Effects of Rashba and Dresselhaus spin-orbit couplings on the critical temperature and paramagnetic limiting field of superconductors with broken inversion symmetry

Transition temperature (T_c) and paramagnetic limiting of a superconductor without spatial inversion symmetry in the presence of both Rashba and Dresselhaus antisymmetric spin-orbit couplings is studied. The critical temperature is derived for anisotropy of the superconducting order parameter, ranging from isotropic s-wave to any pairing state with nonzero angular momentum and mixed parity singlet-triplet states emerge due to spin-orbit coupling (SOC). It will be shown that for unprotected odd parity pairing, pure Rashba and Dresselhaus SOCs have similar effects on the reduction of T_c and for combined effects of the two spin-orbit couplings at fixed SOC, T_c reduced by increasing Dresselhaus component and decreased down to its minimum value in the equal-Rashba-Dresselhaus case. The paramagnetic limiting is also analyzed for spin-singlet pairing and it is shown that the low temperature divergence behavior of paramagnetic limiting is less affected by both Rashba and Dresselhaus SOCs but for fixed SOC strength by increasing Dresselhaus component the paramagnetic limiting field is increased.