{"id":"1e9e0211-8823-487d-8be1-d7b1ac750bc3","arxiv_id":"2412.18446","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"A finite residual heat-conduction term and non-zero zero-bias tunneling conductance show residual density of states in superconducting CsV3Sb5, absent when CDW order is suppressed by Ta doping.","lead":"Researchers measured heat conduction and tunneling spectra in the kagome superconductor CsV3Sb5 at temperatures near absolute zero. They found leftover conducting states inside the superconducting gap, and the absence of these states in a Ta-doped version ties the effect to the material's charge density wave order.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The zero-field κ0/T values are extracted with α free and anomalously >3 for four of five CsV3Sb5 crystals, and scatter by a factor of 3; without fixed-α or per-sample normal-state normalization, the residual DOS claim may be a fitting artifact.","rationale":"The reader's weakest assumption was the causal inference from the single Ta-doped comparison to CDW order. I agree that comparison is under-controlled. However, a more foundational condition for the central claim — the existence of residual DOS in pristine CsV3Sb5 — is the reliability of the zero-field residual term itself. The paper reports α values above 3 for most crystals, which is unusual; in standard thermal-conductivity analyses α lies between 2 and 3 for phonon boundary scattering. The paper attributes the anomaly to thermally excited quasiparticles, but that same population contributes a non-linear temperature dependence that can bias the fitted intercept. The factor-of-3 spread in κ0/T across five crystals is not discussed; for universal nodal transport, such scatter would be unexpected. A fixed-α and fit-range stability check, plus per-sample normal-state normalization, would settle whether the residual DOS claim survives. Because this is a concrete and testable concern, the conditional verdict is appropriate pending re-analysis; no change to the reader's overall verdict is needed.","tokens_in":11354,"tokens_out":6620,"duration_ms":66026,"concrete_test":"Re-analyze the raw zero-field κ/T versus T data for all five CsV3Sb5 crystals (and the Ta-doped crystal) with α fixed to 3 and to 2.5 over the same reported fitting range below 0.5 K, and report the resulting intercept a with its uncertainty. Also vary the upper fit bound to 0.4 K and 0.6 K. If available, measure κ0/T in the normal state for each sample by applying H > Hc2 and report the ratio κ0/T ÷ κN0/T. If a becomes zero or negative for any sample under fixed α, or if the intercept changes by more than its statistical error when the fit range is varied, the residual-DOS claim is not robust.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central evidence for residual DOS is the finite intercept a in fits of κ/T = a + bT^(α−1) below 0.5 K. For CsV3Sb5, the reported α values are 3.87, 3.85, 2.70, 3.28, and 3.19 for samples #1–#5, meaning four of five lie outside the usual 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: a, b, and α are determined simultaneously, and the extrapolated intercept can be strongly correlated with the anomalous power law. No fit residuals or alternative fits are shown. In addition, the five nominally identical crystals yield κ0/T from 0.14 to 0.42 mW K−2 cm−1, a factor-of-3 variation that is not explained. If the residual DOS were intrinsic — for example, in the universal limit for nodal quasiparticles — κ0/T should be approximately sample-independent; the observed scatter suggests either fitting instability, sample-dependent normal-state inclusions, or other extrinsic contributions. Only sample #1 is normalized to its normal-state Wiedemann–Franz value (κN0/T = 4.54 mW K−2 cm−1), so the fractional residual term for the other four samples is unknown. The qualitative contrast with Ta-doped Cs(V0.86Ta0.14)3Sb5 (κ0/T = −0.4 ± 4 μW K−2 cm−1) is large, but that comparison can support the CDW-causality conclusion only if the pristine residual term itself is established; the fitting and scatter issues undercut this foundation.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":11785,"tokens_out":4274,"duration_ms":39859,"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":[{"comment":"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.","section":"§2, Eq. (1)"},{"comment":"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.","section":"§4, Fig. 4"},{"comment":"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.","section":"§2, Fig. 2(a)"}],"minor_comments":[{"comment":"There is a typo in the sentence 'we conducte ultralow-temperature STM measurements'; it should be 'we conducted'.","section":"§3"},{"comment":"The word 'resudual' should be 'residual' in the final paragraph of the main text.","section":"Summary paragraph"},{"comment":"The phrase 'the Tc of CsV3Sb5 is quiet low' should be 'quite low'.","section":"§2"},{"comment":"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.","section":"§2"},{"comment":"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.","section":"References"},{"comment":"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.","section":"§3, Fig. 3(c)"}],"recommendation":"major_revision","confidential_remarks":"The manuscript comes from an experienced group with a strong track record in thermal transport, and the measurement appears careful. The main risk is the robustness of the extrapolated intercept a in the presence of an anomalous power law α, and the causal link to CDW order rests on a single doped sample. These issues should be addressed directly through additional analysis or clear tempering of the claims. I do not see evidence of circularity or fabrication; the fit robustness concern is the primary scientific gate."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper delivers credible bulk evidence that superconducting CsV3Sb5 has a finite residual linear term in zero field, with the Ta-doped control showing none. The five pristine crystals all give nonzero κ0/T, the field dependence rises quickly as expected for nodal or small-gap behavior, and the normal-state Wiedemann–Franz check on sample #1 at 0.4 T is a good calibration. The STM zero-bias conductance is a useful supporting datum, though it is one unquantified spectrum. This package is new in the AV3Sb5 literature, even if the authors' earlier preprint (ref [24]) already pointed in this direction.\n\nThe soft spots are real but not fatal. The fit allows α to float, and four of five α values come out above 3, which is unusual for phonon boundary scattering. With only a and b plus an anomalous α, the intercept can trade off against the power law. I want to see residuals or a fixed-α comparison, especially given that the five κ0/T values scatter from 0.14 to 0.42 mW K−2 cm−1. That factor-of-three spread would be in the plot in a fully gapped or universal-nodal picture, though sample quality can vary. The bigger issue is causal: the paper concludes CDW order is essential from a single Ta-doped composition. Ta doping also raises Tc from 3.0 to 4.9 K, introduces disorder, and changes carrier density. No control isolates CDW suppression as the relevant variable, so the claim goes beyond the data. The abstract's last sentence states it more strongly than the evidence justifies.\n\nEven so, the qualitative contrast between pristine and Ta-doped samples is striking, and the residual-DOS observation itself is likely correct. The paper engages the conflicting literature honestly, citing both fully gapped and nodal reports and discussing residual Fermi arcs as an alternative. I do not see circular reasoning or invented entities. The fitting concern deserves a careful referee, but the normal-state WF validation of the same fitting procedure suggests the method is sound.\n\nWho is this for? Anyone working on kagome superconductors or on heat transport as a probe of gap structure. It deserves a serious referee: the evidence is substantive, the interpretation needs pruning, and the fitting details need explicit scrutiny. I would send it out.","headline":"Solid heat-transport evidence for residual DOS in CsV3Sb5, but the CDW-causality claim overreaches the single-doping comparison.","tokens_in":12392,"tokens_out":1829,"would_cite":true,"duration_ms":20105,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["82D55"],"pacs":["74.25.F-","74.70.Ad"],"model":"deepseek-v4-flash","headline":"Ultralow-temperature heat transport and STM data indicate residual zero-energy states inside the superconducting gap of CsV3Sb5.","keywords":["CsV3Sb5","kagome superconductor","thermal conductivity","residual density of states","charge density wave","nodal superconductivity","residual Fermi arc","zero-bias conductance"],"falsifier":"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.","tokens_in":11191,"feed_emoji":"❄️","tokens_out":5784,"duration_ms":49626,"temperature":0.7,"pith_summary":"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.","feed_headline":"Heat flow reveals leftover zero-energy states in kagome superconductor","feed_subtitle":"CsV3Sb5 keeps conducting heat near absolute zero, linking the effect to charge-density-wave order.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Establishes ultralow-temperature thermal conductivity as a bulk probe of superconducting gap structure.","marker":"[48]"},{"why":"Supplies the fit form κ/T=a+bT^{α-1} used to extract the residual linear term κ0/T.","marker":"[49]"},{"why":"Provides the fully gapped s-wave baseline (InBi) with no residual κ0/T in zero field.","marker":"[51]"},{"why":"Provides the multiband s-wave baseline (NbSe2) with no residual κ0/T in zero field.","marker":"[52]"},{"why":"Provides a d-wave nodal comparison (Tl-2201) whose large κ0/T and field dependence resemble the present data.","marker":"[53]"},{"why":"Shows that Ta doping suppresses the CDW and yields a U-shaped gap with zero DOS, supporting the absence of residual DOS in the doped compound.","marker":"[19]"},{"why":"ARPES evidence of a highly anisotropic superconducting gap with a possible node in CsV3Sb5.","marker":"[43]"},{"why":"Reports residual Fermi arcs in the pair-density-wave state, a proposed origin of the residual DOS.","marker":"[34]"},{"why":"ARPES evidence of isotropic, nodeless gaps in Ta-doped CsV3Sb5, consistent with no residual DOS there.","marker":"[45]"},{"why":"STM observation of a flat-bottom gap with zero DOS in Ta-doped CsV3Sb5, supporting the absence of residual DOS.","marker":"[46]"}],"fun_headline_variants":["Heat flow pinpoints residual states in kagome superconductor gap","CDW order leaves superconducting gap with residual states","Kagome superconductor shows unexpected gap states via heat flow","Heat transport reveals residual states tied to CDW in CsV3Sb5"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Heat flow pinpoints residual states in kagome superconductor gap","CDW order leaves superconducting gap with residual states","Kagome superconductor shows unexpected gap states via heat flow","Heat transport reveals residual states tied to CDW in CsV3Sb5"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00063,"raw_usage":{"total_tokens":2940,"prompt_tokens":1007,"completion_tokens":1933,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":623,"completion_tokens_details":{"reasoning_tokens":1860}},"tokens_in":623,"tokens_out":1933,"duration_ms":13211,"temperature":1.0,"reasoning_tokens":1860,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T04:42:39.893530+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the multiband s-wave baseline (NbSe2) with no residual κ0/T in zero field."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides a d-wave nodal comparison (Tl-2201) whose large κ0/T and field dependence resemble the present data."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Establishes ultralow-temperature thermal conductivity as a bulk probe of superconducting gap structure."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the fit form κ/T=a+bT^{α-1} used to extract the residual linear term κ0/T."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the fully gapped s-wave baseline (InBi) with no residual κ0/T in zero field."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Shows that Ta doping suppresses the CDW and yields a U-shaped gap with zero DOS, supporting the absence of residual DOS in the doped compound."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Reports residual Fermi arcs in the pair-density-wave state, a proposed origin of the residual DOS."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"ARPES evidence of isotropic, nodeless gaps in Ta-doped CsV3Sb5, consistent with no residual DOS there."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"STM observation of a flat-bottom gap with zero DOS in Ta-doped CsV3Sb5, supporting the absence of residual DOS."}],"review_version":1}