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REVIEW 3 major objections 4 minor 36 references

Direct Comparison of Magnetic Penetration Depth in Kagome Superconductors AV$_3$Sb$_5$ (A = Cs, K, Rb)

T0 review · 3 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read The Kagome superconductors CsV3Sb5, KV3Sb5, and RbV3Sb5 all show fully gapped, nodeless superconductivity when their penetration depths are compared with the same scanning SQUID technique.

desk verdict First side-by-side penetration depth comparison across AV3Sb5; the data visibly saturate and argue against nodal superconductivity in K and Rb, but missing error bars and fit-window sensitivity keep the nodeless claim from being conclusive. read the letter →

arxiv 2412.19919 v2 pith:RO46UXDR submitted 2024-12-27 cond-mat.supr-con

Austin Kaczmarek , Andrea Capa Salinas , Stephen D. Wilson , Katja C. Nowack This is my paper · ORCID
classification cond-mat.supr-con
keywords kagomesuperconductorsAV3Sb5magneticpenetrationdepthscanningSQUIDmicroscopysuperconductinggapsymmetryfullygappedsuperconductivitysuperfluiddensitynodal
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 side-by-side measurements of the local magnetic penetration depth in the three Kagome superconductors CsV3Sb5, KV3Sb5, and RbV3Sb5, made with the same scanning SQUID susceptometer. The authors argue that in all three compounds the superconducting gap is fully gapped, with no nodes, contradicting earlier muon-spin-rotation reports of nodal superconductivity in KV3Sb5 and RbV3Sb5. They also find that a single isotropic gap cannot describe the superfluid density, while either a single anisotropic gap or two isotropic gaps fit well. The penetration-depth curves of KV3Sb5 and RbV3Sb5 are nearly identical to each other and distinct from CsV3Sb5, which the authors tie to known similarities in the normal-state electronic structure. If correct, the result establishes the gap symmetry of this family as nodeless and shows that the superconducting state tracks the normal-state band structure.

What carries the argument

The measurement uses a scanning SQUID susceptometer whose concentric field coil and pickup loop generate and detect a local magnetic field; screening currents in the superconductor reduce the mutual inductance according to ΔM(z,T)/M0 = −[1 + (4/a²)(z + λ(T))²]^{-3/2}, where a is the effective coil radius. From this, a dimensionless quantity y is constructed so that Δλ(T) = a(y(z*,T) − y(z*,0)) is independent of the unknown tip-sample height z*. The nodal-versus-gapped diagnosis comes from fitting the low-temperature Δλ(T) to an exponential versus a T^n power law, while the full-temperature analysis fits the raw ΔM(T) to superfluid-density models for a single isotropic gap, a single anisotropic gap with sixfold-symmetric anisotropy, and two isotropic gaps, treating λ0/a as a fit parameter.

What would settle it

Refit the published low-temperature Δλ(T) for KV3Sb5 and RbV3Sb5 to Δλ ∝ T^n with n free and with error bars; if the best-fit exponent approaches or falls below 2, or if the exponential gap extracted from cutoffs between 0.15Tc and 0.35Tc varies by more than about a factor of two, the fully gapped conclusion would be in doubt.

Watch

Extended reading notes

Core claim

The central claim is that the superconducting order parameter in all three AV3Sb5 compounds is fully gapped. At low temperatures, Δλ(T) saturates and fits an exponential form Δλ ∝ $T^{{-1/2}}$ $e^{{-Δ0/kBT}}$ rather than a power law with exponent n ≤ 2; power-law fits require n > 2, which the authors interpret as incompatible with line nodes. The fitted gaps are 1.05 kBTc for CsV3Sb5 and 1.56 and 1.57 kBTc for KV3Sb5 and RbV3Sb5, lower than the BCS weak-coupling value of 1.76 kBTc. Across the full temperature range the superfluid density deviates from single-isotropic-gap behavior but is well captured by a single anisotropic gap or by two isotropic gaps. A rescaling analysis that removes the influence of the absolute penetration depth and gap magnitude shows that KV3Sb5 and RbV3Sb5 share the same gap structure while CsV3Sb5 differs.

Load-bearing premise

The nodeless conclusion depends on assuming that the low-temperature Δλ(T) behavior below about 0.3Tc can reliably distinguish an exponential fully gapped form from a power-law nodal form; the fitted gap for CsV3Sb5 changes from 0.60 to 1.05 kBTc depending on the fit cutoff, and no error bars are shown on the data points.

Editorial extensions

If this is right

  • All three Kagome superconductors are nodeless; power-law fits with n > 2 do not indicate nodes, so the previously reported nodal superconductivity in KV3Sb5 and RbV3Sb5 is not reproduced.
  • Superconductivity in this family is not described by a single isotropic gap: either gap anisotropy or multiple gaps are required to match the superfluid density.
  • KV3Sb5 and RbV3Sb5 have nearly identical penetration-depth and superfluid-density temperature dependences, while CsV3Sb5 is distinct, matching normal-state fermiology and implying that superconductivity inherits normal-state band structure.
  • The low-temperature exponential gap corresponds to the smaller gap in the multigap fits, so low-temperature penetration depth mainly probes the minimum gap on the Fermi surface.

Reading between the lines

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

  • If the nodeless conclusion holds, the earlier muon-spin-rotation evidence for nodes may reflect sample-specific disorder or strain conditions rather than an intrinsic nodal state; a controlled comparison on the same crystals could test this.
  • Because anisotropic and two-gap models are nearly indistinguishable from penetration depth alone, decisive tests of the gap structure will need phase-sensitive probes or momentum-resolved spectroscopies.
  • The observed spatial inhomogeneity in superfluid density means bulk measurements average over regions with different λ0, so local SQUID data may differ from bulk tunnel-diode-oscillator or muon-spin-rotation results even for the same sample, which could explain part of the literature disagreement.
  • The fitted λ0 ranges (195–390 nm for CsV3Sb5, 127–255 nm for KV3Sb5, and 123–247 nm for RbV3Sb5) could be combined with the measured Tc values to estimate superfluid density and test whether it scales with charge-density-wave strength across the family.
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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

3 major / 4 minor

Summary. This manuscript reports scanning SQUID susceptometry measurements of the local magnetic penetration depth in the kagome superconductors CsV3Sb5, KV3Sb5, and RbV3Sb5. From the temperature-dependent mutual inductance, the authors extract Δλ(T) and analyze its low-temperature behavior together with the superfluid density ρs(T) obtained by fitting the raw data to single-isotropic, single-anisotropic, and two-isotropic-gap models. The central claim is that all three compounds are fully gapped (nodeless), in contrast to prior μSR reports of nodal behavior in KV3Sb5 and RbV3Sb5, and that KV3Sb5 and RbV3Sb5 have nearly identical gap structures that differ from CsV3Sb5. The paper also compares the measured Δλ(T) with published data and discusses spatial inhomogeneity and thermalization checks.

Significance. If the central claim is correct, this work would resolve conflicting literature on the pairing symmetry in the AV3Sb5 family and establish a consistent, technique-uniform comparison of penetration depth across all three compounds. The side-by-side measurement approach and the stacking of sample-to-sample, spatial, and thermalization consistency checks are valuable strengths. However, the load-bearing assertion of nodeless superconductivity currently rests on low-temperature fits that are not quantitatively defended; the manuscript itself reports that the extracted gap for CsV3Sb5 shifts from 0.60 to 1.05 kBTc depending on the fit window, and no error bars or statistical model comparison are provided. The superfluid-density analysis, while honestly acknowledging that anisotropic and two-gap models are indistinguishable, does not independently support the nodeless conclusion because the low-temperature exponential form is the only discriminator against power-law behavior.

major comments (3)
  1. [Fig. 2(c)-(e) and Supp. Sec. S11] The central claim that all three compounds are fully gapped rests on the low-temperature Δλ(T) fits, but the discrimination between exponential and power-law behavior is not quantitatively established. No error bars are shown on any data point in Fig. 2, and no goodness-of-fit metric (e.g., χ², residuals, AIC) is reported. The sensitivity to fit window is acknowledged in the main text, where the extracted gap for CsV3Sb5 changes from 0.60 to 1.05 kBTc when the upper fit limit is changed from 0.2 to 0.3 Tc; Supp. Fig. S9 shows similar strong variation of the power-law exponent n. Over the limited range T/Tc < 0.3, a power law with a large exponent (n ≈ 5) can appear very similar to an exponential, so the data as presented do not establish that exponential is significantly preferred over power-law or small-minimum-gap anisotropic models.
  2. [Fig. 2(c)-(e) and main text after Eq. (4)] The claims that 'fits to T² fail to capture the data' and that 'power law fits to T^n yield n>2' are made without any quantitative support. The values n = 3.4, 5.4, and 5.5 for Cs, K, and Rb are presented without confidence intervals, and 'reasonable fits' is not defined. Since a power-law exponent larger than 2 can arise from disorder or from a nodal gap with small but nonzero minimum gap, the statement that n>2 rules out nodes is not justified unless the fit quality and parameter uncertainties are quantified.
  3. [Main text, superfluid density analysis (Eq. (5) and Fig. 3)] The paper correctly states that the anisotropic and two-isotropic-gap models are nearly indistinguishable from the full-temperature-range superfluid density fits. As a consequence, the only quantitative evidence for nodelessness is the low-temperature Δλ(T) exponential fit. This logical dependence makes the first major comment load-bearing: if the exponential-vs-power-law discrimination is not statistically validated, the central conclusion of the paper is not supported by the presented analysis. The authors should either provide a robust statistical comparison (e.g., including propagated noise from the cooling/warming cycles in Supp. Sec. S10 and spatial positions in Supp. Sec. S8) or soften the nodeless claim to 'consistent with a fully gapped state' with explicit caveats.
minor comments (4)
  1. [Main text, Summary paragraph] The sentence 'Analysis of the temperature-dependent superfluid density, s(T )from the behavior expected for a single isotropic gap for all three compounds.' is garbled; it appears to be missing the phrase 'shows deviations from' and should be corrected.
  2. [Main text, after Eq. (4)] There are typographical errors: 'Sepp. Sec. S11' should be 'Supp. Sec. S11', and 'ncrease' should be 'increase'.
  3. [Supp. Sec. S12, Fig. S10 caption] In the figure caption, the models are labeled 'single isotropic gap (iso), single anisotropic gap (aniso), and two isotropic gaps (aniso)'; the last label should be '(iso+iso)' to match the main text notation.
  4. [Supp. Sec. S10, Fig. S8] The thermalization check shows good cooling-warming agreement, but the plotted quantity is |ΔM(T)| normalized by its value at T0; providing the absolute temperature base (T0) and the field-coil excitation parameters would make this check more reproducible.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the nodeless conclusion rests on the direct low-temperature saturation of Δλ(T), while the model-dependent superfluid-density fits are explicitly acknowledged to be underdetermined.

full rationale

The central claim that all three AV3Sb5 compounds are fully gapped is derived from the measured low-temperature behavior of Δλ(T), obtained directly from the raw mutual-inductance data via Eqs. (2) and (3). The observed saturation of Δλ(T)/a at low temperature (Fig. 2b) is an empirical feature independent of the functional fits; the exponential and power-law fits in Figs. 2(c)-(e) and Supp. Sec. S11 are consistency checks rather than equations that re-insert the conclusion. The superfluid-density analysis fits λ0/a and gap parameters to the same ΔM(T) data, and the paper explicitly states that a single anisotropic gap and two isotropic gaps are nearly indistinguishable and that the data do not sufficiently constrain the gap distribution; this is a fitting limitation, not a fitted parameter relabeled as a prediction. Citations to prior work such as Duan et al., Roppongi et al., and point-contact spectroscopy are contextual experimental comparisons, not a uniqueness theorem or ansatz imported from the authors' prior work. The sensitivity of the extracted exponential gap to the fit window (0.60 vs 1.05 kBTc for CsV3Sb5) is a statistical robustness concern, not evidence of circularity. The derivation chain is therefore self-contained with respect to the measured data.

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

The central claims require fitting penetration depth and gap parameters to the measured data. The main free parameters are λ0/a and the gap model parameters; these are not fixed by external experiments. The governing formulas are standard models for these measurements.

free parameters (6)
  • λ0/a (zero-temperature penetration depth over coil radius) = Cs: 0.065-0.074, K: 0.041-0.042, Rb: 0.040-0.042 (unitless)
    Fitted separately for each gap model to the same ΔM(T) data (Table S1); used to convert ΔM to ρs.
  • exponential low-T gap Δ0 = 0.21 meV (Cs), 0.12 meV (K), 0.10 meV (Rb)
    From fits to Eq.4 up to 0.3Tc (Fig.2); sensitive to temperature range, e.g., Cs gives 0.12 meV with cutoff 0.2Tc.
  • power-law exponent n = 3.4 (Cs), 5.4 (K), 5.5 (Rb)
    From fitting Δλ(T)=AT^n over 0<T/Tc<0.3; used to argue n>2 rules out nodes.
  • single isotropic gap Δ0 = Cs: 0.31 meV; K: 0.14 meV; Rb: 0.11 meV
    From fitting ρs(T) model to ΔM(T) (Table S1).
  • anisotropic gap parameters (Δ0, γ) = Cs: 0.53 meV, 0.63; K: 0.17 meV, 0.39; Rb: 0.14 meV, 0.42
    From fitting the sixfold anisotropic gap model (Table S1).
  • two-gap parameters (Δ01, Δ02, α) = Cs: 0.23, 0.60 meV, α=0.51; K: 0.12, 0.24 meV, α=0.64; Rb: 0.10, 0.26 meV, α=0.75
    From fitting the alpha model (Table S1).
assumptions (6)
  • domain assumption Mutual inductance model ΔM/M0 = -1/(1 + (4/a^2)(z+λ)^2)^{3/2} (Eq.1)
    Assumes a semi-infinite superconductor with local penetration depth λ and a point-dipole-like field coil; from Kirtley et al. (Ref. 32). Used to extract Δλ from measured ΔM.
  • domain assumption Cylindrical Fermi surface with quasi-2D superfluid density formula (Eq. S1)
    AV3Sb5 is quasi-2D; this standard expression relates ρsab to the gap function. Introduced in Supp. Sec. S3.
  • domain assumption Gap temperature dependence via Δ(T)=Δ0 tanh((π kBTc/Δ0) sqrt(Tc/T - 1)) (Eq. S2)
    Phenomenological interpolation commonly used in penetration depth fits; not derived in the paper.
  • domain assumption Alpha model ρs(T) = α ρs1 + (1-α) ρs2 for two isotropic gaps (Eq. S3)
    Multigap model borrowed from MgB2 analysis; assumes independent two-band superfluid densities.
  • domain assumption Low-T Δλ behavior: nodes give power law with exponent <2; full gap gives T^{-1/2} exp(-Δ0/kBT) (Eq.4)
    Classification rule from Prozorov and Giannetta (Ref. 20) used to infer nodeless order from saturation.
  • domain assumption Constant SQUID-sample distance z=z* during a temperature sweep (light mechanical contact)
    The extraction of y(T) assumes fixed z*; thermalization checks in Supp. Sec. S10 support this.

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Pith. "Pith review of Direct Comparison of Magnetic Penetration Depth in Kagome Superconductors AV$_3$Sb$_5$ (A = Cs, K, Rb)." pith.science (2026). https://pith.science/paper/RO46UXDR

@misc{pith2026241219919,
  author       = {Pith},
  title        = {Pith review of: Direct Comparison of Magnetic Penetration Depth in Kagome Superconductors AV$_3$Sb$_5$ (A = Cs, K, Rb)},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RO46UXDR}},
  note         = {Machine review of arXiv:2412.19919}
}
abstract

We report measurements of the local temperature-dependent penetration depth, $\lambda(T)$, in the Kagome superconductors AV$_3$Sb$_5$ (A = Cs, K, Rb) using scanning superconducting quantum interference device (SQUID) microscopy. Our results suggest that the superconducting order in all three compounds is fully gapped, in contrast to reports of nodal superconductivity in KV$_3$Sb$_5$ and RbV$_3$Sb$_5$. Analysis of the temperature-dependent superfluid density, $\rho_s(T)$, shows deviations from the behavior expected for a single isotropic gap, but the data are well described by models incorporating either a single anisotropic gap or two isotropic gaps. Notably, the temperature dependences of $\lambda(T)$ and $\rho_s(T)$ in KV$_3$Sb$_5$ and RbV$_3$Sb$_5$ are qualitatively more similar to each other than to CsV$_3$Sb$_5$, consistent with the superconducting phase reflecting features of the normal-state band structure. Our findings provide a direct comparison of the superconducting properties across the AV$_3$Sb$_5$ family.

Figures

Figures reproduced from arXiv: 2412.19919 by the authors.

Figure 1
Figure 1. FIG. 1: (a) Schematic of the SQUID pickup loop with concentric field coil above the sample. An AC current [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: Change in penetration depth ∆ [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: Reduced superfluid density for (a) CsV [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

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