulomb correlations together with the electron-phonon interaction can effectively stabilize a d-wave superconducting state. \textcopyright{} 1996 The American Physical Society.

Physical review. B, Condensed matter•Jan 1, 1996•19 citations
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.
The problem of phonon-mediated and phonon-free contributions to d-wave superconductivity in the two-dimensional Hubbard model has been addressed. Strong local correlations (U\ensuremath{\rightarrow}\ensuremath{\infty} limit) have been incorporated in the slave boson formulation. In order to consider electron-boson and electron-phonon coupling on equal footing, fluctuations of the auxiliary boson fields over their mean-field value have been introduced. The magnitude of effective pairing interactions derived with the help of a canonical transformation indicates that within the weak-coupling theory, phonon-mediated pairing plays a marginal role and can be dominated by a phonon-free pairing mechanism. On the other hand, in the strong-coupling limit (Eliashberg formulation), electron-phonon and electron-phonon-boson interactions can significantly enhance the superconducting transition temperature. It is also shown that Coulomb correlations together with the electron-phonon interaction can effectively stabilize a d-wave superconducting state. \textcopyright{} 1996 The American Physical Society.