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

TL;DR

This paper proposes that a spin singlet $ ext{eta}$-mode, a charge $ ext{±}2$ excitation, explains the $A_{1g}$ Raman resonance in cuprate superconductors, linking superconducting and charge channels.

Contribution

It introduces the $ ext{eta}$-mode as a novel explanation for the $A_{1g}$ Raman resonance, supported by theoretical calculations matching experimental observations.

Findings

The $ ext{eta}$-mode forms a bound state below $2 ext{Delta}$.

The mode's energy aligns with INS resonance in cuprates.

It is a candidate for detection via Raman, X-ray, or EELS.

Abstract

We discuss the possible existence a spin singlet excitation with charge $\pm2$ ($\eta$-mode) originating the $A_{1g}$ Raman resonance in cuprate superconductors. This $\eta$-mode relates the $d$-wave superconducting singlet pairing channel to a $d$-wave charge channel. We show that the $\eta$ boson forms a particle-particle bound state below the $2\Delta$ threshold of the particle-hole continuum where $\Delta$ 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 $2\Delta$ in various SC cuprates compounds. We show that it is a very good candidate for the resonance observed in Raman scattering below the $2\Delta$ peak in the $A_{1g}$ symmetry. Since the $\eta$-mode sits in the $S=0$ channel, it may be observable via Raman, X -ray or Electron Energy Loss Spectroscopy probes.