Phase-shifted Andreev levels in an altermagnet Josephson junction

We compute the effect of a d-wave magnetization (altermagnetism) on the spectrum of bound states (Andreev levels) in a junction between two s-wave superconductors (gap Delta(0) and phase difference phi). Compared to a nonmagnetic junction, the phi dependence of the spectrum is shifted by an offset +/-delta phi, dependent on the spin direction, so that the Andreev levels become spin polarized. In a planar junction, oriented along the crystalline axis of d(xy)-wave symmetry, the excitation energies are determined by the normal-state transmission probability T according to E = Delta(0)root 1 - T sin(2) 1/2 (phi +/- delta phi). We calculate the corresponding Josephson energy and supercurrent, recovering the 0-pi transition of related studies.