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REVIEW 2 major objections 5 minor 70 references

Unconventional superconductivity in a non-centrosymmetric ${\alpha}$-Mn alloy NbTaOs$_{2}$

T0 review · 2 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read This paper argues that the new ternary superconductor NbTaOs2 breaks time-reversal symmetry in its superconducting state, making it the first rhenium-free α-Mn compound with this signature.

desk verdict NbTaOs2 is a genuinely new rhenium-free α-Mn superconductor with solid bulk characterization, but the TRSB headline rests on a tiny relaxation increase whose analysis is underdetermined, and the conclusion overstates the evidence. read the letter →

arxiv 2506.12449 v1 pith:PDTQTJSD submitted 2025-06-14 cond-mat.supr-con

R. K. Kushwaha , Arushi , S. Jangid , P. K. Meena , R. Stewart , A. D. Hillier , R. P. Singh This is my paper · ORCID
classification cond-mat.supr-con
keywords time-reversalsymmetrybreakingnon-centrosymmetricsuperconductoralpha-MnstructuremuonspinrelaxationNbTaOs2superconductinggapantisymmetricspin-orbitcouplingtype-II
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 a new ternary superconductor, NbTaOs2, and argues that its superconducting ground state breaks time-reversal symmetry. The compound crystallizes in the non-centrosymmetric α-Mn structure, and zero-field muon spin relaxation shows a small extra relaxation rate appearing only below the transition temperature, which the authors interpret as a spontaneous internal field of about 0.1 G. If correct, this is the first rhenium-free α-Mn superconductor to show time-reversal symmetry breaking, a status previously associated mainly with rhenium-based members of the family. The same measurements also indicate a fully gapped, moderately coupled pairing state, so the material combines a conventional-looking gap with an unconventional symmetry-breaking signature.

What carries the argument

The central object is the zero-field muon spin relaxation function A(t) = Ai G_KT(t) exp(−(Λt)^β) + Abg, where G_KT is the static Kubo-Toyabe function describing randomly oriented nuclear dipoles. The additional Gaussian relaxation rate Λ is the probe: when Tc is crossed, Λ increases by 0.008(1) μs−1 while the nuclear term is held fixed, and the increase is converted to an internal field through Bint = δΛ/γμ. The structural carrier of the effect is the non-centrosymmetric α-Mn lattice with mixed Nb/Ta 4d/5d sites, which the authors argue enhances antisymmetric spin-orbit coupling.

What would settle it

A decisive check would be a zero-field muon experiment on a series of NbTaOs2 samples with controlled purity: if the extra relaxation below Tc disappears or scales with impurity concentration rather than with the superconducting fraction, the assignment to time-reversal symmetry breaking fails. A second check is to measure the same relaxation increase in a sample with a muon site shifted by chemical substitution, since TRSB fields should follow the superconducting order parameter rather than the local defect environment.

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Extended reading notes

Core claim

The central claim is that NbTaOs2 is an unconventional superconductor in which time-reversal symmetry is broken in the superconducting state. This is inferred from zero-field muon spin relaxation: a static Gaussian Kubo-Toyabe relaxation is observed at all temperatures, and an additional relaxation rate Λ grows below Tc = 2.4 K, corresponding to a spontaneous static field Bint ≈ 0.094 G. Specific heat and transverse-field muon data show a single isotropic nodeless gap with Δ(0)/kBTc ≈ 2.2 and moderate electron-phonon coupling, and the upper critical field reaches the Pauli limit. The authors conclude that NbTaOs2 is the first Re-free α-Mn non-centrosymmetric superconductor with time-reversal symmetry breaking.

Load-bearing premise

The argument relies on the assumption that the muon's nuclear-dipolar relaxation, the initial asymmetry, and the background contribution are exactly the same above and below the superconducting transition, so the small extra relaxation must come from new static internal fields rather than from impurities or a spurious magnetic transition.

Editorial extensions

If this is right

  • The first Re-free α-Mn superconductor with time-reversal symmetry breaking weakens the idea that rhenium content is required for TRSB in this structure family.
  • A fully gapped, moderately coupled superconductor with broken time-reversal symmetry provides a concrete candidate for the intrinsic superconducting diode effect.
  • The spontaneous field scale of about 0.1 G is comparable to other TRSB non-centrosymmetric superconductors, so similar α-Mn ternaries become promising targets for muon-based searches.
  • The closeness of the upper critical field to the Pauli limit suggests antisymmetric spin-orbit coupling is active, linking the broken inversion symmetry to the measured properties.

Reading between the lines

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

  • If the time-reversal symmetry breaking is intrinsic, theory would predict a two-component order parameter such as s+is or s+id for NbTaOs2; a low-temperature specific-heat or Josephson-phase measurement could distinguish such pairing from a single-component state.
  • The disorder-versus-intrinsic question could be settled by comparing the size of the Λ increase with the residual resistivity ratio in samples with different annealing histories, following the idea that disorder alone can induce TRSB.
  • A natural extension is to scan neighboring Re-free α-Mn ternaries, for example substituting Os with other 5d elements, to map which 4d/5d site combinations produce time-reversal symmetry breaking.
  • The same material may exhibit a field-free superconducting diode effect; a transport measurement with an in-plane current and no applied magnetic field would be a direct test.
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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

2 major / 5 minor

Summary. The manuscript reports the synthesis of the ternary non-centrosymmetric α-Mn-type compound NbTaOs2 and characterizes its superconductivity through resistivity, magnetization, specific heat, transverse-field muon spin rotation, and zero-field muon spin relaxation. The authors find bulk type-II superconductivity at Tc≈2.4 K, a fully gapped moderately coupled s-wave-like state with Δ(0)/kBTc≈2.1–2.2 from both specific heat and TF-μSR, and a small (0.008(1) μs⁻¹) increase in the zero-field muon relaxation rate below Tc that they attribute to spontaneous internal fields and hence to time-reversal symmetry breaking. On this basis they claim NbTaOs2 is the first Re-free α-Mn-type compound with TRSB.

Significance. If confirmed, the TRSB claim is significant because the established TRSB cases in α-Mn-type superconductors are mostly Re-based; a Re-free counterexample would sharpen the debate about the role of Re, antisymmetric spin-orbit coupling, and disorder. The fully gapped moderate-coupling s-wave conclusion is well supported: the gap ratios from two independent probes (specific heat: 2.22(1); TF-μSR: 2.02(1) when Eq. (17) is corrected) agree within uncertainties, and the TF-μSR analysis uses standard BCS formulas. The paper is also commendable for reporting detailed raw measurements and fits. The main weakness is that the TRSB evidence rests on one very small relaxation-rate change extracted under fixed nuclear-width parameters, and the analysis does not yet rule out static impurity fields as the source of the extra relaxation.

major comments (2)
  1. [III.E, Eq. (19), Eq. (21), Fig. 5(b)] The central TRSB claim depends on the 0.008(1) μs⁻¹ increase in Λ below Tc. Because the Kubo-Toyabe term and the added Gaussian term are both (near-)Gaussian over the measured time window, ΔZ and Λ are strongly correlated; the authors' decision to fix ΔZ, Ai, and Abg at their normal-state values means that any temperature dependence of the nuclear dipolar width—from thermal contraction, muon diffusion, or dilute static moments—would be absorbed into Λ. The 5 mT longitudinal-field decoupling only establishes that the relaxation is static; it does not discriminate between a TRSB spontaneous field and static impurity fields or a weak magnetic transition, both of which also decouple at 50 G. The manuscript should fit ΔZ as a free parameter with reported correlation contours, provide an independent determination of the nuclear dipolar width, or include control measurements on a non-superconducting analog before the 'first Re-free α-Mn TRSB' claim can be considered established.
  2. [III.E, Eq. (17)] Eq. (17) as written equates σ_fll⁻²(T)/σ_fll⁻²(0) to λ⁻²(T)/λ⁻²(0), but Eq. (16) implies σ_fll ∝ λ⁻², so σ_fll⁻² ∝ λ⁴ and the left side is λ⁴(T)/λ⁴(0), which rises as T approaches Tc and cannot describe the plotted λ⁻²(T) that decreases toward Tc. The intended dirty-limit BCS relation is σ_fll(T)/σ_fll(0) = λ⁻²(T)/λ⁻²(0) = (Δ(T)/Δ(0)) tanh(Δ(T)/2kBT). The equation should be corrected, and the quoted Δ(0)/kBTc = 2.02(1) should be verified with the correct expression.
minor comments (5)
  1. [III.D, Eq. (10)] The λe−ph calculation uses Tc = 2.25(3) K, while Tc values quoted elsewhere are 2.40(2) K from magnetization and specific heat and 2.90(3) K from resistivity; please state the origin of 2.25(3) K and assess the sensitivity of λe−ph (and of the Uemura ratio) to this choice.
  2. [III.E, text after Eq. (16)] The text says the simplified Brandt formula applies under the condition H/Hc2 ≫ 1, but the correct regime is H/Hc2 ≪ 1; at the applied field of 40 mT with Hc2(0) ≈ 4.5 T, H/Hc2 ≈ 0.009, so the text should read H/Hc2 ≪ 1.
  3. [III.E, Eq. (19) and Eq. (21)] The convention for Λ in Eq. (19) should be stated explicitly: with β = 2 the extra term is exp(−Λ²t²), which differs from the conventional Gaussian relaxation form exp(−σ²t²/2) used in the Kubo-Toyabe term; if the conventional form is intended, the conversion Bint = δΛ/γμ in Eq. (21) may need a √2 factor.
  4. [III.C and IV] The compound is incorrectly written as NbTaO2 in the text near Fig. 2(a) and again in Section IV; it should be NbTaOs2.
  5. [III.E, ZF-μSR discussion] The statement that 'the absence of oscillatory components in the LF spectra confirms the absence of magnetic ordering' is too strong; the data show no evidence of long-range magnetic order, but dilute static moments would also fail to produce coherent oscillations.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the paper's central inferences are data-driven fits and standard μSR analyses, not derivations that reduce to their own inputs.

full rationale

The paper's central claims are supported by fitting standard models to independent datasets: BCS isotropic-gap fits to specific heat and transverse-field μSR, Ginzburg–Landau fits to magnetization, and a Kubo–Toyabe-plus-relaxation fit to zero-field μSR. The ZF-μSR relaxation rate Λ is a fitted parameter, and its increase below Tc is an empirical observation from the data; the paper does not assume TRSB in the model and then recover it. The internal field Bint is obtained from δΛ via the standard relation Bint = δΛ/γμ, which is a unit conversion, not an independent prediction that is statistically forced. The gap values from specific heat (Δ(0)/kBTc = 2.22) and TF-μSR (2.02) come from separate measurements and agree, so no fitted parameter is being recycled as a prediction. The 'first Re-free α-Mn TRSB' claim rests on comparative prior μSR null results; although several are from the same research group, they are published external measurements and are used as context rather than as an unverified self-citation that forbids alternatives. No equation in the paper is equivalent to another by construction, and no known result is merely renamed. The potential degeneracy between the Gaussian Kubo–Toyabe term and the extra exp(−Λt)^β decay is a fitting/underdetermination concern about the strength of the TRSB evidence, not a circularity of the derivation; under the governing rules, such a scientific weakness does not raise the circularity score.

Assumptions & free parameters 9 free parameters · 6 assumptions · 0 invented entities

The central claims rest on standard fitted models (BCS, Ginzburg-Landau, Kubo-Toyabe) with several parameters fitted to the measured data. No new particles or forces are introduced. The most consequential interpretive assumption is that the small ZF-muSR relaxation increase below Tc is a spontaneous internal field from TRSB rather than an artifact of impurities or fitting choices.

free parameters (9)
  • Delta(0)/kB Tc (specific heat) = 2.22(1)
    Fitted from the electronic specific heat using the isotropic BCS gap model; a free parameter in the fit.
  • Delta(0)/kB Tc (TF-muSR) = 2.02(1)
    Fitted from the temperature dependence of the inverse penetration depth using the dirty-limit BCS expression.
  • gamma_n (Sommerfeld coefficient) = 8.78(1) mJ mol-1 K-2
    Obtained from the C/T versus T^2 fit in the normal state.
  • beta_3 (phonon coefficient) = 0.316(4) mJ mol-1 K-4
    Fitted in Eq. (7) to the normal-state specific heat.
  • beta_5 (anharmonic coefficient) = 0.108(3) mJ mol-1 K-6
    Fitted in Eq. (7) to the normal-state specific heat.
  • Hc1(0) = 2.85(3) mT
    Obtained by fitting Hc1(T) to the Ginzburg-Landau relation.
  • Hc2(0) = 4.50(1) T
    Obtained by fitting Hc2(T) to the Ginzburg-Landau relation.
  • delta_Lambda = 0.008(1) micros-1
    Increase in the zero-field muon relaxation rate below Tc, extracted from fits of Eq. (19).
  • mu (Coulomb repulsion) = 0.13
    Assumed value from McMillan's model for transition metals, used to compute lambda_e-ph.
assumptions (6)
  • domain assumption BCS isotropic single-gap model describes the superconducting state.
    Used to fit specific heat (Eqs. 12 and 13) and TF-muSR (Eqs. 17 and 18); no anisotropic or multi-gap models are tested.
  • domain assumption Dirty-limit London approximation with a well-ordered triangular vortex lattice.
    Used to relate the TF-muSR depolarization rate to the penetration depth via the Brandt formula (Eq. 16), assuming the low-field limit H/Hc2 << 1, though the text incorrectly states H/Hc2 >> 1.
  • standard math Static Kubo-Toyabe relaxation for randomly oriented nuclear moments.
    Used to fit ZF-muSR spectra (Eq. 20); assumes static and random nuclear dipolar fields.
  • ad hoc to paper The increase in ZF-muSR relaxation below Tc is intrinsic to the superconducting state.
    This is the central interpretation of the data; LF-muSR shows the field is static but cannot exclude static impurity moments that appear near Tc.
  • standard math Ginzburg-Landau theory relations for Hc1(T) and Hc2(T).
    Used to extract zero-temperature critical fields, coherence length, and penetration depth (Eqs. 1, 2, 4, and 5).
  • domain assumption The sample is phase pure with the intended NbTaOs2 composition and homogeneous Nb/Ta site mixing.
    Based on XRD Rietveld refinement and EDAX mapping; any magnetic impurity phase would affect the muon relaxation and the interpretation.

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Pith. "Pith review of Unconventional superconductivity in a non-centrosymmetric ${\alpha}$-Mn alloy NbTaOs$_{2}$." pith.science (2026). https://pith.science/paper/PDTQTJSD

@misc{pith2026250612449,
  author       = {Pith},
  title        = {Pith review of: Unconventional superconductivity in a non-centrosymmetric $\alpha$-Mn alloy NbTaOs$_2$},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PDTQTJSD}},
  note         = {Machine review of arXiv:2506.12449}
}
abstract

Non-centrosymmetric superconductors have emerged as a fascinating avenue for exploring unconventional superconductivity. Their broken inversion and time-reversal symmetries make them prime candidates for realizing the intrinsic superconducting diode effect (SDE). In this work, we synthesize the ternary non-centrosymmetric $\alpha$-Mn alloy NbTaOs$_{2}$ and conduct a comprehensive investigation of its superconducting properties through resistivity, magnetization, specific heat and muon spin rotation/relaxation ($\mu$SR) techniques. Our transverse field-$\mu$SR and specific heat results provide evidence of a moderately coupled, fully-gaped superconducting state. Zero field-$\mu$SR measurements reveal a subtle increase in the relaxation rate below the transition temperature, suggesting time reversal symmetry breaking in the superconducting ground state of NbTaOs$_{2}$.

Figures

Figures reproduced from arXiv: 2506.12449 by the authors.

Figure 1
Figure 1. FIG. 1. (a) Powder XRD pattern of NbTaOs [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. (a) Temperature [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. (a), analyzed using the Debye-Sommerfeld relation (Eq. (7)) C/T = γn + β3T 2 + β5T 4 (7) where γn is the Sommerfeld coefficient (electronic contribution to specific heat), β3 corresponds to the phononic contribution, and β5 captures the higher-order anharmonic effects. The best fit of Eq. (7) to the spe￾cific heat data in the normal state, shown as the red curve in [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: FIG. 4. TF- [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]
Figure 5
Figure 5. Figure 5: (b)), indicating the emergence of a weak sponta￾neous magnetic field. This relaxation rate remains nearly constant above Tc. Further, longitudinal field (LF)-µSR measurements were conducted to rule out the possibility that the ob￾served increase in relaxation originate…
Figure 6
Figure 6. Figure 6: FIG. 6. T [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.