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−δ}

• Published in: Physical review research 2020-05, Vol.2 (2), p.023231
• Main Authors: Lucio Braicovich, Matteo Rossi, Roberto Fumagalli, Yingying Peng, Yan Wang, Riccardo Arpaia, Davide Betto, Gabriella M. De Luca, Daniele Di Castro, Kurt Kummer, Marco Moretti Sala, Mattia Pagetti, Giuseppe Balestrino, Nicholas B. Brookes, Marco Salluzzo, Steven Johnston, Jeroen van den Brink, Giacomo Ghiringhelli
• Format: Article
• Language: English
• ISSN: 2643-1564
• DOI: 10.1103/PhysRevResearch.2.023231

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 ω_{0}, 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/ω_{0})^{2} without detailed microscopic modeling. We then apply these methods to very high-resolution Cu L_{3}-edge RIXS spectra of three Nd_{1+x}Ba_{2−x}Cu_{3}O_{7−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.