Twofold symmetric superconductivity in NbSe2 monolayers with vacancy defects

Monolayer NbSe2, as an Ising superconductor, has attracted considerable attention. Experimentally, its samples inevitably contain defects, yet the effects of these defects on superconductivity remain largely unexplored. Here, we demonstrate that selenium (Se) monovacancies, the most common defects in monolayer NbSe2, critically affect superconductivity. Specifically, Se monovacancies disrupt both the out-of-plane mirror symmetry and the C3z rotational symmetry in pristine monolayer NbSe2, resulting in an asymmetric spin-orbit coupling (SOC). While pristine monolayer NbSe2, which possesses Ising SOC, exhibits an isotropic in-plane upper critical field (Bc2), the asymmetric SOC induced by Se monovacancies leads the in-plane Bc2 to display an anisotropic twofold symmetry in response to the direction of the in-plane magnetic field. Furthermore, Se monovacancies significantly reduce the in-plane spin susceptibility of the superconducting state, causing Bc2 to exceed the Pauli limit only moderately, consistent with experimental observations. These findings provide valuable insights into the role of defects in tuning superconductivity of two-dimensional materials.