Recent discovery of Ising superconductivity protected against in-plane magnetic field by spin-orbit coupling (SOC) has stimulated intensive research interests. The effect, however, was only expected to appear in two-dimensional (2D) noncentrosymmetri
c materials with spin-valley locking. In this work, we proposed a new type of Ising superconductivity in 2D materials with $C_{nz}$ rotational symmetry ($n=3,4,6$). This mechanism, dubbed as type-II Ising superconductivity, is applicable for centrosymmetric materials. Type-II Ising superconductivity relies on the SOC-induced spin-orbital locking characterized by Ising-type Zeeman-like fields displaying opposite signs for opposing orbitals. We found that type-II Ising superconductivity are most prominent around time-reversal invariant momenta and is not sensitive to inversion symmetry breaking. By performing high-throughput first-principles calculations, about one hundred candidate materials were identified. Our work significantly enriches the physics and materials of Ising superconductor, opening new opportunities for fundamental research and practical applications of 2D materials.
Based on ab initio software packages using nonorthogonal localized orbitals, we develop a general scheme of calculating response functions. We test the performance of this method by calculating nonlinear optical responses of materials, like the shift
current conductivity of monolayer WS2, and achieve good agreement with previous calculations. This method bears many similarities to Wannier interpolation, which requires a challenging optimization of Wannier functions due to the conflicting requirements of orthogonality and localization. Although computationally heavier compared to Wannier interpolation, our procedure avoids the construction of Wannier functions and thus enables automated high throughput calculations of linear and nonlinear responses related to electrical, magnetic and optical material properties.
