Schwinger-Keldysh canonical formalism for electronic Raman scattering

TL;DR

This paper develops a Schwinger-Keldysh formalism to comprehensively analyze electronic Raman scattering, including all response types, in superconductors, facilitating better theoretical understanding of experimental spectra in strongly correlated materials.

Contribution

It introduces a unified perturbation formalism for electronic Raman scattering that accounts for resonant, non-resonant, and mixed responses, applicable to superconductors and extendable to X-ray scattering.

Findings

All scattering processes are included in the formalism.

Superconducting gap suppresses single-particle responses.

Cooper pairs contribute only to non-resonant response.

Abstract

Inelastic low-energy Raman and high-energy X-ray scatterings have made great progress in instrumentation to investigate the strong electronic correlations in matter. However, theoretical study of the relevant scattering spectrum is still a challenge. In this article, we present a Schwinger-Keldysh canonical perturbation formalism for the electronic Raman scattering, where all the resonant, non-resonant and mixed responses are considered uniformly. We show how to use this formalism to evaluate the cross section of the electronic Raman scattering off an one-band superconductor. All the two-photon scattering processes from electrons, the non-resonant charge density response, the elastic Rayleigh scattering, the fluorescence, the intrinsic energy-shift Raman scattering and the mixed response, are included. In the mean-field superconducting state, Cooper pairs contribute only to the non-resonant response. All the other responses are dominated by the single-particle excitations and are strongly suppressed due to the opening of the superconducting gap. Our formalism for the electronic Raman scattering can be easily extended to study the high-energy resonant inelastic X-ray scattering.