Effects of Double Magnon Scattering on the Particle-Particle Interaction in the Two-Dimensional Hubbard Model with Next-Nearest-Neighbor Hopping

Abstract

We investigate effects of double scattering by antiferromagnetic spin fluctuation (magnon), denoted as DMS, on both the singlet and triplet particle-particle (p-p) interaction in the two-dimensional Hubbard model. Different band structures with different next-nearest-neighbor hopping parameter but with a fixed electron occupation number of around 0.85 are considered. It is first indicated that due to the retardation of magnon contribution from the p-p and hole-hole (h-h) pair in the intermediate states also arises in the vertex correction, which has sign opposite to that of the usual particle-hole (p-h) pair. The contributions of the p-h pair and of the p-p and h-h pair to the DMS correction are enhanced for large and small momentum transfer (MT), respectively. A model calculation is performed to show that when the Fermi level is near the Van Hove level, the DMS correction becomes comparable to the single magnon results. For singlet pairing state the DMS p-p interaction is repulsive at both large and smal...