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arXiv:1903.08713 · Physical review. B./Physical review. B

Multiband nonequilibrium GW+EDMFT formalism for correlated insulators

Denis Golež, Martin Eckstein, Philipp Werner

Published Dec 11, 2019• 51 citations
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Abstract

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 $GW+\text{EDMFT}$ 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.

DOI
10.1103/physrevb.100.235117

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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.
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.
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 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.
We study the photoexcitation dynamics of correlated band insulators, using nonequilibrium dynamical mean-field theory for the ionic Hubbard model. We find two distinct behaviors, depending on the ratio of the on-site interaction UUU and the bare band gap $\mathrm{\ensuremath{\Delta}}$. For small interactions, the relaxation is characterized by intraband carrier scattering in relatively rigid bands, leading to a nonthermal intermediate state with separate thermal distributions of electrons and holes. This behavior can be viewed as typical for a band insulator with weak interactions. For larger interaction, on the other hand, we observe a strong modification of the electronic spectrum and a filling-in of the gap after photoexcitation, along with a rapid thermalization of the system. The two behaviors therefore provide a dynamical distinction of a correlated band insulator and a band insulator, which can differ even when the spectra of the two systems are similar in equilibrium. The crossover happens when the interaction UUU is comparable to $\mathrm{\ensuremath{\Delta}}$.
The three-band model relevant to high-temperature copper-oxide superconductors is solved using single-site dynamical mean field theory and a tight-binding parametrization of the copper and oxygen bands. For a band filling of one hole per unit cell the metal/charge-transfer-insulator phase diagram is determined. The electron spectral function, optical conductivity, and quasiparticle mass enhancement are computed as functions of electron and hole doping for parameters such that at one hole per cell the paramagnetic phase is insulating and for parameters such that at one hole per unit cell the paramagnetic phase is metallic. The optical conductivity is computed using the Peierls phase approximation for the optical matrix elements. The calculation includes the physics of ``Zhang-Rice singlets.'' The effects of antiferromagnetism on the magnitude of the gap and the relation between correlation strength and doping-induced changes in state density are determined. Three-band and one-band models are compared. The two models are found to yield quantitatively consistent results for all energies less than about 4 eV including energies in the vicinity of the charge-transfer gap. Parameters on the insulating side of the metal/charge-transfer insulator phase boundary lead to gaps which are too large and near-gap conductivities which are too small relative to data. The results place the cuprates clearly in the intermediate correlation regime, on the paramagnetic metal side of the metal/charge-transfer insulator phase boundary.
On the basis of exact diagonalizations, a comparative study of two-particle optical and magnetic, as well as single-particle, excitations is presented for a two-dimensional (2D) multiorbital Hubbard model. For reasonable parameter sets appropriate for the cuprate superconductors, the single-particle excitations display strongly correlated states related to the Zhang-Rice Cu-O singlet construction. These states define the gap (to the upper Hubbard band) at half-filling and become partially occupied by doping holes in our 2\ifmmode\times\else\texttimes\fi{}2 unit-cell system. The optical results, which are the first quantitative calculations performed for realistic parameters of the three-band Hubbard model, clearly show three allowed optical transitions: (i) itinerant motion of the Cu-O singlets, having (for doping concentrations x\ensuremath{\ne}0) a spectral Drude distribution around \ensuremath{\omega}=0 with spectral weight proportional to x; (ii) unbinding of the O hole from the Cu spin in the singlet. This gives, in particular, a strong absorption peak due to singlet\ensuremath{\rightarrow}nonbonding oxygen transitions, again with relative weight \ensuremath{\sim}x.It is roughly centered at \ensuremath{\omega}\ensuremath{\sim}JKondo{\mathit{J}}_{\mathrm{Kondo}}JKondo​, where JKondo{\mathit{J}}_{\mathrm{Kondo}}JKondo​ is the Kondo coupling and \ensuremath{\Delta} the bare Cu-O charge-transfer energy. It is this singlet unbinding that results in the by far dominant absorption structure between Drude and higher-energy Cu-O transitions and not the often discussed ``mid-infrared'' absorption due to transitions between different singlet states. (iii) Cu-O charge-transfer processes at energy \ensuremath{\sim}\ensuremath{\Delta}+Upd{\mathit{U}}_{\mathit{p}\mathit{d}}Upd​. They show a pronounced excitonic effect due to the p-d interaction Upd{\mathit{U}}_{\mathit{p}\mathit{d}}Upd​ and have a reduced spectral weight shifted to higher energies for increased dopings. Findings (i)--(iii) are in general accordance with recent experimental data. Our study of the low-energy absorption is complemented with a numerical scaling analysis of the Drude weight in 1D, where, in particular, we find an interesting violation of Lenz's law for 4n-site Hubbard rings. Finally, the magnetic structure factor is calculated for the 2D case. For finite doping it contains a peak at 2JKondo{\mathit{J}}_{\mathrm{Kondo}}JKondo​, which should be detectable in experiment.