Upper Critical Field and Pairing Symmetry of Ising Superconductors

Motivated by the fact that the measured critical field H_{c2} in various transition metal dichalcogenide superconductors is poorly understood, we reexamine its scaling behavior with temperature and spin-orbit coupling (SOC). By computing the spin-susceptibility in a multipocket system, we find that segments of the Fermi surface (FS) at which the SOC has nodal points can have a contribution orders of magnitude larger than the remaining FS, hence setting the H_{c2}, assuming the presence of a conventional singlet superconducting order parameter. Nodal lines of an Ising SOC in the Brillouin zone are imposed by symmetry, so they cause such nodal points whenever they intersect an FS pocket, which is indeed the case in monolayer NbSe_{2} and TaS_{2}, but not in gated MoS_{2} and WS_{2}. Our analysis reinterprets existing measurements, concluding that a dominant singlet-order parameter on pockets with SOC nodes is consistent with the H_{c2}(T) data for all monolayer Ising superconductors, in contrast to previous contradictory pairing assumptions. Finally, we predict a doping-dependent experimental signature of our theory.