Ising superconductors with in-plane upper critical fields several times higher than the Pauli limits have been discovered recently in transition metal dichacogenides such as MoS2 and NbSe2 thin films [1-3]. These Ising superconductors have very strong Ising spin-orbit couplings (SOC), in the order of 10 to 100meV, which pin electron spins to the out-of-plane directions. This is in contrast to Rashba SOC which pins electron spins to in-plane directions. Here, we explain how Ising SOC can enhance the in-plane upper critical field of Ising superconductors [1-4]. We also show that Ising superconductors can be used to create Majorana fermions by placing a metal wire on top of the Ising superconductor [5], similar to the case of Rashba wire on top of s-wave superconductors. We further show that an applied in-plane magnetic field can drive a monolayer NbSe2 [2,5] and into a nodal topological phase with Majorana flat bands when the applied in-plane field is higher than the Pauli limit but smaller than the upper critical field.

1. J. M. Lu, O. Zeliuk, I. Leermakers, Noah F. Q. Yuan, U. Zeitler, K. T. Law and J. T. Ye, Science 350, 1353 (2015).

2. X. Xi, Z. Wang, W. Zhao, J-H Park, K. T. Law, H. Berger, L. Forró, J. Shan, K. F. Mak,  Nature Physics 12, 139-143 (2016).

3. Y Saito et al. Nature Physics 12, 144-149 (2016).

4. Benjamin T. Zhou, Noah F.Q. Yuan, Hong-Liang Jiang and K. T. Law, Phys. Rev. B 93, 180501 R (2016).

5. Wen-Yu He, Benjamin T. Zhou, James J. He, Ting Zhang and K. T. Law, arXiv:1604.02867.