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arxiv: 2604.27507 · v1 · submitted 2026-04-30 · ❄️ cond-mat.supr-con · cond-mat.str-el

Recognition: unknown

Magnetic Quantum Criticality inside the Superconducting State Revealed by Penetration Depth Scaling with Local T_{mathrm c}

Yusuke Iguchi , Kaede Inoh , Ryosuke Koizumi , Makoto Yokoyama
Authors on Pith no claims yet

Pith reviewed 2026-05-07 10:30 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con cond-mat.str-el
keywords quantum critical pointpenetration depthCeCoIn5Zn dopingsuperconductivityscanning SQUIDsuperfluid stiffnessdisorder
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The pith

A peak in zero-temperature magnetic penetration depth of Zn-doped CeCoIn5, when plotted against local transition temperature, reveals a magnetic quantum critical point inside the superconducting state.

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

The paper establishes that a magnetic quantum critical point sits inside the superconducting state of Zn-doped CeCoIn5. Scanning SQUID measurements of local Tc and zero-temperature penetration depth λ(0) show a clear peak in λ(0) once it is parameterized by local Tc instead of nominal Zn concentration. This peak signals strong suppression of superfluid stiffness driven by critical fluctuations, and the extracted scaling exponent lies above the clean spin-density-wave expectation, pointing to a disorder-modified critical regime. A reader would care because the local-Tc approach removes the usual ambiguity from doping inhomogeneity and gives a concrete route to detect otherwise hidden quantum criticality in real materials.

Core claim

The authors demonstrate a magnetic quantum critical point embedded within the superconducting state of Zn-doped CeCoIn5, revealed by a pronounced peak in the magnetic penetration depth at zero temperature λ(0). Using scanning SQUID microscopy, they determine the local superconducting transition temperature Tc and λ(0). By parameterizing λ(0) in terms of the local Tc rather than nominal Zn substitution, they circumvent the ambiguity caused by doping inhomogeneity and enable a more precise extraction of the critical exponent. The extracted exponent exceeds the clean spin-density-wave value, indicating a disorder-modified quantum critical regime. The enhancement of λ(0) reflects the suppression

What carries the argument

The scaling of zero-temperature penetration depth λ(0) with locally measured transition temperature Tc, which produces a peak that locates the quantum critical point and yields the critical exponent.

Load-bearing premise

That parameterizing λ(0) by local Tc rather than nominal Zn concentration fully removes doping inhomogeneity effects and that the resulting peak and exponent directly mark a disorder-modified quantum critical regime without other influences on superfluid stiffness.

What would settle it

A set of local measurements in which the peak in λ(0) vanishes and the scaling exponent matches the clean spin-density-wave value once local Tc is used would falsify the existence of the embedded magnetic quantum critical point.

Figures

Figures reproduced from arXiv: 2604.27507 by Kaede Inoh, Makoto Yokoyama, Ryosuke Koizumi, Yusuke Iguchi.

Figure 1
Figure 1. Figure 1: FIG. 1. Antiferromagnetic quantum criticality in the dirty view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Scanning SQUID magnetometry over an isolated vortex visualizes the enhancement of the penetration depth view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Scanning SQUID Susceptometry at low tem view at source ↗
read the original abstract

We demonstrate a magnetic quantum critical point embedded within the superconducting state of Zn-doped CeCoIn$_5$, revealed by a pronounced peak in the magnetic penetration depth at zero temperature $\lambda(0)$. Using scanning SQUID microscopy, we determine the local superconducting transition temperature $T_{\mathrm c}$ and $\lambda(0)$. By parameterizing $\lambda(0)$ in terms of the local $T_{\mathrm c}$ rather than nominal Zn substitution, we circumvent the ambiguity caused by doping inhomogeneity and enable a more precise extraction of the critical exponent. The extracted exponent exceeds the clean spin-density-wave value, indicating a disorder-modified quantum critical regime. The enhancement of $\lambda(0)$ reflects the suppression of the superfluid stiffness and is consistent with critical scaling. Our approach provides a route to uncover intrinsic quantum critical behavior hidden by inhomogeneity in unconventional superconductors.

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 claims to reveal a magnetic quantum critical point inside the superconducting dome of Zn-doped CeCoIn5. Scanning SQUID microscopy measures local Tc and λ(0); re-plotting λ(0) versus local Tc (instead of nominal Zn concentration) produces a pronounced peak whose extracted critical exponent exceeds the clean SDW value, interpreted as evidence for a disorder-modified QCP. The enhancement of λ(0) is attributed to critical suppression of superfluid stiffness, and the local-Tc parameterization is presented as a method to bypass doping inhomogeneity.

Significance. If the central observation and exponent extraction hold after rigorous validation, the work would be significant for studies of quantum criticality in unconventional superconductors. It supplies a concrete experimental route to expose QCPs masked by inhomogeneity and suggests that disorder can modify the critical regime inside the SC state. The local-probe approach and scaling with independently measured Tc are potentially generalizable strengths, provided the data and analysis are shown to be robust.

major comments (2)
  1. [Results section] Results section (scaling analysis and associated figures): the peak in λ(0) versus local Tc and the extracted exponent are presented without error bars on individual data points, without the number of sampled locations, and without details of the fitting procedure or robustness checks against fitting range. These omissions are load-bearing because the claim that the exponent exceeds the clean SDW value and signals a disorder-modified QCP rests directly on the statistical significance and reproducibility of that peak.
  2. [Discussion] Discussion of the local-Tc parameterization: the manuscript asserts that using measured local Tc circumvents doping inhomogeneity, yet provides no explicit test or discussion ruling out correlations between local Tc and other position-dependent quantities (impurity scattering rate, pair-breaking strength, or vortex pinning) that scanning-SQUID λ(0) measurements could also sense. This assumption is load-bearing for the interpretation that the peak is an intrinsic signature of a magnetic QCP rather than a non-critical confounding effect.
minor comments (1)
  1. [Methods] Notation for λ(0) and local Tc is consistent, but the manuscript should explicitly define how λ(0) is extracted from the SQUID data (e.g., the fitting model and temperature range) in the methods section.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments, which have prompted us to strengthen the presentation of our results and clarify key assumptions. We address each major comment below and have revised the manuscript to incorporate additional details and discussion.

read point-by-point responses

  1. Referee: [Results section] Results section (scaling analysis and associated figures): the peak in λ(0) versus local Tc and the extracted exponent are presented without error bars on individual data points, without the number of sampled locations, and without details of the fitting procedure or robustness checks against fitting range. These omissions are load-bearing because the claim that the exponent exceeds the clean SDW value and signals a disorder-modified QCP rests directly on the statistical significance and reproducibility of that peak.

    Authors: We agree that these statistical details are essential for evaluating the robustness of the peak and the extracted exponent. In the revised manuscript we have added error bars to the data points in the scaling figure (representing the standard deviation across repeated local measurements at each position). We have also specified the number of sampled locations (typically 30–60 per nominal doping level) in the figure caption and Methods section. The fitting procedure is now described in detail, including the power-law form used to extract the exponent and explicit robustness checks performed by varying the fitting range (e.g., excluding the two lowest and two highest Tc points). These checks confirm that the exponent remains larger than the clean SDW value, supporting our interpretation of a disorder-modified quantum critical regime. revision: yes

  2. Referee: [Discussion] Discussion of the local-Tc parameterization: the manuscript asserts that using measured local Tc circumvents doping inhomogeneity, yet provides no explicit test or discussion ruling out correlations between local Tc and other position-dependent quantities (impurity scattering rate, pair-breaking strength, or vortex pinning) that scanning-SQUID λ(0) measurements could also sense. This assumption is load-bearing for the interpretation that the peak is an intrinsic signature of a magnetic QCP rather than a non-critical confounding effect.

    Authors: The referee rightly notes that the manuscript would be strengthened by explicitly addressing possible correlations between local Tc and other spatially varying quantities that could affect the measured λ(0). While the local-Tc parameterization was introduced primarily to mitigate doping inhomogeneity, we acknowledge that impurity scattering, pair-breaking, or pinning could in principle contribute. In the revised Discussion we have added a paragraph that considers these alternatives and explains why they are unlikely to produce the observed sharp peak at the specific local Tc value that coincides with the bulk QCP location. The peak’s position, the magnitude of the enhancement, and the extracted exponent are all consistent with critical suppression of superfluid stiffness rather than conventional scattering. We have also noted the limitation that a direct experimental decoupling of these effects would require additional local probes not employed here. revision: partial

Circularity Check

0 steps flagged

No significant circularity; result is direct observation from local measurements

full rationale

The paper's chain consists of scanning SQUID measurements of local Tc and λ(0) at the same positions, followed by re-plotting λ(0) against measured local Tc (instead of nominal doping) to reduce scatter from inhomogeneity, observation of a peak, and extraction of a scaling exponent from the resulting curve. This is an empirical data analysis procedure, not a derivation that reduces by construction to its inputs. The peak and exponent emerge from the plotted data rather than being fitted parameters renamed as predictions. No self-definitional loops, load-bearing self-citations, imported uniqueness theorems, or smuggled ansatzes are present in the provided text. The approach is self-contained against the experimental benchmarks described.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard relations between penetration depth and superfluid stiffness plus the assumption that local Tc parameterization isolates intrinsic critical behavior; no new entities are postulated.

free parameters (1)
  • critical exponent
    Extracted from the scaling of λ(0) with local Tc; stated to exceed the clean spin-density-wave value.
axioms (2)
  • domain assumption Zero-temperature penetration depth λ(0) inversely reflects superfluid stiffness and density in the London regime.
    Invoked when linking the observed peak in λ(0) to suppression of superfluid stiffness at the QCP.
  • domain assumption Local Tc measured by scanning SQUID accurately captures the position-dependent superconducting properties despite spatial doping variations.
    Central to the parameterization approach that replaces nominal Zn concentration.

pith-pipeline@v0.9.0 · 5466 in / 1585 out tokens · 90887 ms · 2026-05-07T10:30:16.513219+00:00 · methodology

discussion (0)

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    Fitting Analysis of the penetration depth enhancement at AF-QCP To examine how the extracted critical exponent depends on the fitting procedure, we analyze theλ(0) 2 data using the combined form introduced in the main text, λ(0,Γ) 2 =q(Γ,Γ c, A, C, ν)h(Γ),(S1) where q(Γ,Γ c, A, C, ν) = 1 C+A|Γ−Γ c|3ν−1 (S2) describes the quantum-critical enhancement [6], ...