Role of interlayer coupling in oxide superconductors

The role of interlayer coupling in high-${T}_{c}$ oxide superconductors is considered. Within the assumption that the direct hopping between layers is vanishingly small, we find that the interlayer coupling in the particle-particle channel caused by interactions plays a very important role in the enhancement of ${T}_{c}$ and stabilizes the superconducting order with respect to fluctuations. The interlayer coupling in the particle-hole channel plays a relatively minor role. The introduction of a small interlayer hopping matrix element reduces ${T}_{c}$ in the lowest-order approximation.