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REVIEW 4 major objections 4 minor 43 references

Distinct Uniaxial Stress and Pressure Fingerprint of Superconductivity in the 3D Kagome Lattice Compound CeRu2

T0 review · 4 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Uniaxial stress reshapes the superconducting gap of CeRu2 into a Tc dome, while hydrostatic pressure switches the same compound to nodal pairing.

desk verdict Fresh μSR data on CeRu2 under stress and pressure, but the pairing-symmetry claims outrun the statistics. read the letter →

arxiv 2507.09779 v1 pith:QACUO2TG submitted 2025-07-13 cond-mat.supr-con cond-mat.mtrl-sci

O. Gerguri , D. Das , V. Sazgari , H.X. Liu , C. Mielke III , P. Kràl , S.S. Islam , J.N. Graham
show 11 more authors
V. Grinenko R. Sarkar T. Shiroka J.-X. Yin J. Chang R. Thomale H.H. Klauss R. Khasanov Y. Shi H. Luetkens Z. Guguchia
This is my paper · ORCID
classification cond-mat.supr-concond-mat.mtrl-sci
keywords CeRu23DKagomelatticeuniaxialstresshydrostaticpressuremuonspinrotationsuperconductinggapsymmetrynodalsuperconductivityflatbands
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper reports that the superconducting state of the pyrochlore compound CeRu2 responds very differently to two mechanical knobs. Uniaxial stress applied in the (111) Kagome plane raises and then lowers the critical temperature, forming a dome, and changes the superconducting gap from anisotropic s-wave to isotropic s-wave with no structural transition. Hydrostatic pressure up to 2.2 GPa leaves Tc nearly unchanged but switches the low-temperature superfluid density from exponential to linear behavior, a signature of nodal pairing. The authors position CeRu2 as a 3D Kagome material where flat bands and correlations can be tuned by stress and pressure, offering a way to study how lattice geometry controls pairing symmetry.

What carries the argument

The central observable is the superconducting muon spin relaxation rate σSC, related to the magnetic penetration depth by σSC/γμ = 0.06091 Φ0/λ². Fits of its temperature dependence to anisotropic s-wave, isotropic s-wave, and nodal gap models distinguish the pairing symmetry. The two tuning mechanisms are a piezoelectric uniaxial stress cell for in-plane strain along the Kagome plane and a piston-cylinder hydrostatic pressure cell for isotropic compression; the paper interprets the stress response through stress-induced shifts of flat bands near the Fermi level.

What would settle it

Apply uniaxial stress with a cell that independently measures the in-plane strain tensor while tracking Tc and σSC(T); observing a different dome shape or no gap isotropization for different known stress directions would invalidate the flat-band-shift interpretation. Alternatively, hydrostatic pressure measurements at finer intervals near 1.9 GPa could check whether the linear low-temperature superfluid density emerges discontinuously or smoothly.

Watch

Extended reading notes

Core claim

Using muon spin rotation on a single crystal of CeRu2, the paper claims that uniaxial stress within the (111) Kagome planes produces a non-monotonic, dome-shaped Tc(σ) with a plateau, a maximum near 0.13 GPa, and a 16% suppression at 0.22 GPa, and that the gap anisotropy ratio Δmin/Δmax drops from 0.41 at ambient pressure to a fully isotropic value above 0.07 GPa. The same crystal under hydrostatic pressure up to 1.9 GPa shows essentially constant Tc, but the superfluid density, extracted from the muon relaxation rate, changes from exponential to linear low-temperature behavior, indicating the minimum gap closes and nodal quasiparticles appear. The coexistence of these two pathways—a pairing-symmetry crossover under anisotropic stress and a nodeless-to-nodal transition under isotropic pressure—is presented as a distinct fingerprint of tunable superconductivity in a 3D Kagome lattice.

Load-bearing premise

The load-bearing assumption is that the uniaxial stress is truly uniaxial and acts along a well-defined direction within the (111) plane; the paper notes the exact in-plane direction is not known, so any unintended shear or misalignment could in principle produce the observed dome and gap changes without reflecting intrinsic CeRu2 physics.

Editorial extensions

If this is right

  • Uniaxial stress can tune both Tc and gap symmetry of CeRu2 without any structural phase transition, so the lattice's electronic structure alone responds to strain.
  • Hydrostatic pressure provides an independent knob that preserves Tc but changes the gap structure from nodeless to nodal, meaning pairing symmetry is decoupled from Tc in this material.
  • The stress scale (≤0.22 GPa) is an order of magnitude smaller than the pressure scale (up to 2.2 GPa) for comparable microscopic changes, showing that directional strain is a far more sensitive control parameter.
  • CeRu2 becomes a testbed for theories connecting Kagome flat bands and heavy-fermion correlations to pairing symmetry, since both a smooth-gap crossover and a nodal transition are accessible in one compound.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the flat-band-shift explanation is correct, a stress cell with a controlled in-plane direction should produce an anisotropic dome, with the largest Tc change when strain aligns with the Kagome bond directions.
  • The pressure-induced nodal state could be tested by low-temperature specific heat or penetration depth measurements searching for a T-linear term or a T² dependence expected from line nodes.
  • The paramagnetic upturn seen below 1.5 K under pressure, if intrinsic, may indicate field-induced magnetism or a competing order that couples to the nodal state, rather than pairing alone.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 4 minor

Summary. The manuscript reports muon spin rotation (μSR) measurements on single-crystalline CeRu2 under uniaxial in-plane stress and hydrostatic pressure. The authors claim three main results: (i) uniaxial stress up to 0.22 GPa produces a dome-shaped evolution of Tc, with an initial plateau followed by enhancement and suppression; (ii) uniaxial stress drives a crossover from anisotropic to isotropic s-wave pairing, inferred from fits to the temperature-dependent superfluid density; and (iii) hydrostatic pressure up to 1.9–2.2 GPa leaves Tc largely unchanged but changes the low-temperature superfluid density from exponential to linear behavior, suggesting a nodeless-to-nodal transition. The paper combines a unique experimental setup and compares fits of isotropic s-wave, anisotropic s-wave, and nodal models to the extracted σSC(T).

Significance. If the central claims are substantiated, the paper would provide a valuable demonstration of mechanical tuning of the superconducting pairing in a three-dimensional kagome-type correlated metal, with distinct responses to uniaxial stress versus hydrostatic pressure. The work has clear strengths: it uses high-quality single crystals, combines AC susceptibility with μSR, checks the elastic regime through force-displacement linearity (Fig. 2c), and the ambient-pressure anisotropic s-wave gap ratio (Δmin/Δmax = 0.41) is consistent with previous μSR, NMR, and ARPES reports. The two-axis tuning approach and the proposed connection to flat-band physics are timely and interesting. However, the central pairing-symmetry claims currently rest on model fits without quantitative statistical comparison, a sparse Tc-stress dataset without error bars, and a single pressure point for the purported nodal behavior; these issues must be addressed before the conclusions can be considered established.

major comments (4)
  1. [§II.A, §II.B, Tables I and II, Eq. (5)] The manuscript reports no goodness-of-fit metric (χ², Δχ², AIC, BIC, or residuals) for any of the gap-model fits. In Table I, the anisotropic and isotropic s-wave fits return identical values of λ0 and Δmax at 0.07, 0.10, 0.13, and 0.18 GPa, with no Δmin value listed; the claimed 'crossover to isotropic s-wave' could simply reflect that the data no longer constrain the anisotropy parameter. In Table II, the nodal fit at 1.9 GPa gives Δmax = 1.22(4) meV versus 0.92(3) meV for the s-wave fit, but without a statistical comparison the assertion that the nodal model is 'best' is unsupported. Please provide quantitative model comparisons for all stress and pressure points, and explicitly state whether Δmin was a free parameter, fixed to zero, or constrained during the fits.
  2. [Fig. 1 caption, §II.A] The Fig. 1 caption states that the exact direction of the uniaxial stress within the (111) plane is not known. The interpretation that stress shifts flat bands and drives both the Tc dome and the anisotropic-to-isotropic crossover assumes that the uncontrolled in-plane direction is either irrelevant or reproducibly fixed. If the stress direction varies, or if the stress is not purely uniaxial along the intended plane, the observed Tc variation and the apparent evolution of the fitted gap structure could be artifacts of the stress cell rather than intrinsic properties of CeRu2. Please specify how the sample orientation was verified, how the stress direction was calibrated, and discuss the sensitivity of the conclusions to the unknown in-plane direction.
  3. [§II.A, Fig. 2(a)] The claimed dome-shaped Tc evolution is based on five stress values (0, 0.10, 0.13, 0.19, and 0.22 GPa) with no quoted uncertainties on Tc or on the transition midpoint. Given the definition of Tc as the 50% flux-exclusion midpoint and the absence of error bars, the enhancement between 0.10 and 0.13 GPa is not demonstrably significant. Please report Tc with errors and provide a statistical test (e.g., a fit to a dome function or a comparison of transition widths) to support the non-monotonic claim.
  4. [Abstract, §II.B, §IV (Hydrostatic Pressure Cell), Fig. 4] The abstract states that hydrostatic pressure was applied 'up to 2.2 GPa', whereas the body text and Methods state the maximum pressure is 1.9 GPa, and all presented hydrostatic data are at 0, 1.5, and 1.9 GPa. This inconsistency is confusing and should be corrected. More importantly, the conclusion that hydrostatic pressure induces a nodeless-to-nodal transition rests on a single pressure point at 1.9 GPa, where only one σSC(T) curve supports the linear low-temperature behavior. Please either add at least one additional pressure point above 1.5 GPa or temper the claim by explicitly acknowledging that the evidence for nodal superconductivity is based on one pressure value.
minor comments (4)
  1. [§II.A, Table I] For the anisotropic s-wave rows at 0.07–0.18 GPa, the values of λ0 and Δmax are identical to the s-wave rows and Δmin is left blank; please state explicitly whether Δmin was fixed to Δmax during these fits or whether the fit returned a boundary value, and define the meaning of the blank entry.
  2. [Fig. 3] In Fig. 3, the solid and dashed lines are labelled only in panel (a); please ensure that every panel (a–e) clearly identifies which line corresponds to the isotropic and anisotropic s-wave fits, since the visual comparison is central to the crossover claim.
  3. [§III (Conclusion)] There is a typographical error in 'degress of freedom' in the closing paragraph; it should read 'degrees of freedom'.
  4. [Abstract and §II.B] The phrase 'alters the superfluid density from exponential to linear behavior' is used for the hydrostatic-pressure result, but the paper does not show an explicit fit to an exponential form at ambient pressure in the hydrostatic series; please clarify that this refers to the temperature dependence of σSC(T) (or λ−2(T)) and specify the functional forms used.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: gap-symmetry inferences come from standard model fits to measured μSR relaxation data, not from definitional or self-citational forcing.

full rationale

The paper's main claims are experimental: Tc under stress is read directly from AC susceptibility (Fig. 2), and the superfluid-density evolution is obtained by fitting the measured TF-μSR relaxation rate σSC(T) with the standard local-London model (Eq. 5). The gap-symmetry assignments are model comparisons to the same σSC(T) curves (Tables I and II). This is curve fitting, not a derivation in which the conclusion is encoded in the input: the isotropic s-wave, anisotropic s-wave, and nodal models are not defined from the outcome, and the fitted parameters (λ0, Δmax, Δmin) are free parameters with stated uncertainties. The claim that the anisotropic fit 'provides the best fit' at ambient pressure is corroborated by independent NMR and photoemission gap ratios, so the self-cited μSR result is not load-bearing. The stress-induced evolution toward isotropic pairing and the pressure-induced nodal behavior rest on the fitted parameters changing with applied stress/pressure; no equation reduces one of these conclusions to the fit input by construction. The absence of a reported Δχ2 or likelihood metric for model selection is a statistical-support weakness (correctness risk), but it is not circularity. The paper also explicitly flags open questions ('Whether this 16% reduction in Tc is driven solely by the movement of the Kagome flat band ... remains an open question'; 'A detailed microscopic understanding ... is still required'), which further shows the claims are not presented as closed derivations. The unknown in-plane stress direction is an experimental uncertainty, not a circular step.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The central claims rest on standard muSR analysis of the vortex-lattice field distribution. No new physical entities are introduced. The main assumptions are the local London limit, the gap-model temperature dependence, and the homogeneity of the applied stress and pressure. The fitted gap parameters (lambda0, Delta_max, Delta_min) are extracted from the same data used to infer pairing symmetry, which is a standard but non-independent procedure.

free parameters (3)
  • lambda0 (zero-temperature penetration depth) = 272-311 nm depending on condition and model
    Fitted from the temperature dependence of sigma_SC using Eq. (5); central to the superfluid density analysis.
  • Delta_max (maximum superconducting gap) = 0.72-1.22 meV depending on condition
    Fitted gap magnitude in the isotropic and anisotropic s-wave models.
  • Delta_min (minimum gap in anisotropic model) = 0.34 +/- 0.16 meV at 0 GPa; 0.32 +/- 0.03 meV at 1.5 GPa
    Fitted anisotropy parameter; at other stress values it is not reported, suggesting the fit could not constrain it.
assumptions (6)
  • domain assumption London local approximation (lambda >> xi) applies
    Used in Eq. (5) to relate sigma_SC to lambda(T).
  • domain assumption Gap temperature dependence follows Gamma(T/Tc) = tanh{1.82[1.018(Tc/T - 1)]^0.51}
    Approximation from Carrington and Manzano (ref 43) used in Eq. (5).
  • domain assumption The vortex lattice is a perfect triangular lattice and Ha << Hc2
    Brandt's formula (Eq. 1) relates sigma_SC to lambda^-2.
  • domain assumption Normal-state depolarization is small, temperature independent, and constant below Tc
    Used to extract sigma_SC by subtracting sigma_ns.
  • domain assumption The pressure cell background is correctly described by a single Gaussian component
    Used in the three-component Gaussian fit for the pressure data.
  • domain assumption Uniaxial stress is homogeneous across the sample and the sample remains elastic
    Linear force-displacement response is assumed to indicate uniform stress without structural changes.

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Cite this review

Pith. "Pith review of Distinct Uniaxial Stress and Pressure Fingerprint of Superconductivity in the 3D Kagome Lattice Compound CeRu2." pith.science (2026). https://pith.science/paper/QACUO2TG

@misc{pith2026250709779,
  author       = {Pith},
  title        = {Pith review of: Distinct Uniaxial Stress and Pressure Fingerprint of Superconductivity in the 3D Kagome Lattice Compound CeRu2},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QACUO2TG}},
  note         = {Machine review of arXiv:2507.09779}
}
abstract

The exploration of tunable superconductivity in strongly correlated electron systems is a central pursuit in condensed matter physics, with implications for both fundamental understanding and potential applications. The Laves phase CeRu$_{2}$, a pyrochlore compound, exhibits a three-dimensional (3D) Kagome lattice type geometry giving rise to flat bands and degenerate Dirac points, where band structure features intertwine with strong multi-orbital interaction effects deriving from its correlated electronic structure. Here, we combine muon spin rotation ($\mu$SR), uniaxial in-plane stress, and hydrostatic pressure to probe the superconducting state of CeRu$_{2}$. Uniaxial stress up to 0.22 GPa induces a dome-shaped evolution of the critical temperature $T_{\rm c}$, with an initial plateau, successively followed by enhancement and suppression without any structural phase transition. Stress is further found to drive a crossover from anisotropic to isotropic $s$-wave pairing. In contrast, hydrostatic pressure up to 2.2 GPa leaves $T_{\rm c}$ largely unchanged but alters the superfluid density from exponential to linear behavior at low temperatures, indicative of nodal superconductivity under hydrostatic pressure. Taken together, these results indicate that CeRu$_{2}$ occupies an ideal position in parameter space, enabling highly responsive and multifold tunability of superconductivity in this three-dimensional correlated electronic system. This warrants further quantitative analysis of the interplay between lattice geometry, electronic correlations, and pairing symmetry.

Figures

Figures reproduced from arXiv: 2507.09779 by the authors.

Figure 1
Figure 1. FIG. 1. (a,b) The CeRu [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. (a) The temperature dependence of AC susceptibility, measured under various uniaxial stress values. The dark dash [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. (a-e) The temperature dependence of the superconducting muon spin relaxation rate [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4. The temperature dependence of the superconducting [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

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