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arxiv: 2510.23800 · v1 · submitted 2025-10-27 · ❄️ cond-mat.supr-con · cond-mat.str-el

Observation of a pronounced Hebel-Slichter peak in the spin-lattice relaxation rate and implications for gap and pairing symmetry in LaNiGa₂

P. Sherpa , R. Hingorani , A. Menon , I. Vinograd , C. Chaffey , A. P. Dioguardi , R. Yamamoto , M. Hirata
show 6 more authors
F. Ronning J. R. Badger P. Klavins R. R. P. Singh V. Taufour N. J. Curro
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Pith reviewed 2026-05-18 02:43 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con cond-mat.str-el
keywords Hebel-Slichter peakNQR relaxation rateLaNiGa2pairing symmetrytwo-band superconductivitysinglet pairingtriplet pairingcoherence factors
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The pith

NQR data in LaNiGa2 show a Hebel-Slichter peak that fits two-band singlet pairing with distinct gaps better than non-unitary triplet pairing.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper measures the zero-field NQR spin-lattice relaxation rate in superconducting LaNiGa2 and reports a pronounced Hebel-Slichter coherence peak just below the transition temperature. This peak is compared against theoretical models for different pairing states. The temperature dependence matches a two-band singlet BCS-like state with two distinct gaps that align with earlier measurements. The same data deviate quickly from a two-band internally antisymmetric non-unitary triplet model unless the gaps are forced equal and the state made unitary. If correct, the result questions the prior assignment of time-reversal symmetry breaking to this material.

Core claim

The NQR spin-lattice relaxation rate exhibits a pronounced Hebel-Slichter coherence peak that is well described by a two-band singlet BCS-like pairing with two distinct gaps consistent with previous measurements, while even tiny non-unitarity in a triplet model with unequal gaps causes the peak to diminish rapidly and deviate from the observed data.

What carries the argument

The Hebel-Slichter coherence peak in the zero-field NQR spin-lattice relaxation rate, which is sensitive to superconducting coherence factors and used to test gap magnitudes and singlet versus triplet pairing symmetry through temperature-dependent fits.

If this is right

  • The pairing in LaNiGa2 is consistent with two-band singlet superconductivity rather than non-unitary triplet pairing.
  • Time-reversal symmetry breaking is not supported by the relaxation rate data.
  • The two gaps are distinct in magnitude but the state remains unitary.
  • Earlier proposals identifying LaNiGa2 as a non-unitary triplet superconductor with time-reversal symmetry breaking require re-examination.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The material may lack the topological features previously linked to the non-unitary triplet state.
  • Muon spin relaxation or Kerr rotation measurements could test for the absence of spontaneous fields expected in the triplet scenario.
  • The same coherence-peak analysis could be applied to related nickel-based or topological candidate superconductors to refine pairing assignments.

Load-bearing premise

The temperature dependence of the NQR relaxation rate is dominated by the superconducting gap structure and coherence factors, with negligible contributions from impurity scattering or other relaxation channels.

What would settle it

A direct observation of spontaneous internal magnetic fields below the transition temperature via muon spin relaxation, persisting under conditions where the singlet model fits the NQR peak, would challenge the conclusion that the data favor singlet pairing.

Figures

Figures reproduced from arXiv: 2510.23800 by A. Menon, A. P. Dioguardi, C. Chaffey, F. Ronning, I. Vinograd, J. R. Badger, M. Hirata, N. J. Curro, P. Klavins, P. Sherpa, R. Hingorani, R. R. P. Singh, R. Yamamoto, V. Taufour.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Normalized ( [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
read the original abstract

We report a pronounced Hebel-Slichter coherence peak in the zero field nuclear quadrupolar resonance (NQR) spin-lattice relaxation rate of the topological crystalline superconductor LaNiGa$_2$ in the superconducting state. Previously, a two-band internally antisymmetric non-unitary triplet pairing (INT) state was proposed for this system, with equal spin-pairing and two distinct gaps associated with different spins. A detailed examination of the temperature dependence of the NQR data shows that the data best fit an INT model if the two gaps are equal and the model is unitary. Even a tiny non-unitarity with two unequal gaps causes the coherence peak to diminish rapidly and deviate from the data. On the other hand, the data are well-fit by a two-band singlet BCS-like pairing with two distinct gaps consistent with previous measurements. This raises doubts on the identification of non-unitary triplet-pairing with time-reversal symmetry breaking in this material.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript reports observation of a pronounced Hebel-Slichter peak in the zero-field NQR spin-lattice relaxation rate 1/T1(T) of LaNiGa2 below Tc. It compares the temperature dependence to phenomenological models and concludes that the data are well described by a two-band singlet BCS-like state with two distinct gaps, while even small non-unitarity in the previously proposed internally antisymmetric non-unitary triplet (INT) state rapidly suppresses the peak and deviates from experiment. This is used to question the identification of non-unitary triplet pairing with time-reversal symmetry breaking in the material.

Significance. If the model discrimination is robust, the result would be significant for resolving the pairing symmetry of LaNiGa2, a candidate topological crystalline superconductor. The new NQR data and explicit comparison of coherence factors across singlet and triplet scenarios provide a concrete experimental handle on non-unitarity effects. Credit is due for the clear experimental observation of the peak and for testing the INT proposal against fresh measurements; however, the strength of the conclusion hinges on the validity of the underlying relaxation model.

major comments (2)
  1. Abstract and implied model-comparison section: the central claim that 'even a tiny non-unitarity with two unequal gaps causes the coherence peak to diminish rapidly and deviate from the data' is load-bearing for ruling out the INT state. The manuscript provides no explicit values for the non-unitarity parameter, no calculated suppression factor, and no comparison of deviations against experimental error bars or full temperature curves, making it impossible to verify whether the reported preference for the singlet model is robust or partly by construction from gap magnitudes and spectral weights.
  2. Relaxation-rate modeling (throughout the model fits): the temperature dependence of 1/T1 is assumed to arise exclusively from quasiparticle excitations whose density of states and coherence factors are set by the gap structure. No quantitative bounds are placed on possible impurity scattering (Dynes broadening) or spin-fluctuation contributions that could suppress or mimic the peak height; this assumption is load-bearing for the model discrimination and requires either explicit estimates or sample-variation tests to support.
minor comments (2)
  1. Abstract: the statement that the two gaps are 'consistent with previous measurements' should cite the specific prior works and quote the gap values used in the present fits.
  2. Figure presentation: experimental 1/T1(T) points should include error bars and the full temperature range down to the lowest measured T to allow readers to judge fit quality and the position of the peak.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for the constructive comments. We address each major comment below and indicate the revisions we will make to improve clarity and robustness.

read point-by-point responses

  1. Referee: Abstract and implied model-comparison section: the central claim that 'even a tiny non-unitarity with two unequal gaps causes the coherence peak to diminish rapidly and deviate from the data' is load-bearing for ruling out the INT state. The manuscript provides no explicit values for the non-unitarity parameter, no calculated suppression factor, and no comparison of deviations against experimental error bars or full temperature curves, making it impossible to verify whether the reported preference for the singlet model is robust or partly by construction from gap magnitudes and spectral weights.

    Authors: We agree that additional quantitative detail on the non-unitarity parameter would make the model comparison more transparent and verifiable. In the revised manuscript we will report the specific values of the non-unitarity parameter (the relative magnitude of the imaginary component of the gap) employed in the calculations, together with the resulting suppression factors for the Hebel-Slichter peak height. We will also overlay the full temperature-dependent model curves for several small non-unitarity strengths against the experimental data, including error bars, so that readers can directly assess the magnitude of the deviations. revision: yes

  2. Referee: Relaxation-rate modeling (throughout the model fits): the temperature dependence of 1/T1 is assumed to arise exclusively from quasiparticle excitations whose density of states and coherence factors are set by the gap structure. No quantitative bounds are placed on possible impurity scattering (Dynes broadening) or spin-fluctuation contributions that could suppress or mimic the peak height; this assumption is load-bearing for the model discrimination and requires either explicit estimates or sample-variation tests to support.

    Authors: The analysis follows the conventional quasiparticle framework used for NQR relaxation in multiband superconductors. To address the concern we will add a dedicated paragraph that provides explicit estimates of Dynes broadening using representative values from the literature on related nickel-based compounds and demonstrates that moderate broadening does not remove the pronounced peak seen in the data. We will also briefly discuss the absence of strong spin-fluctuation signatures above Tc. Sample-to-sample variation tests lie outside the scope of the present work, which reports high-quality data from a single well-characterized crystal; we will note this limitation explicitly. revision: partial

Circularity Check

0 steps flagged

NQR relaxation-rate data independently discriminates singlet vs non-unitary triplet models

full rationale

The paper reports new zero-field NQR 1/T1(T) measurements on LaNiGa2 that exhibit a clear Hebel-Slichter peak. Standard coherence-factor expressions for two-band singlet and INT triplet states are evaluated with adjustable gap magnitudes and relative weights; the singlet parametrization reproduces both the peak height and its temperature position while even weakly non-unitary INT states suppress the peak. Because the input data are fresh experimental points independent of the prior INT proposal, and because the model comparison rests on the well-known BCS coherence-factor formulas rather than on any self-derived or self-cited uniqueness theorem, the discrimination does not reduce to a fit-by-construction or to a self-citation chain. No ansatz is smuggled, no known result is merely renamed, and the central claim therefore retains independent empirical content.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The analysis assumes standard BCS coherence factors for the relaxation rate and that the two-band structure can be modeled with independent gaps. No new particles or forces are introduced. Gap values and band weights are fitted parameters.

free parameters (2)
  • two distinct gap magnitudes
    Fitted to reproduce the height and position of the observed coherence peak in the NQR rate.
  • relative spectral weights of the two bands
    Adjusted to match the overall temperature dependence of the relaxation rate.
axioms (2)
  • domain assumption BCS coherence factors govern the spin-lattice relaxation rate in the superconducting state
    Invoked when comparing the measured peak to theoretical curves for singlet versus triplet pairing.
  • domain assumption The NQR signal arises from a single crystallographic site with no significant impurity or vortex contributions below Tc
    Required for the relaxation rate to directly reflect the gap structure.

pith-pipeline@v0.9.0 · 5784 in / 1596 out tokens · 25145 ms · 2026-05-18T02:43:10.452198+00:00 · methodology

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Works this paper leans on

37 extracted references · 37 canonical work pages

  1. [1]

    Quantum Fluctuations in Narrow-band Systems

    In this case, the scattering rates between the quasipar- ticles are dramatically suppressed if the two gaps have different values because energy cannot be conserved in the process. The nuclear resonance frequency is set to ℏωN /kBTc = 10 −4 and 10 −6 in the cases ofd a and dθ, respectively, with no additional broadening included. When the two gaps are equ...

    work page

  2. [2]

    S. Ran, C. Eckberg, Q.-P. Ding, Y. Furukawa, T. Metz, S. R. Saha, I.-L. Liu, M. Zic, H. Kim, J. Paglione, and N. P. Butch, Nearly ferromagnetic spin-triplet supercon- ductivity, Science365, 684 (2019)

    work page 2019

  3. [3]

    E. R. Schemm, W. J. Gannon, C. M. Wishne, W. P. Halperin, and A. Kapitulnik, Observation of broken time- reversal symmetry in the heavy-fermion superconductor UPt3, Science345, 190 (2014)

    work page 2014

  4. [4]

    A. D. Hillier, J. Quintanilla, B. Mazidian, J. F. Annett, and R. Cywinski, Nonunitary triplet pairing in the cen- trosymmetric superconductor LaNiGa2, Phys. Rev. Lett. 109, 097001 (2012)

    work page 2012

  5. [5]

    S. K. Ghosh, M. Smidman, T. Shang, J. F. Annett, A. D. Hillier, J. Quintanilla, and H. Yuan, Recent progress on superconductors with time-reversal symmetry breaking, J. Phys. Condens. Matter33, 033001 (2020)

    work page 2020

  6. [6]

    J. R. Badger, Y. Quan, M. C. Staab, S. Sumita, A. Rossi, K. P. Devlin, K. Neubauer, D. S. Shulman, J. C. Fet- tinger, P. Klavins, S. M. Kauzlarich, D. Aoki, I. M. Vishik, W. E. Pickett, and V. Taufour, Dirac lines and loop at the fermi level in the time-reversal symme- try breaking superconductor LaNiGa 2, Communications Physics5, 22 (2022)

    work page 2022

  7. [7]

    Y. Quan, V. Taufour, and W. E. Pickett, Nonsymmor- phic band sticking in a topological superconductor, Phys. Rev. B105, 064517 (2022)

    work page 2022

  8. [8]

    S. K. Ghosh, G. Csire, P. Whittlesea, J. F. Annett, M. Gradhand, B. ´Ujfalussy, and J. Quintanilla, Quantita- tive theory of triplet pairing in the unconventional super- conductor LaNiGa2, Phys. Rev. B101, 100506 (2020)

    work page 2020

  9. [9]

    Z. F. Weng, J. L. Zhang, M. Smidman, T. Shang, J. Quin- tanilla, J. F. Annett, M. Nicklas, G. M. Pang, L. Jiao, W. B. Jiang, Y. Chen, F. Steglich, and H. Q. Yuan, Two-gap superconductivity in LaNiGa 2 with nonunitary triplet pairing and even parity gap symmetry, Phys. Rev. Lett.117, 027001 (2016)

    work page 2016

  10. [10]

    Ghimire, K

    S. Ghimire, K. R. Joshi, E. H. Krenkel, M. A. Tanatar, Y. Shi, M. Ko´ nczykowski, R. Grasset, V. Taufour, P. P. Orth, M. S. Scheurer, and R. Prozorov, Electron irra- diation reveals robust fully gapped superconductivity in LaNiGa2, Phys. Rev. B109, 024515 (2024)

    work page 2024

  11. [11]

    Sundar, M

    S. Sundar, M. Yakovlev, N. Azari, M. Abedi, D. M. Broun, H. U. ¨Ozdemir, S. R. Dunsiger, D. Zackaria, H. Bowman, P. Klavins, Y. Shi, V. Taufour, and J. E. Sonier, Gap structure of the nonsymmorphic supercon- ductor LaNiGa 2 probed byµSR, Phys. Rev. B109, 104517 (2024)

    work page 2024

  12. [12]

    L. C. Hebel and C. P. Slichter, Nuclear relaxation in su- perconducting aluminum, Phys. Rev.107, 901 (1957)

    work page 1957

  13. [13]

    L. C. Hebel and C. P. Slichter, Nuclear spin relaxation in normal and superconducting aluminum, Phys. Rev.113, 1504 (1959)

    work page 1959

  14. [14]

    Arovas and C

    D. Arovas and C. Wu,Lecture Notes on Superconductiv- ity (A Work in Progress), edited by unknown (unknown, 2019)

    work page 2019

  15. [15]

    D. E. MacLaughlin, Solid state physics (1976) pp. 1–68

    work page 1976

  16. [16]

    R. F. Kiefl, W. A. MacFarlane, K. H. Chow, S. Dun- siger, T. L. Duty, T. M. S. Johnston, J. W. Schneider, J. Sonier, L. Brard, R. M. Strongin, J. E. Fischer, and A. B. Smith, Coherence peak and superconducting en- ergy gap in Rb 3C60 observed by muon spin relaxation, Phys. Rev. Lett.70, 3987 (1993)

    work page 1993

  17. [17]

    Kotegawa, K

    H. Kotegawa, K. Ishida, Y. Kitaoka, T. Muranaka, and J. Akimitsu, Evidence for strong-couplings-wave super- conductivity in MgB2: 11B NMR study, Phys. Rev. Lett. 87, 127001 (2001)

    work page 2001

  18. [18]

    B. W. Statt, Anisotropic gap and quasiparticle-damping effects on NMR measurements of high-temperature su- perconductors, Phys. Rev. B42, 6805 (1990)

    work page 1990

  19. [19]

    Brandow, Characteristic features of the exotic super- conductors, Phys

    B. Brandow, Characteristic features of the exotic super- conductors, Phys. Rep.296, 1 (1998)

    work page 1998

  20. [20]

    Nakai, K

    Y. Nakai, K. Ishida, D. Kikuchi, H. Sugawara, and H. Sato, Evidence fors-wave superconductivity with antiferromagnetic fluctuations in filled skutterudite LaFe4P12: 139La and 31P NMR studies, J. Phys. Soc. Jpn.74, 3370 (2005)

    work page 2005

  21. [21]

    Q.-P. Ding, P. Wiecki, V. K. Anand, N. S. Sangeetha, Y. Lee, D. C. Johnston, and Y. Furukawa, Volovik effect and Fermi-liquid behavior in the s-wave superconductor CaPd2As2: As75 NMR-NQR measurements, Phys. Rev. B93, 140502 (2016)

    work page 2016

  22. [22]

    T. Imai, T. Shimizu, T. Tsuda, H. Yasuoka, T. Taka- 6 batake, Y. Nakazawa, and M. Ishikawa, Nuclear spin- lattice relaxation of 63,65Cu at the Cu(2) sites of the high Tc superconductor YBa2Cu3O7−δ, J. Phys. Soc. Jpn.57, 1771 (1988)

    work page 1988

  23. [23]

    Curro, T

    N. Curro, T. Caldwell, E. Bauer, L. Morales, M. Graf, Y. Bang, A. Balatsky, J. Thompson, and J. Sarrao, Unconventional superconductivity in PuCoGa 5, Nature 434, 622 (2005)

    work page 2005

  24. [24]

    K. K. Tanaka, M. Ichioka, and S. Onari, Site-selective NMR for odd-frequency Cooper pairs around vortex in chiralp-wave superconductors, Phys. Rev. B93, 094507 (2016)

    work page 2016

  25. [25]

    K. K. Tanaka, M. Ichioka, and S. Onari, Local NMR relaxation ratesT −1 1 andT −1 2 depending on thed-vector symmetry in the vortex state of chiral and helicalp-wave superconductors, Phys. Rev. B97, 134507 (2018)

    work page 2018

  26. [26]

    See Supplemental Material at URL-will-be-inserted-by- publisher

    work page

  27. [27]

    Sherpa, I

    P. Sherpa, I. Vinograd, Y. Shi, S. A. Sreedhar, C. Chaf- fey, T. Kissikov, M.-C. Jung, A. S. Botana, A. P. Dio- guardi, R. Yamamoto, M. Hirata, G. Conti, S. Nemsak, J. R. Badger, P. Klavins, I. Vishik, V. Taufour, and N. J. Curro, Absence of strong magnetic fluctuations or inter- actions in the normal state of LaNiGa 2, Phys. Rev. B 109, 125113 (2024)

    work page 2024

  28. [28]

    Balian and N

    R. Balian and N. Werthamer, Superconductivity with pairs in a relative p-wave, Phys. Rev.131, 1 (1963)

    work page 1963

  29. [29]

    P. W. Anderson and P. Morel, Generalized Bardeen Cooper Schrieffer states and the proposed low temper- ature phase of liquid 3He, Phys. Rev.123, 1911 (1961)

    work page 1911

  30. [30]

    J. F. Annett, Symmetry of the order parameter for high-temperature superconductivity, Adv. Phys.39, 83 (1990)

    work page 1990

  31. [31]

    Ramires, Nonunitary superconductivity in complex quantum materials, J

    A. Ramires, Nonunitary superconductivity in complex quantum materials, J. Phys. Condens. Matter34, 304001 (2022)

    work page 2022

  32. [32]

    Coleman,Introduction to Many Body Physics(Cam- bridge University Press, 2015)

    P. Coleman,Introduction to Many Body Physics(Cam- bridge University Press, 2015)

    work page 2015

  33. [33]

    Shimizu, H

    M. Shimizu, H. Amanuma, K. Hachitani, H. Fukazawa, Y. Kohori, T. Namiki, C. Sekine, and I. Shirotani, 75As-NQR studies of superconducting filled skutteru- dites PrRu4As12 and LaRu4As12, J. Phys. Soc. Jpn.76, 104705 (2007)

    work page 2007

  34. [34]

    Q.-P. Ding, K. Nishine, Y. Kawamura, J. Hayashi, C. Sekine, and Y. Furukawa, Suppression of ferromag- netic spin fluctuations in the filled skutterudite super- conductor SrOs4As12 revealed by As75 NMR-NQR mea- surements, Phys. Rev. B100, 054516 (2019)

    work page 2019

  35. [35]

    Yamada, S

    Y. Yamada, S. Kitagawa, T. Ihara, K. Ishida, N. Ue- matsu, D. Hirai, and K. Takenaka, Uniform electronic states and s-wave superconductivity in a strongly disor- dered high-entropy compound X0.6Pt0.4Sb ( X = Ru, Rh, Pd, Ir), Phys. Rev. B112, L020508 (2025)

    work page 2025

  36. [36]

    Takahashi, S

    H. Takahashi, S. Kitagawa, K. Ishida, M. Kawaguchi, A. Ikeda, S. Yonezawa, and Y. Maeno, S-wave supercon- ductivity in the Dirac line-nodal material CaSb2, J. Phys. Soc. Jpn.90, 073702 (2021)

    work page 2021

  37. [37]

    Masuda and A

    Y. Masuda and A. G. Redfield, Nuclear spin-lattice re- laxation in superconducting aluminum, Phys. Rev.125, 159 (1962)

    work page 1962