Superconductivity is commonly destroyed by a magnetic field due to orbital or Zeeman-induced pair breaking. Surprisingly, the spin-valley locking in a two-dimensional superconductor with spin-orbit interaction makes the superconducting state resilient to much stronger magnetic fields. We investigate the spectral properties of such an Ising superconductor in a magnetic field taking into account disorder [1]. The interplay of the in-plane magnetic field and the Ising spin-orbit coupling leads to noncollinear effective fields. We find that the emerging singlet and triplet pairing correlations manifest themselves in the occurrence of “mirage” gaps: at (high) energies of the order of the spin-orbit coupling strength, a gaplike structure in the spectrum emerges that mirrors the main superconducting gap. We show that these mirage gaps are signatures of the equal-spin triplet finite-energy pairing correlations and due to their odd parity are sensitive to intervalley scattering. Furthermore, we study a Josephson junction formed by two Ising superconductors that are in proximity to ferromagnetic layer [2]. This leads to highly tunable spin-triplet pairing correlations which allow to modulate the charge and spin supercurrents through the in-plane magnetic exchange fields. For a junction with a nonmagnetic barrier, the charge current is switchable by changing the relative alignment of the in-plane exchange fields, and a  pi-state can be realized. Furthermore, the phases of both the charge and spin currents aretunable for a junction with a strongly spin-polarized ferromagnetic barrier.

[1] G. Tang, C. Bruder, and W. Belzig, Phys. Rev. Lett. 126, 237001 (2021).
[2] G. Tang, R. Klees, C. Bruder, W. Belzig, preprint.