# MgB2: two gaps, isotope effects and conductor conditions

Connect boron-derived bands and coupled superconducting gaps to isotope experiments, impurity scattering and the conditions that matter for MgB2 conductors.

## Scope

Magnesium diboride, MgB₂, is a useful benchmark for electron–phonon superconductivity with different gap scales on different Fermi-surface sheets. Its 2001 discovery report combined magnetization and resistivity near 39 K in a simple hexagonal compound. This historical temperature is not a universal sample constant or an upper bound on phonon-mediated superconductivity. [R1](#ref-source-fade6558e7eafb2b) [R6](#ref-source-7c4eac077ae5e221)

Boron honeycomb layers provide most of the electronic states near the Fermi level. The approximately cylindrical σ sheets derive mainly from in-plane boron orbitals; the π sheets have substantial out-of-plane character. Strong coupling of σ states to boron bond stretching helps explain the large gap. “Two gaps” is a useful reduction of a momentum-dependent problem: Choi's calculation at 4 K spans 6.4–7.2 meV on σ sheets and 1.2–3.7 meV on π sheets, with averages of 6.8 and 1.8 meV. These are calculated distributions, not two exactly constant measured gaps. [R2](#ref-source-a720b8200872878c) [R6](#ref-source-7c4eac077ae5e221)

## Mathematical assumptions

In an illustrative clean weak-coupling model with a shared cutoff, the linearized equations are $\Delta_i=L(T)\sum_j\lambda_{ij}\Delta_j$. The largest positive eigenvalue of the pairing matrix determines the first instability. Off-diagonal pair-transfer terms can make both gap components nonzero at the same transition, even when their amplitudes differ. For the chosen toy matrix $\lambda=\begin{pmatrix}0.40&0.08\\0.04&0.15\end{pmatrix}$, the leading eigenvalue is approximately 0.4122 and $\Delta_2/\Delta_1\approx0.1526$ at onset. Setting both off-diagonal entries to zero removes the induced second component at the higher transition. These numbers illustrate coupled equations; they are not fitted MgB₂ parameters. [R6](#ref-source-7c4eac077ae5e221) [R7](#ref-source-a9d7d0b720a3bafd)

Pair transfer and impurity interband scattering are different processes. An elastic scattering rate contains impurity matrix elements and connects single-particle states; it must not replace $\lambda_{ij}$ in the pairing equation. Mazin's analysis distinguishes weak σ–π impurity mixing from potentially large scattering within each band. Its normal-state conductivity adds parallel band contributions, so a single residual resistivity cannot uniquely determine the interband rate. Using its illustrated in-plane plasma weights and intraband rates, a simplified residual-conductivity calculation shifts the σ share from about 33% to 92% between the selected clean and dirty examples. This is a model illustration, not a resistivity measurement or a calculation of the full temperature dependence. [R7](#ref-source-a9d7d0b720a3bafd)

For isotope substitutions, $\alpha_i=-\Delta\ln T_c/\Delta\ln M_i$ is a partial coefficient. Bud'ko's rounded 40.2 K and 39.2 K values give $\alpha_{\mathrm B}\approx0.264$ using masses 10 and 11, consistent with the reported $0.26\pm0.03$. Hinks separately measured both elements and reported approximately $\alpha_{\mathrm B}=0.30(1)$ and $\alpha_{\mathrm{Mg}}=0.02(1)$. Their sum near 0.32 differs from the simplest harmonic single-scale expectation of 0.5. This does not uniquely isolate anharmonicity, Coulomb effects or multiband contributions. [R3](#ref-source-22ad55507a1e49c5) [R4](#ref-source-60ffd9b4ef2c9ccd)

## Experimental criteria

The original discovery paper reported a resistive onset of 39 K and an endpoint of 38 K using four probes at zero applied field. Magnetization used zero-field-cooled and field-cooled protocols at 10 Oe; the authors estimated a 49% superconducting volume fraction at 5 K. Their 196 MPa argon pressure was used during hot isostatic synthesis at 973 K for ten hours. It is not the pressure of the superconductivity measurement. Onset, endpoint, magnetic response and synthesis conditions must remain separate fields. [R1](#ref-source-fade6558e7eafb2b)

Bud'ko measured on warming after zero-field cooling in 25 G, using 2% of the low-temperature diamagnetic signal to define onset. The curves were normalized for comparison; their displayed height is not an absolute superconducting volume fraction. Hinks instead cooled to about 20 K in nominal zero field, applied 1 G and recorded on warming, comparing extrapolated onset with a 10% criterion. Its six boron isotope comparisons retain the same criterion within each pair. The natural-Mg samples had higher transition temperatures than the enriched-Mg samples; an unquantified impurity contribution limits the small Mg-isotope inference. The Mg coefficient belongs to Hinks, not Bud'ko's boron-only experiment. For the last 10% pair, the printed temperatures give 0.3049, versus the table's 0.31(1): agreement within stated uncertainty is not exact last-digit reproduction. Recalculating printed temperatures does not refit magnetization or resolve the Hinks manuscript's Mg-mass discrepancy. [R3](#ref-source-22ad55507a1e49c5) [R4](#ref-source-60ffd9b4ef2c9ccd)

Szabó's Cu–MgB₂ point contacts showed small and large gap scales around 2.8 and 7 meV. Their two-component BTK fits kept interface transparency and relative weight fixed across temperature; thermal smearing makes the two contributions harder to separate near the bulk transition. Fields up to 1 T preferentially suppressed the small-gap spectral contribution, helping reveal the large-gap features. This does not mean that 1 T is the bulk upper critical field, and these spectra alone do not determine the relative sign of the gaps. Using a transition temperature of 39 K, the low-temperature gap ratios are approximately 1.67 and 4.17, rather than a single weak-coupling BCS ratio. [R5](#ref-source-69ced9b5dda860f1)

## Limits and disputes

The Choi calculation resolves momentum-dependent gaps. In Fig. 3a, separate empirical fits describe the calculated average gaps with exponents 2.9 for the sigma sheets and 1.8 for the pi sheets; these are not one universal temperature curve. Fig. 3b assumes a 0.1 meV lifetime-broadening parameter. Fig. 4 compares calculated electronic specific heat with three experimental datasets having different transition temperatures, rather than fitting a single specimen's spectroscopy. Szabo's author manuscript fits point-contact conductance with two BTK contributions: their relative weight varies from about 10% to 90% between contacts, while weight and barrier parameter remain fixed during a given temperature series. That contact-dependent weight must not be substituted for Choi's calculated band density-of-states shares. Thermal smearing also obscures separate peaks near the transition. These distinctions support comparing multiple probes; they do not establish gap sign from these spectra or independently reproduce the specific-heat data or Eliashberg calculation. [R5](#ref-source-69ced9b5dda860f1) [R6](#ref-source-7c4eac077ae5e221)

The Hinks author manuscript contains a version issue: Table 1 prints a Mg mass of 25.001 for a sample family, while the methods describe enriched ²⁶Mg. This discrepancy is retained as unresolved pending comparison with the final published table. No Mg-mass refit is presented. The boron ratios use the explicitly printed boron masses and temperatures. Likewise, the Mazin author PDF's generated date is not its submission date; the cited version is the arXiv submission of 1 April 2002. [R4](#ref-source-60ffd9b4ef2c9ccd) [R7](#ref-source-a9d7d0b720a3bafd)

## Discovery implications

Materials development must connect gap physics to usable conductors. A 2026 study of square, 19-filament MgB₂ wire reports a 14.2% filling factor and an engineering-current benchmark at 4.2 K and 6.5 T. This reference is currently checked only through the publisher's indexed summary and the authors' publication record; the electric-field criterion, full methods and coil comparison require further review. Engineering current density uses the whole composite cross-section, unlike a current density normalized to superconducting material alone. Neither operating temperature nor a current-density benchmark should enter a transition-temperature ranking. [R8](#ref-source-39e103ef0175cc7e)

Preserve processing, connectivity, field orientation, temperature and voltage criterion when comparing wires. Increasing intraband disorder, changing band filling and increasing interband impurity mixing are not interchangeable interventions. A useful candidate must satisfy its operating requirements as well as the microscopic pairing model; this article's scoped calculations do not certify a wire or magnet design. [R7](#ref-source-a9d7d0b720a3bafd) [R8](#ref-source-39e103ef0175cc7e)

## Related topics

See [multiband pairing](/scwiki/multiband-pairing), [Eliashberg theory](/scwiki/eliashberg-strong-coupling), [isotope effects](/scwiki/isotope-effect), [Andreev reflection](/scwiki/andreev-reflection) and [critical current](/scwiki/critical-current).

## Material cases

Values describe individual reports, not a ranking. Unknown means the checked source did not supply the field at this review scope.

| Material and sample | Reported temperature | Criterion | Probe | Pressure | State | Evidence |
|---|---|---|---|---|---|---|
| MgB2; Nagamatsu 2001 polycrystalline pellet, zero field | 39 K; Onset 39 K; endpoint 38 K. Synthesis pressure 196 MPa is not measurement pressure. | transition; four-probe-resistive-onset | Four-probe resistivity; separate 10 Oe magnetization | ambient; unknown GPa | unknown | experiment; [source](#ref-source-fade6558e7eafb2b) |
| MgB2; Budko Mg10B2, ZFC warming in 25 G | 40.2 K; Isotope-specific sample; not universal MgB2 Tc. | transition; two-percent-diamagnetic-onset | SQUID magnetization; paired Mg11B2 comparison | ambient; unknown GPa | unknown | experiment; [source](#ref-source-22ad55507a1e49c5) |
| MgB2; Budko Mg11B2, ZFC warming in 25 G | 39.2 K; Isotope-specific sample and criterion. | transition; two-percent-diamagnetic-onset | SQUID magnetization; paired Mg10B2 comparison | ambient; unknown GPa | unknown | experiment; [source](#ref-source-22ad55507a1e49c5) |
| MgB2; Szabo Cu–MgB2 point contact at 4.2 K | 4.2 K; Operating temperature; 2.8/7 meV gap scales are not measured Tc values. | measurement; point-contact-operating-temperature | Differential resistance; two BTK contributions, fields up to 1 T | ambient; unknown GPa | unknown | experiment; [source](#ref-source-69ced9b5dda860f1) |
| MgB2; 2026 square 19-filament IMD wire | 4.2 K; Operating temperature, not Tc; full conductor methods remain open. | measurement; engineering-current-operating-temperature | Indexed summary benchmark at 6.5 T; voltage criterion not reviewed | ambient; unknown GPa | unknown | experiment; [source](#ref-source-39e103ef0175cc7e) |

## Sources

### Ref source-fade6558e7eafb2b

[R1] Superconductivity at 39 K in magnesium diboride (2001). [DOI 10.1038/35065039](https://doi.org/10.1038/35065039). Publication: journal-article. Check: selected-published-methods-figures-check. Checked: 2026-10-18. Published 1 March 2001. Original published pp.63–64 read for MgB2 discovery (not preceding unrelated article); p.64 visually checked. Resistive onset 39 K / endpoint 38 K, 10 Oe magnetization and synthesis196 MPa distinguished. Raw data not reproduced.
### Ref source-a720b8200872878c

[R2] Superconductivity of Metallic Boron in MgB2 (2001). [DOI 10.1103/PhysRevLett.86.4656](https://doi.org/10.1103/PhysRevLett.86.4656). Publication: journal-article. Check: publisher-abstract-check. Checked: 2026-10-18. Published 14 May 2001. Abstract only; band/phonon interpretation, not independently reproduced electronic structure.
### Ref source-22ad55507a1e49c5

[R3] Boron Isotope Effect in Superconducting MgB2 (2001). [DOI 10.1103/PhysRevLett.86.1877](https://doi.org/10.1103/PhysRevLett.86.1877). Publication: journal-article. Check: selected-author-criterion-normalization-check. Checked: 2026-10-20. Author v1 submitted 31 January 2001, pp. 1–2 reread: 25 G ZFC warming, 2% diamagnetic onset and curves normalized to minus one at low temperature; boron-only comparison. Publisher identity and arXiv history checked; v2 exists but its full text and final journal methods were not compared in this follow-up. No raw magnetization refit.
### Ref source-60ffd9b4ef2c9ccd

[R4] The complex nature of superconductivity in MgB2 as revealed by the reduced total isotope effect (2001). [DOI 10.1038/35078037](https://doi.org/10.1038/35078037). Publication: journal-article. Check: selected-author-criterion-table-and-published-abstract-check. Checked: 2026-10-20. Author v1 submitted 12 April 2001, pp. 2–3 and Table 1 p. 7 checked: cooling to about 20 K, 1 G warming, onset and 10% criteria, unquantified impurity caveat. Table 1 visually inspected and six boron comparisons recalculated. Published 24 May 2001; final publisher abstract checked, final table remains unavailable. Printed Mg mass 25.001 versus enriched 26Mg methods leaves the discrepancy unresolved; no Mg-mass regression.
### Ref source-69ced9b5dda860f1

[R5] Evidence for Two Superconducting Energy Gaps in MgB2 by Point-Contact Spectroscopy (2001). [DOI 10.1103/PhysRevLett.87.137005](https://doi.org/10.1103/PhysRevLett.87.137005). Publication: journal-article. Check: selected-author-contact-weight-and-temperature-check. Checked: 2026-10-20. Author v1 submitted 30 May 2001, selected pp. 2–3 reread: Cu contacts, 400 Hz differential resistance, approximately 10%–90% relative weights between contacts, fixed weight and barrier parameter within each temperature series, thermal smearing and fields to 1 T. Journal published 11 September 2001; complete final methods and raw BTK fits not reproduced.
### Ref source-7c4eac077ae5e221

[R6] The origin of the anomalous superconducting properties of MgB2 (2002). [DOI 10.1038/nature00898](https://doi.org/10.1038/nature00898). Publication: journal-article. Check: selected-final-gap-fit-dos-and-heat-capacity-check. Checked: 2026-10-20. Final Nature 418, 758–760, published 15 August 2002. Selected discussion and Figs. 2–4 checked; p. 759 visually re-inspected. Fig. 3a separate empirical fits to calculated averages use exponents 2.9/1.8; Fig. 3b assumes broadening 0.1 meV. Fig. 4 compares three experimental datasets with calculated electronic specific heat. Calculated density-of-states shares are not point-contact weights. No full anisotropic Eliashberg solve or original specific-heat reanalysis.
### Ref source-a9d7d0b720a3bafd

[R7] Superconductivity in MgB2: Clean or Dirty? (2002). [DOI 10.1103/PhysRevLett.89.107002](https://doi.org/10.1103/PhysRevLett.89.107002). Publication: journal-article. Check: selected-author-scattering-transport-check. Checked: 2026-10-18. Journal published 19 August 2002; arXiv v1 submitted 1 April 2002 (PDF generated date 2018 is not submission). Selected pp.1–4, Eqs. 1–3 / Table I and Fig. 3 parameters. Full final-version comparison and impurity supercell calculations not reproduced.
### Ref source-39e103ef0175cc7e

[R8] Square filamentary MgB2 wire fabricated by the internal Mg diffusion method (2026). [Source publication](https://www.sciencedirect.com/science/article/pii/S2772830726000086). Publication: journal-article. Check: publisher-indexed-summary-and-author-bibliography-check. Checked: 2026-10-18. 2026, Superconductivity 17, 100238; identity crosschecked with authors at https://elu.sav.sk/veda-a-vyskum/kniznica/ing-pavol-kovac-drsc/ . Indexed publisher summary only:19 filaments, 14.2% filling, 4.2 K / 6.5 T engineering benchmark. Exact publication date, voltage criterion and full methods remain unreviewed; DOI not yet resolved.

## Claim evidence and conditions

### scwiki-d7-claim-scope-1

Magnesium diboride, MgB₂, is a useful benchmark for electron–phonon superconductivity with different gap scales on different Fermi-surface sheets. Its 2001 discovery report combined magnetization and resistivity near 39 K in a simple hexagonal compound. This historical temperature is not a universal sample constant or an upper bound on phonon-mediated superconductivity.

Evidence: theory. Sources: source-fade6558e7eafb2b, source-7c4eac077ae5e221.

Conditions: Source-specific sample, temperature, probe, isotope and publication version; toy models are not fitted material results.

Verification scope: Selected primary passages and bounded algebra only; final-version/raw-data issues explicitly retained.

### scwiki-d7-claim-scope-2

Boron honeycomb layers provide most of the electronic states near the Fermi level. The approximately cylindrical σ sheets derive mainly from in-plane boron orbitals; the π sheets have substantial out-of-plane character. Strong coupling of σ states to boron bond stretching helps explain the large gap. “Two gaps” is a useful reduction of a momentum-dependent problem: Choi's calculation at 4 K spans 6.4–7.2 meV on σ sheets and 1.2–3.7 meV on π sheets, with averages of 6.8 and 1.8 meV. These are calculated distributions, not two exactly constant measured gaps.

Evidence: theory. Sources: source-a720b8200872878c, source-7c4eac077ae5e221.

Conditions: Source-specific sample, temperature, probe, isotope and publication version; toy models are not fitted material results.

Verification scope: Selected primary passages and bounded algebra only; final-version/raw-data issues explicitly retained.

### scwiki-d7-claim-mathematical-assumptions-1

In an illustrative clean weak-coupling model with a shared cutoff, the linearized equations are $\Delta_i=L(T)\sum_j\lambda_{ij}\Delta_j$. The largest positive eigenvalue of the pairing matrix determines the first instability. Off-diagonal pair-transfer terms can make both gap components nonzero at the same transition, even when their amplitudes differ. For the chosen toy matrix $\lambda=\begin{pmatrix}0.40&0.08\\0.04&0.15\end{pmatrix}$, the leading eigenvalue is approximately 0.4122 and $\Delta_2/\Delta_1\approx0.1526$ at onset. Setting both off-diagonal entries to zero removes the induced second component at the higher transition. These numbers illustrate coupled equations; they are not fitted MgB₂ parameters.

Evidence: theory. Sources: source-7c4eac077ae5e221, source-a9d7d0b720a3bafd.

Source relationship: mixed-source-and-local-derivation. References provide physical context and any explicitly attributed inputs; the stated toy-matrix, parallel-channel or logarithmic-ratio calculation is local algebra, not a reproduced material fit.

Conditions: Source-specific sample, temperature, probe, isotope and publication version; toy models are not fitted material results.

Verification scope: Selected primary passages and bounded algebra only; final-version/raw-data issues explicitly retained.

### scwiki-d7-claim-mathematical-assumptions-2

Pair transfer and impurity interband scattering are different processes. An elastic scattering rate contains impurity matrix elements and connects single-particle states; it must not replace $\lambda_{ij}$ in the pairing equation. Mazin's analysis distinguishes weak σ–π impurity mixing from potentially large scattering within each band. Its normal-state conductivity adds parallel band contributions, so a single residual resistivity cannot uniquely determine the interband rate. Using its illustrated in-plane plasma weights and intraband rates, a simplified residual-conductivity calculation shifts the σ share from about 33% to 92% between the selected clean and dirty examples. This is a model illustration, not a resistivity measurement or a calculation of the full temperature dependence.

Evidence: theory. Sources: source-a9d7d0b720a3bafd.

Source relationship: mixed-source-and-local-derivation. References provide physical context and any explicitly attributed inputs; the stated toy-matrix, parallel-channel or logarithmic-ratio calculation is local algebra, not a reproduced material fit.

Conditions: Source-specific sample, temperature, probe, isotope and publication version; toy models are not fitted material results.

Verification scope: Selected primary passages and bounded algebra only; final-version/raw-data issues explicitly retained.

### scwiki-d7-claim-mathematical-assumptions-3

For isotope substitutions, $\alpha_i=-\Delta\ln T_c/\Delta\ln M_i$ is a partial coefficient. Bud'ko's rounded 40.2 K and 39.2 K values give $\alpha_{\mathrm B}\approx0.264$ using masses 10 and 11, consistent with the reported $0.26\pm0.03$. Hinks separately measured both elements and reported approximately $\alpha_{\mathrm B}=0.30(1)$ and $\alpha_{\mathrm{Mg}}=0.02(1)$. Their sum near 0.32 differs from the simplest harmonic single-scale expectation of 0.5. This does not uniquely isolate anharmonicity, Coulomb effects or multiband contributions.

Evidence: experiment. Sources: source-22ad55507a1e49c5, source-60ffd9b4ef2c9ccd.

Source relationship: mixed-source-and-local-derivation. References provide physical context and any explicitly attributed inputs; the stated toy-matrix, parallel-channel or logarithmic-ratio calculation is local algebra, not a reproduced material fit.

Conditions: Source-specific sample, temperature, probe, isotope and publication version; toy models are not fitted material results.

Verification scope: Selected primary passages and bounded algebra only; final-version/raw-data issues explicitly retained.

### scwiki-d7-claim-experimental-criteria-1

The original discovery paper reported a resistive onset of 39 K and an endpoint of 38 K using four probes at zero applied field. Magnetization used zero-field-cooled and field-cooled protocols at 10 Oe; the authors estimated a 49% superconducting volume fraction at 5 K. Their 196 MPa argon pressure was used during hot isostatic synthesis at 973 K for ten hours. It is not the pressure of the superconductivity measurement. Onset, endpoint, magnetic response and synthesis conditions must remain separate fields.

Evidence: experiment. Sources: source-fade6558e7eafb2b.

Conditions: Source-specific sample, temperature, probe, isotope and publication version; toy models are not fitted material results.

Verification scope: Selected primary passages and bounded algebra only; final-version/raw-data issues explicitly retained.

### scwiki-d7-claim-experimental-criteria-2

Bud'ko measured on warming after zero-field cooling in 25 G, using 2% of the low-temperature diamagnetic signal to define onset. The curves were normalized for comparison; their displayed height is not an absolute superconducting volume fraction. Hinks instead cooled to about 20 K in nominal zero field, applied 1 G and recorded on warming, comparing extrapolated onset with a 10% criterion. Its six boron isotope comparisons retain the same criterion within each pair. The natural-Mg samples had higher transition temperatures than the enriched-Mg samples; an unquantified impurity contribution limits the small Mg-isotope inference. The Mg coefficient belongs to Hinks, not Bud'ko's boron-only experiment. For the last 10% pair, the printed temperatures give 0.3049, versus the table's 0.31(1): agreement within stated uncertainty is not exact last-digit reproduction. Recalculating printed temperatures does not refit magnetization or resolve the Hinks manuscript's Mg-mass discrepancy.

Evidence: experiment. Sources: source-22ad55507a1e49c5, source-60ffd9b4ef2c9ccd.

Source relationship: mixed-source-and-local-derivation. Named papers support the method and figure details; limits on transferring normalized weights, criteria or calculated quantities are editorial reasoning. No independent raw-data or full numerical reproduction.

Conditions: Budko author v1: ZFC warming, 25 G and 2% criterion; Hinks author v1: cooling to about 20 K, 1 G warming, separate onset and 10% pairs; final Hinks table unresolved.

Verification scope: Selected identified author methods/table and final Choi figure captions; source-specific quantitative comparisons, no complete final-author comparison or raw-data reanalysis.

### scwiki-d7-claim-experimental-criteria-3

Szabó's Cu–MgB₂ point contacts showed small and large gap scales around 2.8 and 7 meV. Their two-component BTK fits kept interface transparency and relative weight fixed across temperature; thermal smearing makes the two contributions harder to separate near the bulk transition. Fields up to 1 T preferentially suppressed the small-gap spectral contribution, helping reveal the large-gap features. This does not mean that 1 T is the bulk upper critical field, and these spectra alone do not determine the relative sign of the gaps. Using a transition temperature of 39 K, the low-temperature gap ratios are approximately 1.67 and 4.17, rather than a single weak-coupling BCS ratio.

Evidence: experiment. Sources: source-69ced9b5dda860f1.

Conditions: Source-specific sample, temperature, probe, isotope and publication version; toy models are not fitted material results.

Verification scope: Selected primary passages and bounded algebra only; final-version/raw-data issues explicitly retained.

### scwiki-d7-claim-limits-and-disputes-1

The Choi calculation resolves momentum-dependent gaps. In Fig. 3a, separate empirical fits describe the calculated average gaps with exponents 2.9 for the sigma sheets and 1.8 for the pi sheets; these are not one universal temperature curve. Fig. 3b assumes a 0.1 meV lifetime-broadening parameter. Fig. 4 compares calculated electronic specific heat with three experimental datasets having different transition temperatures, rather than fitting a single specimen's spectroscopy. Szabo's author manuscript fits point-contact conductance with two BTK contributions: their relative weight varies from about 10% to 90% between contacts, while weight and barrier parameter remain fixed during a given temperature series. That contact-dependent weight must not be substituted for Choi's calculated band density-of-states shares. Thermal smearing also obscures separate peaks near the transition. These distinctions support comparing multiple probes; they do not establish gap sign from these spectra or independently reproduce the specific-heat data or Eliashberg calculation.

Evidence: theory. Sources: source-69ced9b5dda860f1, source-7c4eac077ae5e221.

Source relationship: mixed-source-and-local-derivation. Named papers support the method and figure details; limits on transferring normalized weights, criteria or calculated quantities are editorial reasoning. No independent raw-data or full numerical reproduction.

Conditions: Choi final Figs. 2–4 and Szabo author v1 temperature/field spectroscopy: computed gaps, density of states, heat capacity and contact-dependent BTK weights have different meanings.

Verification scope: Selected identified author methods/table and final Choi figure captions; source-specific quantitative comparisons, no complete final-author comparison or raw-data reanalysis.

### scwiki-d7-claim-limits-and-disputes-2

The Hinks author manuscript contains a version issue: Table 1 prints a Mg mass of 25.001 for a sample family, while the methods describe enriched ²⁶Mg. This discrepancy is retained as unresolved pending comparison with the final published table. No Mg-mass refit is presented. The boron ratios use the explicitly printed boron masses and temperatures. Likewise, the Mazin author PDF's generated date is not its submission date; the cited version is the arXiv submission of 1 April 2002.

Evidence: theory. Sources: source-60ffd9b4ef2c9ccd, source-a9d7d0b720a3bafd.

Conditions: Source-specific sample, temperature, probe, isotope and publication version; toy models are not fitted material results.

Verification scope: Selected primary passages and bounded algebra only; final-version/raw-data issues explicitly retained.

### scwiki-d7-claim-discovery-implications-1

Materials development must connect gap physics to usable conductors. A 2026 study of square, 19-filament MgB₂ wire reports a 14.2% filling factor and an engineering-current benchmark at 4.2 K and 6.5 T. This reference is currently checked only through the publisher's indexed summary and the authors' publication record; the electric-field criterion, full methods and coil comparison require further review. Engineering current density uses the whole composite cross-section, unlike a current density normalized to superconducting material alone. Neither operating temperature nor a current-density benchmark should enter a transition-temperature ranking.

Evidence: experiment. Sources: source-39e103ef0175cc7e.

Conditions: Source-specific sample, temperature, probe, isotope and publication version; toy models are not fitted material results.

Verification scope: Selected primary passages and bounded algebra only; final-version/raw-data issues explicitly retained.

### scwiki-d7-claim-discovery-implications-2

Preserve processing, connectivity, field orientation, temperature and voltage criterion when comparing wires. Increasing intraband disorder, changing band filling and increasing interband impurity mixing are not interchangeable interventions. A useful candidate must satisfy its operating requirements as well as the microscopic pairing model; this article's scoped calculations do not certify a wire or magnet design.

Evidence: theory. Sources: source-a9d7d0b720a3bafd, source-39e103ef0175cc7e.

Conditions: Source-specific sample, temperature, probe, isotope and publication version; toy models are not fitted material results.

Verification scope: Selected primary passages and bounded algebra only; final-version/raw-data issues explicitly retained.

## Revision and review

Article ID: scwiki-d7. Revision: ca6e65ff7ad5048561ac. Updated: 2026-10-19T16:30:29.378385+00:00.

Review scope: Selected original sources and follow-up on isotope criteria, contact weights and computed-gap/thermodynamic comparisons; author checks and bounded algebra only.

- Full scientific acceptance, raw-data and full numerical reproduction remain open.
- Hinks v1 table Mg mass conflicts with methods; final table unresolved, no Mg-mass refit presented.
- Several detailed sources use identified author versions; final-version comparisons remain open.
- 2026 wire source is an indexed-summary check only; no conductor design or performance certification.

Source: [D_material_families/D7_MgB2.md](https://github.com/JackZH26/jzis-superconductivity/blob/0a7c9d6696804ec26aa12f8eed68b55c9b3c0fcf/D_material_families/D7_MgB2.md), commit 0a7c9d6696804ec26aa12f8eed68b55c9b3c0fcf, SHA-256 2f2a1ddc3d4cf4a17f548112ddf82587ec4d600dd4b0795483cdc747e4c4a063.