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

•Effect of combined Rashba and Dresselhauls SOCs on superconductivity is studied.•Spin-singlet and triplet pairings are mixed when SOC is present.•Pairing gaps reduce to their minimum values in equal-Rashba–Dresselhauls case.

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.