Abstract
The coupling between lattice and charge degrees of freedom in condensed matter materials is ubiquitous and can often result in interesting properties and ordered phases, including conventional superconductivity, charge density wave order, and metal-insulator transitions. Angle-resolved photoemission spectroscopy and both neutron and non-resonant x-ray scattering serve as effective probes for determining the behavior of appropriate, individual degrees of freedom -- the electronic structure and lattice excitation, or phonon dispersion, respectively. However, each provides less direct information about the mutual coupling between the degrees of freedom, usual through self-energy effects, which tend to renormalize and broaden spectral features precisely where the coupling is strong, impacting ones ability to quantitively characterize the coupling. Here we demonstrate that resonant inelastic x-ray scattering, or RIXS, can be an effective tool to directly determine the relative strength and momentum dependence of the electron-phonon coupling in condensed matter systems. Using a diagrammatic approach for an 8-band model of copper oxides, we study the contributions from the lowest order diagrams to the full RIXS intensity for a realistic scattering geometry, accounting for matrix element effects in the scattering cross-section as well as the momentum dependence of the electron-phonon coupling vertex. A detailed examination of these maps offers a unique perspective into the characteristics of electron-phonon coupling, which complements both neutron and non-resonant x-ray scattering, as well as Raman and infrared conductivity.
Highlights
The ability to characterize excited states and fundamental excitations in solids remains one of the forefront challenges in condensed matter physics
We have utilized a general formalism to investigate the way in which phonons can appear in a RIXS process
Our focus was centered on the cuprates since a large majority of RIXS efforts to date have focused on the Cu L-edge
Summary
The ability to characterize excited states and fundamental excitations in solids remains one of the forefront challenges in condensed matter physics. This issue has important ramifications to our understanding of emergent phenomena such as superconductivity and density wave order. We examine this selectivity of the light-scattering process to determine how and which phonons can be resonantly excited during a resonant x-ray process, and the resulting information that can be obtained about the relative strength and momentum dependence of electron-phonon coupling. We primarily consider an L-edge resonant x-ray scattering, where a core electron is excited into the conduction band, and we assume that the most interesting phonons are those that couple to mobile conduction, valence electrons, or holes. Electron-phonon coupling with atomic specificity, to further complement neutron and IXS measurements
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