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arxiv: 2605.03171 · v1 · submitted 2026-05-04 · ❄️ cond-mat.supr-con · hep-ex

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Nb₃Sn Thin Films Using a Cu-Sn Route for Dark Matter Detection

Andre Juliao

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Pith reviewed 2026-05-08 02:35 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con hep-ex
keywords Nb3Snthin filmsCu-Sn alloysSRF cavitiesaxion detectionquality factorsuperconducting coatingsdark matter
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The pith

A Cu-Sn diffusion method produces Nb3Sn films on copper cavities with 40 percent higher quality factor than bare copper at zero magnetic field.

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

This paper develops a lower-temperature route to apply Nb3Sn superconducting films to copper cavities by diffusing tin from copper-tin alloys into niobium. The technique succeeds at 650 to 750 degrees Celsius, sidestepping damage to the copper that occurs in hotter vapor methods. Cavities coated this way reach quality factors 40 percent above those of plain copper at zero field, which matters for axion searches that need high performance in strong magnets. Two coating sequences were tested, with one chosen for a hexagonal cavity that was evaluated at millikelvin temperatures and up to 9 tesla.

Core claim

The authors establish that solid-state diffusion from Cu-Sn alloys can form uniform Nb3Sn thin films on copper substrates at compatible temperatures, yielding superconducting radio-frequency cavities with quality factors of 77,000 at zero field, 40 percent above bare copper, while providing two practical coating routes for axion search applications.

What carries the argument

The central mechanism is solid-state diffusion of tin from high-tin Cu-Sn alloys into niobium layers to form Nb3Sn at 650-750 degrees Celsius, preserving copper substrate integrity.

If this is right

  • Uniform Nb3Sn coatings become feasible on complex copper cavity shapes.
  • Zero-field performance improves over bare copper, raising potential detector sensitivity.
  • Strain from copper substrate suppresses critical temperature to around 16 K.
  • The method was demonstrated on a hexagonal cavity tested down to 50 millikelvin and 9 tesla.

Where Pith is reading between the lines

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

  • Mitigating the observed drop in quality factor under magnetic fields would directly enhance axion detection capabilities.
  • Alternative strain-relief interlayers could restore higher critical temperatures closer to 18 K.
  • This coating route may apply to other copper-based cryogenic devices beyond dark matter searches.

Load-bearing premise

The quality factor gain observed without magnetic field will carry over to the multi-tesla conditions needed for axion detection.

What would settle it

A direct comparison of the quality factor for the Nb3Sn-coated cavity versus bare copper at 9 tesla would confirm whether the improvement persists in operational magnetic fields.

Figures

Figures reproduced from arXiv: 2605.03171 by Andre Juliao.

Figure 2.1
Figure 2.1. Figure 2.1: Proposed Dark Matter candidates. By Jen Christiansen; Article by Leslie Rosen view at source ↗
Figure 2.2
Figure 2.2. Figure 2.2: Anna Bertha’s hand, imaged using Wilhelm R¨ontgen’s X-ray detector in 1895. view at source ↗
Figure 2.3
Figure 2.3. Figure 2.3: Cloud chamber track used to prove the existence of the positron in 1932 by Carl view at source ↗
Figure 2.4
Figure 2.4. Figure 2.4: Axion-photon coupling strength vs axion mass for cavity haloscopes [ view at source ↗
Figure 2.5
Figure 2.5. Figure 2.5: Axion-photon coupling strength vs axion mass for full axion-photon coupling view at source ↗
Figure 2.6
Figure 2.6. Figure 2.6: Spherical halo containing dark matter surrounding the visible Milky Way disk. view at source ↗
Figure 2.7
Figure 2.7. Figure 2.7: (Upper) Background-subtracted single scans with synthetic axion signals at view at source ↗
Figure 3.1
Figure 3.1. Figure 3.1: Resistivity of Cu with varying levels of purity (Residual resistivity ratio - RRR) view at source ↗
Figure 4.1
Figure 4.1. Figure 4.1: Source material heated and evaporated onto a target. Material is moving from view at source ↗
Figure 4.2
Figure 4.2. Figure 4.2: Vapor pressure curves for common elements [ view at source ↗
Figure 4.3
Figure 4.3. Figure 4.3: An ultra-high vacuum chamber with a working gas (Argon) that hits the target view at source ↗
Figure 4.4
Figure 4.4. Figure 4.4: Thornton structure zone model diagram from [ view at source ↗
Figure 4.5
Figure 4.5. Figure 4.5: Schematic of film that is prepared for cross-section by cutting and gluing together view at source ↗
Figure 4.6
Figure 4.6. Figure 4.6: SEM images of a Nb3Sn film on a Nb substrate that was cut in half, and one half was etched and the other half not etched, and sandwiched together. Focused Ion Beam (FIB) milling: An ion beam mills a trench into the sample, exposing the cross-section in situ with minimal mechanical contact or stress. FIB minimizes damage and provides precise site-specific sectioning, allowing investigation of localized fe… view at source ↗
Figure 4.7
Figure 4.7. Figure 4.7: Example FIB cross section SEM image showing voids above the diffusion layer. view at source ↗
Figure 4.8
Figure 4.8. Figure 4.8: Cross-sectional characterization of a Cu-Sn first film: (a) visible light micrograph view at source ↗
Figure 4.9
Figure 4.9. Figure 4.9: SEM image (a) with (b) EDS point scan and (c) EDS mapping showing elemental view at source ↗
Figure 4.10
Figure 4.10. Figure 4.10: Superconducting Quantum Interference Device (SQUID) schematic showing view at source ↗
Figure 4.11
Figure 4.11. Figure 4.11: Ideal flux response to a small magnetic field for different samples: a) supercon view at source ↗
Figure 4.12
Figure 4.12. Figure 4.12: Simulated SQUID scans for superconductor, ferromagnet, and paramagnet, view at source ↗
Figure 4.13
Figure 4.13. Figure 4.13: Superconducting slab in parallel field with example critical temperature curve view at source ↗
Figure 4.14
Figure 4.14. Figure 4.14: Magnetization of large samples where d ≫ λ and thin films where d ∼ λ. Thin Films. If the superconducting material has a thickness on the same order as the penetration depth, d ∼ λ, the magnetic field cannot be perfectly screened. The material is still diamagnetic but has a smaller magnetic moment |M| < H0 (seen in view at source ↗
Figure 4.15
Figure 4.15. Figure 4.15: Demagnetization affecting magnetic field penetration at the edges for (a) view at source ↗
Figure 4.16
Figure 4.16. Figure 4.16: Schematic of superconducting slab with variable Sn or strain properties view at source ↗
Figure 4.17
Figure 4.17. Figure 4.17: Critical temperature curves for two Nb3Sn samples on Cu substrates. The black curve exhibits a sharp transition (∆Tc ≈ 0.6 K) with Tc onset at ≈ 16 K. The red curve shows a broader transition with a higher Tc onset. Secondary transitions at 6 K (black) and 8 K (red) indicate additional phases. 4.4 RF Characterization of Pillbox Cavities 4.4.1 Measurement Principles and Instrument Configuration To charac… view at source ↗
Figure 4.18
Figure 4.18. Figure 4.18: Experimental apparatuses needed for Q measurement: probe [ view at source ↗
Figure 4.19
Figure 4.19. Figure 4.19: Example vector network analyzer scan for a specific mode at 10 GHz. The view at source ↗
Figure 5.1
Figure 5.1. Figure 5.1: Arrangement of Nb and Sn atoms in Nb3Sn crystal structure [103]. 5.2.2 Nb-Sn Phase Diagram The Nb3Sn compound can form with a varying degree of Sn%, from 16 to 26 at.% Sn, where 25 at.% Sn is the most desirable for superconducting properties [104]. There are other Nb-Sn compounds, Nb6Sn5 and NbSn2, with poor superconducting properties (Tc = 2.8 K, and Tc = 2.68 K respectively). These compounds can form w… view at source ↗
Figure 5.2
Figure 5.2. Figure 5.2: Nb-Sn Phase diagram, where the Nb3Sn compound is highlighted in yellow, and above the purple line shows where Nb6Sn5 and NbSn2 break down [105]. 5.2.3 Nb-Cu-Sn Reactions Adding Cu to a Nb-Sn reaction enables Nb3Sn formation at lower temperatures (650– 750 °C instead of >930 °C). Understanding this ternary reaction requires examining both the Cu-Sn binary system ( view at source ↗
Figure 5.3
Figure 5.3. Figure 5.3: The binary Cu-Sn phase diagram [107]. 73 view at source ↗
Figure 5.4
Figure 5.4. Figure 5.4: Ternary Cu-Nb-Sn phase diagram at 675 ◦C isothermal [108, 109]. 5.2.4 Kinetics of Nb3Sn Formation Nb3Sn forms by a solid-state diffusion reaction. Growth of the Nb3Sn phase at an interface between Cu-Sn and Nb depends on nucleation, followed by continued supply of Sn as Nb3Sn grains grow. However, as the diffusion reaction proceeds, Sn becomes depleted at the reaction front. As the Nb3Sn layer grows, Sn … view at source ↗
Figure 5.5
Figure 5.5. Figure 5.5: ) demonstrates how reduced diffusion paths minimize Sn compositional gradients view at source ↗
Figure 5.6
Figure 5.6. Figure 5.6: Plot of critical temperature Tc as a function of at. Sn% in Nb3Sn. The maximum Tc is associated with at. Sn 25% to 26% [111]. grain boundaries of the film. If the reaction has sufficient time to equilibrate, impurities are expelled from the bulk into the grain boundaries. Understanding the film morphology at nm-scale resolution is essential for correlating final Q measurements with thin-film properties. … view at source ↗
Figure 5.7
Figure 5.7. Figure 5.7: EDS linescan of Nb3Sn film with 25% Sn in the Nb3Sn layer. 5.3.2 Strain Sensitivity Nb3Sn’s critical temperature is also strongly strain-dependent ( view at source ↗
Figure 5.8
Figure 5.8. Figure 5.8: Nb3Sn’s strain-dependent critical temperature for bronze processed Nb3Sn wires under tension and compression [112] view at source ↗
Figure 5.9
Figure 5.9. Figure 5.9: Coefficient of Thermal Expansion (CTE) or Cu, Nb, and Nb view at source ↗
Figure 5.10
Figure 5.10. Figure 5.10: (a) Wire cross section with Nb3Sn filaments [117], and (c) closer look at mi￾crostructure with small grains near the Sn source and large columnar grains farther from the Sn source [118] commonly found in Nb3Sn wires. (b) Cross-section microscopy showing thin film Nb3Sn grains made with the Sn vapor route [119]. 5.4.2 Grain Boundaries Grain boundaries affect Nb3Sn performance differently depending on the… view at source ↗
Figure 5.11
Figure 5.11. Figure 5.11: TEM image from a hot-bronze film on a bronze substrate, where Cu was found view at source ↗
Figure 5.12
Figure 5.12. Figure 5.12: Q factor measurements showing improved performance in samples with Sn view at source ↗
Figure 6.1
Figure 6.1. Figure 6.1: Schematic showing the different multilayers needed for Nb view at source ↗
Figure 6.2
Figure 6.2. Figure 6.2: Thermally evaporated Cu-Sn film with concentration gradient. This gradient view at source ↗
Figure 6.3
Figure 6.3. Figure 6.3: A schematic representation of the Cu substrate with a diffusion layer and bronze view at source ↗
Figure 6.4
Figure 6.4. Figure 6.4: Tc curves for a hot bronze film on sapphire, that has been peeled, and etched and measured at each stage. etching uncovered unreacted Nb and Sn-poor Nb3Sn phases that were magnetically screened in initial SQUID magnetization measurements, which indicates hidden inhomogeneities in the film composition. 6.3.2 Substrate Experiments By understanding the impact the substrate has on Tc, the effects of low Sn c… view at source ↗
Figure 6.5
Figure 6.5. Figure 6.5: Tc curves for substrates: Cu, Cu w/ Ta diffusion barrier, Nb, and sapphire. 6.3.3 Nb Substrate - High Sn Cu-Sn The following Nb substrate experiment varied the Sn content in the Cu-Sn films ( view at source ↗
Figure 6.6
Figure 6.6. Figure 6.6: Cu-Sn phase diagram showing initial source Sn concentration and final Cu-Sn view at source ↗
Figure 6.7
Figure 6.7. Figure 6.7: 4 µm Cu-Sn films with varying Sn content on Nb substrates. Higher temperature consistently increased the critical temperature, given our reaction temperatures of 650 − 750 ◦C ( view at source ↗
Figure 6.8
Figure 6.8. Figure 6.8: T c curves for Nb3Sn films Nb substrates made with varying Sn content, Cu-Sn films, and heat-treatment profiles. 6.3.4 High-Sn Routes Combined with Cu Substrates The final proof-of-principle experiment aimed to understand how the Sn concentration in the final Nb3Sn film was affected by the Cu substrate. This experiment used three different Cu-Sn starting powder concentrations (13, 24, and 33 wt.% Sn) the… view at source ↗
Figure 6.9
Figure 6.9. Figure 6.9: (a) Tc curves for Nb3Sn on Cu substrates with varying reactions and Sn concen￾trations, and (b) a schematic showing the multilayer structure. 6.4 Implications of the Proof-of-Principle Experiments for High-Quality Nb3Sn Films 6.4.1 Hot-Bronze + Post-Reaction The hot-bronze deposition method, where Nb is sputtered at 715 °C onto Cu-Sn, offers rapid Nb-Sn reaction kinetics, approximately 12× faster than wi… view at source ↗
Figure 6.10
Figure 6.10. Figure 6.10: Schematic showing (a) hot-bronze viable route Nb view at source ↗
Figure 6.11
Figure 6.11. Figure 6.11: Schematic of the Nb3Sn film on a Nb substrate, with a 3-D optical imaging showing the surface morphology before and after etching. 107 view at source ↗
Figure 6.12
Figure 6.12. Figure 6.12: Tc curves for best Nb3Sn samples on Cu substrates. Black curve: Recipe 1 (thin Cu-Sn first) with sharp transition, ∆Tc ≈ 1 K. Red curve: Recipe 2 (thick Cu-Sn first) with the highest Tc = 17.7 K onset, but low-Sn Nb3Sn near the surface. Blue curve: Recipe 3 (Nb first) with uniform morphology, but needing longer reaction. 6.5.1 Recipe 1: Thin Cu-Sn First The superconducting transition (black curve in 6.1… view at source ↗
Figure 6.13
Figure 6.13. Figure 6.13: Recipe 1, thin Cu-Sn first: Cross-sectional microscopy imaging structure of thin view at source ↗
Figure 6.14
Figure 6.14. Figure 6.14: Recipe 2, thick Cu-Sn first: first Cross-sectional microscopy imaging multilayer view at source ↗
Figure 6.15
Figure 6.15. Figure 6.15: Recipe 3, Nb First: SEM Image of Nb3Sn film made by depositing Nb onto a Cu substrate/Ta diffusion bilayer. Then Cu-Sn was evaporated onto the Nb and post-reacted. This film had particularly uniform morphology due to the clean interface between Ta and Nb. 112 view at source ↗
Figure 7.1
Figure 7.1. Figure 7.1: Quality factor vs magnetic field measurements for superconducting axion detector view at source ↗
Figure 7.2
Figure 7.2. Figure 7.2: NbTi Bulk Cavity [161]. 114 view at source ↗
Figure 7.3
Figure 7.3. Figure 7.3: NbTi versus copper cavity Quality factor vs Magnetic field [ view at source ↗
Figure 7.4
Figure 7.4. Figure 7.4: NbTi surface resistance for both the walls and end caps calculated using a mode view at source ↗
Figure 7.5
Figure 7.5. Figure 7.5: (a) 7-GHz and (b) 9-GHz cavities halves made by the European collabora view at source ↗
Figure 7.6
Figure 7.6. Figure 7.6: A schematic of the REBCO HTS tape’s architecture [ view at source ↗
Figure 7.7
Figure 7.7. Figure 7.7: REBCO orange slice cavity [15]. 7.2.2 European CERN REBCO Cavity Golm et al. [159] made a REBCO cavity that showed promising results, with minimal magnetic field degradation out to 9 T ( view at source ↗
Figure 7.8
Figure 7.8. Figure 7.8: A REBCO cavity made with the tapes perpendicular to cavity axis [ view at source ↗
Figure 7.9
Figure 7.9. Figure 7.9: Two different cavity geometries: a) optimized for high field use called the cigar view at source ↗
Figure 7.10
Figure 7.10. Figure 7.10: Loaded quality factor versus applied magnetic field for a small 3.9 GHz TESLA view at source ↗
Figure 7.11
Figure 7.11. Figure 7.11: The Nb3Sn cavity made by sputtering from a stoichiometric Nb3Sn target [159]. 123 view at source ↗
Figure 8.1
Figure 8.1. Figure 8.1: SLAC mushroom cavity schematic, where the 2-inch wafer is the superconducting view at source ↗
Figure 8.2
Figure 8.2. Figure 8.2: The 2-inch bronze substrate disks, after Nb deposition and reaction, showing view at source ↗
Figure 8.3
Figure 8.3. Figure 8.3: Samples marked with H2 and PR2 are coupon samples that underwent the same view at source ↗
Figure 8.4
Figure 8.4. Figure 8.4: Quality factor as a function of temperature for 2-inch bronze disk samples view at source ↗
Figure 8.5
Figure 8.5. Figure 8.5: COMSOL simulation showing the change of frequency and quality factor for the view at source ↗
Figure 8.6
Figure 8.6. Figure 8.6: a) Side view and b) cross section of the 8-piece Cu cavity (6 walls, 2 endcaps). view at source ↗
Figure 8.7
Figure 8.7. Figure 8.7: Cavity wall from the 8-piece design that went through a full downselected Nb view at source ↗
Figure 8.8
Figure 8.8. Figure 8.8: Delamination near the edge after heat-treatment for 8-piece cavity wall before view at source ↗
Figure 8.9
Figure 8.9. Figure 8.9: Comparison between normalized cavity measurement and coupon sample SQUID view at source ↗
Figure 8.10
Figure 8.10. Figure 8.10: Model of 8 piece cavity with one Nb3Sn wall and the Rs vs T curve for bulk Cu, cavity with one superconducting wall, and isolated superconducting wall. this hybrid geometry. At 8 T the superconducting state is lost, which is much lower than the predicted > Hc2 = 20 T commonly found in wires. At very low field B0 < 1 T, the superconductor was more resistive than Cu. This experiment proved promising as th… view at source ↗
Figure 8.11
Figure 8.11. Figure 8.11: Quality factor vs Magnetic field for the single wall 8-Piece cavity. At 8 tesla, view at source ↗
Figure 8.12
Figure 8.12. Figure 8.12: Sputtering chamber max clearance, for substrate thickness. view at source ↗
Figure 8.13
Figure 8.13. Figure 8.13: 2-piece Cu cavity. 0.2 liters per minute flow rate) to improve the Cu residual resistivity ratio. After substrate preparation and coating, the cavity was tested at ASC from 2 K to 20 K and then shipped to LLNL for dilution-refrigerator testing down to 50 mK. All RF measurements at LLNL follow a protocol established at ASC (see Sec.8.2.1). 2-piece Cavity Results. The first experiments with the 2-piece he… view at source ↗
Figure 8.14
Figure 8.14. Figure 8.14: Downselected Nb-first recipe coated on the 2-piece cavity design. view at source ↗
Figure 8.15
Figure 8.15. Figure 8.15: Surface Resistance vs Temperature for the two Cu cavity designs, and a com view at source ↗
Figure 8.16
Figure 8.16. Figure 8.16: Dilution fridge setup for Q measurements of the 2-piece cavity in mK temper￾atures. wall regions). For a hybrid cavity with geometric factor Gtotal = 350 Ω, the measured quality factor reflects losses from both materials: 1 Qmeasured = Rs,Cu GCu + Rs,Nb3Sn GNb3Sn (8.2) where GCu = 1050 Ω (1/3 surface coverage) and GNb3Sn = 525 Ω (2/3 coverage). Using the measured Cu cavity surface resistance Rs,Cu = 6.3… view at source ↗
Figure 8.17
Figure 8.17. Figure 8.17: Model and Rs vs T for the 2-piece Nb3Sn cavity. 76,000 for seamless geometry. Assuming the same fractional leakage affects the Nb3Sn mea￾surement, the correction factor is: α = QCu,ideal QCu,measured = 76,000 55,000 = 1.38 (8.4) Applying this correction: QNb3Sn,corrected = α × QNb3Sn,full = 1.38 × (9.6 × 104 ) = 1.3 × 105 (8.5) at B = 0 and T = 50 mK. This corrected value represents the expected perform… view at source ↗
Figure 8.18
Figure 8.18. Figure 8.18: Coating defects at edge regions and endcaps of the two-piece cavity, showing view at source ↗
read the original abstract

Axion dark matter searches require superconducting radio-frequency (SRF) cavities on copper (Cu) substrates with quality factors Q > 10^5 in multi-tesla magnetic fields. Copper reduces thermal noise and allows complex geometries. Nb3Sn is a strong candidate due to its superior superconducting properties. However, uniform high-Tc Nb3Sn thin films on Cu are challenging due to Sn loss and substrate strain. This work uses solid-state diffusion of Sn from high-Sn Cu-Sn alloys into Nb layers to form Nb3Sn at Cu-compatible temperatures (650-750{\deg}C), avoiding the traditional ~1100{\deg}C vapor method. Varying Cu-Sn composition yielded an optimal alloy that maintains high Sn activity. Compositional and thermal expansion analyses showed Tc is suppressed below 18 K by Cu substrate strain. Experiments on Nb and sapphire substrates isolated the strain effects. Two routes were developed: (1) Cu-Sn on Ta-coated Cu with hot Nb sputtering (Tc = 16 K), and (2) Nb on Ta/Cu with Cu-Sn evaporation and ex-situ reaction. Route 2 gave uniform Nb3Sn and was chosen for cavity coating. A hexagonal cavity combining designs from the University of Washington and Center for Axion and Precision Physics was coated using Route 2 and tested to 50 mK and 9 T. At zero field it reached Q = 77,000 (40% above bare Cu's Q = 55,000), but Q dropped sharply in field. Nb3Sn coatings on Cu cavities outperform bare Cu at zero field and provide practical routes for improved axion detectors.

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 reports the fabrication of Nb3Sn thin films on Cu substrates using a novel Cu-Sn solid-state diffusion method at 650-750°C to avoid high-temperature issues with Sn loss. Two routes are developed, with Route 2 (Nb on Ta/Cu with Cu-Sn evaporation and ex-situ reaction) selected for coating a hexagonal SRF cavity combining UW and CAPP designs. The coated cavity is tested at 50 mK up to 9 T, achieving zero-field Q = 77,000 (40% above bare Cu Q = 55,000) but with a sharp Q drop in applied field. Tc is suppressed to 16 K by Cu substrate strain, as isolated via tests on Nb and sapphire substrates. The authors conclude that Nb3Sn coatings on Cu outperform bare Cu at zero field and provide practical routes for improved axion detectors.

Significance. The low-temperature Cu-compatible fabrication route for Nb3Sn films represents a useful technical advance for SRF cavities on Cu, enabling complex geometries and reduced thermal noise relevant to axion dark matter searches. The zero-field Q improvement and strain-effect isolation experiments add concrete value. However, the sharp field-induced Q drop leaves the key multi-tesla performance requirement unaddressed, limiting immediate applicability.

major comments (1)
  1. [Abstract] Abstract: The assertion that the coatings 'provide practical routes for improved axion detectors' (requiring Q > 10^5 in multi-tesla fields) is not supported by the reported results, as the cavity test explicitly shows Q drops sharply once field is applied up to 9 T, with no mechanism (vortex dissipation, coating non-uniformity, or strain) or mitigation strategy described. This makes the extrapolation to the operating regime an untested assumption that is load-bearing for the central application claim.
minor comments (2)
  1. [Abstract] Abstract: The reported Q values (77,000 and 55,000), 40% improvement, and Tc = 16 K are presented without error bars, statistical details, full datasets, or controls for the field-dependent drop, which reduces verifiability of the performance claims.
  2. The manuscript would benefit from expanded discussion of the cavity test conditions and any preliminary steps taken to address field losses, even if preliminary.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful and constructive review of our manuscript. We address the major comment regarding the abstract below and have revised the manuscript to ensure our claims accurately reflect the reported results without overstatement.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The assertion that the coatings 'provide practical routes for improved axion detectors' (requiring Q > 10^5 in multi-tesla fields) is not supported by the reported results, as the cavity test explicitly shows Q drops sharply once field is applied up to 9 T, with no mechanism (vortex dissipation, coating non-uniformity, or strain) or mitigation strategy described. This makes the extrapolation to the operating regime an untested assumption that is load-bearing for the central application claim.

    Authors: We agree that the zero-field Q of 77,000, while 40% higher than bare Cu, falls short of the Q > 10^5 target in multi-tesla fields, and the sharp Q drop observed up to 9 T indicates that field performance requires further development. The phrasing 'practical routes for improved axion detectors' was meant to emphasize the low-temperature (650-750°C) Cu-Sn solid-state diffusion method, which enables uniform Nb3Sn films on Cu substrates and complex geometries while avoiding Sn loss and high-temperature damage to Cu. This fabrication advance directly addresses a key barrier for SRF cavities in axion searches. However, to avoid implying that the current results already achieve the full multi-tesla performance, we will revise the abstract to state that the Nb3Sn coatings on Cu outperform bare Cu at zero field and that the routes provide a practical foundation for developing improved axion detectors. The mechanism of the field-induced Q drop was outside the scope of this work, which focused on process development and zero-field characterization; no mitigation strategy is presented because none was tested here. revision: yes

Circularity Check

0 steps flagged

No circularity: purely experimental report with no derivations or fitted predictions

full rationale

The paper describes fabrication routes, substrate preparation, cavity coating, and direct RF measurements of Q at zero field and up to 9 T. No equations, ansatzes, parameter fits, or theoretical derivations appear in the provided text or abstract. All claims rest on measured values (e.g., Q = 77 000 vs. 55 000) rather than any chain that reduces to its own inputs by construction. Self-citations, if present, are not load-bearing for any derivation because none exists. This matches the default expectation of an honest non-finding for experimental work.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

This experimental materials paper introduces no free parameters, mathematical axioms, or invented entities; it operates within standard superconductivity and thin-film deposition principles.

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