Theoretical study of ac Josephson effect in a double barrier Josephson junction

We study an ac Josephson effect in a SC/I/X/I/SC junction, where SC is an s-wave superconductor, I is an insulator, and X is either a normal metal (NM) or a ferromagnetic metal (FM). Using a tunneling Hamiltonian and Green's function method, we obtain two types of superconducting phase dependent current. One is the Josephson current and the other is the quasiparticle-pair-interference current (QPIC). In a SC/I/NM/I/SC junction, the Josephson critical current (I_{c 1}) and the amplitude of QPIC (I_c2) are functions of the thickness of NM and the applied voltage (V). I_c1 shows a logarithmic divergence called Riedel peak at the gap voltage, V = 2 Δ / e, where Δ is the superconducting gap, and I_c2 shows a discontinuous jump at the gap voltage. These behaviors are similar to these of SC/I/SC junctions. On the other hand, in a SC/I/FM/I/SC junction, I_c1 and I_c2 exhibit the strong dependence on the thickness of FM and changes their signs by crossing the 0-π transition point due to the magnetic exchange splitting between the up- and down-spin bands in FM. It is predicted that the Riedel peak in I_c1 disappears at the 0-π transition and the 0-π transition occurs in I_c2 similarly to I_c1.