  Systems that simultaneously exhibit superconductivity and spin-orbit coupling
are predicted to provide a route toward topological superconductivity and
unconventional electron pairing, driving significant contemporary interest in
these materials. Monolayer transition-metal dichalcogenide (TMD)
superconductors in particular lack inversion symmetry, enforcing a spin-triplet
component of the superconducting wavefunction that increases with the strength
of spin-orbit coupling. In this work, we present an experimental and
theoretical study of two intrinsic TMD superconductors with large spin-orbit
coupling in the atomic layer limit, metallic 2H-TaS$_2$ and 2H-NbSe$_2$. For
the first time in TaS$_2$, we investigate the superconducting properties as the
material is reduced to a monolayer and show that high-field measurements point
to the largest upper critical field thus reported for an intrinsic TMD
superconductor. In few-layer samples, we find that the enhancement of the upper
critical field is sustained by the dominance of spin-orbit coupling over weak
interlayer coupling, providing additional platforms for unconventional
superconducting states in two dimensions.
