eta$ collective mode as A$_{1g}$ Raman resonance in cuprate superconductors

We discuss the possible existence a spin singlet excitation with charge ±2 (η-mode) originating the A 1g Raman resonance in cuprate superconductors. This η-mode relates the d-wave superconducting singlet pairing channel to a d-wave charge channel. We show that the η boson forms a particle-particle bound state below the 2∆ threshold of the particle-hole continuum where ∆ is the maximum d-wave gap. Within a generalized random phase approximation and Bethe-Salpether approximation study, we find that this mode has energies similar to the resonance observed by Inelastic Neutron Scattering (INS) below the superconducting (SC) coherent peak at 2∆ in various SC cuprates compounds. We show that it is a very good candidate for the resonance observed in Raman scattering below the 2∆ peak in the A 1g symmetry. Since the η-mode sits in the S = 0 channel, it may be observable via Raman, X-ray or Electron Energy Loss Spectroscopy probes.