Josephson effects in the spin-triplet superconductor/altermagnet/spin-triplet superconductor junctions: the detection of the intrinsic $\bf{d}$-vector
We study the Josephson effects in the spin-triplet superconductor/altermagnet/spin-triplet superconductor junctions using the Green's function method. It is found that the current-phase difference relationships in the junctions strongly depend on the direction of the $\bf{d}$-vectors in the spin-triplet superconductors and the orientation angle of the altermagnet. For the given orientation angle, the $0$-$π$ transition can be obtained when the $\bf{d}$-vector is rotated. The variations of the critical current of the junctions with the direction of the $\bf{d}$-vector, the orientation angle and the strength of altermagnetism are systematically investigated. These Josephson effects can provide the distinguishable information about the direction of the $\bf{d}$-vector. Compared to the existing research, the proposed altermagnetic Josephson junctions can effectively avoid the negative influence of the magnetic field on the $\bf{d}$-vector and can serve as a feasible scheme for the detection of the intrinsic $\bf{d}$-vector. The obtained $0$-$π$ transition in the junctions can also have potential applications in the design of quantum devices.