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REVIEW 2 major objections 5 minor 52 references

Impact of charge-density-wave pattern on the superconducting gap in V-based kagome superconductors

T0 review · 2 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read K/RbV3Sb5 have fully gapped, nearly isotropic s-wave pairing, unlike CsV3Sb5, and the CDW stacking pattern explains the difference.

desk verdict New penetration-depth data show K/RbV3Sb5 are fully gapped and isotropic, but the CDW-stacking explanation trips on its own numbers for Rb. read the letter →

arxiv 2507.03266 v1 pith:RWS5GFIN submitted 2025-07-04 cond-mat.supr-con

T. Nagashima , K. Ishihara , Y. Yamakawa , F. Chen , K. Imamura , M. Roppongi , R. Grasset , M. Konczykowski
show 7 more authors
B. R. Ortiz A. C. Salinas S. D. Wilson R. Tazai H. Kontani K. Hashimoto T. Shibauchi
This is my paper · ORCID
classification cond-mat.supr-con
keywords kagomesuperconductorsAV3Sb5chargedensitywavesuperconductinggapanisotropypenetrationdepthelectronirradiationbondorderfluctuationsvanHovesingularity
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

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.

What carries the argument

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.

What would settle it

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.

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Extended reading notes

Core claim

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 $T_c$.

Load-bearing premise

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.

Editorial extensions

If this is right

  • 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.

Reading between the lines

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

  • 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.
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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

2 major / 5 minor

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.

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 (2)
  1. [Theoretical analysis, around Fig. 4j] 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.
  2. [Theoretical analysis, paragraph after Fig. 4j] 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.
minor comments (5)
  1. [Abstract] 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.
  2. [Figure 2 caption] In the caption of Fig. 2, "filled brue circles" should read "filled blue circles."
  3. [Text around Fig. 4j] The text uses "greaterorsimilar" for the ≳ symbol; please ensure proper typesetting in the final version.
  4. [Fig. 1f and related text] 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.
  5. [Supplementary Information] 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.

Circularity Check

1 steps flagged · score 4.0 of 10

The measured K/Rb versus Cs gap dichotomy is new and independent, but the causal attribution to CDW stacking is carried by same-group bond-order-fluctuation theory and a hand-set δt that, on the paper's own numbers, fails to remove Rb's vHS pockets.

  1. self citation load bearing [Main text near end of theory section, after Fig. 4j, 'Considering the reported differences in the CDW patterns...']
    "Theoretically, the dxz-orbital vHS states play an essential role in the quantum fluctuations and SC [4, 5]. Therefore, although the stacking pattern of BO in our samples is not experimentally confirmed, we expect substantial BO fluctuations derived by the dxz-orbital vHSs and associated electron correlations only in CsV3Sb5, which induce an anisotropic gap structure in CsV3Sb5 in contrast to an isotropic gap in K/RbV3Sb5."

    The central causal premise—that surviving dxz-orbital vHS pockets generate bond-order fluctuations that produce an anisotropic s-wave gap and enhanced Tc—is cited to Refs [4,5], whose authors (Tazai, Yamakawa, Kontani) are coauthors here. That prior theory was developed to account for the same group's earlier CsV3Sb5 penetration-depth data (Ref [37], overlapping authorship), and is now re-invoked to 'explain' that same compound's anisotropy. The K/Rb side adds a new empirical contrast, so the central claim is not definitionally forced; however, the causal explanation is load-bearing self-citation rather than an independent, externally checked derivation.

full rationale

The experimental content—Meissner-state penetration depth, electron-irradiation impurity control, and the resulting n>2, large Δ0/kBTc for K/Rb versus the smaller Δ0/kBTc for Cs—is self-contained; no SC gap data are used to fit the theoretical parameters. There is no fitted-input-called-prediction or self-definitional reduction. The main circularity concern is the explanatory layer: the paper attributes the gap-anisotropy difference to CDW stacking via the bond-order-fluctuation mechanism of Refs [4,5] by the same Tazai/Kontani group, a mechanism previously constructed to explain the same group's CsV3Sb5 data. That is a genuine self-citation load-bearing step, though the new K/Rb comparison gives the claim independent observational content. In addition, an internal-support gap weakens the theoretical branch: with the hand-set |δt|=0.015 eV, 4|δt|=0.06 eV while the paper's own first-principles |EvHS| values are 0.06 (K), 0.08 (Rb), and 0.10 (Cs) eV; the stated pocket-removal condition 4|δt| ≳ |EvHS| therefore fails for RbV3Sb5, the very compound whose isotropic gap the mechanism is invoked to explain. This is an internal consistency problem rather than a circularity, but it means the CDW-pattern explanation is not currently established for the full K/Rb pair. Overall circularity is moderate: the data are not circular, while the theoretical attribution is substantially self-referential and parameter-sensitive.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

The theoretical framework is assembled from parameters and premises inherited from prior coauthor work and external literature. No new particles or entities are introduced. The free parameters are the model hoppings and δt, which control the van Hove pocket survival and hence the central theoretical narrative. The most fragile assumption is the unmeasured CDW stacking assignment combined with the EvHS mismatch that makes the TrH-TrH pocket-removal argument fail for RbV3Sb5.

free parameters (4)
  • Bond-order hopping modulation |δt| = 0.015 eV
    Introduced by hand to model the CDW state; the vHS splitting and Fermi-pocket survival depend directly on |δt| relative to |EvHS|, and the paper's central theoretical conclusion is sensitive to this ratio.
  • Model van Hove energy |EvHS| in the single-orbital model = ≈ 0.05 eV (model); 0.06, 0.08, 0.10 eV for K, Rb, Cs from first principles
    The condition 4|δt| ≳ |EvHS| is satisfied in the model band structure but is not satisfied for Rb and Cs when first-principles EvHS values are used, creating a mismatch that underpins the theoretical weakness.
  • Kagome lattice hopping parameters (t, tyz, txz-yz, t', t_perp_yz, onsite dyz) = t = 0.5, tyz = 1.0, txz-yz = ±0.05, t' = -0.08, t_perp_yz = 0.02, onsite dyz = 2.3 (eV)
    Taken from prior band-structure fitting by the coauthors (Ref. [49]); not fitted to the SC gap data but load-bearing for the band structure and DOS conclusions.
  • Electron number N = 17.8 for the 24-site model; 11.6 for the single-orbital model
    Set to match the Fermi surface from first principles; the existence and size of the Fermi pockets depend on this choice.
assumptions (4)
  • domain assumption The CDW stacking patterns are TrH-TrH (π-shifted) in K/Rb and TrH-SoD (or 2x2x4 with SoD layers) in Cs.
    Cited from the external literature and not directly measured on the present samples; the authors explicitly write that 'the stacking pattern of BO in our samples is not experimentally confirmed'.
  • domain assumption The dxz-orbital van Hove singularities and bond-order fluctuations dominate the SC pairing and determine the gap anisotropy.
    This is the central premise of the theory from the coauthors' earlier papers (Refs. [4,5]); the new manuscript applies it to explain the measured gap anisotropy difference.
  • domain assumption Low-temperature Meissner-state Δλ(T) is governed by quasiparticle excitations and can be modeled by power-law and single-gap exponential forms.
    Standard for penetration depth analysis, but the single-gap exponential form with a single minimum gap Δ0 is a simplification that affects the extracted anisotropy value.
  • domain assumption Electron irradiation creates nonmagnetic point defects without changing the lattice constant or carrier density.
    The authors state this as the basis for using irradiation to study impurity effects; it is a common assumption for high-energy electron irradiation.

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Cite this review

Pith. "Pith review of Impact of charge-density-wave pattern on the superconducting gap in V-based kagome superconductors." pith.science (2026). https://pith.science/paper/RWS5GFIN

@misc{pith2026250703266,
  author       = {Pith},
  title        = {Pith review of: Impact of charge-density-wave pattern on the superconducting gap in V-based kagome superconductors},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RWS5GFIN}},
  note         = {Machine review of arXiv:2507.03266}
}
abstract

Kagome metals $A$V$_3$Sb$_5$ ($A=$ K, Rb, Cs) provide a compelling platform to explore the interplay between superconductivity (SC) and charge-density-wave (CDW) orders. While distinct CDW orders have been identified in K/RbV$_3$Sb$_5$ versus CsV$_3$Sb$_5$, their influence on the SC order parameter remains unresolved. Here, we investigate low-energy quasiparticle excitations in $A$V$_3$Sb$_5$, uncovering a striking difference in SC gap anisotropy: K/RbV$_3$Sb$_5$ exhibit fully gapped, nearly isotropic $s$-wave states, in contrast to the strongly anisotropic SC gap in CsV$_3$Sb$_5$. Contrary to previous vortex-state studies suggesting nodal SC in K/RbV$_3$Sb$_5$, our Meissner-state measurements in high-quality crystals demonstrate fully gapped states with reduced anisotropy compared to CsV$_3$Sb$_5$. Impurity scattering introduced via electron irradiation in K/RbV$_3$Sb$_5$ has a minimal impact on low-energy excitations, and it induces an increase in the SC transition temperature $T_{\rm c}$, consistent with more isotropic $s$-wave SC competing with CDW order. Our theoretical analysis attributes the observed SC gap anisotropy differences to distinct CDW modulation patterns: the star-of-David structure unique to CsV$_3$Sb$_5$ preserves van Hove singularities near the Fermi level, promoting anisotropic $s$-wave SC with enhanced $T_{\rm c}$ via bond-order fluctuations. These findings establish a systematic framework for understanding the interplay between SC and CDW orders in $A$V$_3$Sb$_5$, driven by electron correlations.

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