Importance of out-of-plane dispersion of the excitation spectrum of superconducting bilayers with Josephson coupling

We study the effect of Josephson coupling between adjacent superconducting layers on the BCS energy spectrum. We find that the interference between the gap functions of two layers can lead to vanishing condensation energy for perpendicular momenta corresponding to the formation of standing waves. We therefore predict a conventional energy spectrum for large interlayer spacings, if the gap of the single layers has no nodes, and in all cases a gapless spectrum for small spacings. Within the experimental error, our numerical results account for the low-temperature dependence of the penetration depth reported in Nd_1.85Ce_0.15CuO₄ and YBa₂Cu₃O_6.9.