Gap structure in noncentrosymmetric superconductors

Gap structure in noncentrosymmetric superconductors with spin-orbit band splitting is studied using a microscopic model of pairing mediated by phonons and/or spin fluctuations. The general form of pairing interaction in the band representation is derived, which includes both the intraband and interband pairing terms. In the case of isotropic interaction (in particular, for a BCS-contact interaction), the interband pairing terms vanish identically at any magnitude of the band splitting. The effects of pairing interaction anisotropy are analyzed in detail for a metal of cubic symmetry with strong spin-orbit coupling. It is shown that if phonons are dominant then the gaps in two bands are isotropic, nodeless, and have in general different amplitudes. Applications to the ${\mathrm{Li}}_2{({\mathrm{Pd}}_{1-x},{\mathrm{Pt}}_x)}_3\mathrm{B}$ family of noncentrosymmetric superconductors are discussed.