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

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 $\phi$ 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.

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