Spin-split Andreev bound states and diode effect in an Ising superconductor Josephson junction

The transition-metal dichalcogenides featuring Ising spin-orbit coupling in so-called Ising superconductors offer a unique system to study the interplay of singlet and triplet superconductivity. The presence of high critical fields, spectral properties such as the mirage gap, and field-tunable charge and spin currents in Ising superconductor Josephson junctions are some of the important features. In this Letter, we study an Ising superconductor Josephson junction with a transparent interface and show that Andreev bound states are spin split due to a relative misorientation of in-plane fields in the superconducting contacts. Correspondingly, supercurrent-phase relations display a strongly nonsinusoidal behavior. Introducing additional spin-polarized channels with low transmission results in a nonreciprocal current-phase relation with a diode effect that can be tuned by the in-plane exchange fields. The diode efficiency reaches high values of the order of 40% and is not sensitive to disorder in the junction. Such structures can be realized in van der Waals heterostructures of two-dimensional superconductors and magnets.