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Theory of ultrafast screening of U in driven charge-transfer insulators: a time-resolved x-ray absorption study

Denis Golež, Eva Paprotzki, Philipp Werner, Martin Eckstein

Published Jan 5, 2026• 0 citations
OpenAlex

Abstract

Recent seminal experiments have utilized time-resolved x-ray absorption spectroscopy (XAS) to investigate the ultrafast photoinduced renormalization of the electron interaction (“Hubbard U”) in Mott and charge transfer insulators. In this paper, we theoretically analyze the change of interactions due to dynamical screening as it is encoded in the XAS signal, using the nonequilibrium GW+EDMFT formalism. Our study shows that XAS is well-suited for measuring this change, but two aspects should be kept in mind if the screening processes are not substantially faster than the valence electron dynamics: (i) Screening in a photoexcited system can affect both the position and the lineshape of the absorption lines. (ii) In general, the effect cannot be captured by the modification of a single interaction parameter. Specifically, an estimate for Δ⁢� extracted from the shift of the XAS lines does not necessarily describe the related shift of the upper Hubbard band. We clarify these aspects using a minimal cluster model and the three-band Emery model for a charge transfer insulator.

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Recent seminal experiments have utilized time-resolved x-ray absorption spectroscopy (XAS) to investigate the ultrafast photoinduced renormalization of the electron interaction (“Hubbard U”) in Mott and charge transfer insulators. In this paper, we theoretically analyze the change of interactions due to dynamical screening as it is encoded in the XAS signal, using the nonequilibrium GW+EDMFT formalism. Our study shows that XAS is well-suited for measuring this change, but two aspects should be kept in mind if the screening processes are not substantially faster than the valence electron dynamics: (i) Screening in a photoexcited system can affect both the position and the lineshape of the absorption lines. (ii) In general, the effect cannot be captured by the modification of a single interaction parameter. Specifically, an estimate for Δ⁢� extracted from the shift of the XAS lines does not necessarily describe the related shift of the upper Hubbard band. We clarify these aspects using a minimal cluster model and the three-band Emery model for a charge transfer insulator.
We present a formalism based on nonequilibrium dynamical mean-field theory (DMFT) which allows to compute the time-resolved x-ray absorption spectrum (XAS) of photoexcited solids. By applying this formalism to the photodoped half-filled and quarter-filled two-orbital Hubbard models in the Mott insulating regime we clarify how the time-resolved XAS signal reflects the nonequilibrium population of different local states. Apart from the missing broadening associated with continuum excitations, the atomic XAS spectrum computed with the nonthermal state populations provides a good approximation to the full nonequilibrium DMFT result. This suggests a route to combine the accurate DMFT description of nonequilibrium states of solids with cluster calculations of the XAS signal.
Cuprate superconductors remain a mysterious and intensely studied class of materials. New insights into their properties may be obtained by driving these systems out of equilibrium by strong laser pulses. Up to now, most theoretical works on photoexcited cuprates have employed a minimalistic single-band description of these complex materials. In order to treat cuprates and other charge transfer insulators more realistically, the authors develop a multiband theoretical scheme based on GW+EDMFT and Hartree-Fock+EDMFT and apply it to the paradigmatic Emery model. They demonstrate that photoexcitations across the charge transfer gap lead to a strong renormalization of this gap by relative band shifts as well as a substantial broadening of the bands. Comparison with several experimental probes on cuprates, e.g., time-resolved ARPES or optical experiments, shows a remarkable agreement with these simulation results. The new theoretical framework opens a path to explore optical manipulations in charge transfer insulators.
We study the dynamics of charge-transfer insulators after a photoexcitation using the three-band Emery model which is relevant for the description of cuprate superconductors. We provide a detailed derivation of the nonequilibrium extension of the multiband GW+EDMFTGW+\text{EDMFT}GW+EDMFT formalism and the corresponding downfolding procedure. The Peierls construction of the electron-light coupling is generalized to the multiband case resulting in a gauge invariant combination of the Peierls intraband acceleration and dipolar interband transitions. We use the formalism to study momentum-dependent (inverse) photoemission spectra and optical conductivities. The time-resolved spectral function shows a strong renormalization of the charge-transfer gap and a substantial broadening of some of the bands. While the upper Hubbard band exhibits a momentum-dependent broadening, an almost rigid band shift is observed for the ligand bands. The inverse photoemission spectrum reveals that the inclusion of nonlocal and interband charge fluctuations results in a very fast relaxation of the holes to the top of the Zhang-Rice singlet band. Consistent with the changes in the spectral function, the optical conductivity shows a renormalization of the charge-transfer gap, which is proportional to the photodoping. The details of the photoinduced changes strongly depend on the dipolar matrix elements, which calls for an ab initio determination of these parameters.
Collective excitations contain rich information about photoinduced transient states in correlated systems. In a Mott insulator, charge degrees of freedom are frozen, but can be activated by photodoping. The energy-momentum distribution of the charge excitation spectrum reflects the propagation of charge degrees of freedom and provides information about the interplay among various intertwined instabilities on the timescale set by the pump. To reveal charge excitations out of equilibrium, we simulate time-resolved x-ray absorption and resonant inelastic x-ray scattering using a Hubbard model. After pumping, the former resolves photodoping, while the latter characterizes the formation, dispersion, weight, and nonlinear effects of collective excitations. Intermediate-state information from time-resolved resonant inelastic x-ray scattering (trRIXS) can be used to decipher the origin of these excitations, including bimagnons, Mott-gap excitations, doublon and single-electron in-gap states, and anti-Stokes relaxation during an ultrafast pump. This paper provides a theoretical foundation for existing and future trRIXS experiments.
Recent angle-resolved photoemission spectroscopy (ARPES) for a newly discovered doped one-dimensional (1D) Mott insulator ${\mathrm{Ba}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{3+\ensuremath{\delta}}$ proposed the presence of attractive charge interactions between neighboring sites if a 1D Hubbard model is employed to describe the material. On the other hand, long-range repulsive charge interactions were proposed to be crucial for understanding the optical excitations of undoped 1D Mott insulators. Motivated by these contrasting proposals, we perform density-matrix renormalization group calculations of the single-particle spectral function as well as dynamical spin and charge structure factors for two kinds of extended 1D Hubbard models. The spectral function for the long-range repulsive model less agrees with the ARPES data as compared with that for the attractive one. The dynamical spin and charge structure factors also exhibit contrasting behaviors between the two models: The attractive model shows less momentum dependence of the integrated weight in the dynamical spin structure factor and more accumulation of the weight on the upper edge of particle-hole-type excitation in the dynamical charge structure factor. These features give a good criterion of an appropriate model for doped 1D Mott insulators, which can be judged by resonant-inelastic x-ray scattering experiments.
We study the dynamics of screening in photodoped Mott insulators with long-ranged interactions using a nonequilibrium implementation of the GW plus extended dynamical mean-field theory formalism. Our study demonstrates that the complex interplay of the injected carriers with bosonic degrees of freedom (charge fluctuations) can result in long-lived transient states with properties that are distinctly different from those of thermal equilibrium states. Systems with strong nonlocal interactions are found to exhibit a self-sustained population inversion of the doublons and holes. This population inversion leads to low-energy antiscreening which can be detected in time-resolved electron-energy-loss spectra.