A universal route to chiral Ising superconductivity in monolayer TaS$_2$ and NbSe$_2$

We investigate Ising superconductivity in two archetypal intrinsic superconductors, monolayer 1H-TaS$_2$ and 1H-NbSe$_2$, in a bottom-up approach. Using ab initio-based tight-binding parameterizations for the relevant low-energy d-bands, the screened interaction is evaluated microscopically, in a scheme including Bloch overlaps. In direct space, the screened potential displays for both systems long-range Friedel oscillations alternating in sign. Upon scaling, the oscillation pattern becomes universal, with the periodic features locked to the lattice. Solving the momentum-resolved gap equations, a chiral ground state with p-like symmetry is generically found. Due to the larger Ising spin-orbit coupling, the chiral gap is more anisotropic in TaS$_2$ than in NbSe$_2$. This is reflected in tunneling spectra displaying V-shaped features for the former, in quantitative agreement with low-temperature scanning tunneling experiments on TaS$_2$. At the same time, our results reconcile the apparent discordance with hard gap tunneling spectra reported for the sibling NbSe$_2$.