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arXiv:2105.05554 · Physical review. B./Physical review. B

Nonequilibrium resonant inelastic x-ray scattering study of an electron-phonon model

Philipp Werner, Martin Eckstein

Published Aug 31, 2021• 9 citations
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Abstract

We use the nonequilibrium dynamical mean-field theory formalism to compute the equilibrium and nonequilibrium resonant inelastic x-ray scattering (RIXS) signal of a strongly interacting fermionic lattice model with a coupling of dispersionless phonons to the total charge on a given site. In the atomic limit, this model produces phonon subbands in the spectral function, but not in the RIXS signal. Electron hopping processes however result in phonon-related modifications of the charge excitation peak. We discuss the equilibrium RIXS spectra and the characteristic features of nonequilibrium states induced by photo-doping and by the application of a static electric field. The latter produces features related to Wannier-Stark states, which are dressed with phonon sidebands. Thanks to the effect of field-induced localization, the phonon features can be clearly resolved even in systems with weak electron-phonon coupling.

DOI
10.1103/physrevb.104.085155

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Abstract Resonant inelastic X-ray scattering (RIXS) detects various types of high- and low-energy elementary excitations in correlated solids, and this tool will play an increasingly important role in investigations of time-dependent phenomena in photo-excited systems. While theoretical frameworks for the computation of equilibrium RIXS spectra are well established, the development of appropriate methods for nonequilibrium simulations is an active research field. Here, we apply a recently developed nonequilibrium dynamical mean field theory (DMFT) based approach to compute the RIXS response of photo-excited two-orbital Mott insulators. The results demonstrate the feasibility of multi-orbital nonequilibrium RIXS calculations and the sensitivity of the quasi-elastic fluorescence-like features and excitation peaks on the nonequilibrium population of the Hubbard bands.
An emerging application of resonant inelastic x-ray scattering (RIXS) is the study of lattice excitations and electron-phonon ( e -ph) interactions in quantum materials. Despite the growing importance of this area of research, the community lacks a complete understanding of how the RIXS process excites the lattice and how these excitations encode information about the e -ph interactions. Here, we present a detailed study of the RIXS spectra of the Hubbard-Holstein model defined on extended one-dimensional lattices. Using the density matrix renormalization group method, we compute the RIXS response while treating the electron mobility, many-body interactions, and core-hole interactions on an equal footing. The predicted spectra exhibit notable differences from those obtained using the commonly adopted Lang-Firsov models, with important implications for analyzing past and future experiments. Our results provide a deeper understanding of how RIXS probes e -ph interactions and set the stage for a more realistic analysis of future experiments.
We develop a framework to evaluate the time-dependent resonant inelastic x-ray scattering (RIXS) signal with the use of nonequilibrium dynamical mean-field theory simulations. The approach is based on the solution of a time-dependent impurity model which explicitly incorporates the probe pulse. It avoids the need to compute four-point correlation functions and can in principle be combined with different impurity solvers. This opens a path to study time-resolved RIXS processes in multiorbital systems. The approach is exemplified with a study of the RIXS signal of a melting Mott antiferromagnet.
Su-Schrieffer-Heeger-like (SSH-like) electron-phonon interactions can drive the formation of light (bi)polarons and several novel states of matter. It is, therefore, prudent to develop experimental protocols for identifying such couplings in real materials and quantifying their strength. Here, we investigate how resonant inelastic x-ray scattering (RIXS) probes electron-phonon interactions in the one-dimensional half-filled Hubbard-SSH model with on-site phonons. Using the density matrix renormalization group method, we compute the full RIXS response and find that the lattice excitations generated during the scattering process inevitably couple to the system's charge and magnetic sectors, resulting in combined multiparticle excitations that cannot be easily disentangled from one another. While this aspect complicates the interpretation of RIXS experiments, we outline how it can be leveraged to identify and quantify SSH-like interactions in quantum materials.
We investigate the nonequilibrium dynamics of the transverse field Ising chain (TFIC) using time-resolved resonant inelastic X-ray scattering (tr-RIXS) in a pump-probe setup within a condensed matter setting. The tr-RIXS spectra reveal distinctive features, including two-kink continua at high energies and oscillatory spectral weight at low energies, both strongly influenced by the pump dynamics. By systematically analyzing the nonequilibrium tr-RIXS cross section under various pump configurations, we demonstrate how the spectra encode detailed information about the system's transient states, capturing instantaneous Hamiltonian parameters and the traversal of equilibrium quantum critical points during dynamic evolution. Notably, we uncover a one-to-one correspondence between oscillatory features in the low-energy spectra and dynamical quantum phase transitions, offering a novel and experimentally accessible approach for their detection. These findings highlight the versatility of tr-RIXS as a powerful tool for studying quantum systems far from equilibrium and their critical phenomena.
Su-Schrieffer-Heeger (SSH)-like electron-phonon (e-ph) interactions can drive the formation of light (bi)polarons and several novel states of matter. It is, therefore, prudent to develop experimental protocols for identifying such couplings in real materials and quantifying their strength. Here, we investigate how resonant inelastic x-ray scattering (RIXS) probes e-ph interactions in the one-dimensional half-filled Hubbard-SSH model with onsite phonons. Using the density matrix renormalization group method, we compute the full RIXS response and find that the lattice excitations generated during the scattering process inevitably couple to the system's charge and magnetic sectors, resulting in combined multi-particle excitations that cannot be easily disentangled from one another. While this aspect complicates the interpretation of RIXS experiments, we outline how it can be leveraged to identify and quantify SSH-like interactions in quantum materials.