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

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 a function of incident photon energy and momentum transfer in several layered cuprates. For CaCuO$_2$, a$_{2−x}$Sr$_{x}$CuO$_{4+δ}$, and YBa$_2$ Cu$_3$ O$_6$ , using a generally accepted theoretical model, we quantitatively estimate the EPC for the bond-stretching mode along the high-symmetry directions (ζ,0) and (ζ,ζ), and as a function of the azimuthal angle φ at fixed q$_{∥}$. We compare our results with theoretical predictions and find that the q$_{∥}$-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 reliably determine the momentum dependence of EPC for the bond-stretching modes of cuprates. ... mehrMoreover, the large experimental basis provided here constitutes a stringent test for advanced theoretical predictions on the EPC.