Directly characterizing the relative strength and momentum dependence of electron-phonon coupling using resonant inelastic x-ray scattering

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.

arXiv comment10 pages, 10 figures

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Cited by in corpus (63)

• Dispersive charge density wave excitations and temperature dependent commensuration in Bi2Sr2CaCu2O8+δ
• Mapping momentum-dependent electron-phonon coupling and non-equilibrium phonon dynamics with ultrafast electron diffuse scattering
• Direct determination of mode-projected electron-phonon coupling in the time-domain
• Mechanisms of electron-phonon coupling unraveled in momentum and time: The case of soft-phonons in TiSe${}_2$
• Strong Superexchange in a $d^{9-\delta }$ Nickelate Revealed by Resonant Inelastic X-Ray Scattering
• Charge order at high temperature in cuprate superconductors
• Spectroscopic Evidence for Charge Order Melting via Quantum Fluctuations in a Cuprate
• Experimental Determination of Momentum-Resolved Electron-Phonon Coupling
• Nature of the charge-density wave excitations in cuprates
• Direct observation of charge order in underdoped and optimally doped Bi${}_2$(Sr,La)${}_2$CuO${}_{6+\delta }$ by resonant inelastic x-ray scattering
• Formation of Incommensurate Charge Density Waves in Cuprates
• Multi-orbital charge density wave excitations and concomitant phonon anomalies in Bi${}_2$Sr${}_2$LaCuO${}_{6+\delta }$
• Polarization resolved Cu $L_3$-edge resonant inelastic x-ray scattering of orbital and spin excitations in NdBa${}_2$Cu${}_3$O${}_{7-\delta }$
• Langevin Simulations of a Long Range Electron Phonon Model
• Coupling between dynamic magnetic and charge-order correlations in the cuprate superconductor Nd${}_{2-x}$Ce${}_x$CuO${}_4$
• Theory for Time-Resolved Resonant Inelastic X-ray Scattering
• Enhanced electron-phonon coupling for charge-density-wave formation in La${}_{1.8-x}$Eu${}_{0.2}$Sr${}_x$CuO${}_{4+\delta }$
• Signature of quantum criticality in cuprates by charge density fluctuations
• 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${}_{7-\delta }$
• Anisotropic damping of the spin fluctuations in doped La2-xSrxCuO4 studied by resonant inelastic x-ray scattering
• Probing the energy conversion pathways between light, carriers and lattice in real time with attosecond core-level spectroscopy
• Mode-selective coupling of coherent phonons to the Bi2212 electronic band structure
• Exploring Quantum Materials with Resonant Inelastic X-Ray Scattering
• Site-selective Probe of Magnetic Excitations in Rare-earth Nickelates using Resonant Inelastic X-ray Scattering
• Charge density waves and Fermi-surface reconstruction in the clean overdoped cuprate superconductor Tl2Ba2CuO6+x
• Demonstration of resonant inelastic X-ray scattering as a probe of exciton-phonon coupling
• Charge Order Lock-in by Electron-Phonon Coupling in La${}_{1.675}$Eu${}_{0.2}$Sr${}_{0.125}$CuO${}_4$
• Decoupling carrier concentration and electron-phonon coupling in oxide heterostructures observed with resonant inelastic x-ray scattering
• High-resolution resonant inelastic x-ray scattering study of the electron-phonon coupling in honeycomb $\alpha$-Li${}_2$IrO${}_3$
• Generalization of the Franck-Condon model for phonon excitations by resonant inelastic X-ray scattering
• High-resolution resonant inelastic soft X-ray scattering as a probe of the crystal electrical field in lanthanides demonstrated for the case of CeRh2Si2
• Dynamical spin susceptibility in La2CuO4 studied by resonant inelastic x-ray scattering
• Identification of a Critical Doping for Charge Order Phenomena in Bi-2212 Cuprates via RIXS
• Probing electron-phonon interactions away from the Fermi level with resonant inelastic x-ray scattering
• Introduction to High-Resolution Inelastic X-Ray Scattering
• Collective nature of orbital excitations in layered cuprates in the absence of apical oxygens
• Doping-dependence of the electron-phonon coupling in two families of bilayer superconducting cuprates
• Observing photo-induced chiral edge states of graphene nanoribbons in pump-probe spectroscopies
• Disparate exciton-phonon couplings for zone center and boundary phonons in solid-state graphite
• Probing the pathway of an ultrafast structural phase transition to illuminate the transition mechanism in Cu2S
• Spin- and time-resolved photoelectron spectroscopy and diffraction studies using time-of-flight momentum microscopes
• Signatures of Mode-Resolved, Nonlocal Electron-Phonon Coupling in Two-Dimensional Spectroscopy
• Collective mode in the SU(2) theory of cuprates
• Beyond the single-site approximation modeling of electron-phonon coupling effects on resonant inelastic X-ray scattering spectra
• Magnon-phonon coupling effects on the indirect K-edge resonant inelastic X-ray scattering spectrum of a 2D Heisenberg antiferromagnet
• Low temperature dynamic polaron liquid in a manganite exhibiting colossal magnetoresistance
• Quantum fluctuations of charge order induce phonon softening in a superconducting cuprate
• Decoupling of Static and Dynamic Charge Correlations revealed by Uniaxial Strain in a Cuprate Superconductor
• Theory of electron-phonon interactions in extended correlated systems probed by resonant inelastic x-ray scattering
• Out-of-phase Plasmon Excitations in the Trilayer Cuprate Bi${}_2$Sr${}_2$Ca${}_2$Cu${}_3$O${}_{10+\delta }$
• Spin-orbital-lattice entanglement in the ideal j=1/2 compound K${}_2$IrCl${}_6$
• Resonant Inelastic X-Ray Scattering in Metals: A Diagrammatic Approach
• Persistence of small polarons into the superconducting phase of Ba${}_{1-x}$K${}_x$BiO${}_3$
• Bulk charge density wave and electron-phonon coupling in superconducting copper oxychlorides
• A set-up for Hard X-ray Time-resolved Resonant Inelastic X-ray Scattering at SwissFEL
• Orbital inversion and emergent lattice dynamics in infinite layer CaCoO${}_2$
• Dynamic charge order from strong correlations in the cuprates
• Signatures of multiple charge excitations in RIXS spectra of metals
• Anisotropic electron damping and energy gap in Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+\delta }$
• Superconducting phase diagram of multi-layer square-planar nickelates
• The doping evolution of the charge density wave and charge density fluctuations in La${}_{2-x}$Sr${}_x$CuO${}_4$
• Theory of dispersive optical phonons in resonant inelastic x-ray scattering experiments
• Superconductivity Reinforces Charge-Density-Wave Phase Coherence across Cuprates