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arxiv: 1907.01770 · v1 · pith:H4UOP4ITnew · submitted 2019-07-03 · ❄️ cond-mat.str-el

Photoinduced electron-electron pairing in the extended Falicov-Kimball model

Ryo Fujiuchi , Tatsuya Kaneko , Yukinori Ohta , Seiji Yunoki This is my paper

Pith reviewed 2026-05-25 10:18 UTC · model grok-4.3

classification ❄️ cond-mat.str-el
keywords photoinduced pairingextended Falicov-Kimball modelexcitonic insulatorSU(2) symmetryelectron-electron correlationtime-dependent exact diagonalizationnonlinear optical response
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The pith

Pulse irradiation induces interband electron-electron pair correlations in the extended Falicov-Kimball model while suppressing initial excitonic correlations via an internal SU(2) structure.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper uses time-dependent exact diagonalization to study photoexcited states of the excitonic insulator in the extended Falicov-Kimball model. It shows that a light pulse creates interband electron-electron pair correlations in the excited states even as the ground-state excitonic electron-hole correlations are suppressed. The photoexcited states include eigenstates of the model that contain a finite number of these electron-electron pairs. The effect traces to an internal SU(2) pairing symmetry that survives on nonbipartite lattices when the band structure is direct, allowing zero-momentum pairs to form.

Core claim

Pulse irradiation induces interband electron-electron pair correlation in the photoexcited states of the EFKM while strongly suppressing the excitonic electron-hole pair correlation of the initial ground state; the photoexcited states contain eigenstates with a finite number of interband electron-electron pairs, and this occurs because of the internal SU(2) pairing structure that is preserved even for nonbipartite lattices with direct-type band structure.

What carries the argument

The internal SU(2) pairing structure of the extended Falicov-Kimball model, which maps photoexcited states onto eigenstates carrying interband electron-electron pairs.

Load-bearing premise

The internal SU(2) pairing structure remains intact and governs the dynamics for the pulses and lattices considered.

What would settle it

Measure the time-dependent interband electron-electron pair correlation function after the pulse; if it fails to rise while the electron-hole correlation falls, or if the post-pulse state does not overlap with eigenstates containing a finite number of electron-electron pairs, the claimed induction mechanism does not hold.

Figures

Figures reproduced from arXiv: 1907.01770 by Ryo Fujiuchi, Seiji Yunoki, Tatsuya Kaneko, Yukinori Ohta.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic band structures of (a) a semimetal ( [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) Excitonic (i.e., electron-hole pair) structure [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a) Time evolution of the on-site electron-electron [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. (a) All the eigenenergies [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Contour plots of (a) the excitonic structure factor [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. (a) On-site electron-electron pair correlation fun [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Time evolution of the electron-electron pair struc [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. (a) All the eigenenergies [PITH_FULL_IMAGE:figures/full_fig_p010_10.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Contour plots of (a) the excitonic structure factor [PITH_FULL_IMAGE:figures/full_fig_p010_9.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Time evolution of (a) the electron-electron [PITH_FULL_IMAGE:figures/full_fig_p011_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. The on-site electron-electron pair correlation fu [PITH_FULL_IMAGE:figures/full_fig_p012_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. (a) Time evolution of the on-site electron-electro [PITH_FULL_IMAGE:figures/full_fig_p013_13.png] view at source ↗
read the original abstract

By employing the time-dependent exact diagonalization method, we investigate the photoexcited states of the excitonic insulator in the extended Falicov-Kimball model (EFKM). We here show that the pulse irradiation can induce the interband electron-electron pair correlation in the photoexcited states, while the excitonic electron-hole pair correlation in the initial ground state is strongly suppressed. We also show that the photoexcited states contains the eigenstates of the EFKM with a finite number of interband electron-electron pairs, which are responsible for the enhancement of the electron-electron pair correlation. The mechanism found here is due to the presence of the internal SU(2) pairing structure in the EFKM and thus it is essentially the same as that for the photoinduced $\eta$-pairing in the repulsive Hubbard model reported recently [T. Kaneko et al., Phys. Rev. Lett. ${\bf 122}$, 077002 (2019)]. This also explains why the nonlinear optical response is effective to induce the electron-electron pairs in the photoexcited states of the EFKM. Furthermore, we show that, unlike the $\eta$-pairing in the Hubbard model, the internal SU(2) structure is preserved even for a nonbipartite lattice when the EFKM has the direct-type band structure, in which the pulse irradiation can induce the electron-electron pair correlation with momentum ${\it {\bf q}}$ = ${\textbf 0}$ in the photoexcited states. We also discuss briefly the effect of a perturbation that breaks the internal SU(2) structure.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The manuscript employs time-dependent exact diagonalization to study the extended Falicov-Kimball model in its excitonic insulator regime. It claims that optical pulse irradiation induces interband electron-electron pair correlations in the photoexcited states while strongly suppressing the excitonic electron-hole correlations present in the ground state. The photoexcited states are shown to contain eigenstates with a finite number of interband electron-electron pairs. The mechanism is attributed to the model's internal SU(2) pairing symmetry, which remains intact for direct-type bands even on nonbipartite lattices (unlike the Hubbard model), enabling q=0 pairing; a brief qualitative discussion of SU(2)-breaking perturbations is included.

Significance. If the numerical results hold, the work establishes a symmetry-protected mechanism for photoinduced electron-electron pairing in an excitonic insulator, extending the η-pairing analogy from the repulsive Hubbard model to a broader class of lattices and band structures. The exact-diagonalization approach supplies direct, non-perturbative evidence for the role of the internal SU(2) structure in nonlinear optical responses, offering a concrete, falsifiable prediction for light-induced pairing that could be tested in related models or materials.

major comments (1)
  1. [Discussion of perturbations] Final discussion section (on perturbations breaking the internal SU(2) structure): the robustness of the reported photoinduced electron-electron pair correlations is asserted to fail under SU(2)-breaking terms, yet the manuscript supplies only a qualitative statement without time-dependent ED data, threshold values for perturbation strength (e.g., next-nearest-neighbor hopping or interaction asymmetry), or any quantitative estimate of how small such terms must remain for the q=0 enhancement to survive. Because all quantitative results are obtained strictly inside the symmetric model, this omission leaves the central claim's applicability to realistic extensions unquantified and load-bearing for the mechanism's generality.
minor comments (2)
  1. [Abstract] The abstract and introduction refer to 'the pulse irradiation' without summarizing the specific pulse parameters (amplitude, frequency, duration) used in the time-dependent simulations; these should be stated explicitly for reproducibility.
  2. [Results section] Notation for the interband electron-electron pair correlation function is introduced without an explicit equation reference in the main text; adding a numbered equation would improve clarity when comparing ground-state and photoexcited values.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive assessment of our work and the constructive comment. We address the major point below.

read point-by-point responses

  1. Referee: Final discussion section (on perturbations breaking the internal SU(2) structure): the robustness of the reported photoinduced electron-electron pair correlations is asserted to fail under SU(2)-breaking terms, yet the manuscript supplies only a qualitative statement without time-dependent ED data, threshold values for perturbation strength (e.g., next-nearest-neighbor hopping or interaction asymmetry), or any quantitative estimate of how small such terms must remain for the q=0 enhancement to survive. Because all quantitative results are obtained strictly inside the symmetric model, this omission leaves the central claim's applicability to realistic extensions unquantified and load-bearing for the mechanism's generality.

    Authors: We agree that the discussion of SU(2)-breaking perturbations is only qualitative, as explicitly noted in the manuscript. The central mechanism relies on the exact internal SU(2) symmetry, which protects the q=0 pairing channel; any breaking term (e.g., next-nearest-neighbor hopping or interaction asymmetry) will lift the degeneracy and suppress the enhancement proportionally to its strength relative to the excitonic gap. While additional time-dependent ED data on perturbed models would be desirable, such calculations are computationally intensive because symmetry breaking enlarges the effective Hilbert space and removes conserved quantities used in the current exact-diagonalization implementation. We will revise the final section to include order-of-magnitude estimates based on the existing ED energy scales, indicating that the perturbation must remain smaller than the photoinduced pairing correlation energy for the effect to survive. revision: partial

Circularity Check

0 steps flagged

Minor self-citation to Hubbard-model mechanism; central EFKM results from independent TD-ED

full rationale

The paper's core results derive from direct time-dependent exact diagonalization of the EFKM Hamiltonian under pulse driving, showing suppression of excitonic correlations and enhancement of interband electron-electron pair correlations. The cited Kaneko et al. PRL (overlapping authors) is invoked only to identify the shared SU(2) origin of the mechanism, without substituting for or reducing the present numerical evidence. The SU(2) structure is stated as a property of the EFKM itself, preserved under the studied conditions, and the perturbation discussion is brief and qualitative. No self-definitional equations, fitted inputs renamed as predictions, or load-bearing uniqueness theorems appear. This is a standard low-level self-citation that does not force the reported findings.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The paper rests on the assumption that the EFKM Hamiltonian possesses an exact internal SU(2) symmetry that survives the time-dependent drive and that exact diagonalization faithfully captures the relevant eigenstates; no free parameters are introduced beyond standard model parameters.

axioms (2)
  • domain assumption The extended Falicov-Kimball model possesses an internal SU(2) pairing symmetry that is preserved under the chosen pulse protocol and lattice geometry.
    Invoked to explain why electron-electron pairs appear after the pulse.
  • domain assumption Time-dependent exact diagonalization on finite clusters accurately represents the photoexcited dynamics of the infinite system.
    Standard assumption for the numerical method used.

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Reference graph

Works this paper leans on

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