mu SR study of time-reversal symmetry constraints and bulk superfluid response in Li 0.95 FeAs

arXiv:2604.14376 · cond-mat.supr-con · Submitted 2026-04-15 · Read on arXiv

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Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: Today's paper: "mu SR study of time-reversal symmetry constraints and bulk superfluid response in Li 0.95 FeAs".

Mira: The gist The ZF-µSR 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.

Kai: First, who's behind it and why it matters.

Title and authors: Kai: So we're moving into the specifics of this paper, "mu SR study of time-reversal symmetry constraints and bulk superfluid response in Li zero point nine five FeAs" <ref:2604.14376#pg1,study of time-reversal symmetry constraints and bulk superfluid response in>. We’ve established that zero-field measurements show no evidence for time-reversal symmetry breaking, so what’s the core story here?

Mira: The core story is using these zero-field measurements to place very strict constraints on the possible superconducting states of this material, specifically ruling out some complex order parameters that would otherwise break time-reversal symmetry.

Lev: From a quantum error correction standpoint, if a state breaks time-reversal symmetry and generates spontaneous magnetic fields, it introduces new kinds of noise or dynamics that we have to account for when designing hardware.

Kai: So the authors are essentially saying that based on the mu SR results, they’re confident that the superconducting state in this material is time-reversal invariant within their measurement sensitivity.

Mira: That means they are disfavoring scenarios involving mixed complex order parameters of the s+is or s+id type, which theorists have discussed for LiFeAs.

Lev: For running experiments on real hardware, that simplifies things because you don't have to worry about spontaneous magnetic fields popping up from the superconducting state itself under low-field conditions.

Kai: And they also rule out chiral or otherwise time-reversal symmetry breaking triplet states that would be expected to generate those spontaneous magnetic fields.

Mira: They are focusing on the fact that mu SR is sensitive enough to detect any change in the electronic relaxation rate on cooling through Tc, and they found nothing there.

Lev: It’s a solid constraint for anyone trying to model the pairing symmetry of these iron-based superconductors.

The paper's summary: Kai: Now let’s look at how they summarize the actual results in this paper, "mu SR study of time-reversal symmetry constraints and bulk superfluid response in Li zero point nine five FeAs" <ref:2604.14376#pg1,study of time-reversal symmetry constraints and bulk superfluid response in>. They focus on two main things: the constraint on time-reversal symmetry and the characterization of the bulk superfluid response.

Mira: On one hand, they use the ZF data to confirm that superconductivity is time-reversal invariant within their experimental limits, which rules out states with intrinsically complex order parameters.

Lev: And on the other hand, they look at transverse-field measurements which show a well-developed vortex response with strong flux pinning and a negligible nonsuperconducting contribution.

Kai: That flux pinning is important because it confirms that we are dealing with a bulk superconducting property, not just something localized to the surface or some tiny defect.

Mira: They also analyze the temperature dependence of the normalized superfluid density, which they successfully fit using an effective two-gap model with parameters one = two point zero(two) meV and two = zero point seven(two) meV <ref:2604.14376#pg1,the temperature dependence of the normalized superfluid density>.

Lev: That two-gap model is what allows them to reconcile the apparent spread of gap values reported by different experimental probes, like ARPES and bulk measurements.

Kai: They use this fitting to show that the bulk superfluid response is dominated by the bands associated with the intermediate gaps gamma and delta, while a weaker band, alpha, only contributes about three percent to the total superfluid density <ref:2604.14376#pg3>.

Mira: That’s a key finding because it supports their conclusion that these intermediate and small gap sheets are what truly dominate the physics of this bulk superconductor.

The paper's improvements: Kai: The paper itself points out a few improvements they made to the study, which is interesting because they are essentially explaining how their method helps clarify ambiguities in other studies.

Mira: They highlight that using mu SR allows them to directly access the intrinsic bulk superfluid response, which was previously hard to isolate when comparing it with surface-sensitive probes.

Lev: And this direct access is what helps reconcile the apparent spread of superconducting gap values reported by different experimental methods in this multiband system.

Kai: They also present the quantitative comparison with ARPES-based band weights, showing how the mu SR response aligns well with those weights.

Mira: Specifically, they show that the relative contributions from the intermediate and small-gap sheets match what you get when you look at the superfluid density dependence on temperature.

Lev: This consistency is quite important for anyone trying to use these materials in devices, because it builds confidence in the parameters they’re getting from these experiments.

Kai: So, essentially, they show that mu SR isn't just another tool; it’s a way to bridge the gap between surface measurements and bulk properties.

Conclusion: Mira: To wrap up this discussion on "mu SR study of time-reversal symmetry constraints and bulk superfluid response in Li zero point nine five FeAs", the main conclusion is that mu SR provides direct access to the intrinsic bulk superfluid response of Li zero point nine five FeAs and helps reconcile the gap scales reported by different experimental probes <ref:2604.14376#pg1,study of time-reversal symmetry constraints and bulk superfluid response in>.

Lev: The effective two-gap fit gives us those specific gap values, one = two point zero(two) meV and two = zero point seven(two) meV, which we can use to model the temperature dependence of the superfluid density <ref:2604.14376#pg1,1 = 2.0(2)$ meV and>.

Kai: It confirms that Li zero point nine five FeAs is a bulk multigap superconductor without detectable time-reversal-symmetry breaking and provides a clear picture of its structure based on the dominant gap contributions <ref:2604.14376#pg1>.

Mira: So, when you’re listening, think about this paper as showing how to use mu SR to reconcile the apparent spread of superconducting gap values reported by different experimental probes in this multiband system.

Lev: For us on the error correction side, it means we have a better handle on what the underlying physics is when we design systems based on these materials.

Kai: That’s all for this paper. Next up, we'll be looking at another fascinating piece of research from arXiv.

PSI Center for Neutron and Muon Sciences CNM · CrystMat Company

cond-mat.supr-con

Submitted: 2026-04-15

Updated: 2026-04-15

Comments: 9 pages, 7 figures

Journal ref: Phys. Rev. B 114, 094509 (2026)

DOI: 10.1103/zlzx-qty2

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Importance score: 83/100

The gist: The gist The ZF-µSR 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.

Key concepts

Time-Reversal Symmetry Breaking
This refers to a property of matter where reversing time (or flipping the magnetic field) results in a different physical state. In superconductors, this breaking would typically generate spontaneous local magnetic fields. The $ƼmSR$ data showed no such change upon cooling through the transition temperature, suggesting the superconducting state is time-reversal invariant.
Superfluid Density
This measures how easily a material flows without resistance when cooled below its critical temperature. The study found that Li0.95FeAs exhibits a two-gap behavior ($Σ1 and Σ2) in its superfluid density, meaning the flow is governed by two distinct energy gaps, which explains why different probes report different gap values.
Muon-Spin Rotation/Relaxation ($ƼmSR$)
This technique uses positive muons implanted into a material to measure local magnetic fields and internal fields. By observing how the muon's spin rotates or relaxes over time, researchers can probe the magnetic environment of the superconducting state, providing direct access to bulk properties like flux pinning and penetration depth.
Multiband Superconductivity
This describes a superconducting state where superconductivity occurs across multiple distinct electronic bands within the material. The analysis showed that while all bands contribute, only those associated with intermediate and small gaps ($γ and ϗ) dominate the bulk superfluid response, helping to explain why surface-sensitive probes see different gap scales.

Terminology

Summary

The gist The ZF-µSR 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.

Superconducting State Characterization

The study investigates zero-field (ZF) and transverse-field (TF) muon-spin rotation/relaxation (µSR) measurements on superconducting Li0.95FeAs grown by a high-pressure self-flux method, revealing bulk superconductivity with a transition temperature of Tc ≃ 16.0 K The ZF-µSR 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 This result places stringent constraints on superconducting states with an intrinsically complex order parameter, i.e. states that break time-reversal symmetry and would be expected to generate spontaneous local magnetic fields

Bulk Superfluid Response Analysis

The TF-µSR 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 ∆1 = 2.0(2) meV and ∆2 = 0.7(2) meV The resulting temperature dependence of the superfluid density is well described by an effective two-gap model By comparing the µSR results with the known multiband electronic structure of LiFeAs, we show that the bulk superfluid response is dominated by the bands associated with the intermediate superconducting gaps (γ and δ) and the small gap (β) The temperature dependence of λ−2ab is presented in the inset of Fig. 6

Reconciliation with Multiband Structure

The analysis shows that the bulk superfluid response is dominated by the bands associated with the intermediate superconducting gaps (γ and δ) and the small gap (β), whereas the α Fermisurface sheet, which hosts the largest gap, contributes only weakly to λ−2ab and is therefore not resolved in the present analysis The ARPES-based band-structure estimate yields relative contributions of about 0.7 and 0.3 for the intermediateand small-gap sheets, respectively, in good agreement with the corresponding weights obtained from the µSR analysis This consistency strongly supports the conclusion that the µSR response is dominated by the γ, δ, and β sheets

Constraints on Time-Reversal Symmetry Breaking

The ZF-µSR data indicate that superconductivity in Li0.95FeAs is time-reversal invariant within the sensitivity of the present experiment This result disfavors scenarios involving mixed complex order parameters of the s+is or s+id type, which have been discussed theoretically for LiFeAs Furthermore, it strongly disfavors chiral or otherwise time-reversal symmetry breaking triplet states that would be expected to generate spontaneous magnetic fields

Magnetic Penetration Depth Determination

From the second moment of the internal field distribution we determine a low-temperature in-plane magnetic penetration depth λab = 245(15) nm The temperature dependence of λ−2ab is presented in the inset of Fig. 6 Using Eq. (3), we obtain λab(1.5 K) = 275(15) nm for 5 mT and 245(15) nm for 10 mT The slightly larger value found at 5 mT is not considered intrinsic; rather, it most likely reflects the fact that this field lies closer to the first critical field Hc1, where the second moment of the vortex-state field distribution is reduced

Conclusion on Superfluid Density

The present work demonstrates that µSR provides direct access to the intrinsic bulk superfluid response of Li0.95FeAs and helps reconcile the apparent spread of superconducting gap values reported by different experimental probes The effective two-gap fit yields ∆1 = 2.0(2) meV, ∆2 = 0.7(2) meV, and ω = 0.61(2) This interpretation explains why the present µSR analysis remains fully compatible with the multiband electronic structure established by ARPES The level of agreement is remarkably good

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µSR study of time-reversal symmetry constraints and bulk superfluid response in Li0.95FeAs Rustem Khasanov,1, ∗ Hubertus Luetkens,1 and Nikolai D. Zhigadlo2 1PSI Center for Neutron and Muon Sciences CNM, 5232 Villigen PSI, Switzerland 2CrystMat Company, CH-8037 Zurich, Switzerland (Dated: April 2026 We report zero-field (ZF) and transverse-field (TF) muon-spin rotation/relaxation µSR measurements on superconducting Li0.95FeAs (Tc ≃ 16.0 K) grown by a high-pressure self-flux method The ZF-µSR 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 TF-µSR 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 λab = 245(15) nm The temperature dependence of the normalized superfluid density is well described by an effective two-gap model with ∆1 = 2.0(2) meV and ∆2 = 0.7(2) meV A quantitative comparison with ARPES-based band weights shows that the µSR 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 Li0.95FeAs as a bulk multigap superconductor without detectable time-reversal-symmetry breaking and show how µSR reconciles the gap scales reported by bulk and surface-sensitive probes in this multiband system I. INTRODUCTION LiFeAs is one of the most intriguing members of the Fe-based superconductors (FeSCs) [1, 2] Unlike many FeSCs, where superconductivity emerges only after chemical doping suppresses magnetic order, LiFeAs is intrinsically superconducting in stoichiometric form, without the need for external chemical substitution or pressure [2–4] Moreover, it does not show long-range magnetic or structural order in the normal state These characteristics make LiFeAs an attractive model system for investigating the intrinsic superconducting properties of FeSCs without the additional complexity introduced by substitutional disorder At the same time, the absence of a nearby ordered phase makes LiFeAs a particularly stringent platform for identifying which electronic instabilities are genuinely relevant for superconductivity Despite this apparent simplicity, the superconducting state of LiFeAs remains a matter of active discussion Angle-resolved photoemission spectroscopy (ARPES) has established a multiband Fermi surface with hole pockets around Γ and electron pockets around M, together with a pronounced disparity in the superconducting gap values on the different Fermi-surface sheets [5–12] A schematic representation of the LiFeAs Fermi surface is shown in Fig.

Improvements for AI systems

  1. Improved analysis of superconducting state constraints: The AI system can now perform zero-field (ZF) muon-spin rotation/relaxation (µSR) measurements and directly interpret results regarding time-reversal symmetry breaking, specifically by identifying that the ZF measurements 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.

  2. Enhanced determination of bulk superfluid properties: The system can now calculate the low-temperature in-plane magnetic penetration depth using the derived relationship, as shown by From the second moment of the internal field distribution we determine a low-temperature in-plane magnetic penetration depth λab = 245(15) nm.

  3. Multigap model reconciliation: The AI can compare experimental gap scales against theoretical band structures, specifically demonstrating how "the µSR 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."

  4. Vortex state characterization: The system can analyze transverse-field (TF) data to confirm a well-developed vortex response with strong flux pinning and a negligible nonsuperconducting contribution, confirming that superconductivity is a bulk property of the sample, by analyzing the Fourier transforms which show the strong suppression of the 10 mT component after ZFC demonstrates pronounced flux pinning.

  5. Gap scale fitting: The system can fit the temperature dependence of the normalized superfluid density using an effective two-gap model with ∆1 = 2.0(2) meV and ∆2 = 0.7(2) meV, providing quantitative parameters for gap scales, which are then compared to other probes to explain discrepancies between bulk and surface-sensitive probes.

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