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REVIEW 3 major objections 6 minor 58 references

Ultralow-temperature heat transport evidence for residual density of states in the superconducting state of CsV3Sb5

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Pith's one-line read Ultralow-temperature heat transport and STM data indicate residual zero-energy states inside the superconducting gap of CsV3Sb5.

desk verdict Solid heat-transport evidence for residual DOS in CsV3Sb5, but the CDW-causality claim overreaches the single-doping comparison. read the letter →

arxiv 2412.18446 v1 pith:6VE3KYNS submitted 2024-12-24 cond-mat.supr-con cond-mat.mtrl-scicond-mat.str-el

C. C. Zhao , L. S. Wang , W. Xia , Q. W. Yin , H. B. Deng , G. W. Liu , J. J. Liu , X. Zhang
show 12 more authors
J. M. Ni Y. Y. Huang C. P. Tu Z. C. Tao Z. J. Tu C. S. Gong Z. W. Wang H. C. Lei Y. F. Guo X. F. Yang J. X. Yin S. Y. Li
This is my paper · ORCID
classification cond-mat.supr-concond-mat.mtrl-scicond-mat.str-el MSC 82D55 PACS 74.25.F74.70.Ad
keywords CsV3Sb5kagomesuperconductorthermalconductivityresidualdensityofstateschargewavenodalsuperconductivityFermiarczero-biasconductance
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

The paper reports ultralow-temperature thermal conductivity and scanning tunnelling measurements that point to unpaired electronic states at zero energy inside the superconducting gap of the kagome superconductor CsV3Sb5. In zero magnetic field, five crystals all show a finite residual linear term κ0/T in the thermal conductivity, and the STM spectrum at 90 mK shows non-zero conductance at zero bias. In the Ta-doped compound Cs(V0.86Ta0.14)3Sb5, where the charge-density-wave order is absent, no such residual term appears. The authors conclude that the CDW order is essential for the residual density of states, and that a nodal s-wave gap or residual Fermi arcs may be its origin.

What carries the argument

The central probe is the residual linear term κ0/T of the thermal conductivity, obtained by fitting κ/T = a + $bT^{{α-1}}$ below 0.5 K. In a fully gapped superconductor this term vanishes as T→0 because no fermionic quasiparticles remain to carry heat; a finite value signals quasiparticle states at zero energy. The same samples are compared with the CDW-free Ta-doped material, and the STM dI/dV zero-bias conductance provides a second, local probe of zero-energy DOS. This combination turns an extrapolated heat-transport intercept into a statement about the superconducting gap structure.

What would settle it

Measure κ0/T of CsV3Sb5 under hydrostatic pressure that suppresses the CDW while superconductivity survives; if a finite zero-field κ0/T persists once the CDW is gone, the claim that CDW order is essential would be disproved.

Watch

Extended reading notes

Core claim

The central claim is that the superconducting state of CsV3Sb5 hosts a residual density of states at zero energy rather than a fully gapped Fermi surface. The evidence is a finite κ0/T extrapolated from κ/T=a+$bT^{{α-1}}$ fits below 0.5 K in zero field, a rapid low-field rise of κ0/T that resembles nodal superconductors, and a non-zero zero-bias conductance in STM at an electronic temperature of 90 mK. By contrast, Cs(V0.86Ta0.14)3Sb5, which lacks CDW order, shows κ0/T ≈ 0 in zero field and a slow field dependence, consistent with nodeless superconductivity. The paper therefore argues that the CDW order is required for the residual DOS, and proposes a nodal s-wave gap without sign reversal or residual Fermi arcs from a pair-density-wave state as possible origins.

Load-bearing premise

The conclusion that CDW order causes the residual DOS rests on a single comparison: the Ta-doped crystal has no CDW and no residual DOS, while pristine CsV3Sb5 has both, with no control showing that Ta substitution itself does not remove the states through disorder or the higher transition temperature.

Editorial extensions

If this is right

  • The superconducting gap of CsV3Sb5 is not fully open: unpaired fermionic states exist at zero energy and conduct heat at the lowest temperatures.
  • The residual DOS is tied to the CDW order, because suppressing the CDW by Ta doping removes the residual linear term.
  • The field dependence of κ0/T supports either nodal quasiparticles or small gaps that are quickly suppressed by field.
  • A nodal s-wave gap without sign reversal, or residual Fermi arcs from pair-density-wave order, would both be consistent with the data.
  • The validation of the Wiedemann-Franz law in the normal state supports the reliability of the heat-transport measurement.

Reading between the lines

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

  • A decisive control would be to suppress the CDW continuously within CsV3Sb5 itself, e.g. by hydrostatic pressure, and check whether κ0/T vanishes with the CDW rather than because of chemical disorder from Ta substitution.
  • If residual Fermi arcs are the origin, κ0/T should show directional anisotropy relative to the CDW or pair-density-wave wavevectors in oriented crystals.
  • The residual DOS should also appear as a finite residual electronic specific-heat coefficient γ and in magnetic-penetration-depth measurements; a direct cross-check would strengthen the claim.
  • The disappearance of the residual DOS with doping could be mapped across a doping series; a smooth correlation with CDW strength, rather than a step at the doping level, would support the causal connection.
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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 / 6 minor

Summary. This manuscript reports ultralow-temperature thermal conductivity measurements on five CsV3Sb5 single crystals and one Ta-doped Cs(V0.86Ta0.14)3Sb5 crystal, along with STM spectroscopy on CsV3Sb5. The zero-field data show a finite residual linear term κ0/T for all five CsV3Sb5 samples, which the authors interpret as evidence for residual zero-energy density of states in the superconducting state. The Ta-doped compound shows no residual term, which the authors connect to the absence of CDW order. The paper proposes nodal s-wave pairing or residual Fermi arcs as possible origins and concludes that CDW order is essential for the residual DOS.

Significance. If the result is robust, this would be important experimental evidence for unpaired fermionic states at zero energy in a kagome superconductor, with implications for the interplay of CDW order and superconductivity. The strengths are the use of a well-established bulk probe, measurements on five nominally identical CsV3Sb5 crystals, validation of the normal-state thermal conductivity against the Wiedemann–Franz law, the observed field dependence of κ0/T showing a rapid low-field increase, and the independent STM measurement. The Ta-doped comparison is suggestive but not yet conclusive. The work would meaningfully constrain gap-structure models for AV3Sb5.

major comments (3)
  1. [§2, Eq. (1)] The fit κ/T = a + bT^(α−1) yields α values of 3.87, 3.85, 2.70, 3.28, and 3.19 for the five CsV3Sb5 samples, i.e., four of five outside the conventional phonon boundary-scattering range of 2–3. The paper attributes this to thermally excited quasiparticles, but that attribution makes the electronic and phonon contributions degenerate in the fit, so the extrapolated intercept a can be strongly correlated with the anomalous power law. To support the central claim of a finite κ0/T, the authors should show fit residuals, perform fits with α fixed in the conventional range, and/or report the covariance between a and α. Without such robustness checks, the finite intercept may be a fitting artifact.
  2. [§4, Fig. 4] The conclusion that CDW order is essential for the residual DOS rests on a single comparison with Cs(V0.86Ta0.14)3Sb5, which has a higher Tc (4.9 K vs 3.0 K) and additional disorder from Ta substitution. These differences could independently suppress the residual DOS. The citation of STM results on CsV2.73Ti0.27Sb5 partially addresses uniqueness, but no thermal-transport control is provided. The authors should either temper the causal claim or provide additional evidence, such as pressure dependence or a second doping series with different disorder characteristics.
  3. [§2, Fig. 2(a)] The five nominally identical CsV3Sb5 crystals yield zero-field κ0/T values from 0.14 to 0.42 mW K−2 cm−1, a factor-of-three variation. Only sample #1 is normalized to its normal-state Wiedemann–Franz value (4.54 mW K−2 cm−1), so the fractional residual term for the other four samples is unknown. This spread is unexplained and could indicate fitting instability, sample-dependent normal-state inclusions, or other extrinsic contributions. The authors should report residual resistivity ρ0 for all samples or otherwise address the sample dependence, because the claim of an intrinsic residual DOS implies some degree of sample independence.
minor comments (6)
  1. [§3] There is a typo in the sentence 'we conducte ultralow-temperature STM measurements'; it should be 'we conducted'.
  2. [Summary paragraph] The word 'resudual' should be 'residual' in the final paragraph of the main text.
  3. [§2] The phrase 'the Tc of CsV3Sb5 is quiet low' should be 'quite low'.
  4. [§2] The fit is described as being performed 'below 0.5 K', but the actual number of points, the lower bound of the fit range, and the fit residuals are not shown; please specify these details for reproducibility.
  5. [References] Reference [43] is an arXiv preprint; please add a peer-reviewed reference if one is available, since this ARPES result is used to support the nodal gap discussion.
  6. [§3, Fig. 3(c)] The STM spectrum is presented as a single spatially averaged curve without quantification of the zero-bias conductance relative to the normal-state conductance or an error estimate; a quantitative statement or a clear qualifier would help.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the residual-DOS claim rests on direct thermal-conductivity and STM measurements, not on self-citation or definition.

full rationale

The central claim is that a finite zero-field residual linear term κ0/T indicates residual DOS in superconducting CsV3Sb5. This is a direct empirical inference from measured heat transport, using the standard fit κ/T = a + bT^(α−1); the intercept is not defined in terms of the residual-DOS conclusion. The paper validates its measurement against the normal-state Wiedemann–Franz law and compares against established nodal and fully gapped benchmarks, and it independently corroborates the residual DOS with STM zero-bias conductance. The Ta-doped comparison is an additional independent control: the authors directly measure that Cs(V0.86Ta0.14)3Sb5 lacks CDW and has zero κ0/T. Although the paper cites prior work by overlapping authors (e.g., refs. 19, 34, 35) for CDW suppression and for residual-Fermi-arc scenarios, those citations are not load-bearing for the existence of the residual DOS, which is established by the present measurements. Concerns about free-α fitting and sample-to-sample scatter are robustness or correctness issues, not circularity, because they do not make the conclusion equivalent to the input by construction. No load-bearing step reduces to its own inputs, and no fitted parameter is renamed as a prediction. Score 0.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

No new theoretical entities are introduced. The quantitative claims rest on fitted intercepts and standard heat-transport phenomenology. The causal role of the CDW is an inference from one Ta-doped composition, which is the weakest load-bearing assumption.

free parameters (3)
  • Residual linear term κ0/T of CsV3Sb5 = 0.14, 0.15, 0.22, 0.35, 0.42 mW K^-2 cm^-1 for samples #1-#5
    Fitted intercept a in κ/T = a + bT^(α-1); the finite value is the central evidence for residual DOS. The factor-of-three spread across samples is not discussed.
  • Fitting power α for CsV3Sb5 = 3.87, 3.85, 2.70, 3.28, 3.19
    Fitted exponent for the phonon term; values >3 are outside the usual 2-3 range and are attributed to thermally excited electrons, indicating model imperfection.
  • Residual linear term κ0/T of Ta-doped Cs(V0.86Ta0.14)3Sb5 = -0.4 ± 4 µW K^-2 cm^-1 (essentially zero)
    Null comparison used to argue that absence of CDW removes residual DOS; the error bar is comparable to the measured value.
assumptions (4)
  • domain assumption A finite κ0/T at zero field in a superconductor implies residual zero-energy quasiparticle DOS.
    Standard heat-transport phenomenology (Refs [48-50]) used to interpret the measured intercept.
  • domain assumption The fitting form κ/T = a + bT^(α-1) correctly separates electronic and phonon contributions below 0.5 K.
    Model from Refs [49,50]; the anomalous α>3 requires the additional assumption of thermally excited electrons.
  • domain assumption The normal-state Wiedemann-Franz law applies, so L0/ρ0 equals the normal-state electronic thermal conductivity.
    The paper verifies this at Hc2 and uses it to calibrate the measurement.
  • ad hoc to paper Ta substitution suppresses the CDW without independently changing the residual DOS through disorder, carrier density, or Tc.
    The CDW-essential conclusion depends on this single-composition comparison; no control for other parameters is provided.

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Pith. "Pith review of Ultralow-temperature heat transport evidence for residual density of states in the superconducting state of CsV3Sb5." pith.science (2026). https://pith.science/paper/6VE3KYNS

@misc{pith2026241218446,
  author       = {Pith},
  title        = {Pith review of: Ultralow-temperature heat transport evidence for residual density of states in the superconducting state of CsV3Sb5},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6VE3KYNS}},
  note         = {Machine review of arXiv:2412.18446}
}
abstract

The V-based kagome superconductors $A$V$_3$Sb$_5$ ($A$ = K, Rb, and Cs) host charge density wave (CDW) and a topological nontrivial band structure, thereby provide a great platform to study the interplay of superconductivity (SC), CDW, frustration, and topology. Here, we report ultralow-temperature thermal conductivity measurements on CsV$_3$Sb$_5$ and Ta-doped Cs(V$_{0.86}$Ta$_{0.14}$)$_3$Sb$_5$ and scanning tunneling microscopy (STM) measurements on CsV$_3$Sb$_5$. The finite residual linear term of thermal conductivity at zero magnetic field suggests the existence of a residual density of states (DOS) in the superconducting state of CsV$_3$Sb$_5$. This is supported by the observation of non-zero conductance at zero bias in STM spectrum at an electronic temperature of 90 mK. However, in Cs(V$_{0.86}$Ta$_{0.14}$)$_3$Sb$_5$, which does not have CDW order, there is no evidence for residual DOS. These results show the importance of CDW order for the residual DOS, and a nodal $s$-wave gap or residual Fermi arc may be the origin of the residual DOS in such an unusual multiband kagome superconductor, CsV$_3$Sb$_5$.

Figures

Figures reproduced from arXiv: 2412.18446 by the authors.

Figure 1
Figure 1. FIG. 1. (a) Temperature dependence of the normalized dc magnetization for CsV [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. (a) Temperature dependence of the in-plane thermal [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 4
Figure 4. FIG. 4. (a) Temperature dependence of the in-plane thermal [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

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Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.