  We study the in-plane critical magnetic field of two-dimensional Ising
superconducting systems, and propose the microscopic theory for these 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 coupling, 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 ultra-thin films.
