Combined effect of Rashba spin-orbit coupling and disorder on s-wave superconducting pairing

Based on the Bogoliubov-de Gennes equation, we investigate the s-wave superconducting pairing in the presence of the Rashba spin-orbit interaction (SOI). We find that the superconducting is still in the singlet pairing when the spin-orbit interaction is included. The pairing potential is always weakened by the SOI due to its destructive effect on the superconductivity, and the pairing strength shows a periodic-like oscillation as the SOI strength changes. The period reflects the relationship between the characteristic length of SOI and the coherent length of superconductivity. When the disorder is also introduced, the pairing potential fluctuates in the space, but the disorder has less influence on the pairing strength than the SOI does. The fluctuation pattern depends on both the disorder and the strength of SOI, suggesting the spatial precesions of spins due to the SOI.