Ising superconductors in in-plane magnetic fields

Transition metal dichalcogenide monolayers are a new class of two-dimensional superconductors. They host a strong intrinsic spin-orbit coupling (SOC), that acts as an effective Zeeman field with opposite, out-of-plane, orientations in the +K and –K corners of the Brillouin zone (valleys). This SOC causes unconventional “Ising pairing” of the Cooper pairs, formed of electrons from opposite valleys with strongly pinned out-of-plane spins. In-plane fields are thus not efficient in breaking the Cooper pairs by the paramagnetic effect, which results in a large enhancement of the in-plane upper critical field – the main signature of Ising superconductivity.

Using a quasiclassical formalism for disordered Ising superconductors, we calculate the in-plane upper critical field, as well as the density of states in the superconducting phase. We show that these quantities are not affected by intravalley scattering, and are determined by the interplay of the SOC and intervalley scattering. The smearing of the density of states with the applied field cannot be captured with the standard Abrikosov-Gor'kov theory. We compare our results with recent experiments.