Momentum-resolved thermodynamics and barrier-free order-parameter collapse in spin-orbit-coupled superconductors under a Zeeman field

Spin-orbit coupling (SOC) can enhance the critical Zeeman field of clean superconductors beyond the Pauli limit. We develop a momentum decomposition of the zero-temperature free energy to investigate spin-singlet $s$-wave superconductors with general time-reversal-symmetric SOC. The SOC component perpendicular to the Zeeman field enhances the critical field and suppresses first-order features, whereas the parallel component favors Pauli-limited thermodynamic behavior. Applying this framework to Rashba superconductors and Ising superconductors with weak Rashba SOC, we identify the origin of the abrupt collapse of the superconducting order parameter at the critical field. Competing angular contributions produce a nearly flat free-energy landscape, allowing a barrier-free order-parameter collapse distinct from the conventional Pauli-limited first-order transition.