Effect of pairing fluctuations on the spin resonance in Fe-based superconductors

The spin resonance observed in the inelastic neutron scattering data on Fe-based superconductors has played a prominent role in the quest for determining the symmetry of the order parameter in these compounds. Most theoretical studies of the resonance employ an RPA-type approach in the particle-hole channel and associate the resonance in the spin susceptibility χS(q,ω) at momentum Q=(π,π) with the spin-exciton of an s+- superconductor, pulled below 2Δ by residual attraction associated with the sign change of the gap between Fermi points connected by Q. Here we explore the effect of fluctuations in the particle-particle channel on the spin resonance. Particle-particle and particle-hole channels are coupled in a superconductor and to what extent the spin resonance can be viewed as a particle-hole exciton needs to be addressed. In the case of purely repulsive interactions, we find that the particle-particle channel at total momentum Q (the π channel) contributes little to the resonance. However, if the interband density-density interaction is attractive and the π resonance is possible on its own, along with spin-exciton, we find a much stronger shift of the resonance frequency from the position of the would-be spin-exciton resonance. We also show that the expected double-peak structure in this situation does not appear because of the strong coupling between particle-hole and particle-particle channels, and ImχS(Q,ω) displays only a single peak.