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

Time reversal and spatial inversion are two key symmetries for conventional Bardeen-Cooper-Schrieffer (BCS) superconductivity . Breaking inversion symmetry can lead to mixed-parity Cooper pairing and unconventional superconducting properties. Two-dimensional (2D) NbSe has emerged as a new non-centrosymmetric superconductor with the unique out-of-plane or Ising spin-orbit coupling (SOC). Here we report the observation of an unusual continuous paramagnetic-limited superconductor-normal metal transition in 2D NbSe. Using tunelling spectroscopy under high in-plane magnetic fields, we observe a continuous closing of the superconducting gap at the upper critical field at low temperatures, in stark contrast to the abrupt first-order transition observed in BCS thin-film superconductors. The paramagnetic-limited continuous transition arises from a large spin susceptibility of the superconducting phase due to the Ising SOC. The result is further supported by self-consistent mean-field calculations based on the ab initio band structure of 2D NbSe. Our findings establish 2D NbSe as a promising platform to explore novel spin-dependent superconducting phenomena and device concepts , such as equal-spin Andreev reflection and topological superconductivity.