The influence of phonon symmetry and electronic structure on the electron-phonon coupling momentum dependence in cuprates

TL;DR

This study uses Cu L3 RIXS measurements to analyze the momentum dependence of electron-phonon coupling in cuprates, highlighting the role of phonon symmetry and electronic structure, and validating RIXS as a reliable tool for such analysis.

Contribution

It demonstrates that Cu L3 RIXS can reliably determine EPC momentum dependence in cuprates and emphasizes the importance of phonon symmetry and electronic structure in interpreting RIXS data.

Findings

EPC magnitude varies with phonon symmetry and electronic structure.

RIXS intensity dependence largely due to phonon symmetry.

Provides extensive data for testing theoretical models.

Abstract

The experimental determination of the magnitude and momentum dependence of electron-phonon coupling (EPC) is an outstanding problem in condensed matter physics. The intensity of phonon peaks in Resonant Inelastic X-ray Scattering (RIXS) spectra can be related to the underlying EPC strength under significant approximations whose validity deserves careful verification. We measured the Cu L$_3$ RIXS phonon intensity as function of incident photon energy and of momentum transfer in several layered cuprates. For CaCuO$_2$, La$_{2-x}$Sr$_{x}$CuO$_{4+\delta}$, and \ch{YBa_2Cu_3O_{6}}, using a generally accepted theoretical model, we estimate quantitatively the EPC for the bond-stretching mode along the high-symmetry directions ($\zeta$,0) and ($\zeta$,$\zeta$), and as a function of the azimuthal angle $\varphi$ at fixed $q_\parallel$. We compare our results with theoretical predictions and we find that the $\mathbf{q}_\parallel$-dependence of the phonon RIXS intensity can be largely ascribed to the phonon symmetry. However, a more satisfactory prediction of the experimental results requires an accurate description of the electronic structure close to the Fermi level. Our extensive investigation indicates that Cu L$_3$ RIXS can be reliably used to determine the momentum dependence of EPC for the bond-stretching modes of cuprates. Moreover, the large experimental basis provided in this article can serve as stringent test for advanced theoretical predictions on the EPC.