Combined effect of Rashba spin-orbit coupling and disorder on the symmetry of superconducting pairing

Abstract

Based on Bogoliubov-de Gennes equation, we investigate the superconducting pairing due to the nearest-neighboring attractive interaction in the presence of the Rashba spin-orbit coupling (SOC). It is found that the superconducting is still of the singlet nature and dominated by the $d$-wave symmetry in the presence of SOC and in the absence of disorder. The pairing strength has decreasing maxima as the SOC strength increases due to its destructive effect on the superconductivity and shows a periodiclike oscillation reflecting the relationship between the characteristic length of SOC and the coherent length of superconductivity. In the presence of SOC and disorder, the pairing has both the singlet and triplet components, and the $s$- and $p$-wave symmetries are induced in addition to the dominant $d$-wave symmetry. The related strengths of different pairing components exhibit complicated dependence on the strengths of the SOC and the disorder.