Nodal superconductivity with spin-triplet component in a noncentrosymmetric weakly-correlated metal

Andriy Smolyanyuk; Angelo Di Bernardo; Elke Scheer; Geetha Balakrishnan; Karsten Held; Marcel Strohmeier; Michael Smidman; Wolfgang Belzig

arxiv: 2606.04742 · v2 · pith:6SEOWDXMnew · submitted 2026-06-03 · ❄️ cond-mat.supr-con · cond-mat.mtrl-sci

Nodal superconductivity with spin-triplet component in a noncentrosymmetric weakly-correlated metal

Marcel Strohmeier , Andriy Smolyanyuk , Karsten Held , Michael Smidman , Geetha Balakrishnan , Wolfgang Belzig , Elke Scheer , Angelo Di Bernardo This is my paper

Pith reviewed 2026-06-28 04:08 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con cond-mat.mtrl-sci

keywords superconductivityspin-triplet pairingnoncentrosymmetricNb18Re82scanning tunneling spectroscopyorder parameter symmetryantisymmetric spin-orbit coupling

0 comments

The pith

Nb18Re82 requires a mixed nodal spin-singlet and spin-triplet order parameter to match its orientation-dependent tunneling spectra.

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

The paper studies the superconductor Nb18Re82, a weakly correlated noncentrosymmetric metal. Tunneling spectra measured on single crystals with different orientations show clear variations. A symmetry-constrained fit to the entire dataset cannot be achieved with a pure spin-singlet gap; it requires adding a spin-triplet component whose amplitude reaches up to half that of the singlet part. This result indicates that antisymmetric spin-orbit coupling can produce substantial parity mixing without strong electron correlations.

Core claim

Symmetry-constrained analysis of the spectroscopic dataset from Nb18Re82 demonstrates that the superconducting order parameter must combine a nodal spin-singlet component with a spin-triplet contribution reaching up to half of the singlet amplitude.

What carries the argument

The mixed spin-singlet plus spin-triplet order parameter whose relative amplitudes are fixed by crystal symmetry and antisymmetric spin-orbit coupling.

If this is right

The pairing symmetry of Nb18Re82 is a mixture of singlet and triplet components.
Antisymmetric spin-orbit coupling alone can generate substantial triplet admixture.
Triplet superconductivity may occur more widely in noncentrosymmetric materials than previously thought.
Similar symmetry analyses can be used on other weakly correlated noncentrosymmetric superconductors.

Where Pith is reading between the lines

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

Surface probes in noncentrosymmetric materials should routinely test for mixed-parity gaps rather than assuming pure singlet behavior.
Theoretical models of pairing in such systems should start with both singlet and triplet channels allowed by the symmetry.
Other rhenium-based or structurally related compounds may exhibit detectable triplet signatures in spectroscopic data.

Load-bearing premise

The orientation-dependent variations in tunneling spectra arise purely from the intrinsic superconducting order parameter symmetry rather than from surface reconstruction, impurity effects, or experimental artifacts.

What would settle it

A demonstration that all observed spectra on different crystal faces can be reproduced by a pure nodal spin-singlet gap without any triplet admixture would falsify the central claim.

read the original abstract

The most compelling evidence for spin-triplet superconductivity has emerged from strongly correlated electron systems, yet whether a substantial spin-triplet component can be realized without strong electronic coupling, by virtue of antisymmetric spin-orbit coupling (ASOC), remains unresolved. We address this question in the weakly-correlated noncentrosymmetric superconductor Nb$_{18}$Re$_{82}$ using low-temperature scanning tunneling spectroscopy on single crystals with different crystallographic orientations. The tunneling spectra exhibit orientation-dependent variations. A symmetry-constrained analysis shows that understanding the complete spectroscopic dataset requires an superconducting order parameter combining a nodal spin-singlet component with a spin-triplet contribution reaching up to half of the singlet amplitude. These results resolve the debated pairing symmetry of Nb$_{18}$Re$_{82}$ and demonstrate that ASOC alone can generate substantial parity mixing, suggesting that triplet superconductivity may be more widespread than previously recognized.

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.

Desk Editor's Note private letter to a colleague

The paper uses orientation-dependent STS to argue for a nodal singlet plus substantial triplet component in weakly correlated Nb18Re82, but the analysis details are missing and surface artifacts remain a plausible alternative explanation.

read the letter

The core claim here is that new tunneling spectra on different crystal orientations of Nb18Re82 require a mixed-parity order parameter with a triplet piece reaching half the singlet amplitude, driven by ASOC alone. This is the main new element: it takes a material already debated in the literature and adds orientation-resolved data to push for sizable triplet mixing without strong correlations.

What the work does is straightforward. It measures spectra on multiple faces, notes the variations, and applies a symmetry-constrained fit that cannot be satisfied by pure singlet pairing. That addresses an open question about whether ASOC can produce large parity mixing in weakly correlated systems, and the abstract states the triplet reaches up to 50 percent of the singlet.

The soft spots are in the execution. No spectra, no fitting details, no error bars, and no explicit checks against surface reconstruction or impurity scattering appear in the available description. The stress-test point lands: different crystal faces often show different terminations in STS, and without topography statistics, LEED, or cross-checks to bulk probes, the orientation dependence could be extrinsic. If that holds, the necessity of the large triplet component is not demonstrated. The free parameter (triplet-to-singlet ratio) also makes the fit flexible, so the claim rests heavily on the assumption that the bulk symmetry is the only source of the observed differences.

This is for people working on noncentrosymmetric superconductors who want to see whether mixed parity is more common than thought. The thinking is clear and engages the literature, but the evidence is not yet sharp enough to stand on its own. It deserves peer review so the data and analysis can be examined directly.

Referee Report

1 major / 1 minor

Summary. The manuscript reports low-temperature scanning tunneling spectroscopy (STS) on single crystals of the weakly-correlated noncentrosymmetric superconductor Nb18Re82 with different crystallographic orientations. The tunneling spectra show orientation-dependent variations. A symmetry-constrained analysis of the full spectroscopic dataset is used to argue that the data require a nodal spin-singlet order parameter combined with a spin-triplet component whose amplitude reaches up to half that of the singlet, arising from antisymmetric spin-orbit coupling (ASOC)-induced parity mixing. The work claims to resolve the pairing symmetry of Nb18Re82 and to show that substantial triplet superconductivity can occur without strong electronic correlations.

Significance. If the central claim holds, the result demonstrates that ASOC alone can produce substantial parity mixing and a sizable triplet component in a weakly-correlated material, expanding the range of systems in which triplet superconductivity may be expected. The symmetry-constrained fitting of the complete orientation-dependent dataset is a methodological strength that allows a quantitative bound on the triplet-to-singlet ratio.

major comments (1)

[Results and Discussion (analysis of orientation-dependent spectra)] The central claim that a triplet amplitude up to 50% of the singlet is required rests on the premise that all observed orientation dependence originates from bulk order-parameter symmetry via ASOC. No quantitative controls (surface termination statistics, LEED, or cross-checks with bulk probes) are presented to exclude surface reconstruction or impurity scattering on different crystal faces as the source of the spectral variations; this assumption is load-bearing for the necessity of the triplet component.

minor comments (1)

[Abstract] The abstract states the triplet contribution reaches 'up to half' the singlet amplitude; the main text should explicitly state the fitted range and its uncertainty for each orientation.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the thoughtful review and for highlighting the importance of confirming that the observed orientation dependence arises from bulk pairing symmetry. We address the major comment below and outline the revisions we will make.

read point-by-point responses

Referee: [Results and Discussion (analysis of orientation-dependent spectra)] The central claim that a triplet amplitude up to 50% of the singlet is required rests on the premise that all observed orientation dependence originates from bulk order-parameter symmetry via ASOC. No quantitative controls (surface termination statistics, LEED, or cross-checks with bulk probes) are presented to exclude surface reconstruction or impurity scattering on different crystal faces as the source of the spectral variations; this assumption is load-bearing for the necessity of the triplet component.

Authors: We agree that direct surface probes such as LEED or quantitative termination statistics are not reported and would provide additional reassurance. However, the global symmetry-constrained fit simultaneously reproduces the entire orientation-dependent dataset only when a substantial triplet component is included; alternative models lacking this component fail to capture the systematic variations across faces. Random surface reconstruction or impurity effects would not be expected to produce spectral changes that align precisely with the bulk crystallographic symmetries and ASOC-induced mixing required by the point-group analysis. We will revise the manuscript to add an explicit discussion of possible surface contributions, including why they are unlikely to mimic the observed symmetry-constrained behavior, and to note the absence of direct surface characterization as a limitation. revision: partial

Circularity Check

0 steps flagged

No significant circularity in symmetry-constrained analysis of new STS data

full rationale

The paper's derivation rests on fresh low-temperature STS spectra acquired on multiple crystallographic orientations of Nb18Re82 single crystals, followed by a symmetry-constrained fit that infers the necessity of a nodal singlet plus substantial triplet component. No equations, self-citations, or ansatzes are shown to reduce the claimed triplet amplitude (up to 50% of singlet) to a prior fitted parameter or to a self-referential definition. The result is presented as required by the orientation-dependent dataset under the assumption that surface effects are negligible; this is an empirical modeling step, not a closed logical loop. The analysis is therefore self-contained against external benchmarks and receives the default non-circularity finding.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard assumptions of noncentrosymmetric superconductivity theory and a fitted amplitude ratio; no invented entities are introduced.

free parameters (1)

triplet-to-singlet amplitude ratio
Determined from fitting the orientation-dependent tunneling spectra; reaches up to 0.5.

axioms (1)

domain assumption The superconducting order parameter in noncentrosymmetric crystals can be decomposed into singlet and triplet components allowed by the point group symmetry.
Invoked in the symmetry-constrained analysis of the spectroscopic dataset.

pith-pipeline@v0.9.1-grok · 5714 in / 1240 out tokens · 42897 ms · 2026-06-28T04:08:29.627644+00:00 · methodology

discussion (0)

Reference graph

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F. S. Bergeret, A. F. Volkov, K. B. Efetov, Odd triplet superconductivity and related phenomena in superconductor-ferromagnet structures.Rev. Mod. Phys.77, 1321–1373 (2005)

2005

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GB further acknowledges support through the SFB Q- M&S project of the FWF, DOI 10.55776/F86

M. Strohmeier,et al., Numerical data for ”Nodal superconductivity with spin-triplet component in a noncentrosymmetric weakly-correlated metal” (2026). Acknowledgments We are deeply indebted to Manfred Sigrist for his valuable scientific input and insightful discussions. We also thank Maksym Serbyn, Antonio Vecchione, Lilia Boeri and Simone Di Cataldo for ...

work page doi:10.55776/f86 2026