Interplay of electron-phonon interaction and electron correlation in high-temperature superconductivity

We study the electron-phonon interaction in the strongly correlated superconducting cuprates. Two types of the electron-phonon interactions are introduced in the t-J model; the diagonal and off-diagonal interactions which modify the formation energy of the Zhang-Rice singlet and its transfer integral, respectively. The characteristic phonon-momentum (q^→) and electron-momentum (k^→) dependence that resulted from the off-diagonal coupling can explain a variety of experiments. The vertex correction for the electron-phonon interaction is formulated in the SU(2) slave-boson theory by taking into account the collective modes in the superconducting ground states. It is shown that the vertex correction enhances the attractive potential for the d-wave paring mediated by phonon with q ^→ = [π(1-δ),0] around δ ≅ 0.3, which corresponds to the half-breathing mode of the oxygen motion.