Occurrence of<i>d</i>-Wave Pairing in the Phonon-Mediated Mechanism of High Temperature Superconductivity in Cuprates

Abstract

The $\mathit{k},{\mathit{k}}^{\ensuremath{'}}$ dependence of spectral function ${\ensuremath{\alpha}}^{2}F(\ensuremath{\Omega},\mathit{k},{\mathit{k}}^{\ensuremath{'}})$ is calculated based on the extended two story house model in which carriers itinerate in the region of local antiferromagnetic ordering composed of the localized spins. The following results are obtained: (1) d-wave pairing occurs even for the phonon mechanism; (2) the out-of-plane phonon modes contribute to the superconductivity in cuprates while those like breathing modes do not contribute significantly; and (3) the electron-phonon interaction in Cu${\mathrm{O}}_{5}$ type cuprates is stronger than in Cu${\mathrm{O}}_{6}$ type cuprates.