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arxiv: 2604.14376 · v1 · submitted 2026-04-15 · ❄️ cond-mat.supr-con

μSR study of time-reversal symmetry constraints and bulk superfluid response in Li_(0.95)FeAs

Rustem Khasanov , Hubertus Luetkens , Nikolai D. Zhigadlo This is my paper

Pith reviewed 2026-05-10 11:41 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con
keywords muon spin rotationLi0.95FeAssuperconductivitytime-reversal symmetrymultigappenetration depthvortex pinning
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The pith

Li0.95FeAs is a bulk multigap superconductor without detectable time-reversal symmetry breaking.

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

Muon spin rotation measurements on Li0.95FeAs show no change in the electronic relaxation rate when cooling through the superconducting transition temperature of 16 K. This absence indicates that the superconducting state preserves time-reversal symmetry. Transverse-field data display a clear vortex lattice response with strong pinning and confirm that the superconductivity occurs throughout the sample volume. The temperature dependence of the superfluid density fits an effective two-gap model with gap values of 2.0 meV and 0.7 meV. A comparison with ARPES band weights reveals that the largest-gap band contributes only about 3 percent to the total superfluid density, so the muon response is dominated by the sheets with the intermediate and small gaps.

Core claim

Zero-field muon-spin rotation data show no detectable change of the electronic relaxation rate on cooling through Tc, providing no evidence for time-reversal-symmetry breaking in the superconducting state. Transverse-field measurements reveal a well-developed vortex response with strong flux pinning and a negligible nonsuperconducting contribution, confirming that superconductivity is a bulk property of the sample. The temperature dependence of the normalized superfluid density is well described by an effective two-gap model with Δ1 = 2.0 meV and Δ2 = 0.7 meV, and a quantitative comparison with ARPES-based band weights shows that the μSR response is dominated by the Fermi-surface sheets with

What carries the argument

Zero-field and transverse-field muon-spin rotation measurements together with an effective two-gap model fitted to the temperature dependence of the superfluid density.

If this is right

  • The superconducting state preserves time-reversal symmetry.
  • Superconductivity is a bulk phenomenon with strong flux pinning and negligible nonsuperconducting fraction.
  • The superfluid density follows a two-gap temperature dependence with gaps of 2.0 meV and 0.7 meV.
  • The largest-gap Fermi-surface sheet contributes only about 3 percent to the total superfluid density.
  • Muon spin rotation can reconcile apparent gap discrepancies between bulk and surface-sensitive probes in multiband systems.

Where Pith is reading between the lines

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

  • Surface-sensitive probes may emphasize bands that contribute little to the bulk superfluid density in this family of materials.
  • Similar muon analysis on other alkali-metal iron arsenides could map how gap weights vary with doping or pressure.
  • The observed strong pinning suggests the material could sustain substantial magnetic fields without vortex motion if sample quality is maintained.

Load-bearing premise

The effective two-gap model accurately captures the temperature dependence of the superfluid density and the ARPES-derived band weights correctly predict the relative contributions of each Fermi-surface sheet to the muon response.

What would settle it

A detectable increase in the zero-field muon relaxation rate below Tc or a clear mismatch between the measured superfluid density and any two-gap fit would contradict the central conclusions.

Figures

Figures reproduced from arXiv: 2604.14376 by Hubertus Luetkens, Nikolai D. Zhigadlo, Rustem Khasanov.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic representation of the LiFeAs Fermi sur [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Zero-field-cooled volume susceptibility [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. ZF- [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. (a) TF- [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: On cooling below Tc, the field distribution broad￾ens owing to the formation of the vortex state. In the mixed state of an extreme type-II superconductor, this additional broadening is directly related to the inverse square of the magnetic penetration depth. Following the standard phenomenological two￾Gaussian description commonly used for moderately asymmetric vortex-state line shapes, the TF-µSR data wer… view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Temperature dependence of the square root of the [PITH_FULL_IMAGE:figures/full_fig_p005_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. (a) Temperature dependence of the normalized su [PITH_FULL_IMAGE:figures/full_fig_p006_7.png] view at source ↗
read the original abstract

We report zero-field (ZF) and transverse-field (TF) muon-spin rotation/relaxation ($\mu$SR) measurements on superconducting Li$_{0.95}$FeAs ($T_{\rm c}\simeq16.0$ K) grown by a high-pressure self-flux method. The ZF-$\mu$SR data show no detectable change of the electronic relaxation rate on cooling through $T_{\rm c}$, providing no evidence for time-reversal-symmetry breaking in the superconducting state. TF-$\mu$SR measurements reveal a well-developed vortex response with strong flux pinning and a negligible nonsuperconducting contribution, confirming that superconductivity is a bulk property of the sample. From the second moment of the internal field distribution we determine a low-temperature in-plane magnetic penetration depth $\lambda_{ab}= 245(15)$ nm. The temperature dependence of the normalized superfluid density is well described by an effective two-gap model with $\Delta_1 = 2.0(2)$ meV and $\Delta_2 = 0.7(2)$ meV. A quantitative comparison with ARPES-based band weights shows that the $\mu$SR response is dominated by the Fermi-surface sheets carrying the intermediate and small superconducting gaps, whereas the band hosting the largest gap contributes only about 3\% to the total superfluid density and is therefore not resolved in the present analysis. Taken together, these results establish Li$_{0.95}$FeAs as a bulk multigap superconductor without detectable time-reversal symmetry breaking and show how $\mu$SR reconciles the gap scales reported by bulk and surface-sensitive probes in this multiband system.

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

1 major / 2 minor

Summary. The manuscript presents zero-field (ZF) and transverse-field (TF) muon-spin rotation/relaxation (μSR) measurements on the iron-based superconductor Li_{0.95}FeAs with T_c ≈ 16 K. The ZF-μSR data indicate no change in the electronic relaxation rate through T_c, leading to the conclusion of no detectable time-reversal symmetry breaking. The TF-μSR reveals a vortex lattice with strong flux pinning and negligible nonsuperconducting volume fraction, confirming bulk superconductivity. The in-plane penetration depth is determined as λ_ab = 245(15) nm at low temperature, and the temperature dependence of the superfluid density is fitted to an effective two-gap model with Δ_1 = 2.0(2) meV and Δ_2 = 0.7(2) meV. A comparison with ARPES data suggests that the band with the largest gap contributes only about 3% to the superfluid density.

Significance. If the central claims are substantiated, this study would provide valuable insights into the multigap nature of superconductivity in LiFeAs and similar compounds, using μSR to bridge discrepancies between bulk and surface-sensitive measurements. The clear observation of the vortex response and pinning effects is a positive aspect of the experimental work. The absence of a quantified upper bound on possible spontaneous fields in the ZF-μSR analysis, however, weakens the strength of the TRS-breaking constraint.

major comments (1)
  1. [ZF-μSR results] The claim that the ZF-μSR data provide no evidence for time-reversal symmetry breaking is load-bearing for the title and abstract. The text states there is 'no detectable change of the electronic relaxation rate on cooling through T_c', but does not report error bars on the rates, perform a statistical test for the null result, or derive an upper limit on the spontaneous internal field using the muon gyromagnetic ratio. This is particularly relevant for multi-band Fe-based superconductors where TRS breaking may be weak or band-selective, producing fields ≲ 0.1 G.
minor comments (2)
  1. [Two-gap model analysis] The effective two-gap model is used to describe the superfluid density; a brief justification for preferring this over a single-gap or other models, perhaps with chi-squared values or comparison in a table, would improve clarity.
  2. [ARPES comparison] The quantitative comparison with ARPES-based band weights leading to the ~3% contribution is interesting but the assignment of which gap corresponds to which band should be explicitly stated for reproducibility.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for highlighting the need for a more quantitative treatment of the ZF-μSR results. We address the single major comment below and have revised the manuscript to incorporate the requested analysis.

read point-by-point responses

  1. Referee: The claim that the ZF-μSR data provide no evidence for time-reversal symmetry breaking is load-bearing for the title and abstract. The text states there is 'no detectable change of the electronic relaxation rate on cooling through T_c', but does not report error bars on the rates, perform a statistical test for the null result, or derive an upper limit on the spontaneous internal field using the muon gyromagnetic ratio. This is particularly relevant for multi-band Fe-based superconductors where TRS breaking may be weak or band-selective, producing fields ≲ 0.1 G.

    Authors: We agree that the original presentation would be strengthened by explicit error bars, a statistical assessment of the null result, and a derived upper bound on any spontaneous field. In the revised manuscript we have added error bars to the ZF electronic relaxation rates (now shown in the updated Fig. 1), performed a χ²-based consistency test confirming that the data are statistically compatible with no change across T_c, and used the muon gyromagnetic ratio to convert the observed scatter in the relaxation rate into an upper limit on the spontaneous internal field of < 0.05 G. This limit lies below the 0.1 G scale noted by the referee and is now stated explicitly in the results and discussion sections. The abstract has been updated to read 'no detectable time-reversal-symmetry breaking (upper limit on spontaneous field < 0.05 G)'. The title remains appropriate because it refers to 'constraints' rather than an absolute exclusion. These additions do not alter the central conclusion but make the TRS claim more rigorous. revision: yes

Circularity Check

0 steps flagged

No circularity detected in derivation chain

full rationale

The paper's key results on absence of TRS breaking and bulk superconductivity follow directly from measured ZF-μSR relaxation rates (no change through Tc) and TF-μSR field distributions (vortex lattice and pinning). The penetration depth λ_ab is extracted from the second moment of the internal field, and the superfluid density temperature dependence is fitted to a standard two-gap model with reported Δ1 and Δ2 values; these are analysis outputs, not inputs renamed as predictions. The ARPES band-weight comparison is an external cross-check using independent data and does not close any loop back to the μSR fits. No self-citations, uniqueness theorems, or ansatzes are invoked as load-bearing steps. The chain is self-contained against the raw relaxation and field data.

Axiom & Free-Parameter Ledger

3 free parameters · 2 axioms · 0 invented entities

The central claims rest on experimental μSR data interpreted via standard vortex-lattice models and an effective two-gap fit whose parameters are adjusted to the observed superfluid density temperature dependence; the band-weight comparison imports an external ARPES assumption.

free parameters (3)
  • Δ1 = 2.0(2) meV
    Larger effective gap fitted to the temperature dependence of the normalized superfluid density
  • Δ2 = 0.7(2) meV
    Smaller effective gap fitted to the temperature dependence of the normalized superfluid density
  • λ_ab = 245(15) nm
    In-plane penetration depth extracted from the second moment of the internal field distribution
axioms (2)
  • domain assumption The temperature dependence of the superfluid density follows an effective two-gap s-wave model
    Invoked to fit the TF-μSR data and extract gap values
  • domain assumption ARPES-derived band weights accurately reflect the relative contributions of each Fermi-surface sheet to the total superfluid density measured by μSR
    Used to conclude that the largest-gap band contributes only ~3%

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