Effects of phonon interaction on pairing in high-Tc superconductors

We study the effects of phonon interaction on the superconducting pairing in the background of a d-wave gap, mediated by antiferromagnetic (AFM) spin fluctuations, using coupled BCS gap equations. We found that phonon interaction can induce a s-wave component to the d-wave gap in the (D+S) form with an interaction anisotropy and in the (D + iS) form without anisotropy, respectively. In either case, however, T-c is not enhanced compared to the pure d-wave pairing without phonon interaction. On the other hand, anisotropic phonon interaction can dramatically enhance the d-wave pairing itself and therefore T-c together with the AFM spin fluctuation interaction. This (D-AFM+D-ph) type pairing exhibits strongly reduced isotope coefficient despite the large enhancement of T-c by phonon interaction. Finally, we study the combined type of (D-AFM+D-ph+iS) gap and calculate the penetration depth and specific heat to be compared with the experiments.