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REVIEW 3 major objections 3 minor 59 references

Discovery of High-Temperature Charge Order and Time-Reversal Symmetry-Breaking in the Kagome Superconductor YRu3Si2

T0 review · 3 major / 3 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read YRu3Si2 combines an 800 K charge order with hidden magnetism and multigap superconductivity.

desk verdict Solid new muSR/XRD study of YRu3Si2 with a convincing 800 K transition, but the TRS-breaking claim below 25 K rests on an unmeasured structural assumption. read the letter →

arxiv 2507.06885 v1 pith:7AR5LHV4 submitted 2025-07-09 cond-mat.supr-con cond-mat.mtrl-sci

P. Kràl , J.N. Graham , V. Sazgari , I. Plokhikh , A. Lukovkina , O. Gerguri , I. Bialo , A. Doll
show 16 more authors
L. Martinelli J. Oppliger S.S. Islam K. Wang M. Salamin H. Luetkens R. Khasanov M.v. Zimmermann J.-X. Yin Ziqiang Wang J. Chang B. Monserrat D. Gawryluk F.O. von Rohr S.-W. Kim Z. Guguchia
This is my paper · ORCID
classification cond-mat.supr-concond-mat.mtrl-sci PACS 74.70.-b74.25.Ha76.75.+i
keywords kagomelatticechargeordertime-reversalsymmetrybreakingmuonspinrotationmultigapsuperconductivityvanHovesingularityYRu3Si2hiddenmagnetism
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 the kagome-lattice superconductor YRu$_3$Si$_2$ hosts a rare coexistence of electronic orders. Combining X-ray diffraction, magnetotransport, muon spin rotation, and density functional theory, the authors find a charge-ordered state with propagation vector $(1/2,0,0)$ and onset $T_{\rm co}\simeq 800$ K, which they identify as a record for kagome systems and for quantum materials broadly. They likewise find time-reversal symmetry breaking below $T_2^*\simeq 25$ K and field-induced magnetism below $T_1^*\simeq 90$ K, with both temperature scales mirrored in a magnetoresistance that reaches 45%. Superconductivity below $T_c=3.4$ K is bulk and nodeless, described by either two isotropic gaps or an anisotropic nodeless gap, making YRu$_3$Si$_2$ a single platform where high-temperature charge order, hidden magnetism, and multigap superconductivity can be studied together.

What carries the argument

The central objects are the $(1/2,0,0)$ charge-ordered state, realized as a $Cccm\to Pmma$ structural transition and stabilized in density functional theory by imaginary phonon modes at the $A$ and $L$ points, and the muon spin rotation technique used as a bulk probe of internal fields. Zero-field muon relaxation detects the static internal fields that signal time-reversal symmetry breaking, while transverse-field muon relaxation in the vortex state yields the temperature-dependent superfluid density used to discriminate superconducting gap models. The electronic structure provides the proposed mechanism: two van Hove singularities near the Fermi level, one in a flat band, survive the charge-order distortion and are invoked as the prerequisite for loop-current order, which the paper identifies as the likely origin of the 25 K TRS-breaking phase.

What would settle it

Perform temperature-dependent X-ray or neutron diffraction on YRu$_3$Si$_2$ with fine steps between 5 K and 50 K: a new superlattice reflection or a lattice-symmetry change at roughly 25 K would show that the zero-field muon relaxation increase comes from a structural transition rather than electronic time-reversal symmetry breaking.

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Extended reading notes

Core claim

The central claim is that YRu$_3$Si$_2$ is a kagome superconductor in which three distinct symmetry-breaking phenomena coexist. A charge-ordered phase with propagation vector $(1/2,0,0)$ forms below $T_{\rm co}\simeq 800$ K, corresponding to a structural transition from the $Cccm$ to the $Pmma$ space group, and the paper argues this is the highest charge-order onset yet seen in a kagome system. Below $T_2^*\simeq 25$ K, zero-field muon spin relaxation increases while a small longitudinal field restores the full muon polarization, indicating static internal fields of about 0.45 G and therefore time-reversal symmetry breaking in the electronic state. High-field muon experiments show a field-induced enhancement of the magnetic response below $T_1^*\simeq 90$ K, and magnetotransport tracks both scales, with magnetoresistance reaching 45%. Density functional theory places two van Hove singularities near the Fermi level, one of them within a flat band, and the authors attribute the TRS-breaking phase to the persistence of multiple van Hove singularities in the charge-ordered state. Superconductivity below $T_c=3.4$ K is bulk, with a gap structure that excludes nodal pairing and is fitted either by two isotropic gaps, $\Delta_1=0.53(1)$ meV and $\Delta_2=0.15(1)$ meV, or by an anisotropic nodeless gap with anisotropy ratio $a=0.20(2)$.

Load-bearing premise

The time-reversal-symmetry-breaking claim rests on the assertion that no structural distortion occurs across $T_2^*\simeq 25$ K, but the paper's X-ray diffraction data are taken at 80, 300, 780, and 880 K, not across that transition.

Editorial extensions

If this is right

  • YRu$_3$Si$_2$ becomes the reference kagome compound for high-temperature charge order, doubling the $T_{\rm co}$ scale set by LaRu$_3$Si$_2$ and suggesting the 132 family can host even higher ordering temperatures.
  • A transition at $T_2^*\simeq 25$ K that breaks time-reversal symmetry without static magnetic order points to an electronic hidden order such as loop currents, so microscopic models of kagome metals must reproduce both the charge-order wave vector and this separate low-temperature transition.
  • Because the magnetoresistance and its temperature derivative track $T_1^*$ and $T_2^*$, transport can serve as a rapid screening tool for the magnetic phases in other kagome compounds.
  • The exclusion of a nodal $d$-wave gap, together with the preference for two isotropic gaps or an anisotropic nodeless gap, constrains the pairing symmetry and supports a correlation-driven, unconventional superconducting mechanism.
  • The Uemura ratio $T_c/\lambda_{\rm eff}(0)^{-2}\simeq 0.10$ places YRu$_3$Si$_2$ in the unconventional-superconductor range, implying a comparatively dilute superfluid density rather than conventional BCS behavior.

Reading between the lines

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

  • If the 800 K charge order is electronic in origin, then chemical pressure on the rare-earth site may push the ordering temperature even higher; an isovalent substitution series on YRu$_3$Si$_2$ would test this trend directly.
  • The two-gap versus anisotropic nodeless ambiguity could be settled by specific-heat or single-crystal penetration-depth measurements; a confirmed small gap near 0.15 meV would imply multigap superconductivity tied to distinct Fermi-surface sheets.
  • A loop-current interpretation of the 25 K phase predicts additional experimental signatures such as an anomalous Kerr rotation or Nernst response near $T_2^*$, which would go beyond the muon evidence presented here.
  • The unusually high $T_{\rm co}$ raises the question of whether the charge order is a lattice-driven (Peierls-like) or electronically driven instability; measuring the order parameter and phonon dispersion across 800 K would distinguish these pictures.
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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

3 major / 3 minor

Summary. The manuscript reports a combined single-crystal X-ray diffraction, magnetotransport, muon spin rotation (μSR), and density functional theory (DFT) study of the kagome superconductor YRu3Si2. It claims a high-temperature charge-ordered state with propagation vector (1/2, 0, 0) and onset Tco ≈ 800 K, time-reversal symmetry (TRS) breaking below T2* ≈ 25 K, field-induced magnetism below T1* ≈ 90 K, and bulk superconductivity at Tc = 3.4 K with either two isotropic full gaps or an anisotropic nodeless gap. The XRD data directly show a structural Cccm-to-Pmma transition near 800 K, and the μSR data show a small increase in zero-field relaxation below 25 K as well as a field-dependent relaxation enhancement. The paper interprets the 800 K transition as charge order on the basis of DFT bond-length arguments, and interprets the low-temperature μSR increase as electronic TRS breaking based on an assertion that no structural distortion occurs across T2*.

Significance. If established, the reported coexistence of record-high charge order, hidden magnetism, and multigap superconductivity in YRu3Si2 would be highly significant for the kagome-condensed-matter field. The experimental effort is substantial: the temperature-dependent XRD maps, the zero-field and high-field μSR datasets, and the superconducting penetration-depth analysis are all carefully presented, including quantitative fits to competing gap models. The comparison with LaRu3Si2 is useful and places the new results in context. However, the two most striking claims — the 800 K charge order and the 25 K TRS breaking — depend on interpretational steps that the current data do not directly support. The underlying measurements appear sound, but the manuscript needs either additional experiments or a substantial rephrasing of the central claims to match the evidence.

major comments (3)
  1. [X-ray diffraction and Fig. 1] The claim that YRu3Si2 exhibits charge order with Tco ≈ 800 K is not directly established by the data presented. The superstructure reflections in Fig. 1a-d demonstrate a structural phase transition from Cccm to Pmma, and the DFT calculations in Fig. 1h-j show that the Pmma structure has Ru-Ru bond-length distortions that the authors call 'charge order characteristics.' However, no measurement of electronic charge modulation (e.g., resonant X-ray scattering, STM, or ARPES) is provided. A lattice distortion alone, even one driven by a phonon instability, does not necessarily imply charge order in the electronic sense. The sentence 'This transition establishes charge order at Tco = 800 K' therefore overstates what the XRD data show; the title and abstract's record-Tco claim should be qualified to a structural transition with DFT-supported charge-order character unless direct evidence is added.
  2. [Zero-field μSR and Fig. 4b] The central claim of time-reversal symmetry breaking below T2* ≈ 25 K is built on the sentence near Fig. 4b: 'Keeping in mind that there is no structural distortion across T2*, we can dismiss changes in the structure being the origin for the increase of relaxation rate.' This assertion is unsupported by any measurement in the paper: the XRD data in Fig. 1 cover 80 K, 300 K, 780 K, and 880 K, with no data between 80 K and 25 K. Given that the material already undergoes a displacive structural transition near 800 K and that the zero-field relaxation increase is small (ΔΓZF ≈ 0.045 μs⁻¹, ≈0.45 G), a subtle lattice distortion or a muon-site change across T2* could produce the observed increase in relaxation via altered nuclear dipolar broadening. The longitudinal-field recovery (Fig. 4a) establishes only that the internal fields are static on the μs timescale, not that they are electronic in origin. Unless dedicated structural data across T2* are provided, the assignment of this phase to electronic TRS breaking is not established.
  3. [High-field μSR and Fig. 5] The interpretation of the high-field μSR data as evidence for a 'hidden magnetic state' and field-induced magnetism below T1* ≈ 90 K (Fig. 5a-c) is underdetermined. The relaxation rate σHTF increases with applied field, but the paper does not exclude field-dependent changes in the muon-site distribution or in the nuclear dipolar background, especially given that the material is being driven near a possible structural instability. The comparison with LaRu3Si2 (Fig. 5b) is interesting, but the difference in field dependence could also reflect differences in muon crystallography or electronic structure rather than a distinct magnetic phase. A direct probe of magnetism (e.g., magnetization or neutron diffraction) or a more detailed μSR lineshape analysis would be needed to support the 'magnetic state' claim.
minor comments (3)
  1. [Main text figure cross-references] The main text mis-references figures: the XRD results are said to be shown in 'Fig. 7a-d' and the structures/DFT results in 'Fig. 7e-j', 'Fig. 7h', and 'Fig. 7j', but the corresponding panels belong to Fig. 1a-j in the captions. Please correct all such cross-references.
  2. [Methods, Eq. (1)] The TF-μSR fit function is described as a two-component functional form, but Eq. (1) sums over i = 0, 1, 2 and Eq. (2) uses a denominator As,1 + As,2 that is inconsistent with the stated sum limits. Please correct the summation indices and the moment equations.
  3. [Reference list and data availability] Reference 29 lists the first author as 'C. M. III' rather than a full name; this should be expanded for clarity. In addition, the data availability statement says data are available on request; depositing the underlying XRD and μSR data in a public repository would improve reproducibility, especially given the record-claim nature of the paper.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the central claims are direct measurements and standard model fits; self-citations are comparative, not load-bearing.

full rationale

The derivation chain is self-contained for the paper's main results. The charge-order transition at Tco ~ 800 K is inferred from superstructure reflections in single-crystal XRD (Fig. 1) and corroborated by DFT phonon calculations of the Pmma phase; neither depends on the LaRu3Si2 results except as a comparison. The superconducting gap structure is obtained by fitting the measured TF-muSR relaxation rate to standard London-model expressions (Eqs. 1-4) and is not a re-labeling of a fitted input. The ZF-muSR increase below T2* ~ 25 K is a measured relaxation-rate change whose static character is established by the recovery of polarization in a 5 mT longitudinal field; the interpretation as TRS breaking relies on the sentence 'Keeping in mind that there is no structural distortion across T2*, we can dismiss changes in the structure being the origin for the increase of relaxation rate.' That sentence is an unsupported assumption -- the XRD data shown stop at 80 K -- but it is not circular, because the muSR data are not derived from the structural claim nor vice versa; it is a correctness risk about an unmeasured alternative, not a reduction of the conclusion to its inputs. Self-citations to LaRu3Si2 (refs 10, 28-30) and to earlier kagome muSR work (refs 8, 9, 39, 42) appear as motivation, analogy, and comparison (e.g., Fig. 5b), but they are not used as the fitting equations or as the evidence for the YRu3Si2 anomalies. No fitted parameter is renamed as a prediction, and no uniqueness theorem from the authors' prior work is invoked to forbid alternative explanations. The paper would be strengthened by a structural probe across T2*, but that is a missing-evidence issue, not a circularity issue.

Assumptions & free parameters 6 free parameters · 5 assumptions · 2 invented entities

The experimental claims are new measurements, not derivations, so the ledger is mostly about interpretive assumptions. The SC gap parameters are fitted values, not predictions. The two invented entities are inferred magnetic phases, not new particles or forces. The 800 K charge-order interpretation and the 25 K TRS-breaking interpretation carry the heaviest unproven assumptions.

free parameters (6)
  • Superconducting gap Delta_1 (two-gap isotropic model) = 0.53(1) meV
    Fitted to the temperature dependence of inverse squared penetration depth in Fig. 3d; it is a fit parameter, not a prediction.
  • Superconducting gap Delta_2 (two-gap isotropic model) = 0.15(1) meV
    Second gap in the two-gap fit, carrying about 7% relative weight; fitted to the same data.
  • Relative weight of the first superconducting gap = 0.93(1)
    Weight ratio between the two gaps in the two-gap model; adjusted to reproduce lambda(T).
  • Anisotropic nodeless gap amplitude and anisotropy ratio = Delta_1 = 0.52(1) meV, a = 0.20(2)
    Alternate model fit to the same lambda(T) data; the paper states both models reproduce the data comparably.
  • Nuclear depolarization contribution sigma_nm = not quoted numerically
    Assumed constant at the normal-state value and subtracted from the total relaxation rate to isolate sigma_SC.
  • Upper critical field mu0Hc2 = 1.0 T at 2 K
    Estimated from field-dependent suppression of the resistive superconducting transition.
assumptions (5)
  • domain assumption The increase in zero-field muon relaxation below T2* arises from static spontaneous internal fields rather than from muon diffusion, impurity magnetism, or a structural change.
    Longitudinal-field repolarization supports static fields, but the absence of a structural distortion across T2* is asserted without a dedicated structural probe in this paper.
  • domain assumption The Cccm-to-Pmma transition near 800 K is electronic charge order, not merely a conventional structural distortion.
    The charge-order label is inferred from DFT displacement patterns and a calculated DOS reduction; no direct charge modulation (e.g., STM or resonant scattering) is measured.
  • domain assumption The P6/mmm phase, not directly observed up to 900 K, is the correct parent structure for the DFT phonon and band structure calculations.
    The paper uses hexagonal twin symmetry to infer the parent phase; this enters all first-principles results.
  • domain assumption DFT with the PBEsol functional and harmonic phonon calculations correctly describes the relative stability and instabilities of the three structures.
    Standard approximations are used without anharmonic corrections or benchmark against experimental phonon data.
  • domain assumption Implanted muons probe a representative bulk distribution of internal fields in the polycrystalline pellet.
    Standard muSR assumption; no muon stopping-site calculation is provided.
invented entities (2)
  • Hidden magnetic state or field-induced magnetism below T1* ~ 90 K
    purpose: Explains the onset of magnetoresistance and the field-enhanced high-field muSR relaxation rate below 90 K.
    Inferred from muSR relaxation rates and transport; no magnetic Bragg peaks or resolved static order parameter are reported.
  • Loop-current order as the origin of TRS breaking below T2*
    purpose: Proposed microscopic explanation for the TRS-breaking phase based on persistent multiple van Hove singularities.
    Attributed on the basis of theoretical proposals (refs. 18 and 44); no direct observation of loop currents is made in this work.

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Cite this review

Pith. "Pith review of Discovery of High-Temperature Charge Order and Time-Reversal Symmetry-Breaking in the Kagome Superconductor YRu3Si2." pith.science (2026). https://pith.science/paper/7AR5LHV4

@misc{pith2026250706885,
  author       = {Pith},
  title        = {Pith review of: Discovery of High-Temperature Charge Order and Time-Reversal Symmetry-Breaking in the Kagome Superconductor YRu3Si2},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7AR5LHV4}},
  note         = {Machine review of arXiv:2507.06885}
}
abstract

The identification of high-temperature unconventional charge order and superconductivity in kagome quantum materials is pivotal for deepening our understanding of geometrically frustrated and correlated electron systems, and for harnessing their exotic properties in future quantum technologies. Here, we report the discovery of a remarkably rich phase diagram in the kagome superconductor YRu$_{3}$Si$_{2}$, uncovered through a unique combination of muon spin rotation (${\mu}$SR), magnetotransport, X-ray diffraction (XRD), and density functional theory (DFT) calculations. Our study reveals the emergence of a charge-ordered state with a propagation vector of (1/2, 0, 0), setting a record onset temperature of 800 K for such an order in a kagome system and for quantum materials more broadly. In addition, we observe time-reversal symmetry (TRS) breaking below $T_{2}^{*}$ ${\simeq}$ 25 K and field-induced magnetism below $T_{1}^{*}$ ${\simeq}$ 90 K, indicating the presence of a hidden magnetic state. These transitions are mirrored in the magnetoresistance data, which show a clear onset at ${\sim}$ $T_{1}^{*}$ and a pronounced increase below ${\sim}$ $T_{2}^{*}$, ultimately reaching a maximum magnetoresistance of 45${\%}$. Band structure calculations identify two van Hove singularities (VHSs) near the Fermi level, one of which resides within a flat band, suggesting a strong interplay between electronic correlations and emergent orders. At low temperatures, we find bulk superconductivity below $T_{\rm c}$ = 3.4 K, characterized by a pairing symmetry with either two isotropic full gaps or an anisotropic nodeless gap. Together, our findings point to a coexistence of high-temperature charge order, tunable magnetism, and multigap superconductivity in YRu$_{3}$Si$_{2}$, positioning it as a compelling platform for exploring correlated kagome physics.

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