Quasiparticle energy spectrum and Josephson current in superconducting SNINS junctions

Through the solution of the Bogoliubov de Gennes equations we analyze the effect of different symmetries of the pair potential on the quasiparticle energy spectrum in SNINS junctions (S: superconductor, N: normal metal and I: Insulator). We find that the energy levels are strongly affected by the symmetry of the pair potential, the width of each normal metal (a and b) and the strength of the insulating barrier. The energy levels equation generalizes previous results in SNS and SIS junctions. The energy dispersion relation depends on the phase difference of the pair potential. The Josephson current is related to the Andreev levels; when a = b ~ xi0 and T << Tc this current is approximately 1/2 of the Josephson current transported in an SIS junctions. In general, we find that for d xy symmetries there is always a zero energy state independent of the value of Z, a and b.