# Superconducting gap: magnitude, nodes and phase

Read gap measurements with their probe and model. Distinguish an excitation scale from evidence for nodes, relative sign or bulk superconductivity.

## Scope

A superconducting gap is an energy scale in a specified excitation spectrum. Its magnitude, momentum dependence and relative phase answer different questions. A suppression of spectral weight is not automatically a superconducting gap, and a fitted gap does not automatically define the temperature of bulk superconductivity. This entry organizes observations and model assumptions rather than ranking materials by a single gap ratio.

Specify whether $\Delta$ denotes an order-parameter amplitude, a quasiparticle excitation threshold or a parameter extracted from a broadened spectrum. The relation between these quantities depends on the model. Keep the measured signal, the fit and the inferred state separate; otherwise apparently similar numbers can describe different observables.

## Mathematical assumptions

For a clean, isotropic, single-band weak-coupling BCS model, the quasiparticle spectrum and zero-temperature limiting ratio are

$$E_{\mathbf k}=\sqrt{\xi_{\mathbf k}^{\,2}+|\Delta|^2},\qquad \frac{2\Delta_0}{k_BT_c}=2\pi e^{-\gamma_E}\simeq3.528.$$

Here $\xi_{\mathbf k}$ is measured from the chemical potential and $\gamma_E$ is Euler's constant. The existing BCS entry checks the gap equation and numerical limit. The ratio is not a universal threshold for identifying superconductivity or an interaction. Strong coupling and anisotropy require their own treatment; Carbotte's review abstract describes deviations from simple BCS results without supplying a universal correction. [R1](#ref-source-ba10e800a1246bf6) [R2](#ref-source-2da854ce10895b5e)

With a constant normal density of states $N_n$ and the same spin convention in numerator and denominator, the ideal normalized density of states at positive excitation energy is

$$\frac{N_s(E)}{N_n}=\begin{cases}0,&0\le E<|\Delta|,\\ E/\sqrt{E^2-|\Delta|^2},&E>|\Delta|.\end{cases}$$

The factor above the edge follows from the change of variable $E=\sqrt{\xi^2+|\Delta|^2}$ with the usual Bogoliubov spectral weights. The ideal edge is singular but integrable. A local numerical check integrates it up to a finite energy and recovers the corresponding normal-state $\xi$ interval. The check assumes no lifetime broadening, gap anisotropy or experimental convolution. [R1](#ref-source-ba10e800a1246bf6)

In this magnitude-only model, replacing a gap by its negative leaves the excitation energies unchanged. Likewise, independently summing two uncoupled spectral contributions cannot recover their relative sign. This is a limited counterexample to inferring phase from a gap magnitude; it does not say that every interference-sensitive spectrum is phase blind.

## Experimental criteria

Use the following as a reporting map adapted from the pinned chapter. Each interpretation needs the stated model and a sample-specific source; these rows do not certify any material dataset. Selected passages now support the listed controls across all seven probe rows. This is a scoped methods check, not an exhaustive experimental protocol, a final-version audit or independent validation.

| Probe | Recorded quantity | What must be controlled |
|---|---|---|
| Tunneling or STS | Differential conductance versus bias | Tip and sample spectra, thermal/instrumental broadening, matrix elements and surface variation [R7](#ref-source-d687e60f83e71f36) |
| ARPES | Momentum-resolved photoemission intensity | Occupation, resolution, matrix elements and surface state; a leading edge is not automatically a gap amplitude [R12](#ref-source-d679e3d02f15050c) [R3](#ref-source-e933e3bbd4beade6) |
| Optical or THz spectroscopy | Frequency-dependent electrodynamic response | Scattering, multiple bands and the model linking absorption to an excitation threshold [R8](#ref-source-aa5ec58b03d1a3ef) [R9](#ref-source-9394f6a65db2d109) |
| Heat capacity | Heat capacity versus temperature and field; entropy inferred by integration | Addenda, sample basis, equilibration, lattice and magnetic backgrounds; no direct phase measurement [R13](#ref-source-18085282135e3fe4) [R3](#ref-source-e933e3bbd4beade6) |
| Penetration depth | Low-energy electromagnetic response | Disorder, geometry/nonlocal response, magnetic or surface contributions and multiband weighting [R14](#ref-source-35bdae325860140f) |
| Thermal transport | Heat conductivity and its low-temperature extrapolation | Impurity scattering, nonsuperconducting regions, multiband response and extrapolation range [R15](#ref-source-63de87eb1fb70b58) |
| Andreev or point-contact spectroscopy | Interface current and conductance | Barrier transparency, heating, contact regime and channel mixing [R10](#ref-source-d09edec8bdd2b452) [R11](#ref-source-dc8f626a5df50714) |

The measured ARPES intensity includes occupation and matrix-element factors, and quantitative analysis also requires resolution and background treatment. A leading-edge displacement therefore needs a model before it is reported as a gap amplitude. For calorimetry, Wang and colleagues separately measure addenda and discuss impurity contributions, normalization and thermal equilibration in their MgB2 sample. Heat capacity is measured; entropy requires an integration and reference choice. [R12](#ref-source-d679e3d02f15050c) [R13](#ref-source-18085282135e3fe4)

Penetration depth and heat transport require different controls. The Prozorov-Giannetta review discusses geometry, nonlocality and magnetic or surface contributions, including competing interpretations of a power law. Shakeripour and colleagues warn that nonsuperconducting regions can contribute to a residual heat-conduction term and that multiband response can obscure a particular gap. These selected methodological cautions do not import the reviews' historical material-symmetry assignments as current verdicts. [R14](#ref-source-35bdae325860140f) [R15](#ref-source-63de87eb1fb70b58)

A tunnel conductance resembles the sample density of states only under counterelectrode and matrix-element assumptions; the selected Fischer review gives the thermal convolution and explains the resolution role of lock-in modulation. Do not identify every conductance peak with $\Delta$. Optical interpretation also depends on scattering and multiband weights: the selected Dressel review compares competing fits, while Seibold and colleagues distinguish DOS peaks, excitation thresholds and collective absorption within a disordered model. These are source-scoped cautions, not a new fit to any specimen. Photoemission and thermodynamic probes constrain other aspects; magnitude-sensitive measurements alone do not determine relative phase. [R3](#ref-source-e933e3bbd4beade6) [R7](#ref-source-d687e60f83e71f36) [R8](#ref-source-aa5ec58b03d1a3ef) [R9](#ref-source-9394f6a65db2d109)

For point contacts, a barrier model is only part of the interpretation. Sheet and colleagues distinguish dissipative thermal contacts from a diffusive regime without significant local heating; non-ballistic does not always mean thermal. Kumar and Sheet show how multiple constrictions can mix responses in a network model. These examples motivate contact controls; they neither diagnose every observed peak nor prove that every unconventional spectrum is an artifact. [R10](#ref-source-d09edec8bdd2b452) [R11](#ref-source-dc8f626a5df50714)

Hardy and colleagues report a strong linear term in the penetration-depth change of YBa2Cu3O6.95 single crystals over approximately 3–25 K using a 900 MHz resonator. This is evidence relevant to low-energy excitations under their sample conditions, not a direct measurement of gap phase. The present check covers the publisher abstract. [R4](#ref-source-b7bc48c845a47b53)

By contrast, Tsuei and Kirtley use scanning SQUID measurements of NCCO/PCCO tricrystals to test phase-sensitive predictions. Their designed frustrated geometry produces a half-flux signal, while two unfrustrated NCCO geometries serve as controls. The inference depends on junction geometry and the associated model, not merely on observing a spectral dip. Selected author-manuscript passages and the control description were checked; the image fits were not independently reproduced. [R6](#ref-source-7700f02a5390b1cf)

## Limits and disputes

Nodes, relative sign and topology are distinct. A low-temperature power law can constrain low-energy excitations without uniquely selecting a pairing representation. A fully open gap on each Fermi-surface sheet can coexist with a relative sign change between sheets. Disorder and sample inhomogeneity must be considered before translating a temperature dependence into a symmetry assignment. [R3](#ref-source-e933e3bbd4beade6)

A zero-bias feature alone is not a unique topology test. Identify its field, temperature, position and junction dependence, then compare explicit alternative models. Likewise, a spectroscopic gap-closing temperature must not silently replace a resistive or thermodynamic $T_c$ in a gap ratio. These are inference and reporting limits, not a claim that one alternative explains every observed feature.

Choi and colleagues' MgB2 result is an anisotropic Eliashberg calculation of distinct band-dependent gap scales. Treat those calculated gaps as theory and compare them with separately identified measurements. The pinned chapter's DOI was mismatched; the correct source is nature00898. That correction does not validate a universal multiband gap ratio or independently reproduce the calculation. [R5](#ref-source-7c4eac077ae5e221)

## Discovery implications

Record the specimen, pressure or strain, temperature criterion, spectral resolution, fit model and uncertainty together. Compare probes on the same or demonstrably comparable specimens. A disagreement can expose a surface effect, background assumption or a second energy scale; it should remain visible until tested.

A useful next measurement distinguishes competing interpretations. Establish which observation would separate a change of magnitude from a change of phase, and which control would rule out a contact artifact or another ordered state. Gap measurements constrain models; they do not replace a complete evidence chain for superconductivity.

## Related topics

Connect to [BCS theory](/scwiki/bcs-weak-coupling), [multiband pairing](/scwiki/multiband-pairing), [s± pairing](/scwiki/s-plus-minus), [specific heat](/scwiki/specific-heat-jump), [critical fields](/scwiki/critical-fields), and [zero resistance](/scwiki/zero-resistance).

## Material cases

No sample-specific material records are included in this article. Model results are not experimental transition temperatures.

## Sources

### Ref source-ba10e800a1246bf6

[R1] Theory of Superconductivity (1957). [DOI 10.1103/PhysRev.108.1175](https://doi.org/10.1103/PhysRev.108.1175). Publication: journal-article. Check: primary-full-text-scoped-check. Checked: 2026-10-18. Selected passages: pp. 1182-1183, Eqs. (2.38)-(2.40), (2.49)-(2.50); p. 1186, Eqs. (3.27)-(3.30). One-spin DOS, gap equation and excitation convention checked. Modern limiting constants are evaluated from the model, not copied from historical rounded values. Full proof, empirical fits and exhaustive correction searches remain outside this review.
### Ref source-2da854ce10895b5e

[R2] Properties of boson-exchange superconductors (1990). [DOI 10.1103/RevModPhys.62.1027](https://doi.org/10.1103/RevModPhys.62.1027). Publication: journal-article. Check: review-abstract-scoped-check. Checked: 2026-10-18. Publisher abstract: Eliashberg treatment and deviations from BCS with strong-coupling corrections. Detailed formulas, numerical predictions and experimental fits are not checked.
### Ref source-e933e3bbd4beade6

[R3] Pairing symmetry in cuprate superconductors (2000). [DOI 10.1103/RevModPhys.72.969](https://doi.org/10.1103/RevModPhys.72.969). Publication: journal-article. Check: review-full-text-scoped-check. Checked: 2026-10-18. Selected journal PDF passages: section II pp. 974–976 on penetration depth, heat capacity, thermal conductivity and photoemission; section IV introduction p. 982 on phase-sensitive tests; pp. 998–999 on universality/impurity caveats. Historical review, not an exhaustive current survey or independent check of every cited experiment.
### Ref source-b7bc48c845a47b53

[R4] Precision measurements of the temperature dependence of lambda in YBa2Cu3O6.95: Strong evidence for nodes in the gap function (1993). [DOI 10.1103/PhysRevLett.70.3999](https://doi.org/10.1103/PhysRevLett.70.3999). Publication: journal-article. Check: primary-abstract-scoped-check. Checked: 2026-10-18. Publisher abstract: single-crystal YBa2Cu3O6.95, 900 MHz resonator, penetration-depth change and linear term around 3–25 K. Full curves, fitting and defect interpretation not independently reproduced; not a phase measurement.
### Ref source-7c4eac077ae5e221

[R5] The origin of the anomalous superconducting properties of MgB2 (2002). [DOI 10.1038/nature00898](https://doi.org/10.1038/nature00898). Publication: journal-article. Check: primary-full-text-scoped-check. Checked: 2026-10-18. Selected passages on pp. 758-759 and Fig. 3: anisotropic Eliashberg calculation, band-dependent gaps and a common calculated transition temperature. Calculated gaps are theory, not direct measurements. Numerical convergence, raw experiments and general multichannel enhancement claims are not verified here.
### Ref source-7700f02a5390b1cf

[R6] Phase-Sensitive Evidence for d-Wave Pairing Symmetry in Electron-Doped Cuprate Superconductors (2000). [DOI 10.1103/PhysRevLett.85.182](https://doi.org/10.1103/PhysRevLett.85.182). Publication: journal-article. Check: author-manuscript-scoped-check. Checked: 2026-10-18. Selected pp. 1–3 and Fig. 3 caption: NCCO/PCCO tricrystals, scanning SQUID, frustrated geometry and two unfrustrated NCCO controls. Raw images, Josephson-vortex fits and uncertainty not independently reproduced. arXiv v2 May 2000; typeset 2018 date is not a new publication. No universal claim across all compositions.
### Ref source-d687e60f83e71f36

[R7] Scanning tunneling spectroscopy of high-temperature superconductors (2007). [DOI 10.1103/RevModPhys.79.353](https://doi.org/10.1103/RevModPhys.79.353). Publication: journal-article. Check: review-author-manuscript-scoped-check. Checked: 2026-10-19. Author review v1, submitted 24 October 2006; associated journal publication 2007. Selected pp. 6-8 and 11: lock-in modulation, two-electrode spectra, thermal convolution and matrix-element/surface limits. Pages 6 and 8 visually checked. Final-version comparison, cited original experiments and raw spectra remain unchecked; typeset 2008 header is not submission history.
### Ref source-aa5ec58b03d1a3ef

[R8] Looking at the superconducting gap of iron pnictides (2011). [DOI 10.1016/j.jpcs.2010.10.004](https://doi.org/10.1016/j.jpcs.2010.10.004). Publication: journal-article. Check: review-author-manuscript-scoped-check. Checked: 2026-10-19. Author review v1, submitted 17 April 2010; associated journal publication 2011. Selected pp. 1-2 discuss alternative gap fits, distinct scattering contributions and film/substrate reflectance; p. 2 visually checked. No re-fitting or review of all underlying experiments; final-version comparison remains open. Typeset 2018 footer is not a new study date.
### Ref source-9394f6a65db2d109

[R9] Application of the Mattis-Bardeen theory in strongly disordered superconductors (2017). [DOI 10.1103/PhysRevB.96.144507](https://doi.org/10.1103/PhysRevB.96.144507). Publication: journal-article. Check: author-manuscript-scoped-check. Checked: 2026-10-19. Publisher abstract and author v1, submitted 6 February 2017, selected pp. 1-2 and Fig. 1 checked; p. 2 visually inspected. Distinguishes DOS peak/threshold and collective optical response in a disordered attractive-Hubbard framework. Full numerical calculation, raw experimental data and final-version comparison were not reproduced.
### Ref source-d09edec8bdd2b452

[R10] Role of critical current on the point-contact Andreev reflection spectra between a normal metal and a superconductor (2004). [DOI 10.1103/PhysRevB.69.134507](https://doi.org/10.1103/PhysRevB.69.134507). Publication: journal-article. Check: selected-author-methods-and-publisher-abstract-check. Checked: 2026-10-19. Author v1 submitted 28 November 2003; journal published 16 April 2004. Selected pp. 4-8 on contact-size variation, ballistic/thermal/diffusive regimes and fitting errors; p. 5 visually checked. Heating statement is regime-dependent. No raw-data reanalysis, complete final-version comparison or universal contact diagnosis.
### Ref source-dc8f626a5df50714

[R11] Nonballistic transport characteristics of superconducting point contacts (2021). [DOI 10.1103/PhysRevB.104.094525](https://doi.org/10.1103/PhysRevB.104.094525). Publication: journal-article. Check: selected-author-methods-and-publisher-abstract-check. Checked: 2026-10-19. Author v4 of 6 October 2020: selected pp. 2, 5-11 and p. 5 visual check of barrier/network-model context. Publisher abstract and 29 September 2021 publication date checked separately. Final abstract additionally reports Nb experiments; those final experiments and full version differences were not reviewed. No network-spectrum or raw-data reproduction.
### Ref source-d679e3d02f15050c

[R12] Angle-resolved photoemission studies of the cuprate superconductors (2003). [DOI 10.1103/RevModPhys.75.473](https://doi.org/10.1103/RevModPhys.75.473). Publication: journal-article. Check: review-author-manuscript-scoped-check. Checked: 2026-10-19. Author review v1 submitted 27 August 2002; journal publication 17 April 2003. Selected pp. 7 and 9 (Eqs. 12 and 21), pp. 37-38 on leading-edge versus gap estimates; p. 9 visually checked. Surface caution also uses the separately identified Tsuei-Kirtley review. No current instrumental-resolution claim, raw-spectrum fit, final-version comparison or audit of all underlying experiments.
### Ref source-18085282135e3fe4

[R13] Specific heat in the superconducting and normal state (2–300 K, 0–16 T), and magnetic susceptibility of the 38 K superconductor MgB2: evidence for a multicomponent gap (2001). [DOI 10.1016/S0921-4534(01)00617-7](https://doi.org/10.1016/S0921-4534(01)00617-7). Publication: journal-article. Check: selected-author-measurement-methods-check. Checked: 2026-10-19. Author v1 submitted 8 March 2001. Selected pp. 3, 6-7, 9 and 16: lattice/electronic separation, separately measured addenda, impurity Schottky contribution, per-gram-atom versus per-mole units and heating/cooling equilibration; p. 9 visually checked. These are sample-specific methods and cautions, not re-extracted gaps or temperatures. Final-version comparison and raw-data reanalysis remain open.
### Ref source-35bdae325860140f

[R14] Magnetic penetration depth in unconventional superconductors (2006). [DOI 10.1088/0953-2048/19/8/R01](https://doi.org/10.1088/0953-2048/19/8/R01). Publication: journal-article. Check: review-author-manuscript-scoped-check. Checked: 2026-10-19. Author review v1 submitted 24 May 2006. Selected pp. 14, 24, 32-34 and 38 on paramagnetism, alternative impurity/nonlocal interpretations, surface contributions and multiband response; p. 24 visually checked. Historical material assignments and FFLO claims are not adopted as current conclusions. No underlying-data reanalysis or full final-version comparison.
### Ref source-63de87eb1fb70b58

[R15] Heat transport as a probe of superconducting gap structure (2009). [DOI 10.1088/1367-2630/11/5/055065](https://doi.org/10.1088/1367-2630/11/5/055065). Publication: journal-article. Check: review-author-manuscript-scoped-check. Checked: 2026-10-19. Author v1 submitted 2 April 2009. Selected pp. 1-2 and 8-9: residual-term extrapolation, impurity response, nonsuperconducting-region caveat and multiband weighting. Historical Sr2RuO4 p-wave assignment and material-specific gap verdicts are not adopted as current conclusions. No raw thermal-transport fits or final-version comparison.

## Claim evidence and conditions

### scwiki-a5-claim-scope-1

A superconducting gap is an energy scale in a specified excitation spectrum. Its magnitude, momentum dependence and relative phase answer different questions. A suppression of spectral weight is not automatically a superconducting gap, and a fitted gap does not automatically define the temperature of bulk superconductivity. This entry organizes observations and model assumptions rather than ranking materials by a single gap ratio.

Evidence: hypothesis. Sources: source-e933e3bbd4beade6.

Conditions: Editorial reporting/inference guidance; sample-specific source, probe and model needed. No additional material measurement certified.

Verification scope: Pinned chapter adapted with stated source-review boundaries; table is a reporting map, not a verified dataset.

### scwiki-a5-claim-scope-2

Specify whether $\Delta$ denotes an order-parameter amplitude, a quasiparticle excitation threshold or a parameter extracted from a broadened spectrum. The relation between these quantities depends on the model. Keep the measured signal, the fit and the inferred state separate; otherwise apparently similar numbers can describe different observables.

Evidence: hypothesis. Sources: source-e933e3bbd4beade6.

Conditions: Editorial reporting/inference guidance; sample-specific source, probe and model needed. No additional material measurement certified.

Verification scope: Pinned chapter adapted with stated source-review boundaries; table is a reporting map, not a verified dataset.

### scwiki-a5-claim-mathematical-assumptions-1

For a clean, isotropic, single-band weak-coupling BCS model, the quasiparticle spectrum and zero-temperature limiting ratio are

Evidence: theory. Sources: source-ba10e800a1246bf6.

Conditions: Clean isotropic single-band weak-coupling spectrum and constant normal DOS; no broadening or fit. Magnitude-only sign invariance is not a statement about all interference experiments.

Verification scope: Selected BCS passages, existing B1 gap-equation check and local DOS state-counting calculation; Carbotte remains abstract-scoped.

### scwiki-a5-claim-mathematical-assumptions-2

$$E_{\mathbf k}=\sqrt{\xi_{\mathbf k}^{\,2}+|\Delta|^2},\qquad \frac{2\Delta_0}{k_BT_c}=2\pi e^{-\gamma_E}\simeq3.528.$$

Evidence: theory. Sources: source-ba10e800a1246bf6.

Conditions: Clean isotropic single-band weak-coupling spectrum and constant normal DOS; no broadening or fit. Magnitude-only sign invariance is not a statement about all interference experiments.

Verification scope: Selected BCS passages, existing B1 gap-equation check and local DOS state-counting calculation; Carbotte remains abstract-scoped.

### scwiki-a5-claim-mathematical-assumptions-3

Here $\xi_{\mathbf k}$ is measured from the chemical potential and $\gamma_E$ is Euler's constant. The existing BCS entry checks the gap equation and numerical limit. The ratio is not a universal threshold for identifying superconductivity or an interaction. Strong coupling and anisotropy require their own treatment; Carbotte's review abstract describes deviations from simple BCS results without supplying a universal correction.

Evidence: theory. Sources: source-ba10e800a1246bf6, source-2da854ce10895b5e.

Conditions: Clean isotropic single-band weak-coupling spectrum and constant normal DOS; no broadening or fit. Magnitude-only sign invariance is not a statement about all interference experiments.

Verification scope: Selected BCS passages, existing B1 gap-equation check and local DOS state-counting calculation; Carbotte remains abstract-scoped.

### scwiki-a5-claim-mathematical-assumptions-4

With a constant normal density of states $N_n$ and the same spin convention in numerator and denominator, the ideal normalized density of states at positive excitation energy is

Evidence: theory. Sources: source-ba10e800a1246bf6.

Conditions: Clean isotropic single-band weak-coupling spectrum and constant normal DOS; no broadening or fit. Magnitude-only sign invariance is not a statement about all interference experiments.

Verification scope: Selected BCS passages, existing B1 gap-equation check and local DOS state-counting calculation; Carbotte remains abstract-scoped.

### scwiki-a5-claim-mathematical-assumptions-5

$$\frac{N_s(E)}{N_n}=\begin{cases}0,&0\le E<|\Delta|,\\ E/\sqrt{E^2-|\Delta|^2},&E>|\Delta|.\end{cases}$$

Evidence: theory. Sources: source-ba10e800a1246bf6.

Conditions: Clean isotropic single-band weak-coupling spectrum and constant normal DOS; no broadening or fit. Magnitude-only sign invariance is not a statement about all interference experiments.

Verification scope: Selected BCS passages, existing B1 gap-equation check and local DOS state-counting calculation; Carbotte remains abstract-scoped.

### scwiki-a5-claim-mathematical-assumptions-6

The factor above the edge follows from the change of variable $E=\sqrt{\xi^2+|\Delta|^2}$ with the usual Bogoliubov spectral weights. The ideal edge is singular but integrable. A local numerical check integrates it up to a finite energy and recovers the corresponding normal-state $\xi$ interval. The check assumes no lifetime broadening, gap anisotropy or experimental convolution.

Evidence: theory. Sources: source-ba10e800a1246bf6.

Source relationship: mixed-source-and-local-derivation. BCS pp. 1182-1183 supply the excitation and one-spin state-counting conventions. The modern normalized positive-energy spectral DOS and finite-edge integral are locally derived with a constant normal DOS and matched spin convention; no measured tunneling curve is fitted.

Conditions: Clean isotropic single-band weak-coupling spectrum and constant normal DOS; no broadening or fit. Magnitude-only sign invariance is not a statement about all interference experiments.

Verification scope: Selected BCS passages, existing B1 gap-equation check and local DOS state-counting calculation; Carbotte remains abstract-scoped.

### scwiki-a5-claim-mathematical-assumptions-7

In this magnitude-only model, replacing a gap by its negative leaves the excitation energies unchanged. Likewise, independently summing two uncoupled spectral contributions cannot recover their relative sign. This is a limited counterexample to inferring phase from a gap magnitude; it does not say that every interference-sensitive spectrum is phase blind.

Evidence: theory. Sources: source-ba10e800a1246bf6.

Conditions: Clean isotropic single-band weak-coupling spectrum and constant normal DOS; no broadening or fit. Magnitude-only sign invariance is not a statement about all interference experiments.

Verification scope: Selected BCS passages, existing B1 gap-equation check and local DOS state-counting calculation; Carbotte remains abstract-scoped.

### scwiki-a5-claim-experimental-criteria-1

Use the following as a reporting map adapted from the pinned chapter. Each interpretation needs the stated model and a sample-specific source; these rows do not certify any material dataset. Selected passages now support the listed controls across all seven probe rows. This is a scoped methods check, not an exhaustive experimental protocol, a final-version audit or independent validation.

Evidence: hypothesis. Sources: source-e933e3bbd4beade6, source-d687e60f83e71f36, source-aa5ec58b03d1a3ef, source-9394f6a65db2d109, source-d09edec8bdd2b452, source-dc8f626a5df50714, source-d679e3d02f15050c, source-18085282135e3fe4, source-35bdae325860140f, source-63de87eb1fb70b58.

Source relationship: context-for-local-derivation. Local editorial reporting map, now checked against selected source passages for each listed row. Fischer pp. 6-8/11: tunneling; Dressel pp. 1-2 and Seibold pp. 1-2: optical response; Sheet pp. 4-8 and Kumar pp. 5-11: point-contact controls. Damascelli pp. 7/9/37-38: ARPES; Wang pp. 3/6-7/9/16: calorimetry; Prozorov-Giannetta pp. 14/24/32-34/38: penetration depth; Shakeripour pp. 1-2/8-9: heat transport. Tsuei-Kirtley pp. 975-976 and section III opening p. 977 distinguish these magnitude-sensitive probes from phase tests. Not an exhaustive protocol, independent review or material certification.

Conditions: Editorial reporting/inference guidance; sample-specific source, probe and model needed. No additional material measurement certified.

Verification scope: Selected source passages mapped to each listed probe control; editorial synthesis, no data reanalysis or exhaustive protocol validation.

### scwiki-a5-claim-experimental-criteria-2

| Probe | Recorded quantity | What must be controlled |
|---|---|---|
| Tunneling or STS | Differential conductance versus bias | Tip and sample spectra, thermal/instrumental broadening, matrix elements and surface variation [R7](#ref-source-d687e60f83e71f36) |
| ARPES | Momentum-resolved photoemission intensity | Occupation, resolution, matrix elements and surface state; a leading edge is not automatically a gap amplitude [R12](#ref-source-d679e3d02f15050c) [R3](#ref-source-e933e3bbd4beade6) |
| Optical or THz spectroscopy | Frequency-dependent electrodynamic response | Scattering, multiple bands and the model linking absorption to an excitation threshold [R8](#ref-source-aa5ec58b03d1a3ef) [R9](#ref-source-9394f6a65db2d109) |
| Heat capacity | Heat capacity versus temperature and field; entropy inferred by integration | Addenda, sample basis, equilibration, lattice and magnetic backgrounds; no direct phase measurement [R13](#ref-source-18085282135e3fe4) [R3](#ref-source-e933e3bbd4beade6) |
| Penetration depth | Low-energy electromagnetic response | Disorder, geometry/nonlocal response, magnetic or surface contributions and multiband weighting [R14](#ref-source-35bdae325860140f) |
| Thermal transport | Heat conductivity and its low-temperature extrapolation | Impurity scattering, nonsuperconducting regions, multiband response and extrapolation range [R15](#ref-source-63de87eb1fb70b58) |
| Andreev or point-contact spectroscopy | Interface current and conductance | Barrier transparency, heating, contact regime and channel mixing [R10](#ref-source-d09edec8bdd2b452) [R11](#ref-source-dc8f626a5df50714) |

Evidence: hypothesis. Sources: source-e933e3bbd4beade6, source-d687e60f83e71f36, source-aa5ec58b03d1a3ef, source-9394f6a65db2d109, source-d09edec8bdd2b452, source-dc8f626a5df50714, source-d679e3d02f15050c, source-18085282135e3fe4, source-35bdae325860140f, source-63de87eb1fb70b58.

Source relationship: context-for-local-derivation. Local editorial reporting map, now checked against selected source passages for each listed row. Fischer pp. 6-8/11: tunneling; Dressel pp. 1-2 and Seibold pp. 1-2: optical response; Sheet pp. 4-8 and Kumar pp. 5-11: point-contact controls. Damascelli pp. 7/9/37-38: ARPES; Wang pp. 3/6-7/9/16: calorimetry; Prozorov-Giannetta pp. 14/24/32-34/38: penetration depth; Shakeripour pp. 1-2/8-9: heat transport. Tsuei-Kirtley pp. 975-976 and section III opening p. 977 distinguish these magnitude-sensitive probes from phase tests. Not an exhaustive protocol, independent review or material certification.

Conditions: Editorial reporting/inference guidance; sample-specific source, probe and model needed. No additional material measurement certified.

Verification scope: Selected source passages mapped to each listed probe control; editorial synthesis, no data reanalysis or exhaustive protocol validation.

### scwiki-a5-claim-experimental-criteria-3

A tunnel conductance resembles the sample density of states only under counterelectrode and matrix-element assumptions; the selected Fischer review gives the thermal convolution and explains the resolution role of lock-in modulation. Do not identify every conductance peak with $\Delta$. Optical interpretation also depends on scattering and multiband weights: the selected Dressel review compares competing fits, while Seibold and colleagues distinguish DOS peaks, excitation thresholds and collective absorption within a disordered model. These are source-scoped cautions, not a new fit to any specimen. Photoemission and thermodynamic probes constrain other aspects; magnitude-sensitive measurements alone do not determine relative phase.

Evidence: hypothesis. Sources: source-e933e3bbd4beade6, source-d687e60f83e71f36, source-aa5ec58b03d1a3ef, source-9394f6a65db2d109.

Source relationship: mixed-source-and-local-derivation. Selected review/model passages support stated interpretation cautions; the combined reporting guidance is editorial. No raw-spectrum fit, universal gap identification or full theory reproduction is claimed.

Conditions: Editorial reporting/inference guidance; sample-specific source, probe and model needed. No additional material measurement certified.

Verification scope: Selected author-version pages and publisher abstract only; final versions and underlying experiments remain outside this follow-up.

### scwiki-a5-claim-experimental-criteria-4

Hardy and colleagues report a strong linear term in the penetration-depth change of YBa2Cu3O6.95 single crystals over approximately 3–25 K using a 900 MHz resonator. This is evidence relevant to low-energy excitations under their sample conditions, not a direct measurement of gap phase. The present check covers the publisher abstract.

Evidence: experiment. Sources: source-b7bc48c845a47b53.

Conditions: Named YBCO single crystals or designed NCCO/PCCO tricrystal geometries and stated probes; no universal material or doping assignment.

Verification scope: Hardy publisher abstract or Tsuei/Kirtley selected author-manuscript passages; raw curves/images/fits not independently reproduced.

### scwiki-a5-claim-experimental-criteria-5

By contrast, Tsuei and Kirtley use scanning SQUID measurements of NCCO/PCCO tricrystals to test phase-sensitive predictions. Their designed frustrated geometry produces a half-flux signal, while two unfrustrated NCCO geometries serve as controls. The inference depends on junction geometry and the associated model, not merely on observing a spectral dip. Selected author-manuscript passages and the control description were checked; the image fits were not independently reproduced.

Evidence: experiment. Sources: source-7700f02a5390b1cf.

Conditions: Named YBCO single crystals or designed NCCO/PCCO tricrystal geometries and stated probes; no universal material or doping assignment.

Verification scope: Hardy publisher abstract or Tsuei/Kirtley selected author-manuscript passages; raw curves/images/fits not independently reproduced.

### scwiki-a5-claim-limits-and-disputes-1

Nodes, relative sign and topology are distinct. A low-temperature power law can constrain low-energy excitations without uniquely selecting a pairing representation. A fully open gap on each Fermi-surface sheet can coexist with a relative sign change between sheets. Disorder and sample inhomogeneity must be considered before translating a temperature dependence into a symmetry assignment.

Evidence: hypothesis. Sources: source-e933e3bbd4beade6.

Conditions: Editorial reporting/inference guidance; sample-specific source, probe and model needed. No additional material measurement certified.

Verification scope: Pinned chapter adapted with stated source-review boundaries; table is a reporting map, not a verified dataset.

### scwiki-a5-claim-limits-and-disputes-2

A zero-bias feature alone is not a unique topology test. Identify its field, temperature, position and junction dependence, then compare explicit alternative models. Likewise, a spectroscopic gap-closing temperature must not silently replace a resistive or thermodynamic $T_c$ in a gap ratio. These are inference and reporting limits, not a claim that one alternative explains every observed feature.

Evidence: hypothesis. Sources: source-e933e3bbd4beade6.

Conditions: Editorial reporting/inference guidance; sample-specific source, probe and model needed. No additional material measurement certified.

Verification scope: Pinned chapter adapted with stated source-review boundaries; table is a reporting map, not a verified dataset.

### scwiki-a5-claim-limits-and-disputes-3

Choi and colleagues' MgB2 result is an anisotropic Eliashberg calculation of distinct band-dependent gap scales. Treat those calculated gaps as theory and compare them with separately identified measurements. The pinned chapter's DOI was mismatched; the correct source is nature00898. That correction does not validate a universal multiband gap ratio or independently reproduce the calculation.

Evidence: theory. Sources: source-7c4eac077ae5e221.

Conditions: Anisotropic Eliashberg calculation for MgB2; calculated gaps are not direct measurements and not a universal ratio.

Verification scope: Choi selected primary pp. 758–759 and Fig. 3, as checked in B12; no independent numerical reproduction.

### scwiki-a5-claim-discovery-implications-1

Record the specimen, pressure or strain, temperature criterion, spectral resolution, fit model and uncertainty together. Compare probes on the same or demonstrably comparable specimens. A disagreement can expose a surface effect, background assumption or a second energy scale; it should remain visible until tested.

Evidence: hypothesis. Sources: source-e933e3bbd4beade6.

Conditions: Editorial reporting/inference guidance; sample-specific source, probe and model needed. No additional material measurement certified.

Verification scope: Pinned chapter adapted with stated source-review boundaries; table is a reporting map, not a verified dataset.

### scwiki-a5-claim-discovery-implications-2

A useful next measurement distinguishes competing interpretations. Establish which observation would separate a change of magnitude from a change of phase, and which control would rule out a contact artifact or another ordered state. Gap measurements constrain models; they do not replace a complete evidence chain for superconductivity.

Evidence: hypothesis. Sources: source-e933e3bbd4beade6.

Conditions: Editorial reporting/inference guidance; sample-specific source, probe and model needed. No additional material measurement certified.

Verification scope: Pinned chapter adapted with stated source-review boundaries; table is a reporting map, not a verified dataset.

### scwiki-a5-claim-experimental-criteria-6

For point contacts, a barrier model is only part of the interpretation. Sheet and colleagues distinguish dissipative thermal contacts from a diffusive regime without significant local heating; non-ballistic does not always mean thermal. Kumar and Sheet show how multiple constrictions can mix responses in a network model. These examples motivate contact controls; they neither diagnose every observed peak nor prove that every unconventional spectrum is an artifact.

Evidence: hypothesis. Sources: source-d09edec8bdd2b452, source-dc8f626a5df50714.

Source relationship: mixed-source-and-local-derivation. Source-specific contact regimes and model constructions support the cautions; their combination as reporting guidance is editorial, not a proof about every experimental spectrum.

Conditions: Contact geometry, elastic and inelastic mean free paths, barrier model and sample-specific spectrum; network examples are not a universal diagnosis.

Verification scope: Selected author-version methods and publisher abstracts; final-version experiments and raw data remain unchecked.

### scwiki-a5-claim-experimental-criteria-7

The measured ARPES intensity includes occupation and matrix-element factors, and quantitative analysis also requires resolution and background treatment. A leading-edge displacement therefore needs a model before it is reported as a gap amplitude. For calorimetry, Wang and colleagues separately measure addenda and discuss impurity contributions, normalization and thermal equilibration in their MgB2 sample. Heat capacity is measured; entropy requires an integration and reference choice. [R12](#ref-source-d679e3d02f15050c) [R13](#ref-source-18085282135e3fe4)

Evidence: hypothesis. Sources: source-d679e3d02f15050c, source-18085282135e3fe4.

Source relationship: mixed-source-and-local-derivation. Source methods and cautions summarized in an editorial comparison; selected historical material assignments are excluded.

Conditions: Source-scoped measurement interpretation; no new gap extraction, symmetry verdict or material certification.

Verification scope: Selected author-version passages and declared limitations; no independent reproduction.

### scwiki-a5-claim-experimental-criteria-8

Penetration depth and heat transport require different controls. The Prozorov-Giannetta review discusses geometry, nonlocality and magnetic or surface contributions, including competing interpretations of a power law. Shakeripour and colleagues warn that nonsuperconducting regions can contribute to a residual heat-conduction term and that multiband response can obscure a particular gap. These selected methodological cautions do not import the reviews' historical material-symmetry assignments as current verdicts. [R14](#ref-source-35bdae325860140f) [R15](#ref-source-63de87eb1fb70b58)

Evidence: hypothesis. Sources: source-35bdae325860140f, source-63de87eb1fb70b58.

Source relationship: mixed-source-and-local-derivation. Source methods and cautions summarized in an editorial comparison; selected historical material assignments are excluded.

Conditions: Source-scoped measurement interpretation; no new gap extraction, symmetry verdict or material certification.

Verification scope: Selected author-version passages and declared limitations; no independent reproduction.

## Revision and review

Article ID: scwiki-a5. Revision: 3be442790cc1a84817fd. Updated: 2026-10-19.

Review scope: Edited pinned A5 chapter, selected BCS/Choi and phase-sensitive primary passages, review passages, Hardy/Carbotte abstracts and an independent ideal-DOS state-counting check. Selected Fischer tunneling, Dressel optical review and Seibold disordered-response author-version passages; identified manuscript dates retained. Selected Sheet and Kumar point-contact author passages, with publisher abstracts checked separately. Selected Damascelli, Wang, Prozorov-Giannetta and Shakeripour author-version methods and interpretation passages mapped to the remaining probe controls.

- Selected source checks do not constitute full scientific validation or independent experimental replication.
- Hardy is abstract-scoped; tricrystal image fits, uncertainties and all underlying review citations were not independently reproduced.
- No sample-specific gap amplitude or transition temperature was re-extracted; calculated gaps are not experimental records.
- The DOS check assumes a clean isotropic constant-DOS mean-field model, not a universal tunneling spectrum.
- All seven listed probe rows have selected source support, but the table is an editorial methods map, not an exhaustive protocol or certified dataset. Full final-version comparisons, underlying experimental data and independent review remain open.

Source: [A_phenomenology/A5_gap_features.md](https://github.com/JackZH26/jzis-superconductivity/blob/0a7c9d6696804ec26aa12f8eed68b55c9b3c0fcf/A_phenomenology/A5_gap_features.md), commit 0a7c9d6696804ec26aa12f8eed68b55c9b3c0fcf, SHA-256 c52c880a645d4cb9d43edfe679bae0c21761f0c0df5166e6915d342b0a7a04e7.