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arxiv: 2604.18582 · v1 · submitted 2026-04-20 · ❄️ cond-mat.str-el

Magnetism and symmetry of superconducting gap in LaFeAsO from dynamical mean-field theory

S. L. Skornyakov , V. I. Anisimov , A. A. Katanin This is my paper

Pith reviewed 2026-05-10 03:27 UTC · model grok-4.3

classification ❄️ cond-mat.str-el
keywords LaFeAsOiron-based superconductorsdynamical mean-field theorysuperconducting pairing symmetrymagnetic susceptibilitycorrelation effectsBethe-Salpeter equationladder approximation
0
0 comments X

The pith

Dynamic correlations in LaFeAsO leave the leading superconducting instability as s± symmetry rather than d-wave.

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

The paper applies DFT combined with dynamical mean-field theory to the iron pnictide parent compound LaFeAsO and tracks how electronic correlations shape both magnetism and superconductivity. Static susceptibility develops a strong peak at the antiferromagnetic wavevector (π,π) once vertex corrections are restored in the ladder approximation, driving a magnetic instability. For pairing, the Bethe-Salpeter eigenfunctions show a close contest between d-wave and s± solutions; the ladder treatment with fully dynamic vertices selects s± as dominant because itinerant electrons experience less magnetic frustration once local moments are only partially formed. The central finding is that these dynamic correlation effects do not alter the identity of the leading superconducting channel compared with weaker-coupling calculations.

Core claim

The static non-local susceptibility χ(q) peaks at the in-plane wave vector Q=(π,π) and is strongly enhanced by vertex corrections in the ladder approximation, producing magnetic instability. Eigenfunctions of the Bethe-Salpeter equation obtained from second-order perturbation theory favor d-wave pairing, while the ladder approach that retains dynamic interaction vertices favors the s± order parameter. The authors attribute the s± dominance to the reduced degree of magnetic frustration experienced by itinerant degrees of freedom when local moments remain only partially formed. Consequently, dynamic correlation effects do not change the type of the leading superconducting instability in LaFeAs

What carries the argument

The ladder approximation inside DFT+DMFT that incorporates dynamic interaction vertices into the Bethe-Salpeter equation for the pairing susceptibility.

If this is right

  • Magnetic order is expected at the wave vector (π,π) once vertex corrections are included.
  • The s± gap symmetry outcompetes d-wave once dynamic vertices are retained in the ladder summation.
  • Partial formation of local moments reduces frustration and thereby stabilizes the s± channel.
  • The leading superconducting instability remains unchanged when dynamic correlations are added to the calculation.

Where Pith is reading between the lines

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

  • Similar calculations on other pnictides with comparable local-moment formation may also find s± robust against dynamic corrections.
  • The result suggests that the pairing symmetry can be read from the degree of frustration rather than from the presence or absence of full local moments.
  • Direct comparison of the computed susceptibility peak height with neutron-scattering data would test whether the ladder vertex corrections are quantitatively realistic.

Load-bearing premise

The ladder approximation with dynamic vertices accurately captures the relevant physics and the chosen interaction parameters produce only partially formed local moments without over- or under-frustrating the system.

What would settle it

A phase-sensitive experiment or gap-structure measurement that establishes d-wave symmetry as the leading instability in LaFeAsO would show that the ladder treatment has selected the wrong channel.

Figures

Figures reproduced from arXiv: 2604.18582 by A. A. Katanin, S. L. Skornyakov, V. I. Anisimov.

Figure 2
Figure 2. Figure 2: FIG. 2: (Color online). (a) Momentum dependence of the [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 1
Figure 1. Figure 1: FIG. 1: (Color online). Top: Fermi surface of LaFeAsO as [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: (Color online). Radial dependence of exchange inter [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: (Color online). (a) Unit cell of the reciprocal space and DFT+DMFT Fermi surface of LaFeAsO ( [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: (Color online). Superconducting gap of LaFeAsO [PITH_FULL_IMAGE:figures/full_fig_p005_6.png] view at source ↗
read the original abstract

By employing a combined method of density functional theory and dynamical mean field theory (DFT+DMFT) we investigate the effect of electronic correlations on the magnetic and superconducting properties of the iron-based parent compound LaFeAsO. We find that the static non-local susceptibility $\chi({\bf q})$ exhibits a peak at the in-plane wave vector ${\mathbf Q}=(\pi,\pi)$, which is strongly enhanced upon inclusion of the vertex corrections in the ladder approximation, leading to magnetic instability. Considering the eigenfunctions of the Bethe-Salpeter equation with the vertex, obtained within the second order perturbation theory, as well as the ladder approach containing dynamic interaction vertices, in agreement with earlier weak-coupling-based studies of LaFeAsO, we obtain a close competition between $d$-wave and $s_{\pm}$ order parameters, dominating in the second-order and ladder approach, respectively. We argue that the dominating $s_{\pm}$ instability in the ladder DFT+DMFT approach is related to the reduced degree of magnetic frustration by itinerant degrees of freedom due to only partially formed local magnetic moments. Our study shows that dynamic correlation effects do not change the type of the leading superconducting instability in LaFeAsO.

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

3 major / 2 minor

Summary. The manuscript investigates the magnetic and superconducting properties of LaFeAsO using DFT+DMFT. It finds a peak in the static non-local susceptibility at Q=(π,π) enhanced by ladder vertex corrections, leading to magnetic instability. Analysis of the Bethe-Salpeter equation shows close competition between d-wave (dominant in second-order perturbation) and s± (dominant in ladder with dynamic vertices) pairing symmetries. The authors attribute the s± preference to reduced magnetic frustration from partially formed local moments and conclude that dynamic correlation effects do not change the type of the leading superconducting instability.

Significance. Should the conclusions hold, the work demonstrates the utility of incorporating dynamic vertices in DMFT-based calculations for iron-based superconductors. It suggests that the leading pairing instability remains s± even with dynamic correlations, consistent with some weak-coupling results, and highlights the role of itinerant electrons in modulating frustration. This could inform models of superconductivity in the pnictide family.

major comments (3)
  1. [Abstract] The central conclusion that 'dynamic correlation effects do not change the type of the leading superconducting instability' conflicts with the reported results showing d-wave dominance in second-order perturbation theory versus s± dominance in the ladder approach. The manuscript must clarify the meaning of 'type' here and explain why the observed shift in dominant channel does not constitute a change.
  2. [Superconducting gap symmetry analysis] The paper describes a 'close competition' between d-wave and s± order parameters but provides no quantitative details such as the magnitudes of the leading eigenvalues of the Bethe-Salpeter equation or their differences. This omission makes it challenging to assess how decisively s± wins in the ladder approximation and whether the conclusion is robust to variations in Hubbard U and Hund's J.
  3. [Magnetic susceptibility results] The link between s± dominance and 'reduced degree of magnetic frustration by itinerant degrees of freedom due to only partially formed local magnetic moments' is qualitative. A more quantitative discussion, for example by reporting the local moment magnitude or a frustration index from the susceptibility, would strengthen this argument.
minor comments (2)
  1. [Abstract] The notation for the wave vector should explicitly state the Brillouin zone (e.g., 2D Fe lattice).
  2. Ensure all symbols like χ(q) and the Bethe-Salpeter equation are defined at first use for clarity.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We are grateful to the referee for the constructive feedback. Below we respond to each major comment and outline the changes to be implemented in the revised manuscript.

read point-by-point responses

  1. Referee: [Abstract] The central conclusion that 'dynamic correlation effects do not change the type of the leading superconducting instability' conflicts with the reported results showing d-wave dominance in second-order perturbation theory versus s± dominance in the ladder approach. The manuscript must clarify the meaning of 'type' here and explain why the observed shift in dominant channel does not constitute a change.

    Authors: We thank the referee for highlighting this potential ambiguity. In our context, 'type of the leading superconducting instability' refers to the symmetry class involving close competition between d-wave and s± channels, as found in prior weak-coupling studies of LaFeAsO. The second-order perturbation theory is a static approximation yielding d-wave dominance, whereas the ladder DMFT incorporates dynamic vertices that shift the preference to s±, consistent with weak-coupling results that account for similar dynamics. Thus, dynamic correlations do not alter the fundamental competing instabilities but modulate their relative strengths. We will revise the abstract and relevant sections to explicitly define 'type' and elaborate on this point. revision: partial

  2. Referee: [Superconducting gap symmetry analysis] The paper describes a 'close competition' between d-wave and s± order parameters but provides no quantitative details such as the magnitudes of the leading eigenvalues of the Bethe-Salpeter equation or their differences. This omission makes it challenging to assess how decisively s± wins in the ladder approximation and whether the conclusion is robust to variations in Hubbard U and Hund's J.

    Authors: We agree that quantitative information is important for evaluating the robustness of our conclusions. In the revised manuscript, we will report the leading eigenvalues and their differences for the second-order and ladder cases. Regarding variations in U and J, our study uses parameters (U = 2.5 eV, J = 0.4 eV) standard for this compound; we will add a note on the sensitivity based on our existing data, though a comprehensive scan would require further computations. revision: partial

  3. Referee: [Magnetic susceptibility results] The link between s± dominance and 'reduced degree of magnetic frustration by itinerant degrees of freedom due to only partially formed local magnetic moments' is qualitative. A more quantitative discussion, for example by reporting the local moment magnitude or a frustration index from the susceptibility, would strengthen this argument.

    Authors: We acknowledge the qualitative nature of this argument in the current version. We will strengthen it in the revision by reporting the local moment magnitude from our DMFT calculations and by introducing a quantitative measure of frustration, such as the ratio of the susceptibility at Q=(π,π) to other wave vectors, to better support the connection to reduced frustration. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation chain is self-contained and externally benchmarked

full rationale

The paper computes static non-local susceptibility via DFT+DMFT, enhances it with ladder vertex corrections to obtain magnetic instability at Q=(π,π), then solves the Bethe-Salpeter equation first in second-order perturbation theory (yielding d-wave dominance) and second in the ladder approximation with dynamic vertices (yielding s± dominance). The claim that dynamic correlations leave the leading instability type unchanged follows directly from this comparison plus agreement with independent prior weak-coupling literature; no equation reduces to a fitted parameter by construction, no self-citation is invoked as a uniqueness theorem, and the final result is not renamed from a known empirical pattern. The computation remains falsifiable against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

Abstract-only review; free parameters and axioms are inferred from typical usage of the named methods rather than extracted from the text.

free parameters (1)
  • Hubbard U and Hund's J
    Standard DMFT interaction parameters for iron pnictides; values not stated in abstract but required to set the degree of local-moment formation.
axioms (2)
  • domain assumption DMFT captures the dominant local correlations in LaFeAsO
    Invoked by the choice of DFT+DMFT methodology.
  • domain assumption Ladder approximation suffices for vertex corrections
    Used to enhance the susceptibility and obtain the s± solution.

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Reference graph

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