초록
We study the effects of phonon interaction on the superconducting pairing in the high $T_c$ superconductors (HTSC). Using coupled BCS gap equations, we found that phonon interaction can induce a s-wave component to the d-wave gap, mediated by Antiferromagnetic (AFM) spin fluctuations, in the (D+iS) form. 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 and $T_c$ itself, 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.