Abstract
Interactions between electrons and lattice vibrations are responsible for a wide range of material properties and applications. Recently, there has been considerable interest in the development of resonant inelastic x-ray scattering (RIXS) as a tool for measuring electron-phonon (e-ph) interactions. Here, we demonstrate the ability of RIXS to probe the interaction between phonons and specific electronic states both near to, and away from, the Fermi level. We perform carbon K-edge RIXS measurements on graphite, tuning the incident x-ray energy to separately probe the interactions of the π* and σ* electronic states. Our high-resolution data reveal detailed structure in the multiphonon RIXS features that directly encodes the momentum dependence of the e-ph interaction strength. We develop a Green’s-function method to model this structure, which naturally accounts for the phonon and interaction-strength dispersions, as well as the mixing of phonon momenta in the intermediate state. This model shows that the differences between the spectra can be fully explained by contrasting trends of the e-ph interaction through the Brillouin zone, being concentrated at the Γ and K points for the π* states while being significant at all momenta for the σ* states. Our results advance the interpretation of phonon excitations in RIXS and extend its applicability as a probe of e-ph interactions to a new range of out-of-equilibrium situations.Received 10 May 2021Revised 18 October 2021Accepted 20 October 2021DOI:https://doi.org/10.1103/PhysRevX.11.041052Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasElectronic structurePhononsPhysical SystemsGraphiteTechniquesResonant inelastic x-ray scatteringCondensed Matter, Materials & Applied Physics
Highlights
Knowledge of the interactions between electrons and phonons is central to understanding a diverse array of condensed matter phenomena
Through careful choice of the incident photon energy, RIXS is able to probe the interactions between phonons and electrons both close to, and away from, the Fermi level
Our results for graphite reveal that the momentum dependence of the interaction strength, GðqÞ, can be highly distinct in these two regimes: For low-energy πà states it is concentrated in small regions around the Γ and K points, while for high-energy σà states it is significant across the Brillouin zone
Summary
Knowledge of the interactions between electrons and phonons is central to understanding a diverse array of condensed matter phenomena. At the resonances of these two states, we find qualitatively different multiphonon excitations in our RIXS spectra, showing a stark difference in the phonon momenta to which they couple. This behavior cannot be captured by the currently available theoretical models, which assume dispersionless phonons [19,28,32] or focus on one-phonon processes [29]. Extend a Green’s-function approach, previously applied to small molecules [30], to treat the full momentum dependence of phonons in a crystalline lattice This model accurately reproduces our experimental spectra at both resonances, revealing contrasting trends of the e-ph interaction strength through the Brillouin zone
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