Unconventional superconductivity in ScIr$_2$ chiral crystal with a kagome lattice

Dariusz Jakub Gawryluk; Igor Plokhikh; JianZhou Zhao; Keqi Xia; Marisa Medarde; Qingfeng Zhan; Tian Shang; Toni Shiroka; Yang Xu

REVIEW 3 major objections 5 minor 148 references

Unconventional superconductivity in ScIr$_2$ chiral crystal with a kagome lattice

T0 review · 3 major / 5 minor · reviewed 2026-08-01 · deepseek-v4-flash

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Pith's one-line read Muon-spin and specific-heat data pin ScIr2−xSix as a two-gap (s+d)-wave superconductor, with one gap containing line nodes.

desk verdict New muSR and SXRD data make ScIr2-xSix a plausible chiral kagome superconductor, but the nodal (s+d) claim rests on borrowed specific heat, not the new muSR. read the letter →

arxiv 2607.16689 v1 pith:5DMTMMSY submitted 2026-07-18 cond-mat.supr-con cond-mat.mtrl-scicond-mat.str-el

Keqi Xia , Jianzhou Zhao , Igor Plokhikh , Marisa Medarde , Yang Xu , Qingfeng Zhan , Dariusz Jakub Gawryluk , Toni Shiroka

show 1 more author

Tian Shang

This is my paper

classification cond-mat.supr-concond-mat.mtrl-scicond-mat.str-el

keywords kagomelatticeunconventionalsuperconductivitytwo-gapmuonspinrotationspecificheatchiralcrystalflatbandsScIr2

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 that ScIr2−xSix, a family of kagome-lattice superconductors, hosts unconventional superconductivity: its low-energy excitations cannot be explained by a single fully gapped order parameter. Combining muon-spin rotation and specific-heat analyses, the authors argue that both the parent ScIr2 and the Si-doped ScIr1.82Si0.18 are described by a two-gap (s+d)-wave model in which one gap is nodeless and the other has line nodes. The paper also establishes that ScIr2 undergoes a cubic-to-rhombohedral structural transition near 190 K, so its low-temperature phase contains a slightly distorted Ir kagome layer and an Ir chiral chain, making it a topological chiral crystal. The significance is that this is a rare kagome system where flat bands near the Fermi level, strong correlations, structural chirality, and unconventional superconductivity coexist, offering a platform to study their interplay.

What carries the argument

The central object is the two-gap 'alpha model' for the superconducting state: both the superfluid density ρsc(T) and the electronic specific heat Ce(T)/T are written as weighted sums of two independent gap contributions, with the same weight w, maximum gaps Δ1 and Δ2, and angular gap functions gk = 1 (s-wave) or gk = cos2φ (d-wave) used in both fits. Carrying the argument is the combination of this model with transverse-field muon-spin data for the penetration depth and with zero-field muon-spin data showing preserved time-reversal symmetry; the latter eliminates the point-node (s+p) option, leaving (s+d) as the preferred two-gap description. Band-structure calculations supply the multiband

What would settle it

Measure the zero-field electronic specific heat on the exact same ScIr2 and ScIr1.82Si0.18 batches used for the muon-spin experiments, then re-run the two-gap fits: if the low-temperature Ce/T data are fully reproduced by a nodeless (s+s)-wave model with the same fitted parameters, the nodal d-wave component would disappear. Alternatively, repeat transverse-field muon-spin rotation at a substantially higher applied field (e.g., 100 mT rather than 30 mT), where the s-gap is suppressed and the nodal d-component should become more visible in the temperature dependence of the superfluid density.

Watch

Extended reading notes

Core claim

The central claim is that the superconducting pairing in ScIr2−xSix is unconventional and multigap. The temperature-dependent superfluid density, measured by transverse-field muon-spin rotation, and the zero-field electronic specific heat can both be accurately fitted by a two-gap (s+d)-wave model: an isotropic s-wave gap plus a d-wave gap whose cos2φ angular dependence produces line nodes. The d-wave weight is about 20%, so the nodeless component dominates, which explains why the low-temperature superfluid density is only weakly temperature-dependent. Time-reversal symmetry is preserved in the superconducting state, ruling out the tested (s+p)-wave and chiral p-wave options. Band-structure

Load-bearing premise

The discrimination between (s+d) and (s+s) pairing relies on the zero-field specific-heat data from a separate study being taken on samples with essentially the same actual silicon content as the muon-spin samples, and on the phonon background being adequately captured by a simple γn+βT2+δT4 subtraction; if either fails, the inferred d-wave weight could be an artifact of the fit.

Editorial extensions

If this is right

ScIr2−xSix is an unconventional, multigap superconductor, so any single-gap fully gapped description is inadequate for its low-energy thermodynamics and superfluid response.
Because time-reversal symmetry is preserved, chiral p-wave or (s+p)-wave pairing is excluded in the bulk; the data point to a nodeless-plus-nodal combination, i.e., an (s+d)-type state.
The multiband electronic structure, with multiple Fermi-surface sheets and flat bands near the Fermi level, means the pairing likely arises from a mix of electron-phonon coupling on some bands and spin/charge-fluctuation-mediated pairing on the flat-band-dominated band.
ScIr2 is a noncentrosymmetric chiral crystal at low temperature, making it a candidate for mixed-parity pairing and for exotic surface superconductivity, even if the bulk state preserves time-reversal symmetry.
The (Ca,Sr,Ba,Zr,Th)Ir2 sister compounds, with tunable spin-orbit coupling, become natural next targets for testing how SOC strength affects the nodal gap structure and the pairing symmetry.

Reading between the lines

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

If the (s+d) assignment is correct, a clear testable prediction is that increasing the applied magnetic field in transverse-field muon-spin experiments should suppress the s-wave gap more strongly than the d-wave gap, making the nodal signature more prominent in the superfluid density; conversely, if that does not happen, an anisotropic but nodeless single-gap fit may be the more economical descri
The two-dome superconducting phase diagram in Si content could be reinterpreted as a structural effect: in the first dome the material is rhombohedral with a reduced density of states from antisymmetric spin-orbit splitting, while in the second dome it is cubic with flat bands closer to the Fermi level; this suggests that flat-band-based DOS arguments taken from the cubic structure alone may be mi
The paper's own caveat about 'comparable Si concentrations' between the muon-spin samples and the reference specific-heat samples implies an unstated fragility: a direct measurement of specific heat on the identical batches used for muon-spin would settle whether the claimed d-wave component is real or an artifact of sample mismatch.
Given the preserved time-reversal symmetry in the bulk, the most interesting extension is the surface state: a chiral crystal with strong spin-orbit coupling could harbor topological or chiral surface superconductivity even when the bulk is a TRS-preserving s+d superconductor, and surface-sensitive probes such as scanning tunneling microscopy or Kerr rotation would be the natural 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.

Desk Editor's Note

read the letter

Quick take: this is a competent muSR plus single-crystal XRD study. The genuinely new results are the structural transition in ScIr2 to a chiral R32 phase at ~190 K, confirmed by SXRD with a clear refinement contrast, and the TF/ZF-muSR characterization showing preserved time-reversal symmetry and a two-gap superfluid density. The paper is worth a serious referee, but the headline pairing conclusion—two-gap (s+d) with one nodal gap—is less secure than the writing suggests.

What it does well: the SXRD refinement distinguishing R32 from Fd-3m at 80 K is convincing (chi2 of 1.02 vs 19.7). The ZF-muSR spectra are clean and the absence of TRS breaking is solid. The superfluid-density analysis is standard, and the data alone clearly rule out single-gap d- and p-wave models. The band-structure calculations are reasonable support for multiband physics and flat bands near EF.

The soft spot is exactly where you pointed. Table 1 shows that TF-muSR alone hardly differentiates (s+s) from (s+d): reduced chi2 values are 4.4 vs 5.4 for ScIr2 and 3.1 vs 2.4 for the doped sample. The decisive discrimination comes from Ce/T, where (s+s) gives chi2 >20 and (s+d) gives about 3. Those specific-heat data were not measured in this work; they are taken from the authors' previous paper, Ref. [51]. The Figure 4 caption states only that the samples have "comparable Si concentrations" because the same preparation method was used. That is an assertion, not a demonstration. If the actual Si content differs, or if the phonon subtraction C/T = gamma_n + beta T^2 + delta T^4 is inadequate—and beta for ScIr1.82Si0.18 is only 0.20(3) mJ/mol-K^4, small enough to absorb electronic contributions—the inferred d-wave weight could be a fitting artifact. The authors themselves acknowledge that higher-field muSR is the test that could distinguish the two models, but they do not perform it.

I want to be fair: none of this invalidates the structural result or the unconventional character in a broad sense. The paper is honest about the model-selection logic, and the claim is conditional rather than absurd. But the phrase "solid evidence" in the conclusion overreaches. The central argument holds up only if the sample-matching assumption is accepted, and that is the load-bearing assumption to flag.

Who gets value: the kagome-superconductor and noncentrosymmetric-superconductor communities. I would not cite it in my own near-term work, but I would bring it to a reading group focused on muSR-based pairing determinations.

Recommendation: send to peer review. Ask the authors to either provide higher-field muSR data, demonstrate the Si-content match between the two sample batches with a direct measurement, or soften the conclusion to "consistent with (s+d) rather than (s+s)."

Referee Report

3 major / 5 minor

Summary. This manuscript reports a combined muon-spin spectroscopy (μSR), single-crystal X-ray diffraction (SXRD), electrical transport, magnetization, and density-functional-theory study of the kagome superconductors ScIr2 and ScIr1.82Si0.18. The authors claim that ScIr2 undergoes a cubic-to-rhombohedral (R32) structural transition near 190 K that produces a chiral Ir chain, and that both compounds exhibit unconventional superconductivity described by a two-gap (s+d)-wave model in which one gap is nodal. The pairing-symmetry assignment is based on fits of six gap models to the temperature-dependent superfluid density inferred from transverse-field μSR and to zero-field electronic specific-heat data taken from the authors' earlier work (Ref. [51]). Zero-field μSR shows preserved time-reversal symmetry, which is used to exclude chiral (s+p) pairing.

Significance. If the central claim holds, the paper identifies a rare kagome superconductor with structural chirality and unconventional, partially nodal pairing, making ScIr2–xSix a valuable platform for studying the interplay of flat bands, correlations, topology, and superconductivity. The manuscript contributes new experimental data of good quality: TF- and ZF-μSR measurements, SXRD identification of the R32 phase, and DFT band structures showing flat bands near the Fermi level. These are significant assets. However, the (s+d) pairing conclusion is not established by the new μSR data alone; it is decided by a reanalysis of specific-heat data from a previous paper. The significance is therefore contingent on resolving the sample-matching and phonon-subtraction issues identified below.

major comments (3)

[§2.4 / Table 1 / Fig. 4] The assignment of (s+d) pairing is not determined by the new μSR data. In Table 1, the reduced χ² for (s+s) versus (s+d) from the superfluid-density fits are 4.4 vs 5.4 for ScIr2 and 3.1 vs 2.4 for ScIr1.82Si0.18; for ScIr2 the (s+s) model is actually slightly better. The decisive discrimination (χ²_r >20 vs 3.1/2.64) comes entirely from the Ce/T fits using zero-field data from Ref. [51]. The Figure 4 caption only asserts that 'comparable Si concentrations are expected' and relabels the Ref. [51] sample ScIr1.75Si0.25 as ScIr1.82Si0.18; the actual Si content of that specific-heat sample is not measured. The phonon subtraction C/T = γn + βT² + δT⁴ is also fragile: for ScIr1.82Si0.18, β = 0.20(3) mJ/mol·K⁴ is very small and could absorb low-temperature electronic contributions, biasing Ce/T in the region T/Tc < 0.3 where (s+s) and (s+d) differ. Please either measure Ce/T on the same sample
[§2.4 / Table 1] The text in §2.4 states that in the two-gap Ce/T fit 'w, Δ1, and Δ2' are 'the same parameters as for the superfluid-density fits'. However, Table 1 lists different numerical values for the μSR and Ce/T fits; for example, for ScIr2 with the (s+d) model, w = 0.8 for μSR but 0.63 for Ce/T, and Δ1 = 0.27 meV for μSR but 0.39 meV for Ce/T. Please clarify whether the Ce/T fits were constrained to the μSR-derived parameters or were fitted independently. If they were fitted independently, the claim of a single consistent two-gap model is weaker; if they were constrained, Table 1 and the fits must be corrected. As written, this inconsistency prevents the reader from judging the actual degree of constraint in the combined analysis.
[§2.3 / §4] The authors correctly state in §2.3 that 'TF-μSR measurements in a higher magnetic field can distinguish between these two cases', citing CuIr2Te4 as an example. This discriminating experiment is not performed in the present work, and the (s+d) conclusion instead relies on the borrowed Ce/T data. Given that the new μSR data alone do not select (s+d), the conclusion of unconventional superconductivity would be considerably strengthened by carrying out the acknowledged high-field μSR experiment on the same samples, or by explicitly tempering the concluding claim until such data are available.

minor comments (5)

[Experimental Section] Typo: 'bewteen' should read 'between'.
[Fig. 6 caption] Typo: 'analogus' should read 'analogous'.
[Fig. 4 caption] The sentence 'the extra phases observed in previous studies also resulted in lower actual Si concentrations' is unclear; please rephrase to state explicitly how the composition of the Ref. [51] sample was inferred.
[Eq. (3)] The notation in Eq. (3) — the Fermi-surface average, the integration variable ε, and the angular dependence gk — is not fully specified. Please define the average ⟨...⟩_FS and the relation between ε and k explicitly.
[Table 1] The table headings 'Δ0^{μSR} (meV), w' and 'Δ0^{Ce/T} (meV), w' are ambiguous. Separate columns for Δ1, Δ2 and w would improve readability and avoid confusion between the two fits.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the (s+d)-wave conclusion is a model-selection result using independent muSR and specific-heat data; the main limitations are sample-matching and fit fragility, not definitional circularity.

full rationale

The paper's claimed derivation chain is empirical: TF-muSR gives lambda_eff^-2(T), six gap models (Eq. 3) are fitted to it, the same models are applied to zero-field Ce/T data from Ref. [51] via Eq. (4), and the reduced chi-square values in Table 1 are compared. This is standard model selection, not a derivation in which the conclusion is assumed. The (s+d)-wave choice is not forced by construction: Table 1 shows that the muSR data alone do not discriminate between (s+s) and (s+d) (ScIr2: 4.4 vs 5.4; ScIr1.82Si0.18: 3.1 vs 2.4), and the decisive discrimination comes from the Ce/T data. Those specific-heat data are external (Ref. [51], a different group), so there is no self-citation chain making the result load-bearing on the authors' own prior claims. The Figure 4 caption's statement that 'comparable Si concentrations are expected' and the fragility of the phonon subtraction C/T=gamma_n+beta T^2+delta T^4 are real limitations and correctness risks, but they are not circular: the gap symmetry is not defined in terms of the sample composition, nor is any fitted parameter renamed as an independent prediction. The paper explicitly says the models 'reproduce' and 'describe' the data, not that the data are predicted by a theory derived from the model parameters. No uniqueness theorem is imported from the authors' prior work, and no ansatz is smuggled in via citation: the s-, p-, d-wave gap functions and the two-gap alpha-model are standard, openly stated functional forms. The only self-citations (e.g., Refs. [58] and [101]) are illustrative comparisons or methodological precedents, not load-bearing proof of the central claim. Thus, although the strength of the conclusion may be debated on statistical or sample-matching grounds, the derivation chain is not circular in the sense of reducing to its own inputs by construction.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central claim rests on fitted α-model parameters, a phonon-background assumption, an impurity-phase assumption, an assumed sample-composition match, and DFT band-structure interpretation. No new particles, mediators, or conserved quantities are introduced; 'flat bands', 'chiral chain', and 'topological chiral crystal' are structural/electronic characterizations of the known material.

free parameters (4)

ScIr2: gap amplitudes Δ1, Δ2 and weight w (s+d model) = µSR: Δ1=0.27(1), Δ2=0.35(1) meV, w=0.8; Ce/T: Δ1=0.39(2), Δ2=0.40(2) meV, w=0.63
Fit parameters of the two-gap α-model to λ_eff^-2(T) and Ce/T; the values are not independently predicted and differ between the two datasets.
ScIr1.82Si0.18: gap amplitudes Δ1, Δ2 and weight w (s+d model) = µSR: Δ1=0.60(3), Δ2=0.73(3) meV, w=0.8; Ce/T: Δ1=0.47(3), Δ2=0.54(3) meV, w=0.6
Fit parameters of the two-gap α-model for the doped compound; again fitted rather than predicted.
Normal-state specific-heat coefficients γn, β, δ = ScIr2: γn=14.8(2) mJ/mol K², β=1.6(4) mJ/mol K⁴, δ=0.03(2) mJ/mol K⁶; doped: γn=16.6(1), β=0.20(3), δ=0.016(2)
Obtained by fitting C/T=γn+βT²+δT⁴ to the prior specific-heat data [51] and subtracted to extract the electronic contribution.
Effective magnetic penetration depth λ0 = 425(3) nm (ScIr2), 680(3) nm (ScIr1.82Si0.18)
Output of the superfluid-density fits; used to estimate Hc1 and to place the compounds in the Tc vs λ_eff^-2 phase diagram.

assumptions (5)

domain assumption α-model BCS gap equations (Eq. 3 and Eq. 4) with angle-dependent gap functions gk=1, sinθ, cos2φ
Used to interpret superfluid density and specific heat; assumes a single spherical Fermi surface and no multiband coupling within each gap component.
domain assumption Normal-state phonon background is fully captured by βT²+δT⁴ over the whole measured range
Required to extract Ce/T from the specific-heat data of Ref. [51]; an imperfect subtraction would bias the low-temperature electronic specific heat.
ad hoc to paper The Ir3Si5 impurity phase in ScIr1.82Si0.18 has negligible effect on the superconducting muon relaxation rate
Stated in the Experimental Section without quantitative phase fraction or a dedicated impurity-control experiment.
ad hoc to paper The specific-heat sample in Ref. [51] has comparable actual Si content to the muSR sample, despite different nominal compositions
The Figure 4 caption says 'comparable Si concentrations are expected', but no direct composition measurement is presented for the specific-heat sample.
domain assumption DFT-PBE band structure with SOC accurately locates the flat bands and DOS peak near EF
The explanation connecting flat bands to superconductivity and to the structural transition relies on these calculations; no experimental band-structure measurement is shown.

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Pith. "Pith review of Unconventional superconductivity in ScIr$_2$ chiral crystal with a kagome lattice." pith.science (2026). https://pith.science/paper/5DMTMMSY

@misc{pith2026260716689,
  author       = {Pith},
  title        = {Pith review of: Unconventional superconductivity in ScIr$_2$ chiral crystal with a kagome lattice},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5DMTMMSY}},
  note         = {Machine review of arXiv:2607.16689}
}

abstract

Materials with a kagome lattice host exotic quantum phenomena driven by the interplay between band topology, spin-orbit coupling, magnetism, and electronic correlations. While magnetism of kagome materials has been widely investigated, their unconventional superconductivity (SC) remains largely unexplored due to the limited availability of suitable materials. Here, we report evidence of unconventional SC in the ScIr$_{2-x}$Si$_{x}$ family by combining muon-spin spectroscopy measurements with band-structure calculations. The parent ScIr$_2$ undergoes a structural phase transition from a high-$T$ cubic- to a low-$T$ rhombohedral phase, while the Ir kagome layer remains, albeit slightly distorted. Although the structural transition is suppressed by Si substitution, the superconducting pairing of ScIr$_{2-x}$Si$_{x}$ remains well described by a two-gap model. Since at least one of the gaps has nodes, this indicates an unconventional SC. Its unconventional nature can be explained by the distinct flat bands occurring near the Fermi level, leading to strong electronic correlations in the ScIr$_{2-x}$Si$_{x}$ family. Moreover, the low-$T$ phase of ScIr$_2$ exhibits an Ir chiral chain; therefore, it can be classified as a topological chiral crystal. Overall, the unusual properties of the ScIr$_{2-x}$Si$_{x}$ family make it an interesting, albeit rare, system for studying the interplay between unconventional SC, flat bands, and chirality.

Figures

Figures reproduced from arXiv: 2607.16689 by the authors.

**Figure 1.** Phase diagram and crystal structure. a) Superconducting phase diagram of ScIr2−xSix (0 ≤ x ≤ 0.35). Superconducting transition temperatures determined from the specific heat Cp were taken from Ref. [51]. Note that, previously the same compound was dubbed Sc2 Ir4−xSix (0 ≤ x ≤ 0.7) [51], where the nominal Si concentrations were used. b) Temperature-dependent electrical resistivity ρ(T) (left axis) and its derivative … view at source ↗

**Figure 2.** Characterization of superconductivity. a) Temperature-dependent magnetic susceptibility χ(T) for ScIr2 and ScIr1.82Si0.18. Magnetic susceptibility data were collected using both field-cooled (FC) and zero-field-cooled (ZFC) protocols in an applied magnetic field of 1 mT. Magnetic susceptibility data were normalized to their lowest-temperature value. b) Upper critical fields Hc2 of ScIr2 and ScIr1.82Si0.18. The inset… view at source ↗

**Figure 3.** Exploring the superconducting pairing via TF-µSR. a,b) TF-µSR spectra collected in the superconducting and normal states in an applied magnetic field of 30 mT for ScIr2 (a) and ScIr1.82Si0.18 (b). All the spectra were collected using a FC protocol. Solid lines through the data are fits to Eq. (1). c,d) FFT of the relevant µSR spectra in panels (a) and (b) for ScIr2 (c) and ScIr1.82Si0.18 (d). e,f) Superfluid density… view at source ↗

Figures from the paper (4 more)

**Figure 4.** Figure 4: Electronic specific heat. a,b) Normalized electronic specific heat Ce/γn T as a function of the reduced temperature T/Tc for ScIr2 (a) and ScIr1.82Si0.18 (b). The different lines represent fits to the various models, analogous to those used to analyze the superfluid de…

**Figure 5.** Figure 5: Preserved TRS in the superconducting state of ScIr2−xSix . a,b) ZF-µSR spectra of ScIr2 (a) and ScIr1.82Si0.18 (b), collected in their superconducting (0.3 K) and normal (2 and 4 K) states. Solid lines through the data are fits to Eq. (2) using the Kubo-Toyabe relaxati…

**Figure 6.** Figure 6: Electronic band structures. a,b) First Brillouin zone of ScIr [PITH_FULL_IMAGE:figures/full_fig_p022_6.png]

**Figure 7.** Figure 7: Chiral crystal structure and surface states of ScIr [PITH_FULL_IMAGE:figures/full_fig_p023_7.png]

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