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REVIEW 4 major objections 5 minor 56 references

Superconducting Properties on Two-dimensional Quasicrystal (Ta$_{0.95}$Cu$_{0.05}$)$_{1.6}$Te Studied with $^{125}$Te-NMR

T0 review · 4 major / 5 minor · reviewed 2026-08-03 · deepseek-v4-flash

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Pith's one-line read NMR of a quasicrystal superconductor reveals a nodeless s-wave gap with a suppressed coherence peak.

desk verdict First microscopic NMR look at a quasicrystal superconductor, with a clean 1/T1 gap signature but an over-claimed pairing-symmetry assignment. read the letter →

arxiv 2511.04208 v1 pith:5SXZVMRA submitted 2025-11-06 cond-mat.supr-con

H. Matsudaira , S. Kitagawa , K. Ishida , Y. Tokumoto , K. Tomiyama , K. Edagawa This is my paper · ORCID
classification cond-mat.supr-con
keywords quasicrystalsuperconductor125TeNMRHebel-Slichtercoherencepeaks-wavesuperconductinggapBogoliubovparitymixingKnightshiftTa1.6Te
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

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.

What carries the argument

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.

What would settle it

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.

Watch

Extended reading notes

Core claim

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

Load-bearing premise

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.

Editorial extensions

If this is right

  • 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.

Reading between the lines

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

  • 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.
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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

4 major / 5 minor

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.

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 (4)
  1. [Supplemental Material, 'Numerical calculation of 1/T1 with SC models'; main text around Fig. 3] 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
  2. [Fig. 3 inset; Supplemental 'Relaxation curves'] 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.
  3. [Knight-shift discussion; K = Kspin + Korb + Kdia; Fig. 5(c)] 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.
  4. [NMR spectrum variation in the SC state; Fig. 5(a,b); Table I] 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.
minor comments (5)
  1. [Fig. 3 caption] 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.'
  2. [Inset of Fig. 3] 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.
  3. [Conclusion] The phrase 'unambiguously strange' is informal; please replace with a more precise formulation.
  4. [References] Reference [20] still contains the placeholder 'XXX'; the supplemental-material URL should be inserted.
  5. [Fig. 4] 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).

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the gap is read off the same 1/T1 data with an Arrhenius fit, but the paper's non-trivial claim is the anomalous suppression of the coherence peak, which is a discrepancy from an external s-wave model, not a fitted prediction.

full rationale

The paper's main quantitative result, 2Δ(0)/kBTc = 3.04, is obtained directly from the Arrhenius plot of the measured (T1T)s/(T1T)n in the inset of Fig. 3. The s-wave model curve in Fig. 3 uses this same value ('We used 2Δ(0)/kBTc = 3.04, which was evaluated from above Arrhenius plot, and δ/Δ(0) = 0.4'), so the agreement below Tc/2 is partly a restatement of the fitted gap rather than an independent prediction. However, the paper does not present the gap as a prediction; it transparently identifies it as an evaluated quantity. The load-bearing claim—that the coherence peak is unusually small—is not forced by that fit: the s-wave calculation with a strongly broadened DOS (δ/Δ(0)=0.4) overestimates the peak, and the paper compares the peak height against external Eilenberger-theory curves, so the discrepancy is an independent observation, not a consequence of the fitted parameters. The supplemental model without the coherence factor, which can also reproduce the low-temperature data (Fig. S4), is explicitly acknowledged: 'the possibility of spin-triplet pairing cannot be excluded from the 1/T1T results.' That admission makes the s-wave assignment partially underdetermined by the data, but underdetermination is not circularity. The exclusion of the triplet fit relies on external theory [12] (Takemori, Arita, Sakai), not on the authors' own prior work. The Knight-shift and parity-mixing discussion is explicitly speculative ('might suggest') and is not used to derive the central gap or coherence-peak results. The citations to [16] and [18] involve overlapping authors, but those references are used for supporting parameters (e.g., μ0Hc from specific heat) and for comparison with Hc2, not as the basis of the paper's independent NMR findings. The manuscript contains no self-definitional construction, no fitted parameter renamed as a prediction, and no self-citation chain that forces the central claim. Therefore the score is 0.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central experimental quantities rest on standard NMR relaxation theory and BCS s-wave DOS formulas. The main ad hoc inputs are the fitted gap ratio 2Δ/kBTc=3.04 and the DOS broadening δ/Δ=0.4 (plus δ/Δ=0.05 in the supplemental no-coherence-factor fit). Domain assumptions include the single-exponential slow-component selection, the K_orb≈0 decomposition of the Knight shift, and the transferability of Penrose-lattice/QC theories to this Ta-Te compound. No new entities (particles, forces) are introduced.

free parameters (3)
  • 2Δ(0)/kBTc = 3.04
    Extracted from the Arrhenius slope of (T1T)_s/(T1T)_n vs Tc(H)/T at 0.26 T (Fig. 3 inset). Used as an input to the s-wave model curve.
  • δ/Δ(0) for s-wave model with coherence factor = 0.4
    Chosen to broaden the quasiparticle density of states in the s-wave model to try to reproduce the small coherence peak; the authors note even this large broadening cannot fully explain the HS-peak suppression.
  • δ/Δ(0) for no-coherence-factor fit = 0.05
    Used in the supplemental triplet-like (no-coherence-factor) model to match 1/T1 below Tc/2; chosen to keep the DOS edge sharp.
assumptions (5)
  • domain assumption The nuclear magnetization recovery follows a single exponential R(t)∝exp(-t/T1) for I=1/2; the slow component below 0.3 K represents the bulk 1/T1, while the faster component is an RF-heating artifact.
    Used in Supplemental 'Relaxation curves' to determine all 1/T1 values, especially the low-temperature exponential tail that fixes 2Δ/kBTc.
  • domain assumption The observed 125Te Knight shift is dominated by the spin part; the orbital shift K_orb≈0 because the Korringa product approximately agrees.
    Used to interpret the small SC-state Knight-shift decrease as a nearly unchanged spin susceptibility; the measured K is 0.1% vs Korringa-predicted 0.16%, a 1.6x discrepancy that does not uniquely fix K_orb.
  • domain assumption Theoretical predictions for attractive-Hubbard/Penrose-lattice quasicrystals (refs 11-15), including smearing of the Bogoliubov DOS peak and possible triplet/parity-mixed pairing, apply to this Ta-based quasicrystal.
    Used to interpret the suppressed Hebel-Slichter peak and the unchanged NMR spectrum as quasiperiodicity-driven rather than ordinary disorder or resolution effects.
  • standard math The Eilenberger-theory curves for HS-peak height vs H/Hc2 in conventional s-wave superconductors are an appropriate benchmark for this material.
    Used in Fig. 4 to argue that the measured HS peak is below both clean and Born-limit expectations.
  • domain assumption The Hc2(0) and Hc values used to derive λ and κ are accurate; κ=Hc2/(√2 Hc) and λ=κξ describe the vortex field distribution.
    Used in the Supplemental estimate of K_dia and to argue that vortex-induced line broadening should be negligible.

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Cite this review

Pith. "Pith review of Superconducting Properties on Two-dimensional Quasicrystal (Ta$_{0.95}$Cu$_{0.05}$)$_{1.6}$Te Studied with $^{125}$Te-NMR." pith.science (2026). https://pith.science/paper/5SXZVMRA

@misc{pith2026251104208,
  author       = {Pith},
  title        = {Pith review of: Superconducting Properties on Two-dimensional Quasicrystal (Ta$_0.95$Cu$_0.05$)$_1.6$Te Studied with $^125$Te-NMR},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5SXZVMRA}},
  note         = {Machine review of arXiv:2511.04208}
}
abstract

Physical properties in the normal and superconducting (SC) state are investigated with $^{125}$Te-nuclear magnetic resonance (NMR) measurements in a quasicrystal $\mathrm{(Ta_{0.95}Cu_{0.05})_{1.6}Te}$, which was a recently discovered superconductor with the SC transition temperature $T_{\mathrm{c}}$ = 0.94 K. The nuclear spin-lattice relaxation rate $1/T_1$ shows a coherence peak just below $T_{\mathrm{c}}$, followed by an exponential decrease down to 0.1 K. The overall temperature dependence of $1/T_1$ is in good agreement with an $s$-wave SC model with a SC gap slightly smaller than the BCS value. However, the coherence peak is unusually small, which may be attributable to a reduced Bogoliubov peak theoretically predicted for quasicrystals. Furthermore, $^{125}$Te-NMR spectra show almost no broadening nor shift in the SC state, suggesting that an unusual SC state such as parity mixing might be realized in the Ta$_{1.6}$Te superconductor.

Figures

Figures reproduced from arXiv: 2511.04208 by the authors.

Figure 1
Figure 1. FIG. 1. (a) Temperature dependence of the ac susceptibility [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. (a) Temperature dependence of the Knight shift of [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. FIG. 4. Height of the HS peak as a function of [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figures from the paper (2 more)
Figure 5
Figure 5. Figure 5: FIG. 5. Typical [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]
Figure 3
Figure 3. Figure 3: The square markers represent the experimental data [PITH_FULL_IMAGE:figures/full_fig_p010_3.png]

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Reviewed August 3, 2026 · model on record in the stance chip above.