Calculation of transition temperatures of superconductor-metal sandwiches and superlattices

The transition temperatures of superconductor-metal sandwiches and superlattices have been calculated. We have studied the bi-layer and infinite superlattice cases for varying layer thicknesses. We employ the eigenfunction expansion of the de Gennes kernal near the critical temperature as implemented by Takahashi and Tachiki. We have modified these equations and results by consistently including a cut-off at the Debye frequency in the associated matrix elements of this theory and by approximately diagonalizing the eigenvalue equations. Our results show a much steeper decrease of transition temperature with layer thickness than the Werthammer one-mode approximation. In the limit of a thin superconducting layer on an infinite normal layer we find T_c = 0 at a smaller thickness than that previously calculated by de Gennes.