Density of states of a layered S/N d-wave superconductor

We calculate the density of states of a layered superconductor in which there are two layers per unit cell. One of the layers contains a d-wave pairing interaction while the other is a normal metal. The goal of this article is to understand how the d-wave behaviour of the system is modified by the coupling between the layer-types. This coupling takes the form of coherent, single particle tunneling along the c-axis. We find that there are two physically different limits of behaviour, which depend on the relative locations of the Fermi surfaces of the two layer-types. We also discuss the interference between the interlayer coupling and pairing interaction and we find that this interference leads to features in the density of states.