Microscopic theory of in-plane critical field in two-dimensional Ising superconducting systems

In this talk, I will show our theoretical attempts to study the in-plane critical magnetic field of two-dimensional Ising superconducting systems, and to propose the microscopic theory for these systems with or without inversion symmetry[1]. Protected by certain specific spin-orbital interaction which polarizes the electron spin to the out-of-plane direction, the in-plane critical fields largely surpass the Pauli limit and show remarkable up-turn in the zero temperature limit. The impurity scattering and Rashba spin orbital scattering, treated on equal-footing in the microscopic framework, both weaken the critical field but in qualitatively different manners. The microscopic theory is consistent with recent experimental results in Pb[2,3] and stanine[4] superconducting ultra-thin films.