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REVIEW 4 major objections 5 minor 47 references

Pressure induced transition from chiral charge order to time-reversal symmetry-breaking superconducting state in Nb-doped CsV$_3$Sb$_5$

T0 review · 4 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read Muon-spin and pressure data argue that in Nb-doped CsV3Sb5, suppressing the chiral charge order with about 0.85 GPa reveals a superconducting state that breaks time-reversal symmetry.

desk verdict A serious experimental paper with a genuinely new depth-resolved finding, but the headline TRS-breaking superconducting claim rests on an unverified assumption about charge order suppression, and the text has a numeric inconsistency that must be fixed. read the letter →

arxiv 2411.18744 v1 pith:WHG6BWNZ submitted 2024-11-27 cond-mat.supr-con cond-mat.mtrl-sci

J.N. Graham , S.S. Islam , V. Sazgari , Y. Li , H. Deng , G. Janka , Y. Zhong , O. Gerguri
show 14 more authors
P. Kral A. Doll I. Bialo J. Chang Z. Salman A. Suter T. Prokscha Y. Yao K. Okazaki H. Luetkens R. Khasanov Z. Wang J.-X. Yin Z. Guguchia
This is my paper · ORCID
classification cond-mat.supr-concond-mat.mtrl-sci
keywords kagomesuperconductorCsV3Sb5Nbdopingchargeordertime-reversalsymmetrybreakinghydrostaticpressuremuonspinrotationsuperconductinggap
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

The paper sets out to show that in the kagome superconductor Cs(V0.93Nb0.07)3Sb5, hydrostatic pressure converts the normal-state chiral charge order into a superconducting state that spontaneously breaks time-reversal symmetry. In the bulk of the crystal at ambient pressure, muon-spin rotation detects internal magnetic fields below T* ≈ 40 K, well below the charge-order onset at TCO ≈ 58 K, whereas near the surface the magnetic signal appears at TCO and is about twice as strong. Applying pressure raises both Tc (from 4.5 K to 7 K) and the superfluid density, and once the pressure exceeds about 0.85 GPa the superconducting state exhibits a nodeless gap together with weak internal fields below Tc, which the authors read as evidence for chiral pairing. If correct, the result would show that a single tuning parameter, pressure, can dial a kagome metal from a charge-ordered normal state into a time-reversal-breaking superconductor, and it would strengthen the case that such pairing is a generic feature of the AV3Sb5 family.

What carries the argument

The experimental engine is muon spin rotation (µSR), in which spin-polarized muons implanted in the crystal precess in the local magnetic field; in zero field an exponential relaxation rate Γ measures the distribution of static internal fields, and an increase in Γ below a transition temperature is the standard signature of spontaneously broken time-reversal symmetry. The paper combines three variants: zero-field and high-field µSR to separate electronic from nuclear contributions, low-energy µSR to tune the muon implantation depth between about 1 nm and 120 nm (revealing the surface-bulk difference), and transverse-field µSR under hydrostatic pressure to extract the superfluid density from the muon depolarization rate. The data-analysis identity connecting the superconducting relaxation rate to the London penetration depth, σsc(T)/γµ = 0.06091 Φ0/λ²(T), then converts measured relaxation rates into gap structure and superfluid density values.

What would settle it

Look for the 2×2 charge-order superstructure or its ~20 meV gap under pressure: if x-ray scattering, STM, or transport measurements at 1.2 GPa show that charge order persists or is only partially suppressed, then the TRS-breaking signal below Tc cannot be cleanly assigned to superconductivity. Alternatively, measure zero-field µSR in a Nb-doped sample with charge order fully suppressed chemically; the absence of any internal-field increase below Tc would directly contradict the claim.

Watch

Extended reading notes

Core claim

At ambient pressure, bulk Nb0.07-CVS breaks time-reversal symmetry (the symmetry between forward and backward time evolution, whose breaking reveals itself in spontaneous static internal fields) below T* = 40 K, while its 2×2 chiral charge order sets in at TCO = 58 K; low-energy muon-spin rotation shows the magnetic signal begins at TCO near the surface, within about 20 nm, and is roughly twice as strong as in the bulk. Nb doping raises Tc from 2.5 K to 4.4 K, and hydrostatic pressure further enhances Tc to about 7 K and doubles the superfluid density. Above a critical pressure pcr ≈ 0.85 GPa, the superconducting state shows a nodeless (fully gapped) pairing symmetry and, from zero-field muon-spin rotation, weak internal fields appear only below Tc, indicating broken time-reversal symmetry in the superconducting state itself. The authors interpret the combination of a full gap and broken time-reversal symmetry as compatible with a chiral dx2-y2 + idxy or px + ipy pairing state, and they note the same TRS-breaking response below Tc in undoped CsV3Sb5 at 1.78 GPa and in Ta-doped CsV3Sb5 with suppressed charge order.

Load-bearing premise

The load-bearing premise is that hydrostatic pressure above about 0.85 GPa fully suppresses charge order in Nb0.07-CVS, so the time-reversal-symmetry-breaking fields seen below Tc are intrinsic to the superconducting state and not remnants of the charge-ordered normal state; the paper states this assumption explicitly in the Discussion when interpreting the pressure data.

Editorial extensions

If this is right

  • If the central claim holds, pressure is a clean switch between two broken-symmetry states in the same material: chiral charge order at ambient pressure and TRS-breaking (likely chiral) superconductivity above about 0.85 GPa.
  • The nodeless gap plus TRS breaking points to a chiral pairing state (dx2-y2+idxy or px+ipy), which would make Nb0.07-CVS a concrete platform for studying chiral or topological superconductivity.
  • The near-linear scaling between Tc and superfluid density across pressure suggests a common unconventional pairing mechanism shared by the kagome AV3Sb5 family.
  • The surface-bulk difference (T* = 40 K bulk versus TCO = 58 K surface) implies that surface-sensitive probes can overestimate the TRS-breaking onset, so reported onset temperatures should be accompanied by depth information.

Reading between the lines

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

  • The depth-dependent decoupling suggests a natural experiment: map T* as a function of muon implantation depth at several Nb dopings; if the surface-bulk difference tracks charge-order strength, the near-surface TRS signal is likely charge-order driven, while the bulk 40 K signal may be a separate order.
  • If the pressure-induced TRS-breaking superconducting state is generic, compounds with fully suppressed charge order (Ta-doped and K, Rb, Cs compounds under pressure) should all show the same weak internal fields below Tc; a systematic comparison of their field strengths would test whether the pairing state is universal.
  • A testable extension of the Tc-superfluid-density scaling is to measure λ−2 at pressures up to 2.2 GPa; if the linear relation persists beyond the first-order jump, the enhancement would look like a continuous evolution of pairing strength rather than a simple consequence of charge-order suppression.
  • Because the assignment of the TRS signal to superconductivity rests on charge order being fully suppressed at 0.85 GPa, a direct high-pressure structural probe of Nb0.07-CVS would either validate or correct that assignment.
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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

4 major / 5 minor

Summary. The paper presents a muon spin rotation/relaxation (μSR), AC susceptibility, and scanning tunnelling microscopy study of the Nb-doped kagome superconductor Cs(V0.93Nb0.07)3Sb5 (Nb0.07-CVS) under doping, hydrostatic pressure, magnetic field, and muon implantation depth. The authors report three main findings: (1) in the normal state at ambient pressure, time-reversal symmetry (TRS) breaking occurs below T* = 40 K in the bulk, decoupled from the charge-order onset at TCO = 58 K, while near the surface (within ~20 nm) the TRS-breaking signal is doubled and onsets at TCO; (2) hydrostatic pressure raises Tc from 4.5 K to about 7 K, doubles the superfluid density, and changes the superconducting gap structure from a single nodeless s-wave gap to a two-gap structure at 0.8 GPa and back to a single nodeless gap at 1.2 GPa; and (3) zero-field μSR at 1.2 and 1.5 GPa shows an increase in the relaxation rate below Tc, which the authors interpret as TRS breaking in the superconducting state, possibly indicating chiral superconductivity.

Significance. If the central claims hold, this paper would provide a comprehensive and depth-resolved picture of how TRS breaking evolves from the normal-state charge-ordered phase to the superconducting phase in a kagome superconductor, supported by an unusually complete combination of μSR techniques (ZF, TF, high-field, and low-energy depth profiling) and pressure tuning. The authors explicitly acknowledge the importance of ruling out electric-field-gradient effects by using high-field μSR controls, which is a methodological strength. The reported pressure phase diagram and the gap-structure analysis are useful additions to the kagome superconductivity literature. However, the most novel claim — that the superconducting state above pcr breaks TRS — rests on an assumption that charge order is fully suppressed under pressure in Nb0.07-CVS, which is not directly measured in this compound. Because the normal state of the same material already exhibits TRS breaking at ambient pressure, this missing control is load-bearing. The paper is therefore significant if the assumption can be substantiated, but the current evidence is conditional rather than conclusive.

major comments (4)
  1. [§IV, Discussion and §III] The central claim of a TRS-breaking superconducting state above pcr relies on the assumption that charge order is fully suppressed for p > 0.85 GPa. The manuscript states in Section IV: 'we assume that the charge order is suppressed with pressure, as has been measured in other AV3Sb5 compounds', and in Section III: 'At 0.8 GPa, the pressure brings the system into the optimal Tc region of the phase diagram, where charge order is fully suppressed'. No direct measurement of charge order under pressure (e.g., XRD, neutron, or STM at pressure) is reported for Nb0.07-CVS. Since the same compound exhibits normal-state TRS breaking below T* = 40 K at ambient pressure, a remnant of this signal above Tc at 1.2 GPa could be misidentified as a superconducting-order-induced increase. To support the claim, the authors should measure the ZF-μSR relaxation rate in the normal state just above Tc at p > pcr, or provide a direct probe of charge-order suppression under pressure for this specific stoichiometry without relying on extrapolation from other AV3Sb5 compounds.
  2. [§II, Fig. 2c] The high-field μSR data are presented only in normalized form, so the reader cannot judge the absolute magnitude of the 8-T relaxation enhancement or its relation to the nuclear baseline. The authors argue that the 8-T increase confirms the magnetic origin of the TRS-breaking signal, but without absolute relaxation rates and a quantitative estimate of the nuclear contribution remaining at 8 T, it is difficult to exclude field-dependent artifacts or a partial suppression of the nuclear signal. Please provide the unnormalized σ(T) for each applied field, including the 0.01 T and 8 T data, with the nuclear contribution explicitly modeled.
  3. [§III, Fig. 6b and Methods] The zero-field μSR measurements under pressure are performed in a double-wall MP35N/CuBe pressure cell, yet the manuscript does not describe how the pressure-cell background was separated from the sample signal or whether the cell contributes a temperature-dependent relaxation. The reported increase in Γ below Tc is small (roughly 0.02–0.03 μs−1 in Fig. 6b), comparable in magnitude to the ambient-pressure normal-state signal. Given this, a pressure-cell background with any temperature dependence around Tc could mimic or mask the effect. The authors should show the raw ZF asymmetry spectra at 1.2 GPa, state the sample signal fraction for the pressure runs, and discuss the temperature stability of the cell background.
  4. [§IV, Discussion point (2)] The statement that 'the sharp and well-defined transition from the low-TC to high-TC state strongly indicates a first-order phase transition' is not fully supported by the presented AC susceptibility data. The transition at 0.8 GPa is broad and the phase diagram is constructed from discrete pressure points, so a continuous evolution or a two-phase coexistence region cannot be excluded. The presence of a first-order transition is not essential to the main conclusions, but the claim should be moderated unless thermodynamic evidence (e.g., hysteresis in pressure) is provided.
minor comments (5)
  1. [§III] In Section III, the word 'superconuctor' should be 'superconductor'.
  2. [Fig. 1 caption] The caption contains the fragment 'LH2nmBias=1V' and 'LH2nmBias=20mV', which appear to be formatting artifacts; these should be readable axis labels (e.g., 'Bias (mV)').
  3. [Methods and Table I] In Table I, the header 'λ(T >0) (nm)' is ambiguous and should be clarified; presumably the quantity is the zero-temperature London penetration depth λ(0), not a value at arbitrary positive temperature.
  4. [Reference 13] The author name 'J. X. YIn' in reference 13 should be 'J.-X. Yin'.
  5. [Data availability] The data availability statement includes the phrase 'named incorrectly in file'; this is informal and should be corrected or removed.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; the experimental derivations are self-contained, with only an explicit non-circular assumption about pressure suppressing charge order.

full rationale

The paper's derivation chain is an experimental muon-spin rotation/relaxation, STM, and AC susceptibility study. The normal-state TRS-breaking signal is inferred from standard zero-field and high-field muon relaxation fits (Eqs. 1 and 3), and the superconducting gap, superfluid density, and pairing symmetry are extracted from standard London-model analyses (Eqs. 4 and 5). These fits determine parameters (sigma, Gamma, lambda, Delta, Tc) from measured spectra; the reported correlations, such as the nearly linear scaling between Tc and superfluid density and the increased relaxation rate below Tc, are observational statements about those fitted parameters, not quantities defined to equal the inputs. No equation reduces to its own input, and no fitted parameter is renamed as a prediction. The only load-bearing interpretive step is the Discussion's explicitly stated assumption that pressure suppresses charge order in Nb0.07-CVS based on prior measurements in other AV3Sb5 compounds (refs 10 and 12, some by the same group). This is an extrapolation and a potential correctness risk, but it is not circular: the cited prior results are independent measurements on other compounds, not outputs of the present paper's analysis, and the present data do not force those conclusions. The paper is therefore self-contained against its own measurements, and no significant circularity is present.

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

The paper introduces no new theoretical entities. Its load-bearing assumptions are experimental and interpretational: the London model for superfluid density, the constancy of the nuclear relaxation background, the complete suppression of charge order by pressure, and the magnetic origin of the observed relaxation rate increases. These assumptions are standard for muon spin rotation studies, but the pressure-suppression assumption is stated as a prior rather than directly measured in this compound.

free parameters (5)
  • London penetration depth lambda = 316(5) nm (text) or 381 nm (Table I)
    Extracted from the temperature dependence of the muon spin depolarization rate using the London model (Eq. 4). The inconsistency between text and table is a concern.
  • Superconducting gap amplitude Delta_1 = 0.59 meV (ambient) to 1.56 meV (1.2 GPa)
    Fitted in the gap structure analysis for each pressure. The value changes with pressure and is used to support the nodeless gap claim.
  • Second gap amplitude Delta_2 (at 0.8 GPa) = 3.5(9) meV
    Introduced to model the broadened superfluid density at 0.8 GPa with a two-gap nodeless model.
  • Phase fraction omega (at 0.8 GPa) = 0.73(4)
    Relative weight of the two gap components in the double-gap fit at 0.8 GPa.
  • Critical temperature Tc = 4.7 K (text) or 3.0 K (Table I) at ambient; about 7 K at 1.2 GPa
    Determined from fits of the superfluid density and from AC susceptibility. The inconsistency between text and Table I is a red flag.
assumptions (5)
  • domain assumption The London model relation between the superconducting muon depolarization rate and the penetration depth (Eq. 4) is valid for this vortex lattice.
    Used to convert sigma_sc to lambda^-2; assumes a perfect triangular vortex lattice and the local London limit.
  • domain assumption The nuclear contribution to the muon relaxation rate is temperature-independent and can be subtracted in quadrature to isolate the superconducting contribution.
    Used to extract sigma_sc from sigma_tot. If the nuclear contribution changes below Tc, the superfluid density estimates would be biased.
  • ad hoc to paper Hydrostatic pressure above pcr fully suppresses charge order.
    Stated explicitly in Section IV ('we assume that the charge order is suppressed with pressure, as has been measured in other AV3Sb5 compounds'). This assumption is load-bearing for attributing TRS breaking below Tc to the superconducting state.
  • domain assumption The increase in high-field muon relaxation rate below T* originates from static internal magnetic fields (time-reversal symmetry breaking) and not from field-induced effects or muon-site changes.
    Used to confirm the magnetic origin of the normal-state TRS breaking signal. The argument that a high magnetic field quantizes nuclear moments and leaves the electronic contribution intact is the basis for this assumption.
  • domain assumption The TrimSP-simulated muon implantation profiles accurately represent the depth distribution in Nb0.07-CVS.
    The depth-dependent study relies on these profiles to assign mean implantation depths and to compare surface and bulk responses.

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Cite this review

Pith. "Pith review of Pressure induced transition from chiral charge order to time-reversal symmetry-breaking superconducting state in Nb-doped CsV$_3$Sb$_5$." pith.science (2026). https://pith.science/paper/WHG6BWNZ

@misc{pith2026241118744,
  author       = {Pith},
  title        = {Pith review of: Pressure induced transition from chiral charge order to time-reversal symmetry-breaking superconducting state in Nb-doped CsV$_3$Sb$_5$},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WHG6BWNZ}},
  note         = {Machine review of arXiv:2411.18744}
}
abstract

The experimental realisation of unconventional superconductivity and charge order in kagome systems \textit{A}V$_3$Sb$_5$ is of critical importance. We conducted a highly systematic study of Cs(V$_{1-x}$Nb$_x$)$_3$Sb$_5$ with $x$=0.07 (Nb$_{0.07}$-CVS) by employing a unique combination of tuning parameters such as doping, hydrostatic pressure, magnetic fields, and depth, using muon spin rotation, AC susceptibility, and STM. We uncovered tunable magnetism in the normal state of Nb$_{0.07}$-CVS, which transitions to a time-reversal symmetry (TRS) breaking superconducting state under pressure. Specifically, our findings reveal that the bulk of Nb$_{0.07}$-CVS (at depths greater than 20 nm from the surface) experiences TRS breaking below $T^*=40~$K, lower than the charge order onset temperature, $T_\mathrm{CO}$ = 58 K. However, near the surface (within 20 nm from the surface), the TRS breaking signal doubles and onsets at $T_\mathrm{CO}$, indicating that Nb-doping decouples TRS breaking from charge order in the bulk but synchronises them near the surface. Additionally, Nb-doping raises the superconducting critical temperature $T_\mathrm{C}$ from 2.5 K to 4.4 K. Applying hydrostatic pressure enhances both $T_\mathrm{C}$ and the superfluid density by a factor of two, with a critical pressure $p_\mathrm{cr}$ ${\simeq}$ 0.85 GPa, suggesting competition with charge order. Notably, above $p_\mathrm{cr}$, we observe nodeless electron pairing and weak internal fields below $T_\mathrm{C}$, indicating broken TRS in the superconducting state. Overall, these results demonstrate a highly unconventional normal state with a depth-tunable onset of TRS breaking at ambient pressure, a transition to TRS-breaking superconductivity under low hydrostatic pressure, and an unconventional scaling between $T_\mathrm{C}$ and the superfluid density.

Figures

Figures reproduced from arXiv: 2411.18744 by the authors.

Figure 1
Figure 1. FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. a presents µSR measurements at 5 K in ZF and longitudinal fields (LF - field is applied parallel to the muon spin polarisation) up to 20 mT. To be consistent with previous works, the ZF data were fit with a Gaus￾sian Kubo-Toyabe depolarisation function multiplied by an exponential term27: A GKT ZF (t) =  1 3 + 2 3 (1 − σ 2 t 2 )exp  − σ 2 t 2 2  exp(−Γt)+Abkg (1) where σ/γµ (γµ/2π = 135.5 MHz/T is the muon gyro￾… view at source ↗
Figure 3
Figure 3. FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p013_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8 [PITH_FULL_IMAGE:figures/full_fig_p013_8.png]

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