Spin-triplet superconductor–quantum anomalous Hall insulator–spin-triplet superconductor Josephson junctions: 0−π transition, ϕ0 phase, and switching effects

Abstract

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−π transition can be realized when one rotates the d vectors from the parallel to the junction plane to the perpendicular direction. The ϕ0 phase with nonzero Josephson current at zero phase difference can be obtained as long as dxdz≠0. For the nonparallel configuration, the 0−π transition and the ϕ0 phase still exist. The condition for the formation of the ϕ0 phase becomes dRx≠0. The switch effects of the Josephson current are found in both configurations when the d vectors are rotated in the xy 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 ϕ0 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.

Source-reported materials — not catalogue approval

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