Energy Gap Structure in Bilayer Oxide Superconductors

We consider a model for bilayer superconductors where an interlayer pairing amplitude $\Delta_\perp$ co-exists with intralayer pairing $\Delta_\|$ of $d_{x^2 - y^2}$ symmetry. This model is motivated by a recent photoemission experiment reporting the splitting of the nodes of the energy gap. In addition to offering a natural explanation of this observation, the model has a number of new experimental consequences. We find that the new state is accompanied by a spontaneous breaking of the tetragonal symmetry. We also find that the out-of-phase oscillation of $\Delta_\perp$ and $\Delta_\|$ gives rise to a new Raman active mode. The phase of $\Delta_\perp$ may also become imaginary, leading to a state which breaks time reversal symmetry, which may have important implications for tunnelling experiments.