Determining the electron-phonon coupling in superconducting cuprates by resonant inelastic x-ray scattering: Methods and results on Nd1+xBa2-xCu3 O7-δ

The coupling between lattice vibration quanta and valence electrons can induce charge-density modulations and decisively influence the transport properties of materials, e.g., leading to conventional superconductivity. In high-critical-temperature superconductors, where electronic correlation is the main actor, the actual role of electron-phonon coupling (EPC) is being intensely debated theoretically and investigated experimentally. We present an in-depth study of how the EPC strength can be obtained directly from resonant inelastic x-ray scattering (RIXS) data through the theoretical approach derived by Ament et al. [Europhys. Lett. 95, 27008 (2011)EULEEJ0295-507510.1209/0295-5075/95/27008]. The role of the model parameters (e.g., phonon energy ω0, intermediate state lifetime 1/Γ, EPC matrix element M, and detuning energy ω) is thoroughly analyzed, providing general relations among them that can be used to make quantitative estimates of the dimensionless EPC g=(M/ω0)2 without detailed microscopic modeling. We then apply these methods to very high-resolution Cu L3-edge RIXS spectra of three Nd1+xBa2-xCu3O7-δ films. For the insulating antiferromagnetic parent compound, the value of M as a function of the in-plane momentum transfer is obtained for Cu-O bond-stretching (breathing) and bond-bending (buckling) phonon branches. For the underdoped and the nearly optimally doped samples, the effects of Coulomb screening and of charge-density-wave correlations on M are assessed. In light of the anticipated further improvements of the RIXS experimental resolution, this work provides a solid framework for an exhaustive investigation of the EPC in cuprates and other quantum materials.