Electronic states and currents in superconducting multilayers

We obtain full, exact numerical solutions for eigenvalue problems of the Bogoliubov-de Gennes (BdG) equations for the case of superconducting multilayers. Furthermore, the transport current was calculated. This powerful numerical calculation enables us to get solutions for systems with arbitrary barrier and pair potentials where the Fermi-wavelength for quasi-electrons and quasi-holes is comparable to the size of the Cooper pair and coherence length. We apply this new method to one-dimensional SIS and SNS junctions, where S is a superconductor, I is an insulator, and N is a normal metal. It was found that even in this simple system the Josephson current differs from the perfect sinusoidal function and its components through continuous and quasi-bound states have a variety of directions and magnitudes owing to the wave nature of quasi-electrons and quasi-holes.