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arxiv: 1907.04033 · v1 · pith:O22PSLYUnew · submitted 2019-07-09 · ❄️ cond-mat.supr-con

Two-Gap Superconductivity in CaFe_(0.88)Co_(0.12)AsF Revealed by Temperature Dependence of the Lower Critical Field H_(c1)^c(T)

Teng Wang , Yonghui Ma , Wei Li , Jianan Chu , Lingling Wang , Jiaxin Feng , Hong Xiao , Zhuojun Li
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Tao Hu Xiaosong Liu Gang Mu
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Pith reviewed 2026-05-25 00:14 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con
keywords two-gap superconductivitylower critical fieldCaFe0.88Co0.12AsF1111 iron pnictidesuperfluid densityantiferromagnetic exchange pairing
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The pith

A kink in the temperature dependence of the lower critical field reveals two superconducting gaps in CaFe0.88Co0.12AsF.

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

The paper measures the out-of-plane lower critical field H_c1^c as a function of temperature in the cobalt-doped fluorine-based 1111 iron pnictide superconductor with Tc of 21 K. A distinct kink appears in the H_c1^c(T) curve that the authors attribute to the presence of two separate superconducting gaps. Fitting the data to a two-gap model gives gap sizes of 0.86 meV and 4.48 meV, with the smaller gap contributing 74 percent of the total superfluid density and the larger gap 26 percent. This two-gap structure is used to argue that the pairing mechanism is better described by local antiferromagnetic exchange interactions than by Fermi surface nesting.

Core claim

The temperature dependence of the lower critical field H_c1^c(T) in CaFe0.88Co0.12AsF displays a pronounced kink that indicates two-gap superconductivity. Fitting this curve to a two-gap model yields superconducting gaps of Δ1 = 0.86 meV accounting for 74% of the superfluid density and Δ2 = 4.48 meV accounting for 26%. These results favor the local antiferromagnetic exchange pairing picture compared to the Fermi surface nesting scenario.

What carries the argument

The kink in H_c1^c(T) analyzed with a two-gap model that separates contributions to the superfluid density from each gap.

If this is right

  • The smaller gap of 0.86 meV supplies 74% of the superfluid density while the larger gap of 4.48 meV supplies the remaining 26%.
  • The two-gap structure supports local antiferromagnetic exchange as the dominant pairing interaction rather than Fermi-surface nesting.
  • The extracted gap magnitudes and weights apply specifically to the out-of-plane response in this Co-doped 1111 compound.
  • The kink position and shape in H_c1^c(T) directly encode the relative superfluid-density contributions of each gap.

Where Pith is reading between the lines

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

  • Similar kinks could appear in other 1111 compounds if their lower critical fields are measured with comparable temperature resolution.
  • Independent probes such as specific-heat or tunneling spectroscopy might show corresponding features at the same two energy scales.
  • If the local-exchange picture holds, related materials with stronger local moments should exhibit even more pronounced two-gap signatures.
  • The dominance of the small gap suggests that low-energy quasiparticles control most of the magnetic penetration depth behavior.

Load-bearing premise

The observed kink arises only from two distinct isotropic gaps whose sizes and density weights can be extracted directly from the temperature curve without significant effects from anisotropy or impurities.

What would settle it

A high-precision measurement on cleaner samples in which the kink is absent and the full temperature dependence fits a single-gap model would falsify the two-gap claim.

read the original abstract

Gap symmetry and structure are crucial issues in understanding the superconducting mechanism of unconventional superconductors. Here we report an in-depth investigation on the out-of-plane lower critical field $H_{c1}^{c}$ of fluorine-based 1111 system superconductor CaFe$_{0.88}$Co$_{0.12}$AsF with $T_c$ = 21 K. A pronounced two-gap feature is revealed by the kink in the temperature dependent $H_{c1}^c(T)$ curve. The magnitudes of the two gaps are determined to be $\Delta_1$ = 0.86 meV and $\Delta_2$ = 4.48 meV, which account for 74% and 26% of the total superfluid density respectively. Our results suggest that the local antiferromagnetic exchange pairing picture is favored compared to the Fermi surface nesting scenario.

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 / 2 minor

Summary. The manuscript reports measurements of the out-of-plane lower critical field H_c1^c(T) in the 1111 iron-based superconductor CaFe_{0.88}Co_{0.12}AsF (T_c = 21 K). A kink in H_c1^c(T) is interpreted as direct evidence for two-gap superconductivity; fitting to a two-band model yields gaps Δ1 = 0.86 meV (74% weight) and Δ2 = 4.48 meV (26% weight). The authors conclude that this favors a local antiferromagnetic exchange pairing scenario over Fermi-surface nesting.

Significance. If the kink is robustly established as arising from two isotropic gaps and the extracted parameters are reproducible, the work would add a concrete data point to the multi-gap phenomenology of 1111 compounds and supply a potential discriminator between pairing channels. The strength of the claim, however, rests entirely on the quality and transparency of the H_c1^c(T) data set and the model fit.

major comments (2)
  1. [Abstract] Abstract and main text: the gap magnitudes and superfluid-density weights are obtained exclusively by fitting the measured H_c1^c(T) curve to the standard two-band clean-limit expression; no raw data, error bars, fitting procedure, or goodness-of-fit metrics are shown, rendering it impossible to judge whether the kink unambiguously supports the quoted values or whether the model is post-hoc.
  2. The central interpretation assumes that the observed kink arises solely from two distinct isotropic gaps with no significant contributions from gap anisotropy, impurity scattering, vortex pinning, or demagnetization effects. The manuscript does not present explicit tests or arguments excluding these alternatives, which directly affects the load-bearing claim that the data reveal two-gap superconductivity.
minor comments (2)
  1. [Abstract] The abstract states that the results 'suggest' a preference for local AF exchange pairing; a brief discussion of why the two-gap structure itself distinguishes the pairing channel (as opposed to being compatible with both scenarios) would strengthen the mechanistic claim.
  2. Notation: the superfluid-density weights (74 % and 26 %) should be explicitly tied to the fitting parameters in any equation or table that presents the two-gap model.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive review of our manuscript on two-gap superconductivity in CaFe_{0.88}Co_{0.12}AsF. The comments highlight important issues of data transparency and alternative interpretations, which we address point by point below. We have revised the manuscript to improve clarity and strengthen the presentation while maintaining the core conclusions based on the observed kink in H_{c1}^c(T).

read point-by-point responses

  1. Referee: [Abstract] Abstract and main text: the gap magnitudes and superfluid-density weights are obtained exclusively by fitting the measured H_c1^c(T) curve to the standard two-band clean-limit expression; no raw data, error bars, fitting procedure, or goodness-of-fit metrics are shown, rendering it impossible to judge whether the kink unambiguously supports the quoted values or whether the model is post-hoc.

    Authors: We agree that the original manuscript did not provide sufficient transparency regarding the raw data and fitting details. In the revised version, we will add a dedicated figure displaying the raw H_{c1}^c(T) data points with error bars, include a detailed description of the two-band clean-limit model and the fitting procedure (including initial parameters and constraints), and report quantitative goodness-of-fit metrics such as the reduced chi-squared value. These additions will allow independent assessment of whether the kink supports the reported values Δ1 = 0.86 meV (74% weight) and Δ2 = 4.48 meV (26% weight). The two-gap model yields a substantially better fit than a single-gap model, consistent with the visible kink. revision: yes

  2. Referee: The central interpretation assumes that the observed kink arises solely from two distinct isotropic gaps with no significant contributions from gap anisotropy, impurity scattering, vortex pinning, or demagnetization effects. The manuscript does not present explicit tests or arguments excluding these alternatives, which directly affects the load-bearing claim that the data reveal two-gap superconductivity.

    Authors: We acknowledge that the manuscript would benefit from explicit discussion of alternative explanations. In the revision, we will add a paragraph addressing these points: the sample exhibits low residual resistivity indicative of minimal impurity scattering; demagnetization corrections were applied based on the sample geometry; vortex pinning effects typically produce smoother temperature dependences rather than a distinct kink; and while gap anisotropy cannot be fully ruled out without additional probes, the isotropic two-gap model provides an excellent fit without requiring anisotropy parameters. We maintain that the data support two-gap superconductivity as the most parsimonious interpretation, though complementary measurements (e.g., specific heat) would further strengthen the case. revision: partial

Circularity Check

0 steps flagged

No significant circularity; experimental kink fitted to standard two-gap model

full rationale

The paper reports direct measurement of H_c1^c(T) showing a kink, then applies the established two-band clean-limit superfluid density expression to extract gap magnitudes and weights. This is ordinary parameter extraction from data using a pre-existing model, not a derivation that reduces to its own inputs by construction. No self-citations, uniqueness theorems, or ansatzes are invoked as load-bearing steps in the provided text. The central claim rests on the independent experimental feature (the kink) rather than on any fitted quantity being renamed as a prediction.

Axiom & Free-Parameter Ledger

3 free parameters · 1 axioms · 0 invented entities

The claim rests on fitting two free gap parameters and their weights to the temperature-dependent lower critical field data under a two-gap model; the model itself is a standard domain assumption rather than derived in the work.

free parameters (3)
  • Δ1 = 0.86 meV
    Smaller gap magnitude fitted to low-T portion of H_c1^c(T)
  • Δ2 = 4.48 meV
    Larger gap magnitude fitted to high-T portion of H_c1^c(T)
  • weight1 = 74%
    Fraction of superfluid density assigned to smaller gap
axioms (1)
  • domain assumption Temperature dependence of H_c1 can be described by a two-gap BCS-like expression whose parameters directly give the gap magnitudes and superfluid weights
    Invoked to convert the observed kink into numerical gap values

pith-pipeline@v0.9.0 · 5733 in / 1374 out tokens · 40391 ms · 2026-05-25T00:14:19.990540+00:00 · methodology

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Reference graph

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