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

Abstract

We discuss the possible existence a spin singlet excitation with charge $\pm 2$ ($\eta$-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.

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• Evolution of spectral and transport quantities with doping in the SU(2) theory of cuprates
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• The phase diagram of the underdoped cuprates at high magnetic field
• Calculation of an enhanced A1g symmetry mode induced by Higgs oscillations in the Raman spectrum of high-temperature cuprate superconductors
• Collective mode in the SU(2) theory of cuprates
• A model for the neutron resonance in HgBa${}_2$CuO${}_{4+\delta }$
• Many-body physics-induced selection rules: application to Raman spectroscopy