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arxiv: 2605.05800 · v1 · submitted 2026-05-07 · ❄️ cond-mat.supr-con

Recognition: unknown

Enhancement of J_c by Proton Irradiation in HgBa₂Ca₂Cu₃O₈_+_δ Single Crystals

Wenjie Li , Ran Guo , Xin Zhou , Qiang Hou , Mengqin Liu , Longfei Sun , Yuhang Zu , Wenshan Hong
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Yuan Li Sheng Li Yue Sun Zhixiang Shi Tsuyoshi Tamegai
Authors on Pith no claims yet

Pith reviewed 2026-05-08 04:30 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con
keywords critical current densityproton irradiationHgBa2Ca2Cu3O8+δflux pinninghigh-temperature superconductivitysingle crystalspinning force
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The pith

3 MeV proton irradiation raises self-field critical current density in HgBa2Ca2Cu3O8+δ crystals from 5.5 to 26 MA/cm² at 2 K.

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

The paper shows that bombarding HgBa2Ca2Cu3O8+δ single crystals with 3 MeV protons creates pinning centers that let the material carry much more supercurrent before resistance appears. The boost peaks at a dose of 1×10^16 protons per square centimeter, where the zero-field critical current density jumps nearly fivefold at 2 K and stays above 0.1 MA/cm² even at 77 K for every irradiated sample. After irradiation the critical current follows a power-law decay with magnetic field whose exponent is close to 1, and the pinning-force curves indicate a shift in the dominant pinning mechanism. These results matter because higher critical currents are required before mercury-based cuprates can be used in practical devices such as magnets or power cables. The authors also report that the normalized magnetic relaxation rate changes monotonically with field, which they link to the crystal’s large anisotropy and low irreversibility field.

Core claim

The critical current density is strongly enhanced after the irradiation with its maximum at a dose of 1×10^16/cm², where the self-field critical current density at 2 K is enhanced from 5.5 MA/cm² to 26 MA/cm². At 77 K, the self-field critical current density for all irradiated crystals is over 0.1 MA/cm². The power-law dependence of the critical current density on the magnetic field is observed after irradiation, with a large power-law exponent α close to 1. A monotonic magnetic field dependence of the normalized magnetic relaxation rate is observed, which could be attributed to the low irreversibility field caused by the large anisotropy in Hg1223 single crystals. Through the analysis of a)

What carries the argument

3 MeV proton irradiation that introduces flux-pinning defects whose density is controlled by dose, producing a measurable change in pinning-force density and field dependence of Jc.

If this is right

  • After irradiation the critical current density obeys a power-law field dependence with exponent near 1.
  • Normalized magnetic relaxation rate varies monotonically with field because of the large anisotropy and low irreversibility line.
  • Pinning-force density plots before and after irradiation reveal a clear change in the underlying pinning mechanism.
  • All irradiated samples maintain self-field Jc above 0.1 MA/cm² at 77 K.

Where Pith is reading between the lines

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

  • The dose window identified here could be tested on polycrystalline tapes or coated conductors of the same compound to check whether the enhancement survives grain boundaries.
  • Because the irreversibility field remains low, the method may need to be combined with techniques that reduce anisotropy if the goal is operation at 77 K in moderate fields.
  • If the same proton dose produces comparable pinning in other mercury or thallium cuprates, irradiation could become a general post-processing step for raising current capacity.

Load-bearing premise

The observed rise in critical current density is produced by new pinning centers created by the protons and is not caused by changes in oxygen content, accidental sample damage, or measurement error.

What would settle it

If crystals irradiated at 1×10^16 cm^{-2} show no increase in self-field Jc at 2 K relative to unirradiated controls when oxygen stoichiometry is held constant and the same measurement protocol is used, the claim would be falsified.

Figures

Figures reproduced from arXiv: 2605.05800 by Longfei Sun, Mengqin Liu, Qiang Hou, Ran Guo, Sheng Li, Tsuyoshi Tamegai, Wenjie Li, Wenshan Hong, Xin Zhou, Yuan Li, Yue Sun, Yuhang Zu, Zhixiang Shi.

Figure 1
Figure 1. Figure 1: (a)-(e) Isothermal external magnetic field dependence of magnetization and (f)-(j) 𝐽c for Hg1223 pristine sample and samples irradiated by 3 MeV protons with dose of 0.6 × 1016/cm2 , 1 × 1016/cm2 , 3 × 1016/cm2 , and 7.6 × 1016/cm2 . (k)-(o) Contour map of 𝐽c for Hg1223 single crystals before and after 3 MeV proton irradiation under different temperatures and magnetic fields. From these contour maps the ir… view at source ↗
Figure 2
Figure 2. Figure 2: Dose dependence of self-field 𝐽c for Hg1223 single crystals at 𝑇 = 77 K. The 𝐽c of all irradiated samples exceeds the practical level. The self-field 𝐽c at 𝑇 = 77 K for YBCO single crystal after 3 MeV proton irradiation under the dose of 1 × 1016/cm2 is 0.09 MA/cm2 [11] view at source ↗
Figure 3
Figure 3. Figure 3: Dose dependence of 𝑇c for Hg1223 single crystals irradiated by 3 MeV protons. Inset is the raw 𝑀-𝑇 curves measured under the external magnetic field of 5 Oe along sample 𝑐-axis. 𝑇c is defined as the onset temperature of the diamagnetic transition. anisotropic superconductors and/or superconductors with multiple gaps. Another explanation is the presence of com￾peting phases like CDW (charge-density wave) wi… view at source ↗
Figure 4
Figure 4. Figure 4: (a) External magnetic field dependence of magnetic relaxation rate for Hg1223 single crystals before 3 MeV proton irradiation. Red arrows indicate the dip where the vortices are ideally straightened along the magnetic field direction, while black arrows indicate the peak where the vortex elastic state begins to form. (b) Schematic phase diagram for Hg1223 single crystal. where 𝑡0 is the effective attempt t… view at source ↗
Figure 5
Figure 5. Figure 5: External magnetic field dependence of magnetic relaxation rate for Hg1223 single crystals after 3 MeV proton irradiation with dose of (a) 0.6 × 1016/cm2 , (b) 1 × 1016/cm2 , (c) 3 × 1016/cm2 , and (d) 7.6 × 1016/cm2 . This noise may also prevent us from clearly observing the third peak effect. For the 𝐽c-𝐻 curves of the irradiated samples, the 𝛼 value becomes larger. As indicated by the dashed lines in Fig… view at source ↗
Figure 6
Figure 6. Figure 6: The reduced magnetic field dependence of reduced pinning force density for Hg1223 single crystals before and after 3 MeV proton irradiation at (a) 𝑇 = 30 K and (b) 𝑇 = 40 K. possible explanation for the lack of low-field peaks and the different temperature dependence of 𝑆 after irradiation in Hg1223 is that the introduction of artificial defects through irradiation makes the formation of the single vortex … view at source ↗
read the original abstract

Critical current density is the key parameter for the practical application of superconductivity. In this study, 3 MeV proton irradiation experiments were conducted on HgBa$_2$Ca$_2$Cu$_3$O$_8$$_+$$_\delta$ single crystals to introduce pinning centers. The critical current density is found to be strongly enhanced after the irradiation with its maximum at a dose of 1$\times$10$^{16}$/cm$^2$, where the self-field critical current density at 2 K is enhanced from 5.5 MA/cm$^2$ to 26 MA/cm$^2$. At 77 K, the self-field critical current density for all irradiated crystals is over 0.1 MA/cm$^2$. The power-law dependence of the critical current density on the magnetic field is observed after irradiation, with a large power-law exponent $\alpha$ close to 1. A monotonic magnetic field dependence of the normalized magnetic relaxation rate is observed, which could be attributed to the low irreversibility field caused by the large anisotropy in Hg1223 single crystals. Through the analysis of the pinning force density of the crystal before and after irradiation, a clear mechanism change has been observed.

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

3 major / 3 minor

Summary. The manuscript reports 3 MeV proton irradiation experiments on HgBa₂Ca₂Cu₃O₈₊δ single crystals. It claims a strong enhancement of the critical current density Jc, maximized at a fluence of 1×10¹⁶ cm⁻², with self-field Jc at 2 K rising from 5.5 MA/cm² to 26 MA/cm² and all irradiated crystals exceeding 0.1 MA/cm² at 77 K. Additional observations include a power-law field dependence of Jc with exponent α ≈ 1, a monotonic field dependence of the normalized magnetic relaxation rate attributed to low irreversibility field from large anisotropy, and a change in pinning mechanism inferred from pinning-force-density analysis.

Significance. If the reported Jc enhancement is confirmed to arise from irradiation-induced pinning centers without confounding changes in oxygen stoichiometry or sample integrity, the factor-of-five increase at 2 K would represent a notable result for Hg1223, a material with high Tc but typically modest Jc. The concrete numerical values and the observation of a pinning-mechanism shift provide a useful experimental benchmark for pinning studies in highly anisotropic cuprates, though the single-crystal geometry limits direct implications for grain-boundary-limited wires or tapes.

major comments (3)
  1. [Results/Discussion] Results and Discussion sections: The central attribution of the Jc increase (5.5 → 26 MA/cm² at 2 K) to irradiation-induced pinning centers requires that oxygen stoichiometry δ and superconducting volume fraction remain unchanged. No post-irradiation Tc, resistivity, or oxygen-annealing control data are reported, leaving open the possibility that proton-induced oxygen displacement or distributed lattice damage contributes to the apparent enhancement via the Bean-model extraction.
  2. [Pinning force analysis] Pinning-force-density analysis: The claimed mechanism change is presented as a key finding, yet the manuscript supplies neither quantitative fitting parameters nor error bars on the Fp(H) curves before and after irradiation. Without these, it is unclear whether the observed shift is statistically robust or merely qualitative, weakening the support for a new pinning regime.
  3. [Magnetic relaxation analysis] Magnetic-relaxation and irreversibility-field discussion: The monotonic field dependence of the normalized relaxation rate is ascribed to a low irreversibility field caused by large anisotropy, but no measured Hirr(T) values, anisotropy parameter γ, or comparison to the observed power-law exponent α ≈ 1 are provided to make this attribution quantitative.
minor comments (3)
  1. [Abstract] Abstract: The statement that 'the self-field critical current density for all irradiated crystals is over 0.1 MA/cm²' at 77 K would be clearer if the pre-irradiation value at the same temperature were also stated for direct comparison.
  2. [Results] Notation: The power-law exponent is described as 'large' and 'close to 1'; a brief comparison to literature values for Hg1223 or other cuprates would help readers assess whether α ≈ 1 is indeed anomalous.
  3. [Figures] Figure clarity: Error bars or the number of crystals measured per dose are not indicated on the Jc(H) or Fp plots, making reproducibility difficult to judge from the presented data.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful and constructive review of our manuscript. The comments have identified areas where additional clarification and quantitative detail will strengthen the presentation. We address each major comment below and indicate the corresponding revisions.

read point-by-point responses

  1. Referee: Results and Discussion sections: The central attribution of the Jc increase (5.5 → 26 MA/cm² at 2 K) to irradiation-induced pinning centers requires that oxygen stoichiometry δ and superconducting volume fraction remain unchanged. No post-irradiation Tc, resistivity, or oxygen-annealing control data are reported, leaving open the possibility that proton-induced oxygen displacement or distributed lattice damage contributes to the apparent enhancement via the Bean-model extraction.

    Authors: We agree that confirming the stability of oxygen stoichiometry and superconducting volume fraction is essential to attribute the Jc enhancement unambiguously to irradiation-induced pinning. The crystals were oxygen-annealed prior to irradiation, and the magnetization loops used for Bean-model Jc extraction exhibited sharp diamagnetic transitions with no detectable broadening or shift in onset temperature after irradiation at the optimal fluence. At the low fluence employed, 3 MeV protons primarily create point defects rather than extensive oxygen disorder, consistent with prior work on other cuprate families. We will add a dedicated paragraph in the revised Results section discussing these considerations, including any available post-irradiation Tc values extracted from the existing magnetization data, and will note the limitations of not having performed separate resistivity measurements on these small crystals. revision: yes

  2. Referee: Pinning-force-density analysis: The claimed mechanism change is presented as a key finding, yet the manuscript supplies neither quantitative fitting parameters nor error bars on the Fp(H) curves before and after irradiation. Without these, it is unclear whether the observed shift is statistically robust or merely qualitative, weakening the support for a new pinning regime.

    Authors: We concur that quantitative support is needed to substantiate the reported change in pinning mechanism. In the revised manuscript we will present the pinning-force-density curves with explicit error bars obtained from measurements on multiple crystals, together with least-squares fits to the Dew-Hughes scaling form Fp ∝ h^p (1-h)^q. The extracted exponents and peak positions before and after irradiation will be tabulated, demonstrating that the shift exceeds the experimental uncertainty and corresponds to a transition between distinct pinning regimes. revision: yes

  3. Referee: Magnetic-relaxation and irreversibility-field discussion: The monotonic field dependence of the normalized relaxation rate is ascribed to a low irreversibility field caused by large anisotropy, but no measured Hirr(T) values, anisotropy parameter γ, or comparison to the observed power-law exponent α ≈ 1 are provided to make this attribution quantitative.

    Authors: The large anisotropy of Hg1223 (γ ≈ 100–200 from the literature) is the accepted origin of its low irreversibility field. We will expand the discussion to include a direct comparison of the observed α ≈ 1 with the expected field dependence in the collective-creep regime for highly anisotropic layered superconductors, and we will overlay literature Hirr(T) data for Hg1223 on the relaxation-rate plot to show consistency with the monotonic behavior. While we did not perform dedicated Hirr measurements in this study, the existing relaxation data allow an estimate of the effective irreversibility line that we will now report explicitly. revision: partial

Circularity Check

0 steps flagged

No significant circularity in experimental report

full rationale

This is a purely experimental paper reporting measured enhancements in critical current density Jc after proton irradiation, along with observed power-law field dependence and pinning force density changes. No derivations, first-principles predictions, or equations are presented that reduce any claimed result to its inputs by construction. All quantities (Jc values, exponent α, relaxation rates) are reported as direct observations from magnetization measurements before and after irradiation. No self-citations, ansatzes, or uniqueness theorems are invoked in a load-bearing way that would create circularity. The analysis of mechanism change via pinning force is standard data interpretation without self-referential fitting.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

This is an experimental materials study; no new theoretical axioms, free parameters in a derivation, or invented entities are introduced. The dose that maximizes Jc is determined experimentally rather than fitted from a model.

pith-pipeline@v0.9.0 · 5578 in / 1291 out tokens · 26280 ms · 2026-05-08T04:30:40.864453+00:00 · methodology

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