{"id":"9e470ba4-edd4-43f3-9b6a-c621fe154d49","arxiv_id":"2412.19919","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"Penetration depth measurements on all three AV3Sb5 kagome superconductors saturate at low temperature, indicating fully gapped superconductivity in each compound.","lead":"Scanning SQUID microscopy was used to measure the magnetic penetration depth of the three kagome superconductors CsV3Sb5, KV3Sb5, and RbV3Sb5. The data indicate all three are fully gapped, with KV3Sb5 and RbV3Sb5 more similar to each other than to CsV3Sb5.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Nodeless conclusion rests on unquantified exponential-vs-power-law discrimination: no error bars, and the extracted gap for CsV3Sb5 shifts from 0.60 to 1.05 kBTc across fit windows, so the low-T fits do not yet establish full gapping.","rationale":"The paper is a careful experimental comparison and its central claim is plausible: all three AV3Sb5 compounds show low-temperature saturation of Δλ, and the low-T exponential fits give sensible gap values that align with the small gap from the multigap fits. The side-by-side SQUID methodology, the direct fitting of raw ΔM(T) rather than processed ρs(T), and the explicit checks of thermalization and spatial inhomogeneity are genuine strengths. However, the decisive inference from 'saturation plus exponential fit' to 'nodeless' is only as strong as the ability to distinguish exponential from power-law behavior in the T/Tc<0.3 window, and that ability is not quantified anywhere in the paper or supplement. The fit-range sensitivity admitted in the main text for CsV3Sb5 (0.60 vs 1.05 kBTc) and the cutoff-dependent n in Supp. Fig. S9 are warning signs: a single exponential with a stable gap would not shift by 75% across reasonable windows, and a true power law would not show n drifting with cutoff. In the absence of error bars or a statistical model comparison, the qualitative statements 'T^2 fails' and 'exponential agrees' are not enough to support the strong contrast drawn with earlier nodal reports. This is the same concern the reader identified, and it justifies the CONDITIONAL verdict. A quantitative reanalysis of the raw traces, with noise from repeated sweeps and positions propagated, would either confirm the nodeless classification or show that the available data are compatible with a small-gap anisotropic or dirty-nodal scenario. Thus I do not change the reader's verdict.","tokens_in":17265,"tokens_out":10355,"duration_ms":106952,"concrete_test":"Use the raw, unnormalized ΔM(T,z*) traces and construct pointwise uncertainties from repeated cooling/warming sweeps (Supp. Sec. S10) and from the several measured positions/samples (Supp. Secs. S7-S8). For each compound, fit Δλ(T)/a over T/Tc < t_max for t_max = 0.15, 0.20, 0.25, 0.30, and 0.35 to (i) A T^n, (ii) B T^2, and (iii) C T^{-1/2} e^{-Δ/T}, with n and Δ free. Compare models with AIC/BIC or a likelihood-ratio test. If the exponential model is not preferred by ΔAIC > 10 for every t_max for KV3Sb5 and RbV3Sb5, and with Δ stable within errors, then the central claim that these two compounds are fully gapped is not established by this dataset. Report the same comparison after including a T-linear nodal contribution with disorder.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central 'fully gapped/nodeless' claim depends entirely on the low-temperature Δλ(T) analysis of Fig. 2(c)-(e) and Supp. Sec. S11. The paper asserts that T^2 fits fail, that T^n fits require n>2, and that exponential fits agree with the data, but no error bars, goodness-of-fit metric, or statistical model comparison is provided. This matters because the discriminating signal is small: the entire low-T change is Δλ/a ≲ 5×10^-3, and the extracted gap for CsV3Sb5 shifts from 0.60 to 1.05 kBTc when the fit window is changed from 0.2Tc to 0.3Tc, as stated in the main text. Supp. Fig. S9 shows the power-law exponent n and the exponential gap both vary strongly with the fit cutoff; that is exactly the behavior expected when a curved, noisy trace can be described by different functional forms over a limited range. Without propagating the measurement noise, for example from the cooling/warming cycles in Supp. Sec. S10 or from repeated positions in Supp. Sec. S8, and without quantifying which model is preferred, the data do not yet establish that exponential is significantly better than a power law with a large exponent or an anisotropic-gap model with a small minimum gap. The superfluid-density fits honestly admit that anisotropic and two-gap models are indistinguishable; the low-T fit is the only quantitative evidence for nodelessness, and it is not quantitatively defended.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":17549,"tokens_out":3644,"duration_ms":37394,"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":[{"comment":"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.","section":"Fig. 2(c)-(e) and Supp. Sec. S11"},{"comment":"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.","section":"Fig. 2(c)-(e) and main text after Eq. (4)"},{"comment":"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.","section":"Main text, superfluid density analysis (Eq. (5) and Fig. 3)"}],"minor_comments":[{"comment":"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.","section":"Main text, Summary paragraph"},{"comment":"There are typographical errors: 'Sepp. Sec. S11' should be 'Supp. Sec. S11', and 'ncrease' should be 'increase'.","section":"Main text, after Eq. (4)"},{"comment":"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.","section":"Supp. Sec. S12, Fig. S10 caption"},{"comment":"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.","section":"Supp. Sec. S10, Fig. S8"}],"recommendation":"major_revision","confidential_remarks":"The paper addresses a timely and contested question in the kagome superconductor community, and the direct comparison across all three compounds is a clear strength. The main concern is that the central nodeless claim is not statistically supported as presented; this is a fixable issue if the authors add error propagation and a formal model comparison. I do not see evidence of circularity or invention of entities; the analysis is standard. The fit-window sensitivity that the authors honestly report actually undermines the conclusion until addressed quantitatively. The manuscript is within the scope of the journal and, after major revision, could become a valuable reference."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Here's my take. The genuinely new thing is the side-by-side penetration depth data for all three AV3Sb5 compounds taken with one technique and one sensor family, plus the new K and Rb data that look different from the muSR nodal reports. The paper does what it should: it shows raw ΔM fits, includes thermalization and spatial inhomogeneity checks in the supplement, and is upfront that the superfluid density data cannot distinguish an anisotropic single gap from two isotropic gaps. That honesty is real and earns credit.\n\nThe central nodeless claim rests on the low-temperature Δλ(T) saturation. Visually, in Fig.2(b), the curves do saturate, and that is the strongest piece of evidence. The exponential fits are supportive but not decisive. No error bars appear on any Δλ(T) point, and the paper does not quantify whether an exponential is significantly better than a power law with n between 3 and 5. The supplement shows that n and Δ0 drift with the fit window; for CsV3Sb5 the extracted gap shifts from 0.60 to 1.05 kBTc between cutoffs at 0.2 and 0.3 Tc. The authors disclose this shift, which is good, but they do not resolve it. Since the prior muSR claims are nodal and this paper argues the opposite, the missing error bars matter: the discriminating signal is small and the curve shapes are close.\n\nThe superfluid density analysis is solid as far as it goes. The single isotropic gap is clearly inadequate, and both the anisotropic and two-gap models fit. The paper does not overclaim there—it explicitly says the penetration depth cannot distinguish these scenarios. The fit parameters in the table are plausible, and the λ0 ranges are reasonable.\n\nCitation pattern looks fine. They cite the conflicting muSR work, the point-contact work, and the prior CsV3Sb5 measurements. No suspicious self-citation behavior.\n\nOverall: this is a serious experimental contribution that likely shifts the balance toward fully gapped superconductivity in KV3Sb5 and RbV3Sb5, but the quantitative case would be stronger with error bars and a formal model comparison. I'd send it to peer review and ask for those additions. It is not a desk reject by any means.","headline":"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.","tokens_in":18164,"tokens_out":2194,"would_cite":true,"duration_ms":23149,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"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.","keywords":["kagome superconductors","AV3Sb5","magnetic penetration depth","scanning SQUID microscopy","superconducting gap symmetry","fully gapped superconductivity","superfluid density","nodal superconductivity"],"falsifier":"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.","tokens_in":17006,"feed_emoji":"🧲","tokens_out":5305,"duration_ms":48975,"temperature":0.7,"pith_summary":"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.","feed_headline":"SQUID scans find nodeless gaps in all three Kagome superconductors","feed_subtitle":"Low-temperature penetration depth rules out nodal pairing and pairs KV3Sb5 with RbV3Sb5, not CsV3Sb5.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Supplies the prior muon-spin-rotation reports of nodal superconductivity in KV3Sb5 and RbV3Sb5 that this paper directly contradicts.","marker":"[12]"},{"why":"Provides the theoretical basis for relating the temperature dependence of the penetration depth to nodal versus fully gapped gap structures.","marker":"[20]"},{"why":"Prior penetration-depth study of CsV3Sb5 reporting nodeless superconductivity; used for comparison and for the sensitivity of fitted gap values to temperature cutoff.","marker":"[21]"},{"why":"Prior bulk penetration-depth study of CsV3Sb5 reporting anisotropic s-wave pairing; used for comparison and for the sensitivity of fitted gap values to temperature cutoff.","marker":"[23]"},{"why":"Point-contact spectroscopy study indicating fully gapped superconductivity in KV3Sb5 and CsV3Sb5, cited as consistent with the present result.","marker":"[30]"},{"why":"Describes the gradiometric micro-SQUID susceptometer design that the measurement relies on.","marker":"[31]"},{"why":"Supplies the mutual-inductance model connecting the measured ΔM to the penetration depth λ(T).","marker":"[32]"},{"why":"Quantum-oscillation study showing KV3Sb5 and RbV3Sb5 have more similar normal-state fermiology to each other than to CsV3Sb5, supporting the paper's interpretation of the superconducting differences.","marker":"[34]"}],"fun_headline_variants":["SQUID scans: all three Kagome superconductors have nodeless gaps","Direct penetration depth comparison finds full gaps in Kagome family","KV3Sb5 and RbV3Sb5 share gap structure, CsV3Sb5 differs","Nodeless gaps in all Kagome superconductors, but gaps differ","Penetration depth rules out nodal pairing across AV3Sb5 series"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["SQUID scans: all three Kagome superconductors have nodeless gaps","Direct penetration depth comparison finds full gaps in Kagome family","KV3Sb5 and RbV3Sb5 share gap structure, CsV3Sb5 differs","Nodeless gaps in all Kagome superconductors, but gaps differ","Penetration depth rules out nodal pairing across AV3Sb5 series"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000236,"raw_usage":{"total_tokens":1525,"prompt_tokens":987,"completion_tokens":538,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":603,"completion_tokens_details":{"reasoning_tokens":437}},"tokens_in":603,"tokens_out":538,"duration_ms":5526,"temperature":1.0,"reasoning_tokens":437,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T23:47:06.500562+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":"Guguchia, C","cited_arxiv_id":null,"evidence_quote":"Supplies the prior muon-spin-rotation reports of nodal superconductivity in KV3Sb5 and RbV3Sb5 that this paper directly contradicts."},{"cited_title":"Prozorov and R","cited_arxiv_id":null,"evidence_quote":"Provides the theoretical basis for relating the temperature dependence of the penetration depth to nodal versus fully gapped gap structures."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Prior penetration-depth study of CsV3Sb5 reporting nodeless superconductivity; used for comparison and for the sensitivity of fitted gap values to temperature cutoff."},{"cited_title":"Roppongi, K","cited_arxiv_id":null,"evidence_quote":"Prior bulk penetration-depth study of CsV3Sb5 reporting anisotropic s-wave pairing; used for comparison and for the sensitivity of fitted gap values to temperature cutoff."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Point-contact spectroscopy study indicating fully gapped superconductivity in KV3Sb5 and CsV3Sb5, cited as consistent with the present result."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Describes the gradiometric micro-SQUID susceptometer design that the measurement relies on."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the mutual-inductance model connecting the measured ΔM to the penetration depth λ(T)."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Quantum-oscillation study showing KV3Sb5 and RbV3Sb5 have more similar normal-state fermiology to each other than to CsV3Sb5, supporting the paper's interpretation of the superconducting differences."}],"review_version":1}