{"id":"32d8a922-9867-4939-85fb-48c49ebb10ad","arxiv_id":"2507.03266","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"K/RbV3Sb5 show fully gapped, nearly isotropic s-wave superconductivity, while CsV3Sb5 has a strongly anisotropic gap; the difference is attributed to distinct charge-density-wave stacking patterns.","lead":"The paper measures how electric fields penetrate three kagome superconductors and finds that potassium and rubidium versions have a simple, uniform superconducting gap while the cesium version has an uneven one. It links this difference to the specific pattern of charge order in each crystal, which could explain why the cesium compound superconducts at a higher temperature.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The paper's own parameters do not satisfy the stated pocket-removal condition for RbV3Sb5, so the proposed CDW mechanism does not explain its isotropic gap.","rationale":"The reader's weakest assumption correctly identifies the quantitative failure of the 4|δt| versus |EvHS| criterion for Rb. Rechecking the numbers in the main text confirms the inconsistency: with |δt|=0.015 eV and |EvHS|=0.08 eV for Rb, the condition does not hold. Because the entire explanation for the K/Rb isotropic gap rests on removing these vHS pockets, this is the most load-bearing weakness in the theoretical part of the paper. The experimental observation of a fully gapped, impurity-robust state in K/Rb is not challenged by this concern; the issue is specifically the attribution of that observation to the TrH-TrH CDW pattern. The paper's own acknowledgment that the stacking is not experimentally confirmed on these samples widens, rather than closes, the gap between mechanism and measurement. A first-principles determination of δt in the CDW state would settle the concern: if δt is large enough, the mechanism survives; if not, the framework is not supported for Rb and the verdict should remain conditional pending either a revised criterion or revised parameters. Since this is the same concern identified by the reader, the recommended verdict is unchanged: CONDITIONAL.","tokens_in":15274,"tokens_out":9125,"duration_ms":109233,"concrete_test":"Extract the dxz-orbital hopping modulation δt from a first-principles band-structure calculation of the CDW-distorted RbV3Sb5 with the π-shifted TrH-TrH stacking, and check whether 4|δt| ≥ |EvHS| ≈ 0.08 eV is satisfied. In the same calculation, recompute the folded Fermi surface and dxz DOS at E_F; if small pockets survive or no hybridization gap opens at Γ, the proposed pocket-removal mechanism fails for Rb and the paper's central CDW-pattern explanation is not established.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central theoretical claim is that the TrH-TrH bond-order stacking in K/RbV3Sb5 removes the dxz-orbital van Hove Fermi pockets, leaving an isotropic s-wave gap, while the TrH-SoD stacking in CsV3Sb5 preserves one pocket and yields anisotropic s-wave pairing promoted by bond-order fluctuations. The removal step is explicitly conditioned on 4|δt| ≳ |EvHS| in the main-text discussion of Fig. 4g. The paper uses |δt| = 0.015 eV, so 4|δt| = 0.06 eV. The paper's quoted first-principles |EvHS| values are 0.06 eV (K), 0.08 eV (Rb), and 0.10 eV (Cs). Thus the criterion is only marginally satisfied for K (0.06 ≥ 0.06) and fails for Rb (0.06 < 0.08). Since RbV3Sb5 is one of the two compounds whose isotropic gap is the headline experimental result, the stated mechanism is not internally consistent for exactly the case it is invoked to explain. The paper also acknowledges that the CDW stacking in its measured samples is not experimentally confirmed, so the argument cannot fall back on an alternative stacking without additional data. The issue is quantitative and potentially fixable if first-principles δt in Rb is larger than the illustrative 0.015 eV, but as written the explanation for Rb is unsupported.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper reports magnetic penetration depth measurements on K/RbV3Sb5 using the tunnel diode oscillator technique in the Meissner state, combined with controlled electron irradiation, and compares the results with a previous study of CsV3Sb5. The authors find that K/RbV3Sb5 exhibit fully gapped, nearly isotropic s-wave superconductivity, with minimal change in the penetration depth upon irradiation and an increase in Tc with disorder, whereas CsV3Sb5 shows a strongly anisotropic s-wave gap that is suppressed by impurities. They attribute this difference to distinct CDW stacking patterns: the TrH-TrH stacking in K/Rb is argued to remove the dxz-orbital van Hove Fermi pockets, while the TrH-SoD stacking in Cs preserves one pocket, leading to anisotropic s-wave pairing and enhanced Tc via bond-order fluctuations. The paper claims to establish a systematic SC-CDW framework across the AV3Sb5 family.","tokens_in":15591,"tokens_out":5710,"duration_ms":63780,"significance":"The experimental findings are significant and timely: they provide bulk, Meissner-state evidence for fully gapped isotropic s-wave pairing in K/RbV3Sb5, contradicting earlier nodal-gap suggestions, and they systematically compare the gap anisotropy across the entire AV3Sb5 family using a phase-sensitive impurity-dependence approach. The observation that Tc increases with electron irradiation in K/Rb, opposite to Cs, is a valuable constraint on the SC-CDW competition. If the theoretical attribution is correct, the paper would establish a direct link between CDW stacking patterns and the superconducting gap structure. The theoretical model is not fitted to the SC data, and the experimental analysis is careful, including multiple fitting forms and error estimates. However, the theoretical explanation currently suffers from a quantitative inconsistency for RbV3Sb5, which weakens the central claim as written.","major_comments":[{"comment":"The pocket-removal condition for the TrH-TrH state is stated as 4|δt| ≳ |EvHS|, and the text sets |δt| = 0.015 eV and quotes |EvHS| = 0.06, 0.08, and 0.10 eV for K, Rb, and Cs, respectively. With these values, 4|δt| = 0.06 eV, so the condition is only marginally satisfied for K (0.06 eV ≥ 0.06 eV) and fails for Rb (0.06 eV < 0.08 eV). Consequently, the model does not predict the disappearance of the two dxz-orbital Fermi pockets in RbV3Sb5, which is one of the two compounds whose isotropic gap is a headline experimental result. The central theoretical attribution for Rb is therefore not supported by the paper's own parameters; the authors should either provide material-specific values of δt (e.g., from first-principles calculations) or revise the mechanism.","section":"Theoretical analysis, around Fig. 4j"},{"comment":"The authors explicitly state that \"the stacking pattern of BO in our samples is not experimentally confirmed.\" Since the proposed explanation of the gap isotropy in K/RbV3Sb5 relies on the TrH-TrH stacking and the gap anisotropy in CsV3Sb5 on the TrH-SoD stacking, the connection between the measured gap structure and the assumed CDW pattern is conditional on an unverified assumption. The paper should either provide evidence for the stacking in the measured crystals or discuss how robust the conclusions are to alternative stacking patterns.","section":"Theoretical analysis, paragraph after Fig. 4j"}],"minor_comments":[{"comment":"The abstract mentions \"previous vortex-state studies suggesting nodal SC in K/RbV3Sb5,\" but the main text only cites a µSR study (Ref. [44]) for this; please clarify the relevant literature or adjust the wording.","section":"Abstract"},{"comment":"In the caption of Fig. 2, \"filled brue circles\" should read \"filled blue circles.\"","section":"Figure 2 caption"},{"comment":"The text uses \"greaterorsimilar\" for the ≳ symbol; please ensure proper typesetting in the final version.","section":"Text around Fig. 4j"},{"comment":"The actual values of Δ0/kBTc and their error bars are shown in Fig. 1f but are not quoted in the text; including representative values would make the quantitative claim easier to assess.","section":"Fig. 1f and related text"},{"comment":"The Supplementary Information, which is said to discuss the discrepancy with the µSR study, is not included in the arXiv submission; please ensure it is available for review or summarize the discussion in the main text.","section":"Supplementary Information"}],"recommendation":"major_revision","confidential_remarks":"The core experimental result is strong and likely publishable in a high-quality journal, but the theoretical explanation for RbV3Sb5 is internally inconsistent with the stated model parameters. The issue is fixable by performing first-principles estimates of the bond-order parameter δt for RbV3Sb5, or by reframing the claim to acknowledge the marginal parameter regime. The paper would also benefit from addressing the unverified stacking assumption more prominently. These are surmountable concerns, so I do not recommend rejection, but a major revision is appropriate."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"First, the experiment. The Meissner-state penetration depth data for pristine and electron-irradiated K/RbV3Sb5 are new and directly contradict the muSR-based nodal-gap claim. The power-law exponents n>2, exponential low-T behavior, and irradiation insensitivity all point to a fully gapped, sign-preserving, nearly isotropic s-wave state. The contrast with CsV3Sb5, where irradiation flattens the gap and suppresses Tc, is clean and internally consistent. That experimental part should stand.\n\nThe theoretical synthesis is more fragile. The claim is that TrH-TrH stacking in K/Rb removes the dxz van Hove pockets, while TrH-SoD in Cs preserves one, giving anisotropic s-wave pairing and higher Tc. The pocket removal requires 4|δt| ≳ |EvHS|. With |δt| = 0.015 eV, 4|δt| = 0.06 eV. The paper quotes EvHS ≈ 0.06, 0.08, 0.10 eV for K, Rb, Cs. So the condition barely holds for K and fails for Rb. That means the stated mechanism does not predict pocket removal in Rb, one of the two compounds the headline result is about. The authors also admit the stacking pattern in their measured samples is not experimentally confirmed, so they cannot fall back on a different stacking without new data.\n\nIs this fatal? No. The experimental result is independent of the theory. Even if the mechanism is wrong or incomplete for Rb, the fully gapped isotropic s-wave finding still stands. But as written, the explanation for Rb is unsupported. This is a quantitative inconsistency that a referee should press on. A sensitivity analysis of δt, or first-principles δt for Rb, could fix it.\n\nThe citation pattern is fine. The model parameters come from the authors' earlier work, which is legitimate. They also cite competing literature. The paper is honest about the unconfirmed stacking.\n\nBottom line: the experiment deserves serious peer review, and the paper should not be desk-rejected. The theory section needs work, but the data are valuable.","headline":"New penetration-depth data show K/RbV3Sb5 are fully gapped and isotropic, but the CDW-stacking explanation trips on its own numbers for Rb.","tokens_in":16234,"tokens_out":3487,"would_cite":true,"duration_ms":37136,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"K/RbV3Sb5 have fully gapped, nearly isotropic s-wave pairing, unlike CsV3Sb5, and the CDW stacking pattern explains the difference.","keywords":["kagome superconductors","AV3Sb5","charge density wave","superconducting gap anisotropy","penetration depth","electron irradiation","bond order fluctuations","van Hove singularity"],"falsifier":"Measure the low-temperature Fermi surface of clean RbV3Sb5 by angle-resolved photoemission with enough resolution to see the folded zone-center pockets: if small $d_{xz}$-orbital pockets are present, the TrH-TrH pocket-removal mechanism that is supposed to make the gap isotropic is not operating.","tokens_in":1916,"feed_emoji":"⚛️","tokens_out":4857,"duration_ms":151774,"temperature":0.7,"pith_summary":"K/RbV3Sb5 and CsV3Sb5 are often treated as close relatives, but this paper finds a sharp difference in their superconducting order: K/RbV3Sb5 show a fully gapped, nearly isotropic $s$-wave state, while CsV3Sb5 shows a strongly anisotropic gap. The authors argue this is not a sample-quality artefact; instead, the different three-dimensional stacking of the charge-density-wave (CDW) bond order reshapes the electronic band structure. The tri-hexagonal stacking in K/Rb opens a gap that removes the small $d_{xz}$-orbital van Hove pockets, whereas the star-of-David-containing stacking in Cs keeps those pockets, feeding bond-order fluctuations that make pairing anisotropic and raise $T_c$. If correct, this gives the AV3Sb5 family a single microscopic framework linking CDW pattern to superconducting gap symmetry, and it contradicts an earlier muon-spin-rotation report of nodal gaps in K/Rb.","feed_headline":"CDW stacking decides kagome gap anisotropy","feed_subtitle":"K/RbV3Sb5 are fully gapped and nearly isotropic; CsV3Sb5 is strongly anisotropic, same family, different stacking.","key_machinery":"The load-bearing object is the $d_{xz}$-orbital kagome-lattice band in the $2\\times2\\times2$ CDW state, folded so the three van Hove points move to the zone center $\\Gamma$. In-plane hopping is modulated by $\\delta t$, with $\\delta t>0$ for the tri-hexagonal (TrH) bond order and $\\delta t<0$ for the star-of-David (SoD) bond order; the vertical stacking of these patterns decides the low-energy spectrum. The identity carrying the argument is the condition $4|\\delta t| \\gtrsim |E_{\\rm vHS}|$: when it holds, the TrH-TrH stacking opens a hybridization gap around $\\Gamma$ and removes the $d_{xz}$ Fermi pockets, while a TrH-SoD stacking leaves one pocket alive. The paper uses a three-dimensional $(d_{xz}, d_{yz})$ kagome model to show that pocket survival tracks the stacking, and connects the surviving pockets to bond-order fluctuations that produce anisotropic $s$-wave pairing.","core_discovery":"The central discovery is that the superconducting order parameter in KV3Sb5 and RbV3Sb5 is an isotropic, sign-preserving $s$-wave gap, established by Meissner-state penetration depth measurements showing exponential low-temperature behavior with $n > 2$ and by irradiation studies in which low-energy excitations stay almost unchanged. In CsV3Sb5 the same measurement protocol yields a strongly anisotropic gap that becomes more isotropic with irradiation. The paper attributes this contrast to the CDW bond-order stacking: a $\\pi$-shifted tri-hexagonal (TrH-TrH) pattern in K/Rb reconstructs the $d_{xz}$-orbital band so that the three van Hove points merge at the folded $\\Gamma$ point and, under hybridization, the small Fermi pockets disappear; the TrH-SoD pattern in Cs keeps one such pocket, and the associated bond-order fluctuations drive anisotropic $s$-wave pairing with a higher $T_c$.","pith_inferences":["The paper's stated parameters ($|\\delta t|=0.015$ eV and $|E_{\\rm vHS}|\\approx0.08$ eV for Rb) do not satisfy its own pocket-removal condition $4|\\delta t| \\gtrsim |E_{\\rm vHS}|$ for Rb, so the isotropic-gap explanation for Rb currently rests on a premise the numbers do not clearly support; low-temperature ARPES on RbV3Sb5 would test it directly.","If the stacking mechanism is right, the same logic predicts that any AV3Sb5 variant whose CDW stacking develops a star-of-David component should show anisotropic gap and enhanced Tc, a testable prediction the paper does not explicitly state.","The irradiation-induced Tc increase in K/Rb could be converted into a quantitative measure of SC-CDW competition strength, for example by fitting the slope $dT_c/d\\rho_0$ to a model with a single competing-order coupling, giving a pressure-free way to compare competition across the whole family."],"forward_implications":["KV3Sb5 and RbV3Sb5 have sign-preserving isotropic s-wave gaps, so ordinary nonmagnetic impurities should not suppress their Tc, consistent with the observed Tc increase on irradiation.","The charge-density-wave order competes with superconductivity in K/Rb: irradiation that lowers TCDW raises Tc, so tuning CDW strength is a route to controlling Tc in this family.","In CsV3Sb5 the CDW stacking preserves the dxz-orbital van Hove pockets, and the resulting bond-order fluctuations are the reason its gap is anisotropic and its Tc is higher; removing the star-of-David layers should remove both effects.","The double-peaked superconducting dome in CsV3Sb5 under pressure or doping likely reflects a change in CDW stacking and bond-order fluctuation strength rather than a simple density-of-states effect."],"supporting_citations":[{"why":"Supplies the CsV3Sb5 penetration-depth and irradiation data used as the anisotropic-gap baseline, plus the two-band nodeless s-wave model this paper extends.","marker":"[37]"},{"why":"The earlier muon-spin-rotation report of nodal superconductivity in K/RbV3Sb5 that this paper's Meissner-state measurements contradict.","marker":"[44]"},{"why":"Establishes the different CDW stackings between K/Rb (TrH) and Cs (TrH with SoD) that the mechanism relies on.","marker":"[27]"},{"why":"Documents the structural evolution through CDW order that supports assigning TrH stacking to K/Rb and SoD-containing stacking to Cs.","marker":"[28]"},{"why":"Reports coexistence of trihexagonal and star-of-David motifs in the CDW, the basis for keeping a SoD layer in the Cs model.","marker":"[33]"},{"why":"Provides the bond-order-fluctuation theory connecting dxz-orbital van Hove singularities to anisotropic s-wave superconductivity.","marker":"[4]"},{"why":"Gives the three-dimensional (dxz, dyz) kagome lattice model used for the density-of-states calculations shown in the paper's main-text figure.","marker":"[49]"},{"why":"Recent ARPES observation of coexisting isotropic and anisotropic gaps in CsV3Sb5 that supports the two-band picture used for the anisotropic case.","marker":"[43]"}],"fun_headline_variants":["Kagome superconductors: CDW stacking sets gap shape","CDW pattern dictates superconducting gap in kagome metals","Isotropic vs anisotropic: CDW stacking shapes kagome gaps","Kagome gap anisotropy traced to CDW stacking pattern","Same family, different gaps: CDW stacking matters in kagome"],"cache_read_input_tokens":18176,"weakest_assumption_plain":"The explanation relies on the CDW pattern in K and Rb actually erasing the small electronic pockets tied to the van Hove points; with the paper's own numbers that erasure criterion is met for K but not for Rb, so if the pockets survive in Rb the isotropic-gap story for Rb loses its support.","fun_headline_variants_meta":{"raw":{"variants":["Kagome superconductors: CDW stacking sets gap shape","CDW pattern dictates superconducting gap in kagome metals","Isotropic vs anisotropic: CDW stacking shapes kagome gaps","Kagome gap anisotropy traced to CDW stacking pattern","Same family, different gaps: CDW stacking matters in kagome"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000563,"raw_usage":{"total_tokens":2743,"prompt_tokens":1087,"completion_tokens":1656,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":703,"completion_tokens_details":{"reasoning_tokens":1571}},"tokens_in":703,"tokens_out":1656,"duration_ms":10529,"temperature":1.0,"reasoning_tokens":1571,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T20:14:47.834047+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the low-temperature Fermi surface of clean RbV3Sb5 by angle-resolved photoemission with enough resolution to see the folded zone-center pockets: if small $d_{xz}$-orbital pockets are present, the TrH-TrH pocket-removal mechanism that is supposed to make the gap isotropic is not operating.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"The earlier muon-spin-rotation report of nodal superconductivity in K/RbV3Sb5 that this paper's Meissner-state measurements contradict."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Establishes the different CDW stackings between K/Rb (TrH) and Cs (TrH with SoD) that the mechanism relies on."},{"cited_title":"& Kontani, H","cited_arxiv_id":null,"evidence_quote":"Provides the bond-order-fluctuation theory connecting dxz-orbital van Hove singularities to anisotropic s-wave superconductivity."}],"review_version":1}