Interplay of p-wave pairing potential and spin–orbit coupling in two-dimensional noncentrosymmetric superconductors

•Both SOC and pairing potential play important roles on superconductivity.•The role of SOC on Cooper pairings is determined by pairing potential.•There is a critical pairing potential which can be enhanced by SOC.

Both pairing potential and spin–orbit coupling (SOC) play important roles in two-dimensional noncentrosymmetric superconductivity. Supposing that p-wave pairing potential is present between quasiparticles, spin–singlet pairs arise and mix with spin–triplet pairs in the electron space. Our results show that the effect of SOC on the electron superconducting order parameters is different below and above a critical pairing potential V¯C. If the pairing potential V¯V¯C, increasing SOC leads to increment of the spin–singlet pairing, but reduction of the triplet one. Moreover, V¯C increases with SOC.