Gap-function anisotropy and collective modes in a bilayer superconductor with Cooper-pair tunneling

We study the gap-function anisotropy and collective mode spectrum (ω≤2Δ) of the Anderson-Chakravarty model for high-Tc oxides based on Cooper-pair tunneling in a bilayer (with strength TJ). For both s-wave and d-wave pairing in the layers, the shape of the gap around the Fermi surface is strongly dependent on TJ. Besides the usual Anderson-Bogoliubov phase and Littlewood-Varma amplitude modes, we find branches (optical phononlike modes) involving fluctuations of the relative phase and amplitude of the order parameters of the two layers. These modes are the dynamic signature of the Cooper-pair tunneling model since their energy and damping depends critically on the relative magnitudes of the Cooper-pair tunneling strength (TJ) and the pairing interaction (g), but not significantly on the symmetry of the pairing. The generalization to a trilayer system (which can arise in Bi, Tl, and Hg copper oxides) is briefly discussed.