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Superconductivity in a two-dimensional superconductor with Rashba and Dresselhaus spin-orbit couplings

We present a general model with both Rashba and Dresselhaus spin-orbit couplings to describe a two-dimensional noncentrosymmetric superconductor. The combined effects of the two spin-orbit couplings on superconductivity are investigated in the framework of mean-field theory. We find that the Rashba and Dresselhaus spin-orbit couplings result in similar effects on superconductivity if they are present solely in the system. Mixing of spin-singlet and triplet pairings in electron band is induced under the assumption that each quasiparticle band is p-wave paired. If the two types of spin-orbit couplings appear jointly, both the singlet and triplet pairings are weakened and decreased down to their minimum values in the equal-Rashba-Dresselhaus case.