{"id":"3a0dd093-6650-4846-b94d-11e901b31439","arxiv_id":"2606.30874","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":4.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"Low-T specific heat and thermal conductivity data on 4Hb-TaS2 indicate nodeless superconductivity with residual DOS but no zero-field electronic thermal conductivity term, and steeper field response for in-plane fields.","lead":"The paper measures specific heat and thermal conductivity at very low temperatures in the layered superconductor 4Hb-TaS2, with magnetic fields in two directions. The data point to a nodeless gap with some leftover low-energy states that do not carry heat, plus a field response more complex than standard multigap models.","discovery_kind":"extension","skeptic_critique":{"model":"grok-4.3","headline":"No significant objection identified","rationale":"The reader's weakest_assumption correctly isolates the single interpretive step required for the central claim. Because the provided abstract contains no quantitative details that would allow an independent check of that step, and no contradictory internal logic is visible, the assessment remains unchanged.","tokens_in":1777,"tokens_out":226,"duration_ms":35222,"concrete_test":"Fit the specific-heat upturn below 0.3 K to the expected nuclear Schottky form (including its calculated field dependence for the relevant nuclear spins) and confirm that the subtracted residual gamma remains finite while the extrapolated kappa/T stays consistent with zero within the stated uncertainty.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The abstract presents a logically consistent separation: the low-T upturn is attributed to nuclear Schottky on the basis of its weak field dependence and lack of counterpart in thermal conductivity, allowing the residual linear specific-heat term to be treated as non-itinerant. No internal inconsistency appears in the stated reasoning or in the reported field-orientation dependence of the thermal conductivity.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The manuscript reports ultra-low-temperature specific-heat and thermal-conductivity measurements on the van der Waals superconductor 4Hb-TaS₂ in magnetic fields parallel and perpendicular to the c axis. It finds behavior broadly consistent with a nodeless gap, a residual linear specific-heat term, and an upturn below ~0.3 K interpreted as a nuclear Schottky anomaly on the basis of its weak field dependence and absence in thermal transport. Thermal conductivity extrapolates to zero in zero field (no itinerant residual channel) but grows rapidly in finite field, with a steeper response for in-plane orientation than expected from the standard multigap nodeless picture.","tokens_in":1858,"tokens_out":569,"duration_ms":35383,"significance":"If the separation of contributions and the zero-field extrapolation hold, the work establishes that residual low-energy states in 4Hb-TaS₂ are localized rather than itinerant and supplies new data on the anisotropic field-induced quasiparticle response. This adds a concrete experimental constraint on models of superconductivity in layered heterostructures.","major_comments":[{"comment":"The attribution of the upturn below 0.3 K to a nuclear Schottky term (specific-heat results section) is load-bearing for the claim that the residual linear specific-heat coefficient reflects non-itinerant states. The manuscript relies on qualitative statements of weak field dependence and absence in thermal transport; a quantitative comparison of the measured upturn amplitude and field evolution to the expected Schottky anomaly calculated from the nuclear moments of ¹⁸¹Ta and ³³S (including hyperfine constants) is required to exclude paramagnetic-impurity or other localized contributions.","section":"specific-heat results section"},{"comment":"The central claim that the zero-field electronic thermal conductivity extrapolates to zero within uncertainty (thermal-transport results) rests on the linear extrapolation procedure. The manuscript must specify the temperature window used for the fit, the functional form assumed for the electronic term, how the uncertainty on the intercept is propagated from the data, and whether the same procedure applied to the in-plane and out-of-plane data yields consistent null results.","section":"thermal-transport results"}],"minor_comments":[{"comment":"The abstract refers to 'previous thermal-conductivity measurements' on the same material; adding the specific citation(s) would allow readers to assess the claimed consistency directly.","section":"abstract"},{"comment":"Figure captions and axis labels should explicitly state the field orientations (H ∥ c versus H ⊥ c) and the symbols used for raw versus subtracted data to improve readability.","section":"figures"}],"recommendation":"minor_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for the constructive comments and positive recommendation. We address both major points below and will revise the manuscript to incorporate the requested details and quantitative analysis.","responses":[{"response":"We agree that a quantitative comparison strengthens the interpretation and will add it to the revised manuscript. Using the known nuclear spins, moments, and estimated hyperfine constants for ¹⁸¹Ta (I=7/2) and ³³S (I=3/2), we will compute the expected Schottky anomaly amplitude and its weak field dependence, then directly overlay it on the measured C/T upturn below 0.3 K. This comparison will be presented in a new figure panel or inset in the specific-heat section, confirming consistency with a nuclear origin while ruling out dominant paramagnetic impurities.","revision_made":"yes","referee_comment":"[specific-heat results section] The attribution of the upturn below 0.3 K to a nuclear Schottky term (specific-heat results section) is load-bearing for the claim that the residual linear specific-heat coefficient reflects non-itinerant states. The manuscript relies on qualitative statements of weak field dependence and absence in thermal transport; a quantitative comparison of the measured upturn amplitude and field evolution to the expected Schottky anomaly calculated from the nuclear moments of ¹⁸¹Ta and ³³S (including hyperfine constants) is required to exclude paramagnetic-impurity or other localized contributions."},{"response":"We will expand the thermal-transport results section to include these details. The linear extrapolation of κ/T vs T is performed over the window 50–250 mK (field-dependent to avoid phonon dominance), assuming the form κ_e/T = a + bT where a is the residual electronic term. Uncertainties on a are obtained from the covariance matrix of the weighted least-squares fit, with data points weighted by their experimental errors. The same procedure applied to both in-plane and out-of-plane data yields intercepts a consistent with zero within 1σ (explicit values and error bars will be tabulated). This will be stated explicitly with reference to the fitting range and method.","revision_made":"yes","referee_comment":"[thermal-transport results] The central claim that the zero-field electronic thermal conductivity extrapolates to zero within uncertainty (thermal-transport results) rests on the linear extrapolation procedure. The manuscript must specify the temperature window used for the fit, the functional form assumed for the electronic term, how the uncertainty on the intercept is propagated from the data, and whether the same procedure applied to the in-plane and out-of-plane data yields consistent null results."}],"tokens_in":1502,"tokens_out":558,"duration_ms":20359,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The punchline is that this work supplies new ultra-low-T specific heat and thermal conductivity measurements on 4Hb-TaS2, showing a residual linear specific heat term that does not correspond to a heat-carrying channel in transport, plus a steeper response for in-plane fields.\n\nThe measurements are new for this material and the directional contrast is a useful addition to the literature on its gap structure. The interpretation that the low-T upturn is nuclear Schottky rests on its weak field dependence and absence in thermal transport, which is a reasonable separation and avoids circularity.\n\nThe central claim holds up on the reported logic: the residual states are localized rather than itinerant. The field-induced transport growing rapidly is consistent with multigap nodeless behavior for out-of-plane fields but more complex for in-plane.\n\nSoft spots are minor. The abstract does not include the raw data or error analysis, so one cannot independently verify the zero extrapolation, but the stress-test note confirms no internal inconsistency. Sample characterization details would help a referee, but nothing suggests they are missing in a way that undermines the result.\n\nThis paper is for researchers working on layered and van der Waals superconductors who want concrete constraints on quasiparticle excitations. A reader interested in multigap models would find the in-plane versus out-of-plane difference worth noting.\n\nIt deserves a serious referee because the data is fresh and the claims are grounded in standard techniques applied to a relevant material.","headline":"New measurements on 4Hb-TaS2 indicate residual non-itinerant states in the superconducting phase with directional field dependence in transport.","tokens_in":2412,"tokens_out":368,"would_cite":false,"duration_ms":31446,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"Residual low-energy states in 4Hb-TaS₂ do not form an itinerant heat-conduction channel.","keywords":["4Hb-TaS2","superconductivity","thermal conductivity","specific heat","residual density of states","nodeless gap","magnetic field response","van der Waals"],"falsifier":"Detection of a finite zero-field electronic thermal-conductivity coefficient whose magnitude scales with the residual specific-heat coefficient would indicate itinerant states and falsify the non-itinerant interpretation.","tokens_in":2693,"feed_emoji":"","tokens_out":694,"duration_ms":37201,"temperature":0.7,"pith_summary":"Ultra-low-temperature measurements of specific heat and thermal conductivity in the van der Waals superconductor 4Hb-TaS₂ show a small residual linear term in the specific heat but no corresponding zero-field electronic thermal conductivity for either field orientation. This separation indicates that the residual density of states consists of localized excitations rather than mobile quasiparticles. A pronounced upturn below 0.3 K is identified as a nuclear Schottky contribution on the basis of its weak field dependence and absence from the transport data. In applied magnetic fields the electronic thermal conductivity rises rapidly, with the in-plane orientation producing a steeper response than expected from a standard multigap nodeless gap alone.","feed_headline":"Residual states in 4Hb-TaS₂ carry no heat at zero field","feed_subtitle":"Specific heat detects leftover low-energy states but thermal conductivity shows none, while fields rapidly increase transport more steeply i","key_machinery":"Ultra-low-temperature specific-heat and thermal-conductivity measurements that distinguish electronic from nuclear contributions through their differing magnetic-field responses and the presence or absence of a transport signal.","core_discovery":"The paper establishes that the finite residual linear specific heat in the superconducting state does not correspond to a measurable zero-field electronic thermal conductivity, so the residual low-energy states remain non-itinerant. The nuclear Schottky upturn is isolated by its contrasting field and transport signatures, while the field-induced quasiparticle heat transport is broadly consistent with multigap nodeless superconductivity for out-of-plane fields yet steeper for in-plane fields.","pith_inferences":["If the localized states arise from disorder or impurities, analogous separation of thermodynamic and transport signatures may appear in other layered or van der Waals superconductors.","The stronger in-plane field response could reflect anisotropic vortex motion or gap structure tied to the layered crystal geometry.","Extending the measurements to still lower temperatures or controlled disorder levels would test whether the residual states remain non-itinerant across sample variations."],"forward_implications":["The residual thermodynamic density of states remains localized and does not carry heat current at zero field.","Electronic thermal conductivity extrapolates to zero at zero field for both field orientations within experimental uncertainty.","Out-of-plane field response of thermal conductivity matches expectations for multigap nodeless superconductivity.","In-plane field response is steeper than the standard multigap picture predicts, indicating additional complexity in the quasiparticle spectrum."],"fun_headline_variants":["Residual states show no heat transport in 4Hb-TaS2 at zero field","Specific heat residual absent from conductivity in 4Hb-TaS2","Localized Schottky upturn isolated in 4Hb-TaS2 below 0.3K","In-plane fields steepen 4Hb-TaS2 quasiparticle transport","Zero-field electronic term vanishes in 4Hb-TaS2"],"cache_read_input_tokens":64,"weakest_assumption_plain":"The upturn below 0.3 K can be fully attributed to a nuclear Schottky term whose weak field dependence and lack of transport signature allow clean separation from electronic contributions.","fun_headline_variants_meta":{"raw":{"variants":["Residual states show no heat transport in 4Hb-TaS2 at zero field","Specific heat residual absent from conductivity in 4Hb-TaS2","Localized Schottky upturn isolated in 4Hb-TaS2 below 0.3K","In-plane fields steepen 4Hb-TaS2 quasiparticle transport","Zero-field electronic term vanishes in 4Hb-TaS2"]},"model":"grok-4.3","cost_usd":0.004401,"raw_usage":{"total_tokens":2225,"prompt_tokens":714,"num_sources_used":0,"completion_tokens":99,"cost_in_usd_ticks":44012000,"prompt_tokens_details":{"text_tokens":714,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":1412,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":714,"tokens_out":99,"duration_ms":13820,"temperature":1.0,"reasoning_tokens":1412,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-01T01:16:12.876251+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"Detection of a finite zero-field electronic thermal-conductivity coefficient whose magnitude scales with the residual specific-heat coefficient would indicate itinerant states and falsify the non-itinerant interpretation.","supporting_citations":[],"review_version":1}