Inelastic light scattering from collective modes in a layered superconductor with Cooper-pair tunneling

In a superconducting bilayer with Cooper-pair tunneling (TJ 0) between the layers, it has been recently predicted that there should exist in-phase and out-of-phase phase and amplitude fluctuations of the order parameters of the two layers. As a way of observing these phase modes, we calculate the inelastic light scattering from a semi-infinite superconducting superlattice with a bilayer basis. For simplicity, we ignore surface modes. We show that the bulk phase-modes show up as resonances in the isotropic Raman light scattering intensity at finite momentum transfer parallel to the surface. Our specific calculations are for s-wave superconductors but similar results are expected for d-wave pairing. The size of the energy gap of the out-of-phase modes is strongly dependent on the ratio of TJ and the intralayer pairing interaction g, as well as particle-hole damping.