Pair potential and density of states in proximity-contact superconducting–normal-metal double layers

The self-consistent pair potential and the density of states in a proximity-contact superconducting-normal (S-N) finite double layer are discussed in the clean limit. The finite reflection coefficient R at the interface is explicitly taken into account. It is shown that the depression of the pair potential near the S-N interface is significant even when the layer width is as small as the coherence length. We assume that there is no pairing interaction in the N side, and as a result there is no pair potential. It is found, however, that the N-side density of states has an effective energy gap. In the S side, the density of states in the energy range below the pair potential is finite and has a remarkable structure in contrast to the bulk superconductor. The nuclear spin-lattice relaxation rate ${\mathit{T}}_1^{\mathrm{-}1}$ is also calculated. The enhancement of ${\mathit{T}}_1^{\mathrm{-}1}$ just below the transition temperature is found on both sides, which qualitatively agrees with experiments.