  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) noncentrosymmetric 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.
