Phase dependent energy levels of bound states and D.C. Josephson current in unconventional superconductor/ferromagnetic insulator/unconventional superconductor junctions

Properties of the DC Josephson effects in unconventional-superconductors under the presence of an exchange field in the insulator are studied theoretically. The current-phase relation of the DC Josephson current I(phi) and the temperature dependence of the maximum Josephson current I-C(T) are calculated for various pairing symmetries and crystal orientations as a function of the exchange interaction strength (I-m). The influences of the spin-orbit coupling are also discussed. The phase dependent energy levels of quasiparticle bound states are sensitive to the magnitude of I-m, orientaions of the junctions, and especially parities of two supercondctors. When the two superconductors have d-wave symmetries, I-C(T) shows non-monotonous behavior on the magnitude of I-m, and accordingly the Josephson junction changes between 0-junction and pi-junction. On the other hand, when the two superconductors have different parities, e.g. s-wave and p-wave, the Josephson current is largely suppressed due to SU(2) symmetry in the spin space in the absence of I-m. However, the Josephson current rapidly recovers with the increase of I-m because of the breakdown in SU(2) symmetry. These anomalous features can be used as a criteria for the identification of the pairing symmetries in novel superconductors.