Andreev reflection and tunneling spectrum in a superlattice of metal-superconductor junctions

The tunneling spectrum of an electron and a hole in a superlattice of NS junctions is computed using the BTK approach and the transfer matrix method. It shows sharp resonances at some energies above the superconducting gap. The sharper the resonance is the more layers the superlattice has. We find for the first time a mechanism to balance the incident and outgoing currents on the superlattice by averaging over the phase between the incident electron and the incident hole. This mechanism is more natural and physical than those in literatures.