We study the in-plane critical magnetic field of two-dimensional Ising superconducting systems and propose the microscopic calculation for these disordered two-dimensional superconducting systems with or without inversion symmetry. Protected by certain specific spin-orbit 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 upturn in the zero-temperature limit. The impurity scattering and Rashba spin-orbit interaction, 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 stanene and Pb superconducting ultrathin films.

中文翻译：

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二维伊辛超导系统平面内临界场的微观理论

我们研究了二维伊辛超导系统的面内临界磁场，并提出了具有或没有反演对称性的这些无序二维超导系统的微观计算。受某些特定的自旋轨道相互作用的保护，该相互作用使电子自旋向平面外方向极化，平面内的临界场大大超过了保利极限，并在零温度极限处表现出明显的上翻。在微观框架中以平等的基础处理杂质的散射和Rashba自旋轨道的相互作用，都削弱了临界场，但在质上有不同的方式。微观理论与锡和铅超导超薄膜的最新实验结果一致。