Interlayer tunneling in a strongly correlated electron-phonon system

We discuss the role of interlayer tunneling for superconducting properties of strongly correlated (U-->infinity limit) two-layer Hubbard model coupled to phonons. Strong correlations are taken into account within the mean-field approximation for auxiliary boson fields. To consider phonon-mediated and interlayer tunneling contribution to superconductivity on equal footing we incorporate the tunneling term into the generalized Eliashberg equations. This leads to the modification of the phonon-induced pairing kernel and implies a pronounced enhancement of the superconducting transition temperature in the d-wave channel for moderate doping. In numerical calculations the two-dimensional band structure has been explicitly taken into account. The relevance of our results for high-temperature superconductors is briefly discussed.