Resonant states and currents in superconducting multilayers

We calculated electronic states and Josephson currents for superconducting multilayers with one-dimensional SISIS and SNSNS junctions, where S is a superconductor, I, an insulator, and N, a normal metal. We obtained numerical solutions of the Bogoliubov-de Gennes equations for the case where the Fermi wavelength of quasi-electrons and quasi-holes is comparable to the coherence length, barrier width, and thickness of the intermediate superconductor. It was found that the maximum Josephson current has a peak structure as a function of barrier height slightly above the Fermi energy, because of resonant tunneling of quasi-electrons and quasi-holes. Though the maximum Josephson current of the SNSNS double junction is smaller than that of the SNS single junction, the maximum Josephson current of the SISIS junction is larger than that of the SIS junction for a range of barrier heights above the Fermi energy. The Josephson current is a superposition of sin(φ/2) and sin φ terms, where φ is a phase difference of the superconductors in both ends. The sin(φ/2) term is dominant for the SISIS junction, while the sin φ term dominates the SNSNS junction, and their coefficients vary continuously as a function of the barrier height.