Spectral properties of disordered Ising superconductors with singlet and triplet pairing in in-plane magnetic fields

We study the spectral properties of disordered superconducting transition metal dichalcogenide monolayers, known as Ising superconductors, subjected to in-plane magnetic fields. In addition to the conventional singlet pairing, we also consider the recently proposed equal-spin triplet pairing, which couples to the singlet at finite in-plane magnetic fields. While both singlet and triplet order parameters are immune to intravalley scattering, they are significantly affected by intervalley scattering. In the realistic regime of strong intrinsic Ising spin-orbit coupling, we find that the properties of the superconductor are well described by a simple formula reminiscent of the well-known Abrikosov-Gor'kov theory, but with a modified self-consistency condition. Our results enable straightforward self-consistent calculation of singlet and triplet order parameters and the density of states of disordered Ising superconductors, which can be particularly useful for interpreting recent tunneling spectroscopy experiments in these systems. We also investigate the high-energy features in the density of states, the so-called mirage gaps, and discuss how they are modified by triplet pairing.