# Type-II Ising superconductivity in two-dimensional materials with strong spin-orbit coupling

## TL;DR

This paper introduces a new type of Ising superconductivity, called type-II, which occurs in centrosymmetric 2D materials with strong spin-orbit coupling and is characterized by spin-orbital locking, expanding the scope of Ising superconductors.

## Contribution

The study proposes and characterizes a novel type of Ising superconductivity in centrosymmetric 2D materials with $C_{nz}$ symmetry, supported by first-principles calculations identifying numerous candidate materials.

## Key findings

- Type-II Ising superconductivity relies on SOC-induced spin-orbital locking.
- It is most prominent around time-reversal invariant momenta.
- Approximately one hundred candidate materials were identified.

## Abstract

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.