Spin-Orbit-Parity-Coupled Superconductivity in Topological Monolayer WTe₂

Recent experiments reported gate-induced superconductivity in the monolayer 1T'-WTe₂ which is a two-dimensional topological insulator in its normal state. The in-plane upper critical field B_c2 is found to exceed the conventional Pauli paramagnetic limit B_p by one to three times. The enhancement cannot be explained by the conventional spin-orbit coupling which vanishes due to inversion symmetry. In this Letter, we unveil some distinctive superconducting properties of centrosymmetric 1T'-WTe₂ which arise from the coupling of spin, momentum and band parity degrees of freedom. As a result of this spin-orbit-parity coupling (SOPC): (i) there is a first-order superconductor-metal transition at B_c2 that is much higher than the Pauli paramagnetic limit Bp, (ii) spin-susceptibility is anisotropic with respect to in-plane directions and can result in possible anisotropic B_c2, and (iii) the B_c2 exhibits a strong gate dependence as the spin-orbit parity coupling is significant only near the topological band crossing points. The importance of SOPC on the topologically nontrivial inter-orbital pairing phase is also discussed. Our theory generally applies to centrosymmetric materials with topological band inversions.