Spin-triplet superconductor-quantum anomalous Hall insulator-spin-triplet superconductor Josephson junctions: 0-pi transition, phi(0) phase, and switching effects

We study the Josephson effect in spin-triplet superconductor-quantum anomalous Hall insulator-spin-triplet superconductor junctions using the nonequilibrium Green's function method. The current-phase difference relations show strong dependence on the orientations of the d vectors in superconductors. We focus on two d-vector configurations, a parallel one with the left and right d vectors being in the same direction and a nonparallel one with the left d vector fixed at the z axis. For the parallel configuration, the 0-pi transition can be realized when one rotates the d vectors from the parallel to the junction plane to the perpendicular direction. The phi(0) phase with nonzero Josephson current at zero phase difference can be obtained as long as d(x)d(z) not equal 0. For the nonparallel configuration, the 0-pi transition and the cb o phase still exist. The condition for the formation of the phi(0) phase becomes d(Rx) not equal 0. The switch effects of the Josephson current are found in both configurations when the d vectors are rotated in the phi(0) plane. Furthermore, the symmetries satisfied by the current-phase difference relations are analyzed in detail by the operations of the time-reversal, mirror-reflections, the spin-rotation, and the gauge transformation, which can well explain the above selection rules for the phi(0) phase. Our results reveal the peculiar Josephson effect between spin-triplet superconductors and the quantum anomalous Hall insulator, which provide helpful phases and effects for device designs. The distinct current-phase difference relations for different orientations may be used to determine the direction of the d vector in the spin-triplet superconductor.