{"id":"4dc73b91-7549-44b5-af38-a4e73080e69c","arxiv_id":"2511.04208","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"125Te-NMR on a Ta-based quasicrystal superconductor finds a full s-wave-like gap 2Δ/kBTc≈3.04 with a suppressed Hebel-Slichter peak and almost no SC-state Knight-shift change.","lead":"NMR measurements on the quasicrystal superconductor (Ta0.95Cu0.05)1.6Te show an s-wave-like superconducting gap slightly weaker than BCS and an unusually small coherence peak. A nearly unchanged NMR spectrum below Tc is interpreted cautiously as possible unconventional pairing, but that part rests on weaker evidence.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"1/T1 data do not uniquely select s-wave pairing: the supplement's triplet no-coherence-factor model fits the same data with a sharper DOS edge, so the abstract's 'good agreement with an s-wave model' is underdetermined.","rationale":"The reader's weakest assumption concerns the secondary parity-mixing inference and is correct: the vortex broadening is unobservably small and K_orb is not pinned down. But that concern does not reach the main 1/T1 result. The more load-bearing issue is that the paper's own supplement admits the 1/T1 data cannot exclude triplet pairing; the s-wave assignment depends on the theoretical prediction that quasiperiodicity smears the DOS, the very effect the paper claims to observe. This makes the central 's-wave' statement partly circular and is therefore the right target for a decisive test. I would keep the verdict CONDITIONAL rather than reject: the raw observations (coherence peak, exponential tail, 2Δ/kBTc≈3.04, suppressed HS peak) are solid and would survive, but the abstract should not present s-wave pairing as uniquely established unless a statistical model comparison or an independent probe (e.g., single-crystal Knight-shift / spin-susceptibility decomposition) resolves the degeneracy.","tokens_in":12849,"tokens_out":9604,"duration_ms":102424,"concrete_test":"Digitize the 0.26 T 1/T1T data from Fig. 3 and the two model curves from Fig. S4; compute the weighted residuals over the full range 0.1 K–1.5 K for (i) the s-wave coherence-factor model with δ/Δ=0.4 and (ii) the triplet no-coherence-factor model with δ/Δ=0.05, and also (iii) an s-wave model with a Gaussian gap/Tc distribution chosen to match the HS-peak suppression. If fit (ii) or (iii) gives a comparable or better chi-square than fit (i) while also capturing the peak height, then the abstract's 'good agreement with an s-wave model' should be softened to 'nodeless full gap with suppressed coherence peak; pairing symmetry not determined by 1/T1 alone.'","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that the relaxation data establish 'an s-wave SC model with a SC gap slightly smaller than the BCS value' is weakened by the paper's own supplementary model comparison. In Supplemental Fig. S4 and the accompanying text, a full-gap model without the coherence factor—the form appropriate to triplet pairing—reproduces the same 1/T1T data below Tc/2 with a much smaller DOS broadening (δ/Δ=0.05) than the s-wave fit used in Fig. 3 (δ/Δ=0.4). The authors state explicitly that 'the possibility of spin-triplet pairing cannot be excluded from the 1/T1T results.' The only ground for discarding the triplet fit is the theoretical expectation that quasiperiodicity broadens the DOS edge, with the argument that a sharp edge is 'inconsistent with the theoretical predictions' [12]. But that expectation is precisely the hypothesis the 1/T1 measurement is offered to support. Thus the pairing-symmetry part of the central claim is not independently established; the data are consistent with a nodeless gap plus a suppressed coherence peak, but the assignment to singlet s-wave (and the 'slightly smaller than BCS' as a singlet property) rests on the same quasiperiodicity assumption under test. The gap magnitude and the suppression of the coherence peak remain, but the abstract's 'good agreement with an s-wave SC model' is a model-selection conclusion, not a unique experimental result.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript reports 125Te-NMR measurements on the dodecagonal quasicrystal superconductor (Ta0.95Cu0.05)1.6Te in the normal and superconducting states. From 1/T1T, the authors observe a small Hebel-Slichter coherence peak below Tc and an exponential decrease at lower temperatures; an Arrhenius analysis yields 2Δ(0)/kBTc = 3.04, slightly below the BCS value. The data are compared with an s-wave BCS model with a broadened quasiparticle DOS (δ/Δ = 0.4); while the low-temperature decay is reproduced, the calculated coherence peak remains larger than observed, and this suppression is attributed to quasiperiodicity-induced smearing of the Bogoliubov DOS peak. The NMR spectra show essentially no line broadening or Knight-shift decrease in the superconducting state, which the authors suggest may point to an unusual superconducting state, such as parity-mixed/triplet pairing.","tokens_in":13148,"tokens_out":10150,"duration_ms":88170,"significance":"If the conclusions were firm, this would be important microscopic evidence on the superconducting gap in a quasicrystal superconductor and on the predicted suppression of the coherence peak in Penrose-lattice models. The experimental work is careful in important respects: the heat-up test, the I×T check that the spectra are taken in the superconducting state, and the normal-state Korringa analysis are all valuable. The main quantitative observation—a nodeless gap with 2Δ/kBTc ≈ 3.04 and a strongly suppressed coherence peak—appears robust to the model-selection issue discussed below. However, the paper's stronger claim of 's-wave' pairing, and the interpretation of the unchanged Knight shift as evidence for unusual pairing, are underdetermined by the presented data; some of this is acknowledged by the authors in the supplemental material.","major_comments":[{"comment":"Supplemental Fig. S4 and the accompanying text state that a full-gap model without the coherence factor—the form corresponding to triplet pairing—reproduces the same 1/T1T data below Tc/2 with δ/Δ = 0.05, and that 'the possibility of spin-triplet pairing cannot be excluded from the 1/T1T results.' The only stated reason for rejecting this fit is that a sharp DOS edge is inconsistent with the quasiperiodicity prediction of Ref. [12], which is the very hypothesis the measurements are meant to test. In addition, the s-wave curve in Fig. 3 is not an independent prediction: it uses 2Δ/kBTc = 3.04 obtained from the same data, and δ/Δ = 0.4 is an adjustable broadening. The data therefore establish a nodeless gap with a suppressed coherence peak, but they do not uniquely select the s-wave (coherence-factor) model. The abstract and conclusion should be reworded to distinguish consistency with s-w","section":"Supplemental Material, 'Numerical calculation of 1/T1 with SC models'; main text around Fig. 3"},{"comment":"The central quantitative claim 2Δ/kBTc = 3.04 is read off an Arrhenius plot with no error bars, no stated fit range, and no discussion of the uncertainty introduced by excluding the faster relaxation component below 0.3 K (Supplemental Fig. S1). Since this value is used in the model curves and compared with the BCS value, the authors should report the fitted slope with a confidence interval, show the fit range and residuals, and justify the exclusion of the fast component. Without this, the 'slightly smaller than BCS' statement is not quantitatively falsifiable.","section":"Fig. 3 inset; Supplemental 'Relaxation curves'"},{"comment":"The inference that the ~0.03% Knight-shift decrease is anomalously small relies on the assumption Korb ≈ 0. The normal-state Korringa check gives K = 0.16% from 1/T1T, while the observed K is ~0.10%, leaving room for an orbital contribution of up to ~0.06%—twice the size of the measured SC-state decrease. With such an orbital term, the observed decrease could be most of the spin response, and no parity-mixed/triplet component would be needed. The authors should provide a quantitative bound on Korb (e.g., from the T-independent shift and estimated hyperfine couplings) or substantially soften the parity-mixing suggestion.","section":"Knight-shift discussion; K = Kspin + Korb + Kdia; Fig. 5(c)"},{"comment":"The absence of Redfield broadening is presented as inconsistent with conventional type-II behavior and is used to motivate vortex pinning. However, for the parameters in Table I (μ0Hc ≈ 2.65 mT, λ ≈ 1.04×10^5 Å, κ ≈ 1.2×10^3), the vortex-lattice field spread is expected to be of order μ0Hc1 ≈ 10 μT, corresponding to ~0.15 kHz in 125Te frequency units—far below the ~20 kHz spectral linewidth. The unchanged line shape is therefore expected for a conventional type-II superconductor with such a large penetration depth, and it carries little information about vortex pinning or internal field homogeneity. Please compute and report the expected field distribution, or remove the claim that the absence of broadening is anomalous.","section":"NMR spectrum variation in the SC state; Fig. 5(a,b); Table I"}],"minor_comments":[{"comment":"The caption 'nuclear spin-lattice relaxation rate divided by T1/T1T' is garbled; it should read '1/T1T' or 'spin-lattice relaxation rate divided by temperature.'","section":"Fig. 3 caption"},{"comment":"The axis label appears as 'Tc(H) ~ T 3(T1T)s/(T1T)n Tc(H)/T' in the typeset text; please confirm that the horizontal axis is Tc(H)/T and correct the typesetting.","section":"Inset of Fig. 3"},{"comment":"The phrase 'unambiguously strange' is informal; please replace with a more precise formulation.","section":"Conclusion"},{"comment":"Reference [20] still contains the placeholder 'XXX'; the supplemental-material URL should be inserted.","section":"References"},{"comment":"When comparing the Hebel-Slichter peak height with the Eilenberger curves, the H/Hc2 values for the three fields should be stated explicitly, and it should be noted that the model curves assume zero applied field (or specify the field used in the calculation).","section":"Fig. 4"}],"recommendation":"major_revision","confidential_remarks":"This is a valuable experimental study of superconductivity in a quasicrystal, and the data on the suppressed coherence peak are of genuine interest. The main obstacle to acceptance is the overstatement in the abstract and conclusion: the supplement itself admits that the 1/T1T data cannot exclude triplet pairing, so the 's-wave' claim should be recalibrated. The Knight-shift interpretation also needs a quantitative bound on Korb, and the Redfield-broadening discussion should be reconciled with the very large penetration depth. These are fixable within revision, so I recommend major revision rather than rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The 1/T1 data are a genuinely new and useful result: the first microscopic probe of the superconducting gap in a quasicrystal superconductor. The coherence peak and exponential decay are clearly resolved, and 2Delta/kBTc ~ 3.04 is consistent with bulk specific heat. The heat-up test and I*T drop show the NMR signal comes from the SC state. That is solid experimental work.\n\nThe paper is honest about the main soft spot. The supplementary model without the coherence factor (the triplet form) fits the same 1/T1 data below Tc/2 with delta/Delta = 0.05, and the authors say so. Their reason for discarding it is that a sharp DOS edge is inconsistent with the theoretical prediction that quasiperiodicity smears the Bogoliubov peak, which is the hypothesis the measurement is meant to test. That is a real circularity. The abstract's 'good agreement with an s-wave model' is too confident. The data establish a nodeless full gap with a suppressed coherence peak; they do not uniquely select singlet s-wave pairing.\n\nOther soft spots are minor. There are no error bars on 1/T1 or the HS-peak heights, which matters when comparing to Eilenberger curves. The unchanged spectrum in the SC state is expected to be invisible given lambda ~ 10^5 Angstrom; the vortex field spread is orders of magnitude below the 20-kHz linewidth. The Knight-shift analysis assumes K_orb ~ 0 even though the Korringa estimate is 0.16% vs the measured 0.10%, so the small shift decrease could be a conventional spin response. The parity-mixing sentence is explicitly speculative, so I take it as a suggestion, not a finding.\n\nThis paper is for the quasicrystal-superconductivity community and anyone working on NMR of disordered superconductors. The data deserve serious referee time. My recommendation: send it to review with a clear request to add error bars, show the triplet fit in the main text, and soften the abstract. With those changes it would be a good contribution.","headline":"First microscopic NMR look at a quasicrystal superconductor, with a clean 1/T1 gap signature but an over-claimed pairing-symmetry assignment.","tokens_in":13742,"tokens_out":2361,"would_cite":true,"duration_ms":21855,"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":"NMR of a quasicrystal superconductor reveals a nodeless s-wave gap with a suppressed coherence peak.","keywords":["quasicrystal superconductor","125Te NMR","Hebel-Slichter coherence peak","s-wave superconducting gap","Bogoliubov peak","parity mixing","Knight shift","Ta1.6Te"],"falsifier":"Measure the 125Te NMR Knight shift over a range of applied fields up to Hc2 and construct a K-χ plot to separate the orbital and spin contributions. If the spin part does not show the full Yosida-like decrease expected for an s-wave superconductor (or if a Redfield-like broadening appears at high fields), the parity-mixing inference would be falsified; the s-wave gap result would stand unless the 1/T1 fits are shown to be non-unique.","tokens_in":1617,"feed_emoji":"🔬","tokens_out":4910,"duration_ms":80789,"temperature":0.7,"pith_summary":"This paper reports 125Te nuclear magnetic resonance measurements on the quasicrystal superconductor (Ta0.95Cu0.05)1.6Te, which superconducts at 0.94 K. The nuclear spin-lattice relaxation rate 1/T1 shows a coherence peak just below Tc and then an exponential decay, which the authors fit with an s-wave full-gap model having 2Δ(0)/kBTc = 3.04, slightly below the BCS value of 3.52. The coherence peak is much smaller than conventional s-wave theory predicts, and the paper attributes this to quasiperiodicity smearing the Bogoliubov peak in the quasiparticle density of states. The NMR spectrum barely changes below Tc, with almost no line broadening and only a small Knight-shift decrease, which the authors cautiously suggest may indicate an unusual superconducting state such as parity-mixed or spin-triplet pairing. If correct, these measurements provide a microscopic local-probe look at how quasiperiodicity alters superconductivity.","feed_headline":"NMR on quasicrystal superconductor finds s-wave gap, muted peak","feed_subtitle":"125Te nuclear spin-lattice relaxation reveals a nodeless superconducting gap with a suppressed coherence peak.","key_machinery":"The central object is the Hebel-Slichter coherence peak in the nuclear spin-lattice relaxation rate 1/T1, whose size and temperature dependence directly probe the superconducting gap symmetry and quasiparticle density of states. The authors compare the measured 1/T1 to a conventional s-wave full-gap calculation with a rectangularly broadened density of states (width 2δ, height 1/2δ) and to the coherence-peak height as a function of H/Hc2 against Eilenberger-theory curves. The almost unchanged NMR spectrum below Tc is used to infer a uniform local field, which the authors attribute either to intrinsic vortex pinning or, speculatively, to parity-mixed pairing.","core_discovery":"The paper claims that the superconducting gap in the quasicrystal (Ta0.95Cu0.05)1.6Te is isotropic and nodeless, with 2Δ(0)/kBTc = 3.04, and that the coherence peak in 1/T1 is strongly suppressed even when a large density-of-states broadening is included in the s-wave model. The authors interpret this as the first experimental evidence that the quasiparticle density-of-states divergence at the gap edge is smeared by the quasiperiodic structure, as predicted by tight-binding models on Penrose lattices. They further report that the NMR spectrum shows almost no shift or broadening below Tc, and argue that this could signal an unconventional pairing state such as parity mixing, though they prese","pith_inferences":["The parity-mixing inference is much weaker than the s-wave gap result: using the paper's own parameters (μ0Hc2 = 4.6 T, μ0Hc = 2.65 mT, κ ≈ 1.2×10^3, λ ≈ 10^5 Å), the expected vortex-lattice field spread is only of order 10^-7 T, about 10^4 times smaller than the 20-kHz NMR linewidth, so the absence of broadening carries little information.","A K-χ plot or a careful measurement of the orbital Knight shift would be needed to determine whether the observed ~0.03% shift decrease is the full spin response; if the orbital term is sizable, the unconventional-pairing suggestion would lose its basis.","Comparing the same 1/T1 analysis on the approximant crystals Ta97Te60 and Ta181Te112 would help isolate the effect of quasiperiodicity from ordinary disorder.","The intrinsic vortex-pinning scenario predicts a disordered vortex lattice with an unusually narrow field distribution, which could be tested with small-angle neutron scattering or scanning Hall probe microscopy on single crystals."],"forward_implications":["Confirms that a bulk quasicrystal can host a conventional nodeless s-wave-like superconducting gap, with a gap ratio 2Δ(0)/kBTc ≈ 3.04, slightly smaller than the BCS value.","Provides experimental support for theories that predict the Bogoliubov peak in the quasiparticle density of states is smeared in quasicrystals, which would explain the unusually small coherence peak.","The near-absence of NMR line broadening below Tc suggests a very uniform local field, consistent with an extremely large penetration depth and weak diamagnetic screening.","A marginal Knight-shift decrease, if it is truly due to a small spin susceptibility change, would be consistent with proposals that parity-mixed or spin-triplet pairing is possible without translational symmetry.","Motivates future single-crystal and high-field NMR measurements to separate quasiperiodicity-driven effects from ordinary disorder-driven spin-orbit scattering."],"fun_headline_variants":["Quasicrystal superconductor: s-wave gap, suppressed NMR peak","NMR shows nodeless gap in quasicrystal superconductor","Suppressed coherence peak hints at quasicrystal effects in superconductor","Ta-Cu-Te quasicrystal has s-wave gap but weak coherence peak","125Te-NMR finds s-wave gap and muted peak in quasicrystal"],"cache_read_input_tokens":14848,"weakest_assumption_plain":"The unconventional-pairing suggestion depends on the assumption that a conventional superconducting state would have produced a measurable change in the NMR spectrum; given the very large penetration depth and the uncertainty in the orbital Knight shift, the observed absence of broadening and small shift may instead reflect extreme type-II parameters.","fun_headline_variants_meta":{"raw":{"variants":["Quasicrystal superconductor: s-wave gap, suppressed NMR peak","NMR shows nodeless gap in quasicrystal superconductor","Suppressed coherence peak hints at quasicrystal effects in superconductor","Ta-Cu-Te quasicrystal has s-wave gap but weak coherence peak","125Te-NMR finds s-wave gap and muted peak in quasicrystal"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000315,"raw_usage":{"total_tokens":1637,"prompt_tokens":775,"completion_tokens":862,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":519,"completion_tokens_details":{"reasoning_tokens":764}},"tokens_in":519,"tokens_out":862,"duration_ms":7910,"temperature":1.0,"reasoning_tokens":764,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-03T23:45:00.537026+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the 125Te NMR Knight shift over a range of applied fields up to Hc2 and construct a K-χ plot to separate the orbital and spin contributions. If the spin part does not show the full Yosida-like decrease expected for an s-wave superconductor (or if a Redfield-like broadening appears at high fields), the parity-mixing inference would be falsified; the s-wave gap result would stand unless the 1/T1 fits are shown to be non-unique.","supporting_citations":[],"review_version":1}