Phase and Amplitude Modes in a Superconductor with Interlayer Pair Tunneling

Chakravarty, Sudb{}, Anderson, and Strong have introduced a simple model for high Tc oxides based on the effect of Cooper pair tunneling in a bilayer (with strength TJ) with s-wave pairing (g) in the layers. We discuss the order parameter fluctuations of this model. Besides the usual Anderson-Bogoliubov phase and Littlewood-Varma amplitude modes, we find new out-of-phase phase and amplitude modes. Their energy and damping depend critically on whether TJ>g or ${T}J