Superconducting gap symmetry from repulsive interactions in the spin-singlet state

Abstract

We obtained the superconducting gap equation in terms of the effective T-scattering matrix. We considered the gap symmetry in both singlet and triplet states as well as in charge and spin channels. We show that the superconducting gap for the repulsive interactions in the spin-singlet state exists in the charge channel only, and the gap has s-wave symmetry (ℓ=0, where ℓ is the orbital quantum number of a pair) or d-wave (ℓ=2) symmetry. We also show that in the 2D case, the strongly anisotropic s-wave gap might have nodes in the direction of the nesting wave vector and may resemble the d x 2− y 2 gap symmetry. We show that there is a gap for the attractive interactions in the spin channel only. Such a gap indicates the phase transition into superfluid state which is similar to liquid 3He. The gap due to pairing instability for the attractive interactions in the spin channel has p-wave symmetry (ℓ=1) for the spin-triplet state with m s=±1 or p-wave symmetry (ℓ=1) for the spin-triplet state with m s=0.