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Time reversal and spatial inversion are two key symmetries for conventionalBardeen-Cooper-Schrieffer (BCS) superconductivity. Breaking inversion symmetrycan lead to mixed-parity Cooper pairing and unconventional superconductingproperties. Two-dimensional (2D) NbSe$_2$ has emerged as a newnon-centrosymmetric superconductor with the unique out-of-plane or Isingspin-orbit coupling (SOC). Here, we report the observation of an unusualcontinuous paramagnetic-limited superconductor-normal metal transition in 2DNbSe$_2$. Using tunneling spectroscopy under high in-plane magnetic fields, weobserve a continuous closing of the superconducting gap at the upper criticalfield at low temperatures, in stark contrast to the abrupt first-ordertransition observed in BCS thin film superconductors. The paramagnetic-limitedcontinuous transition arises from a large spin susceptibility of thesuperconducting phase due to the Ising SOC. The result is further supported byself-consistent mean-field calculations based on the ab initio band structureof 2D NbSe$_2$. Our findings establish 2D NbSe$_2$ as a promising platform forexploring novel spin-dependent superconducting phenomena and device concepts,such as equal-spin Andreev reflection and topological superconductivity.

An unusual continuous paramagnetic-limited superconducting phase transition in 2D NbSe$_2$