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The coupling between lattice vibration quanta and valence electrons caninduce charge density modulations and decisively influence the transportproperties of materials, e.g. leading to conventional superconductivity. Inhigh critical temperature superconductors, where electronic correlation is themain actor, the actual role of electron-phonon coupling (EPC) is beingintensely debated theoretically and investigated experimentally. We present anin-depth study of how the EPC strength can be obtained directly from resonantinelastic x-ray scattering (RIXS) data through the theoretical approach derivedby Ament et al. [EPL 95, 27008 (2011)]. The role of the model parameters (e.g.phonon energy $\omega_0$, intermediate state lifetime $1/\Gamma$, EPC matrixelement $M$, and detuning energy $\Omega$) is thoroughly analyzed, providinggeneral relations among them that can be used to make quantitative estimates ofthe dimensionless EPC $g = (M/\omega_0)^2$ without detailed microscopicmodeling. We then apply these methods to very high resolution Cu $L_3$ edgeRIXS spectra of three Nd$_{1+x}$Ba$_{2-x}$Cu$_3$O$_{7-\delta}$ films. For theinsulating antiferromagnetic parent compound the value of $M$ as a function ofthe in-plane momentum transfer is obtained for Cu-O bond-stretching (breathing)and bond-bending (buckling) phonon branches. For the underdoped and the nearlyoptimally doped samples, the effects of Coulomb screening and ofcharge-density-wave correlations on $M$ are assessed. In light of theanticipated further improvements of the RIXS experimental resolution, this workprovides a solid framework for an exhaustive investigation of the EPC incuprates and other quantum materials.

physical review research

Determining the Electron-Phonon Coupling in Superconducting Cuprates by  Resonant Inelastic X-ray Scattering: Methods and Results on  Nd$_{1+x}$Ba$_{2-x}$Cu$_3$O$_{7-\delta}$