Enhancement of superconducting correlation due to interlayer tunneling.

Interlayer single particle tunneling between the $Cu-O$ layers suppress the in-plane short range magnetic order (which is modeled as spin density wave (SDW) insulator). Doping over the SDW state kills perfect nesting of the Fermi surface (FS) in certain directions and hence SDW gap reduces to zero in those directions of the FS. Coupling between the planes through interlayer tunneling ($t_{\perp}$) further suppresses the in-plane magnetic SDW-gap and hence becomes anisotropic. Superconductivity arises in the gapless regions of the FS under the `modified spin bag' mechanism. We show that the highest $T_c$ can only be obtained for non-zero $t_{\perp}$ based on this mechanism.