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arxiv: 2606.05092 · v1 · pith:3V2O2SFEnew · submitted 2026-06-03 · ❄️ cond-mat.str-el

η-pairing in metallic and particle-hole asymmetric systems

Philipp Werner , Aaram J. Kim , Lei Geng This is my paper

Pith reviewed 2026-06-28 04:03 UTC · model grok-4.3

classification ❄️ cond-mat.str-el
keywords η-pairingnonequilibrium DMFTMott insulatorsphoto-dopingparticle-hole asymmetrydoublon holonsuperconductivity
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The pith

η-pairing remains stable under particle-hole asymmetry in large-gap Mott insulators and appears in photo-excited metallic states with quasiparticle population inversion.

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

The work examines whether η-pairing, a route to nonthermal superconductivity, survives when particle-hole symmetry is broken or when the system is metallic rather than a large-gap insulator. Earlier numerical studies were limited to symmetric insulators, yet experiments often involve metals. Steady-state nonequilibrium dynamical mean-field theory with a third-order strong-coupling solver shows the order persists across a range of fillings and doublon-holon imbalances provided the effective temperatures stay low, while temperature asymmetry between doublons and holons suppresses it. In metallic cases that develop a three-peak local density of states, the order can form even with positive temperatures once the low-energy quasiparticle band exhibits population inversion.

Core claim

In the strongly correlated regime with large Mott gap and low effective doublon and holon temperatures, η-pairing is robust against changes in total filling and an imbalance in the doublon and holon density. An asymmetry in the effective doublon and holon temperatures can however strongly suppress the order parameter. In photo-doped metallic systems with a three-peak structure in the local density of states, η-pairing can be realized in set-ups with positive doublon and holon temperatures and a population inversion in the low-energy quasi-particle band.

What carries the argument

Steady-state nonequilibrium dynamical mean-field theory with a strong-coupling impurity solver truncated at third order, used to track the η-pairing order parameter under photo-doping.

If this is right

  • η-pairing order survives deviations from half-filling when doublon and holon effective temperatures remain low.
  • Densities of doublons and holons can be imbalanced without destroying the order under the same low-temperature condition.
  • Asymmetry between doublon and holon temperatures strongly reduces the order parameter.
  • In metallic systems that develop three-peak local spectra, population inversion in the quasiparticle band allows η-pairing at positive temperatures.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The results indicate that experiments on real, imperfectly symmetric materials could still observe η-pairing if effective temperatures are controlled.
  • Similar order may appear under other nonequilibrium driving protocols that produce population inversion without requiring particle-hole symmetry.
  • The findings tie the stability of the order to the separation of energy scales between the Mott gap and the low-energy band.

Load-bearing premise

The third-order truncation of the strong-coupling impurity solver is accurate enough to capture the emergence and stability of η-pairing.

What would settle it

If η-pairing vanishes at moderate deviations from half-filling or fails to appear in three-peak metallic systems even with quasiparticle inversion, the reported robustness would not hold.

Figures

Figures reproduced from arXiv: 2606.05092 by Aaram J. Kim, Lei Geng, Philipp Werner.

Figure 1
Figure 1. Figure 1: FIG. 1: Top panel: Illustration of a nonequilibrium distrib [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Phase diagram of the half-filled Hubbard model with [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: OCA spectral functions [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: OCA and TOA spectral functions for [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Left panel [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: OCA spectral functions [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗
read the original abstract

Light-induced superconducting-like states have been reported in several classes of correlated materials. From a theoretical point of view, the induction of $\eta$-pairing is a promising route to nonthermal superconductivity. Numerical studies of photo-doped Mott systems revealed $\eta$-pairing states with very high effective critical temperatures. These investigations were however restricted to particle-hole symmetric states in large-gap Mott insulators, while the experiments were performed on strongly correlated metallic systems. It is thus relevant to explore if $\eta$-pairing also exists in non-particle-hole symmetric setups and in photo-excited metallic states. Here we use steady-state nonequilibrium dynamical mean field theory combined with a strong-coupling impurity solver up to third order to investigate this issue. We find that in the strongly correlated regime with large Mott gap, and for low effective doublon and holon temperatures, $\eta$-pairing is robust against changes in the total filling and an imbalance in the doublon and holon density. An asymmetry in the effective doublon and holon temperatures can however strongly suppress the order parameter. In photo-doped metallic systems with a three-peak structure in the local density of states, $\eta$-pairing can be realized in set-ups with positive doublon and holon temperatures and a population inversion in the low-energy quasi-particle band.

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

2 major / 1 minor

Summary. The manuscript uses steady-state nonequilibrium DMFT with a strong-coupling impurity solver truncated at third order to study η-pairing. It reports that, in the large-gap Mott regime at low effective doublon/holon temperatures, the order is robust to changes in total filling and doublon-holon imbalance (though suppressed by temperature asymmetry), and that η-pairing can be realized in photo-doped metals possessing a three-peak local DOS together with population inversion in the quasiparticle band.

Significance. If the truncation is shown to be controlled, the results would usefully extend prior particle-hole-symmetric insulator studies to the asymmetric and metallic regimes that are closer to experiment. The work employs an established nonequilibrium DMFT framework and directly solves the steady-state equations rather than relying on fitted parameters.

major comments (2)
  1. [Methods] Methods section (description of the impurity solver): the central claims on the stability of η-pairing and the emergence of population-inversion-driven order rest on the third-order truncation; the manuscript provides no convergence checks with fourth-order terms, comparisons to alternative solvers, system-size dependence, or error estimates on the order parameter and effective temperatures in the relevant regimes.
  2. [Results (metallic regime)] Results on metallic systems: the claim that η-pairing appears with positive doublon/holon temperatures and three-peak DOS requires explicit demonstration that the truncation does not artifactually stabilize the order parameter; without such validation the metallic-regime finding remains provisional.
minor comments (1)
  1. [Abstract] Abstract and figure captions: statements of numerical findings would be strengthened by brief mention of the truncation order and any available convergence indicators.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the detailed report and constructive suggestions. We address the two major comments below. We agree that the absence of explicit convergence tests for the third-order truncation is a limitation that should be discussed more explicitly, and we will revise the manuscript accordingly by adding caveats and references to prior benchmarks. However, performing new fourth-order calculations or solver comparisons is not feasible within the current study.

read point-by-point responses

  1. Referee: [Methods] Methods section (description of the impurity solver): the central claims on the stability of η-pairing and the emergence of population-inversion-driven order rest on the third-order truncation; the manuscript provides no convergence checks with fourth-order terms, comparisons to alternative solvers, system-size dependence, or error estimates on the order parameter and effective temperatures in the relevant regimes.

    Authors: We acknowledge that the manuscript lacks explicit convergence checks with fourth-order terms or alternative solvers. The third-order strong-coupling expansion is a controlled approximation in the large-U limit and has been benchmarked in prior equilibrium and nonequilibrium DMFT studies for similar Mott regimes (e.g., Refs. on iterated perturbation theory extensions). In the large-gap insulator regime studied here, the effective temperatures are low and the gap is large, where higher-order corrections are expected to be small. We will add a dedicated paragraph in the Methods section discussing the expected accuracy, citing relevant benchmarks, and noting that quantitative error bars on the order parameter are not provided. System-size dependence is not applicable as this is a DMFT calculation (infinite dimensions). revision: partial

  2. Referee: [Results (metallic regime)] Results on metallic systems: the claim that η-pairing appears with positive doublon/holon temperatures and three-peak DOS requires explicit demonstration that the truncation does not artifactually stabilize the order parameter; without such validation the metallic-regime finding remains provisional.

    Authors: We agree that the metallic-regime results are more sensitive to the truncation and that additional validation would be desirable. The emergence of η-pairing in this regime is tied to the population inversion in the quasiparticle band and the three-peak DOS structure, which is absent in the equilibrium metallic state. We will revise the discussion to emphasize that the order vanishes when the inversion is suppressed (e.g., by increasing the effective temperature), providing indirect evidence against a pure truncation artifact. However, we cannot perform fourth-order calculations or direct comparisons here, so the metallic finding should indeed be viewed as suggestive rather than fully validated. revision: partial

standing simulated objections not resolved
  • Explicit convergence checks with fourth-order truncation, alternative impurity solvers, or quantitative error estimates on the order parameter would require substantial new computational work and code modifications that are beyond the scope of the present study.

Circularity Check

0 steps flagged

No circularity: results from direct numerical solution of nonequilibrium DMFT equations

full rationale

The paper reports numerical findings on η-pairing obtained via steady-state nonequilibrium DMFT combined with a strong-coupling impurity solver truncated at third order. The central claims concern robustness of the order parameter against filling and asymmetry in the large-gap regime and its realization in metallic three-peak DOS setups; these emerge from solving the DMFT equations rather than from any analytical derivation, fitted parameter renamed as prediction, or self-referential definition. No load-bearing self-citations, uniqueness theorems imported from prior author work, or ansatzes smuggled via citation are present in the provided text. The method is a standard computational approach whose outputs are independent of the target observables by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claims rest on the domain assumption that the chosen DMFT + truncated impurity solver faithfully represents the physics of η-pairing; no free parameters or invented entities are mentioned in the abstract.

axioms (1)
  • domain assumption Steady-state nonequilibrium DMFT combined with a strong-coupling impurity solver truncated at third order is sufficient to determine the stability of η-pairing order.
    Invoked in the description of the computational approach used to obtain all reported results.

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discussion (0)

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Reference graph

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