Orientation-dependent Josephson effect in spin-singlet superconductor/altermagnet/spin-triplet superconductor junctions

We study the Josephson effect in the spin-singlet\nsuperconductor/altermagnet/spin-triplet superconductor junctions using the\nGreen's function method. The current-phase difference relationships in the\njunctions strongly depend on the orientation of altermagnet and the types of\nthe Cooper pairs. For the orientation angle equal to odd multiples of $\\pi/4$,\nthe current-phase difference relationships are of the $\\sin{2\\phi}$ type, which\nare irrespective of the pairing wave functions in superconductors. For the\nother orientation angles, the emergence of the lowest order current becomes\npossible and its form, $\\sin\\phi$ or $\\cos\\phi$, depends on the pairing wave\nfunctions in superconductors. The $\\phi_{0}$ phase and the $0$-$\\pi$ transition\ncan be realized in our junctions due to the appearance of the lowest order\ncurrent. The selection rules for the lowest order current are presented. The\nsymmetric relations satisfied by the current-phase difference relationships are\nanalyzed through considering the transformations of the junctions under the\nmirror reflection, the time-reversal and the spin rotation operations. Our\nresults not only provide a method to detect the intrinsic spin-triplet\nsuperconductivity but also possess application values in the design of the\nfield-free quantum devices.\n