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.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 matterJan 1, 199619 citations

Electron-Phonon Coupling in the t-J Model

Andrei S. Mishchenko

Bulletin of the American Physical SocietyMar 24, 20050 citations

Coupling to Optical Phonons in the One-Dimensional t - J Model: Effects on the Superconducting Fluctuations and Phase Separation

R. Fehrenbacher

The one-dimensional $t\ensuremath{-}J$ Holstein model is studied by exact diagonalization of finite rings using a variational approximation for the phonon states. Because of renormalization effects induced by the phonons, for intermediate electron-phonon coupling, the phase separation boundary, and with it the region of dominating superconducting fluctuations is shifted substantially to smaller values of $J/t$ as compared to the pure $t\ensuremath{-}J$ model. Superconducting correlations are weakened through charge density wave interactions mediated by the phonons. Possible consequences for the high- ${T}_{c}$ oxides are discussed.The one-dimensional $t\ensuremath{-}J$ Holstein model is studied by exact diagonalization of finite rings using a variational approximation for the phonon states. Because of renormalization effects induced by the phonons, for intermediate electron-phonon coupling, the phase separation boundary, and with it the region of dominating superconducting fluctuations is shifted substantially to smaller values of $J/t$ as compared to the pure $t\ensuremath{-}J$ model. Superconducting correlations are weakened through charge density wave interactions mediated by the phonons. Possible consequences for the high- ${T}_{c}$ oxides are discussed.

arXiv:cond-mat/9605190Physical Review LettersSep 9, 199613 citations

J/t

as compared to the pure $t\ensuremath{-}J$ model. Superconducting correlations are weakened through charge density wave interactions mediated by the phonons. Possible consequences for the high-

{T}_{c}

oxides are discussed.