# Heavy-fermion superconductors: correlations, gaps and magnetic phases

Explore CeCu2Si2, CeCoIn5 and uranium compounds through thermodynamic evidence, competing gap models and condition-specific magnetic phases.

## Scope

Heavy-fermion superconductors pair electrons in a strongly renormalized metallic state. Their large low-temperature electronic heat capacity and magnetic response reflect interactions involving partially filled f shells, not unusually heavy atoms moving as Cooper pairs. CeCu₂Si₂ established this class in 1979; the discovery paper reported a transition near 0.5 K. Different compositions and probes need not reproduce that exact number. The family is a laboratory for competing correlations rather than a single pairing mechanism. [R1](#ref-source-0ebda9b697c1f7fd) [R5](#ref-source-5962cf8038597944)

Kondo screening, conduction-electron-mediated magnetic interactions, hybridization and valence changes provide useful organizing ideas. Doniach's competition between magnetic order and a compensated state is a model framework. Proximity to a magnetic boundary does not by itself identify the pairing interaction or predict a superconducting transition. Uranium compounds also require attention to itinerant 5f character and strong spin–orbit coupling; a label borrowed from a cerium compound is not a complete microscopic description. [R2](#ref-source-1bdac37fd450eb32) [R6](#ref-source-e7c77a3327daf5c6) [R9](#ref-source-15aec45a868e9fb9)

## Mathematical assumptions

In a Fermi-liquid regime, the electronic coefficient $\gamma=\lim_{T\to0}C_e/T$ is proportional to the renormalized density of states. A finite-temperature value of total $C/T$ is not automatically that limit. Petrovic's CeCoIn₅ report gives about 290 mJ mol⁻¹ K⁻² above 2.5 K but a much larger low-temperature normal-state value under field. Thus its apparent $\Delta C/(\gamma T_c)\approx4.5$ cannot be converted mechanically into a coupling strength using a temperature-independent normal-state baseline. [R5](#ref-source-5962cf8038597944)

Kittaka's CeCu₂Si₂ analysis subtracts a nuclear term. With numerical field $h$ in tesla and temperature $t$ in kelvin, its empirical expression is $C_n/T=(7.4h^2+0.1)t^{-3}\times10^{-6}$ J mol⁻¹ K⁻². At 60 mK it gives approximately 0.00046, 0.111 and 0.309 J mol⁻¹ K⁻² for 0, 1.8 and 3 T. These recalculations illustrate the size of the correction; they are not a new fit or evidence that any arbitrary subtraction is acceptable. [R3](#ref-source-2764bce38246bfae)

Pang's simplified band-mixing model uses $|\Delta(\varphi)|=\sqrt{a^2\cos^2(2\varphi)+b^2\sin^2(2\varphi)}$ at zero temperature. For nonzero amplitudes on the assumed cylinder, the minimum is $\min(|a|,|b|)$; exchanging them preserves angular averages. The reported S-type fit uses $a=2.5k_BT_c$ and $b=0.58k_BT_c$. This magnitude does not specify the full band matrix or its time-reversal properties. A scalar chiral gap can have the same magnitude; that algebraic coincidence does not equate the two physical states. [R4](#ref-source-e721bddb9ef11661)

## Experimental criteria

The CeCu₂Si₂ specific-heat study used a 13.8 mg S-type crystal, measurements down to 40 mK and a nuclear correction constrained by high-field normal-state data. It reported low-energy behavior consistent with full gaps and no detected in-plane angular oscillation within stated sensitivity. The result constrains quasiparticles weighted strongly by thermodynamics; it is not a universal exclusion of every possible small-band node. The author manuscript's February 2014 version must not be dated from its later PDF generation stamp. [R3](#ref-source-2764bce38246bfae)

Pang measured penetration-depth shifts down to about 40 mK using a tunnel-diode oscillator. Keep each reported temperature tied to its sample and criterion:

| Sample | Criterion in Pang | Approximate temperature |
|---|---|---|
| S-type | Resistive onset | 0.65 K |
| S-type | Zero resistivity | 0.60 K |
| S-type | Superconducting specific-heat anomaly | 0.64 K |
| S-type | Penetration-depth onset | 0.62 K |
| A/S-type | Resistive onset | 0.62 K |
| A/S-type | Superconducting specific-heat anomaly | 0.53 K |
| A/S-type | Antiferromagnetic specific-heat anomaly | 0.70 K; not superconducting Tc |

Low-temperature exponential fits extend to 0.12 K. Finite-window power-law fits are also reported; their exponents increase as the upper fitting temperature decreases. This supports a low-temperature full gap without uniquely selecting the pairing state. Superfluid-density conversion assumes a zero-temperature penetration depth of 2000 Å, and both two-gap s-wave and d+d fits describe it. The paper's sign-change argument additionally invokes earlier neutron and NQR evidence; it is not a direct phase measurement by the oscillator. Its later heat-capacity fit uses data digitized from Kittaka. Raw-data refitting and the complete supplement remain outside this scoped review. [R4](#ref-source-e721bddb9ef11661)

For CeCoIn₅, the discovery study combined zero resistance, magnetic shielding and a heat-capacity anomaly near 2.3 K. It also found substantially different upper critical fields parallel and perpendicular to the c axis. Later neutron work found magnetic order that disappears with superconductivity at the high-field boundary. A coupled magnetic Q phase therefore cannot be described as a clean demonstration of a standalone textbook FFLO state. [R5](#ref-source-5962cf8038597944) [R7](#ref-source-fda01ade7737b638)

## Limits and disputes

CeCu₂Si₂ should not be assigned an unqualified textbook nodal d-wave label. Full-gap thermodynamics, sign-sensitive interpretations and band structure must be reconciled. Its pressure response adds another question: Holmes measured resistivity and ac heat capacity above 6 GPa in helium and interpreted anomalies near 4.5 GPa through valence fluctuations. That interpretation is a proposed mechanism, not a direct measurement of a unique pairing interaction. [R3](#ref-source-2764bce38246bfae) [R4](#ref-source-e721bddb9ef11661) [R6](#ref-source-e7c77a3327daf5c6)

UPt₃ has multiple superconducting phases and Kerr evidence constraining time-reversal symmetry. Heating, field training and the phase being probed matter. This does not uniquely select f-wave symmetry or establish a topological device. URhGe and UCoGe provide coexistence evidence for ferromagnetism and superconductivity, but their magnetic and superconducting transition temperatures are distinct. Their respective field responses cannot be exchanged between compounds. [R8](#ref-source-d3edee404071ac81) [R9](#ref-source-15aec45a868e9fb9) [R10](#ref-source-a4695ba5bfa789f3)

UTe₂ requires particularly careful qualifiers. Antiferromagnetic neutron fluctuations, transverse high-field fluctuations and sample-dependent Kerr results probe different conditions. The 2023 Kerr study found no spontaneous signal in the tested single-transition samples; it does not negate every other superconducting phase. No single large upper critical field, fluctuation spectrum or null Kerr observation determines spin structure and topology together. [R11](#ref-source-df199ac9453d6985) [R13](#ref-source-15cfc4a2f9587af0) [R14](#ref-source-dd4e897d833ce69c)

## Discovery implications

The 2025 UTe₂ halo study mapped transport boundaries with pulsed fields, generally near 0.63 K, using resistance and contactless proximity-detector measurements. Tilting away from the b axis revealed an extended high-field region. The experiment reached approximately 73 T; extrapolated persistence beyond that field is not a measured upper boundary. Its multicomponent triplet interpretation remains a model conclusion. Supplementary sample details, heating corrections and the deposited raw data have not been independently reanalyzed here. [R12](#ref-source-0c4d7cebb12a0d5b)

The 2026 transverse-fluctuation study measured the normal state at 4 K; superconducting phase boundaries at 300 mK were comparisons with earlier work. Neither temperature is a newly measured transition temperature in that experiment. Discovery records should retain the sample, pressure, field direction, probe and criterion, then compare mechanisms across compatible conditions. The goal is to identify informative constraints, not rank unrelated temperatures or convert candidate topology into an established engineering capability. [R13](#ref-source-15cfc4a2f9587af0)

## Related topics

Continue with [antiferromagnetic fluctuations](/scwiki/spin-fluctuation-pairing), [ferromagnetic fluctuations](/scwiki/ferromagnetic-fluctuations), [specific heat](/scwiki/specific-heat-jump), [multiband pairing](/scwiki/multiband-pairing), [f-wave candidates](/scwiki/f-wave) and [pair-density waves](/scwiki/pair-density-wave).

## 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 |
|---|---|---|---|---|---|---|
| CeCu2Si2 (aliases: heavy fermion, heavy fermions); Pang S-type crystal | 0.64 K; Approximate thermodynamic transition; resistive onset and zero-resistance criteria differ. | transition; specific-heat-anomaly | Specific heat | ambient; unknown GPa | unknown | experiment; [source](#ref-source-e721bddb9ef11661) |
| CeCu2Si2 (aliases: heavy fermion, heavy fermions); Pang A/S-type crystal | 0.53 K; Superconducting anomaly; separate antiferromagnetic anomaly near 0.7 K is not Tc. | transition; specific-heat-anomaly | Specific heat | ambient; unknown GPa | unknown | experiment; [source](#ref-source-e721bddb9ef11661) |
| CeCu2Si2 (aliases: heavy fermion, heavy fermions); Kittaka S-type crystal, base temperature | 0.04 K; Base measurement temperature, not superconducting transition. | measurement; heat-capacity-base-temperature | Quasi-adiabatic heat pulse | ambient; unknown GPa | unknown | experiment; [source](#ref-source-2764bce38246bfae) |
| CeCoIn5 (aliases: heavy fermion, heavy fermions); Petrovic discovery single crystals | 2.3 K; Discovery sample transition; not a family-wide fixed value. | transition; zero-resistance-and-shielding | Resistivity and diamagnetic shielding; corroborating heat-capacity anomaly | ambient; unknown GPa | unknown | experiment; [source](#ref-source-5962cf8038597944) |
| UTe2 (aliases: heavy fermion, heavy fermions); Lewin pulsed-field transport, general run condition | 0.63 K; Operating temperature, not a measured Tc or exact upper critical field. | measurement; pulsed-field-operating-temperature | Resistance and proximity-detector oscillator; angle-dependent fields to around 73 T | ambient; unknown GPa | unknown | experiment; [source](#ref-source-0c4d7cebb12a0d5b) |
| UTe2 (aliases: heavy fermion, heavy fermions); Zambra normal-state high-field fluctuation study | 4 K; Normal-state measurement; earlier 300 mK phase boundaries are a separate dataset. | normal-state; normal-state-fluctuation-temperature | Pulsed-field magnetic fluctuation probe | ambient; unknown GPa | unknown | experiment; [source](#ref-source-15cfc4a2f9587af0) |
| CeCu2Si2 (aliases: heavy fermion, heavy fermions); Pang S-type crystal, Fig. 1A | 0.65 K; Approximate onset; distinct from zero resistivity at about 0.60 K and specific heat at 0.64 K. | transition; resistive-onset | Resistivity | ambient; unknown GPa | unknown | experiment; [source](#ref-source-e721bddb9ef11661) |
| CeCu2Si2 (aliases: heavy fermion, heavy fermions); Pang S-type crystal, Fig. 1A | 0.6 K; Approximate zero-resistivity criterion; onset is about 0.65 K. | transition; zero-resistivity | Resistivity | ambient; unknown GPa | unknown | experiment; [source](#ref-source-e721bddb9ef11661) |
| CeCu2Si2 (aliases: heavy fermion, heavy fermions); Pang A/S-type crystal, Fig. 1B | 0.62 K; Approximate transport onset; same sample has a distinct superconducting specific-heat anomaly near 0.53 K. | transition; resistive-onset | Resistivity | ambient; unknown GPa | unknown | experiment; [source](#ref-source-e721bddb9ef11661) |
| CeCu2Si2 (aliases: heavy fermion, heavy fermions); Pang S-type crystal, Fig. 2A inset | 0.62 K; Approximate penetration-depth onset; not a specific-heat or resistive criterion. | transition; penetration-depth-onset | Tunnel-diode oscillator frequency shift | ambient; unknown GPa | unknown | experiment; [source](#ref-source-e721bddb9ef11661) |
| CeCu2Si2 (aliases: heavy fermion, heavy fermions); Pang A/S-type crystal, Fig. 1B | 0.7 K; Antiferromagnetic ordering anomaly, not superconducting Tc. Separate superconducting specific-heat anomaly near 0.53 K. | measurement; antiferromagnetic-specific-heat-anomaly | Specific heat | ambient; unknown GPa | unknown | experiment; [source](#ref-source-e721bddb9ef11661) |
| CeCu2Si2 (aliases: heavy fermion, heavy fermions); Pang penetration-depth measurement, base temperature | 0.04 K; Approximate measurement floor, not a transition temperature; low-temperature fits extend to 0.12 K. | measurement; penetration-depth-base-temperature | Tunnel-diode oscillator | ambient; unknown GPa | unknown | experiment; [source](#ref-source-e721bddb9ef11661) |

## Sources

### Ref source-0ebda9b697c1f7fd

[R1] Superconductivity in the Presence of Strong Pauli Paramagnetism: CeCu2Si2 (1979). [DOI 10.1103/PhysRevLett.43.1892](https://doi.org/10.1103/PhysRevLett.43.1892). Publication: journal-article. Check: publisher-abstract-check. Checked: 2026-10-18. Published 17 December 1979. Abstract checked for historical discovery and approximately 0.5 K; complete original measurements not reviewed.
### Ref source-1bdac37fd450eb32

[R2] The Kondo lattice and weak antiferromagnetism (1977). [DOI 10.1016/0378-4363(77)90190-5](https://doi.org/10.1016/0378-4363(77)90190-5). Publication: journal-article. Check: publisher-indexed-abstract-check. Checked: 2026-10-18. July 1977. Indexed abstract identifies a model competition, not a universal phase diagram. Full publisher endpoint unavailable.
### Ref source-2764bce38246bfae

[R3] Multiband Superconductivity with Unexpected Deficiency of Nodal Quasiparticles in CeCu2Si2 (2014). [DOI 10.1103/PhysRevLett.112.067002](https://doi.org/10.1103/PhysRevLett.112.067002). Publication: journal-article. Check: selected-author-methods-and-supplement-check. Checked: 2026-10-18. Journal published 12 February 2014; author v2 submitted 13 February 2014. Selected pp.1–3 and supplemental p.6 read; p.6 visually checked. Nuclear subtraction and heavy-band sensitivity retained. PDF generated date 2018 is not submission. Final-version comparison and raw-data refit remain open.
### Ref source-e721bddb9ef11661

[R4] Fully gapped d-wave superconductivity in CeCu2Si2 (2018). [DOI 10.1073/pnas.1720291115](https://doi.org/10.1073/pnas.1720291115). Publication: journal-article. Check: selected-published-sample-probe-and-fit-boundaries. Checked: 2026-10-20. Published online 8 May 2018; issue 22 May 2018. Selected Results, Figs. 1–3/5 captions and Methods checked. Separate S/A-S resistive, specific-heat and penetration-depth criteria; approximately 40 mK TDO base and 0.12 K fit cutoff. Superfluid-density conversion uses lambda(0)=2000 Angstrom; two-gap s-wave and d+d fits, calibration caveat and digitized Kittaka heat capacity distinguished. Sign-change arguments additionally use cited earlier probes. Figure pixels, complete supplement and raw fits not rechecked in this follow-up.
### Ref source-5962cf8038597944

[R5] Heavy-fermion superconductivity in CeCoIn5 at 2.3 K (2001). [DOI 10.1088/0953-8984/13/17/103](https://doi.org/10.1088/0953-8984/13/17/103). Publication: journal-article. Check: selected-author-discovery-thermodynamics-check. Checked: 2026-10-18. Author v1 submitted 7 March 2001. Selected discovery, growth, heat-capacity baseline and field-orientation passages, pp.2–5, read. Final journal-version comparison and original data reanalysis remain open.
### Ref source-e7c77a3327daf5c6

[R6] Signatures of valence fluctuations in CeCu2Si2 under high pressure (2004). [DOI 10.1103/PhysRevB.69.024508](https://doi.org/10.1103/PhysRevB.69.024508). Publication: journal-article. Check: publisher-abstract-check. Checked: 2026-10-18. Published 15 January 2004. Abstract: helium pressure medium, simultaneous resistivity/ac heat capacity above 6 GPa and proposed valence interpretation around 4.5 GPa. Full methods not reviewed.
### Ref source-fda01ade7737b638

[R7] Coupled superconducting and magnetic order in CeCoIn5 (2008). [DOI 10.1126/science.1161818](https://doi.org/10.1126/science.1161818). Publication: journal-article. Check: original-abstract-index-check. Checked: 2026-10-18. Original abstract indexed at PubMed read. Online 21 August 2008; issue 19 September 2008. Magnetic order collapses with superconductivity; finite-momentum interpretation is not direct imaging. Publisher fulltext returned 403; complete methods not reviewed.
### Ref source-d3edee404071ac81

[R8] Observation of broken time-reversal symmetry in the heavy-fermion superconductor UPt3 (2014). [DOI 10.1126/science.1248552](https://doi.org/10.1126/science.1248552). Publication: journal-article. Check: selected-author-manuscript-check. Checked: 2026-10-18. Reused scoped primary reading from C6 in this project. Selected pp.1–6, Fig.2 on p.11 visually checked, and sample/apparatus passages on p.13. Published July2014; author upload October2014. Heating and training limits retained; full final-version and raw-data comparison open.
### Ref source-15aec45a868e9fb9

[R9] Coexistence of superconductivity and ferromagnetism in URhGe (2001). [DOI 10.1038/35098048](https://doi.org/10.1038/35098048). Publication: journal-article. Check: publisher-abstract-scoped-check. Checked: 2026-10-18. Reused scoped primary reading from B4 in this project. Aoki et al. publisher indexed abstract: ambient-pressure thermodynamic evidence, with qualified triplet interpretation. Corrects inherited35065045, which identifies unrelated semiconductor melting research. Full data not reanalyzed.
### Ref source-a4695ba5bfa789f3

[R10] Superconductivity on the Border of Weak Itinerant Ferromagnetism in UCoGe (2007). [DOI 10.1103/PhysRevLett.99.067006](https://doi.org/10.1103/PhysRevLett.99.067006). Publication: journal-article. Check: publisher-abstract-scoped-check. Checked: 2026-10-18. Reused scoped primary reading from B4 in this project. Huy et al. original abstract: ambient-pressure bulk signatures. Curie3K and best-sample resistive0.8K are distinct; no sample Tc extracted here. Full curves not reviewed.
### Ref source-df199ac9453d6985

[R11] Resonance from antiferromagnetic spin fluctuations for superconductivity in UTe2 (2021). [DOI 10.1038/s41586-021-04151-5](https://doi.org/10.1038/s41586-021-04151-5). Publication: journal-article. Check: publisher-passages-scoped-check. Checked: 2026-10-18. Reused scoped primary reading from B4 in this project. Duan et al. publisher indexed abstract and Extended Data Fig.7 text checked: AFM resonance and no FM signal above background within specified window. Complete spectra and raw data not reproduced; not an exclusion of all FM fluctuations.
### Ref source-0c4d7cebb12a0d5b

[R12] High-field superconducting halo in UTe2 (2025). [DOI 10.1126/science.adn7673](https://doi.org/10.1126/science.adn7673). Publication: journal-article. Check: selected-published-pulsed-field-methods-check. Checked: 2026-10-18. Published 31 July 2025. Selected pp.512–513 methods and boundary interpretation read; p.512 visually checked. Pulsed-field maximum around 73 T is distinct from extrapolation. Supplement and dataset not reanalyzed; no full order-parameter reconstruction.
### Ref source-15cfc4a2f9587af0

[R13] Giant transverse magnetic fluctuations at the edge of re-entrant superconductivity in UTe2 (2026). [DOI 10.1038/s41467-026-71899-7](https://doi.org/10.1038/s41467-026-71899-7). Publication: journal-article. Check: publisher-passages-scoped-check. Checked: 2026-10-18. Reused scoped primary reading from B4 in this project. Zambra et al., published29April2026. Selected introduction/results, Eq.1 and Fig.1 caption checked:4K normal state, pulsedfields to60T, transverse relative to applied field;300mK phase boundaries reproduced from earlier work. No raw-data or complete spectral/pairing-kernel reconstruction. Publisher indexed record gives article 3742, not inherited 3814; current full HTML endpoint unavailable.
### Ref source-dd4e897d833ce69c

[R14] Fate of Time-Reversal Symmetry Breaking in UTe2 (2023). [DOI 10.1103/PhysRevX.13.041019](https://doi.org/10.1103/PhysRevX.13.041019). Publication: journal-article. Check: selected-author-manuscript-check. Checked: 2026-10-18. Reused scoped primary reading from C6 in this project. Selected pp.2–3 and methods pp.5–6; Fig.1 p.3 visually checked. Kerr sample set distinguished from susceptibility set. Final publisher abstract checked; full version comparison open.

## Claim evidence and conditions

### scwiki-d8-claim-scope-1

Heavy-fermion superconductors pair electrons in a strongly renormalized metallic state. Their large low-temperature electronic heat capacity and magnetic response reflect interactions involving partially filled f shells, not unusually heavy atoms moving as Cooper pairs. CeCu₂Si₂ established this class in 1979; the discovery paper reported a transition near 0.5 K. Different compositions and probes need not reproduce that exact number. The family is a laboratory for competing correlations rather than a single pairing mechanism.

Evidence: experiment. Sources: source-0ebda9b697c1f7fd, source-5962cf8038597944.

Conditions: Material, sample, pressure, field direction and probe-specific conditions; model amplitudes and operating temperatures are not measured transition temperatures.

Verification scope: Selected primary passages and bounded algebra; full scientific acceptance and original-data reproduction remain open.

### scwiki-d8-claim-scope-2

Kondo screening, conduction-electron-mediated magnetic interactions, hybridization and valence changes provide useful organizing ideas. Doniach's competition between magnetic order and a compensated state is a model framework. Proximity to a magnetic boundary does not by itself identify the pairing interaction or predict a superconducting transition. Uranium compounds also require attention to itinerant 5f character and strong spin–orbit coupling; a label borrowed from a cerium compound is not a complete microscopic description.

Evidence: theory. Sources: source-1bdac37fd450eb32, source-e7c77a3327daf5c6, source-15aec45a868e9fb9.

Conditions: Material, sample, pressure, field direction and probe-specific conditions; model amplitudes and operating temperatures are not measured transition temperatures.

Verification scope: Selected primary passages and bounded algebra; full scientific acceptance and original-data reproduction remain open.

### scwiki-d8-claim-mathematical-assumptions-1

In a Fermi-liquid regime, the electronic coefficient $\gamma=\lim_{T\to0}C_e/T$ is proportional to the renormalized density of states. A finite-temperature value of total $C/T$ is not automatically that limit. Petrovic's CeCoIn₅ report gives about 290 mJ mol⁻¹ K⁻² above 2.5 K but a much larger low-temperature normal-state value under field. Thus its apparent $\Delta C/(\gamma T_c)\approx4.5$ cannot be converted mechanically into a coupling strength using a temperature-independent normal-state baseline.

Evidence: theory. Sources: source-5962cf8038597944.

Conditions: Material, sample, pressure, field direction and probe-specific conditions; model amplitudes and operating temperatures are not measured transition temperatures.

Verification scope: Selected primary passages and bounded algebra; full scientific acceptance and original-data reproduction remain open.

### scwiki-d8-claim-mathematical-assumptions-2

Kittaka's CeCu₂Si₂ analysis subtracts a nuclear term. With numerical field $h$ in tesla and temperature $t$ in kelvin, its empirical expression is $C_n/T=(7.4h^2+0.1)t^{-3}\times10^{-6}$ J mol⁻¹ K⁻². At 60 mK it gives approximately 0.00046, 0.111 and 0.309 J mol⁻¹ K⁻² for 0, 1.8 and 3 T. These recalculations illustrate the size of the correction; they are not a new fit or evidence that any arbitrary subtraction is acceptable.

Evidence: theory. Sources: source-2764bce38246bfae.

Conditions: Material, sample, pressure, field direction and probe-specific conditions; model amplitudes and operating temperatures are not measured transition temperatures.

Verification scope: Selected primary passages and bounded algebra; full scientific acceptance and original-data reproduction remain open.

### scwiki-d8-claim-mathematical-assumptions-3

Pang's simplified band-mixing model uses $|\Delta(\varphi)|=\sqrt{a^2\cos^2(2\varphi)+b^2\sin^2(2\varphi)}$ at zero temperature. For nonzero amplitudes on the assumed cylinder, the minimum is $\min(|a|,|b|)$; exchanging them preserves angular averages. The reported S-type fit uses $a=2.5k_BT_c$ and $b=0.58k_BT_c$. This magnitude does not specify the full band matrix or its time-reversal properties. A scalar chiral gap can have the same magnitude; that algebraic coincidence does not equate the two physical states.

Evidence: theory. Sources: source-e721bddb9ef11661.

Source relationship: mixed-source-and-local-derivation. The reference supplies the simplified quadrature model and fitted amplitudes. Extrema, exchange invariance and scalar/matrix magnitude comparison are local algebra; they do not establish the full quasiparticle spectrum or equivalent symmetry.

Conditions: Material, sample, pressure, field direction and probe-specific conditions; model amplitudes and operating temperatures are not measured transition temperatures.

Verification scope: Selected primary passages and bounded algebra; full scientific acceptance and original-data reproduction remain open.

### scwiki-d8-claim-experimental-criteria-1

The CeCu₂Si₂ specific-heat study used a 13.8 mg S-type crystal, measurements down to 40 mK and a nuclear correction constrained by high-field normal-state data. It reported low-energy behavior consistent with full gaps and no detected in-plane angular oscillation within stated sensitivity. The result constrains quasiparticles weighted strongly by thermodynamics; it is not a universal exclusion of every possible small-band node. The author manuscript's February 2014 version must not be dated from its later PDF generation stamp.

Evidence: experiment. Sources: source-2764bce38246bfae.

Conditions: Material, sample, pressure, field direction and probe-specific conditions; model amplitudes and operating temperatures are not measured transition temperatures.

Verification scope: Selected primary passages and bounded algebra; full scientific acceptance and original-data reproduction remain open.

### scwiki-d8-claim-experimental-criteria-2

Pang measured penetration-depth shifts down to about 40 mK using a tunnel-diode oscillator. Keep each reported temperature tied to its sample and criterion:

| Sample | Criterion in Pang | Approximate temperature |
|---|---|---|
| S-type | Resistive onset | 0.65 K |
| S-type | Zero resistivity | 0.60 K |
| S-type | Superconducting specific-heat anomaly | 0.64 K |
| S-type | Penetration-depth onset | 0.62 K |
| A/S-type | Resistive onset | 0.62 K |
| A/S-type | Superconducting specific-heat anomaly | 0.53 K |
| A/S-type | Antiferromagnetic specific-heat anomaly | 0.70 K; not superconducting Tc |

Low-temperature exponential fits extend to 0.12 K. Finite-window power-law fits are also reported; their exponents increase as the upper fitting temperature decreases. This supports a low-temperature full gap without uniquely selecting the pairing state. Superfluid-density conversion assumes a zero-temperature penetration depth of 2000 Å, and both two-gap s-wave and d+d fits describe it. The paper's sign-change argument additionally invokes earlier neutron and NQR evidence; it is not a direct phase measurement by the oscillator. Its later heat-capacity fit uses data digitized from Kittaka. Raw-data refitting and the complete supplement remain outside this scoped review.

Evidence: experiment. Sources: source-e721bddb9ef11661.

Source relationship: mixed-source-and-local-derivation. The paper reports sample/probe temperatures and alternative model fits. Keeping magnetic ordering, transport criteria and measurement floors separate is editorial interpretation; fit agreement alone is not a phase-sensitive identification of a unique order parameter.

Conditions: Pang final Figs. 1–3/5 and Methods; distinct S and A/S crystals, probe-specific transitions, approximately 40 mK base temperature and 0.12 K low-temperature fit cutoff. Superfluid density assumes lambda(0)=2000 Angstrom. AFM anomaly is not superconducting Tc.

Verification scope: Selected published results, figure captions and Methods checked; no new figure-pixel inspection, raw-data fit or full supplement review.

### scwiki-d8-claim-experimental-criteria-3

For CeCoIn₅, the discovery study combined zero resistance, magnetic shielding and a heat-capacity anomaly near 2.3 K. It also found substantially different upper critical fields parallel and perpendicular to the c axis. Later neutron work found magnetic order that disappears with superconductivity at the high-field boundary. A coupled magnetic Q phase therefore cannot be described as a clean demonstration of a standalone textbook FFLO state.

Evidence: experiment. Sources: source-5962cf8038597944, source-fda01ade7737b638.

Conditions: Material, sample, pressure, field direction and probe-specific conditions; model amplitudes and operating temperatures are not measured transition temperatures.

Verification scope: Selected primary passages and bounded algebra; full scientific acceptance and original-data reproduction remain open.

### scwiki-d8-claim-limits-and-disputes-1

CeCu₂Si₂ should not be assigned an unqualified textbook nodal d-wave label. Full-gap thermodynamics, sign-sensitive interpretations and band structure must be reconciled. Its pressure response adds another question: Holmes measured resistivity and ac heat capacity above 6 GPa in helium and interpreted anomalies near 4.5 GPa through valence fluctuations. That interpretation is a proposed mechanism, not a direct measurement of a unique pairing interaction.

Evidence: experiment. Sources: source-2764bce38246bfae, source-e721bddb9ef11661, source-e7c77a3327daf5c6.

Conditions: Material, sample, pressure, field direction and probe-specific conditions; model amplitudes and operating temperatures are not measured transition temperatures.

Verification scope: Selected primary passages and bounded algebra; full scientific acceptance and original-data reproduction remain open.

### scwiki-d8-claim-limits-and-disputes-2

UPt₃ has multiple superconducting phases and Kerr evidence constraining time-reversal symmetry. Heating, field training and the phase being probed matter. This does not uniquely select f-wave symmetry or establish a topological device. URhGe and UCoGe provide coexistence evidence for ferromagnetism and superconductivity, but their magnetic and superconducting transition temperatures are distinct. Their respective field responses cannot be exchanged between compounds.

Evidence: experiment. Sources: source-d3edee404071ac81, source-15aec45a868e9fb9, source-a4695ba5bfa789f3.

Conditions: Material, sample, pressure, field direction and probe-specific conditions; model amplitudes and operating temperatures are not measured transition temperatures.

Verification scope: Selected primary passages and bounded algebra; full scientific acceptance and original-data reproduction remain open.

### scwiki-d8-claim-limits-and-disputes-3

UTe₂ requires particularly careful qualifiers. Antiferromagnetic neutron fluctuations, transverse high-field fluctuations and sample-dependent Kerr results probe different conditions. The 2023 Kerr study found no spontaneous signal in the tested single-transition samples; it does not negate every other superconducting phase. No single large upper critical field, fluctuation spectrum or null Kerr observation determines spin structure and topology together.

Evidence: experiment. Sources: source-df199ac9453d6985, source-15cfc4a2f9587af0, source-dd4e897d833ce69c.

Conditions: Material, sample, pressure, field direction and probe-specific conditions; model amplitudes and operating temperatures are not measured transition temperatures.

Verification scope: Selected primary passages and bounded algebra; full scientific acceptance and original-data reproduction remain open.

### scwiki-d8-claim-discovery-implications-1

The 2025 UTe₂ halo study mapped transport boundaries with pulsed fields, generally near 0.63 K, using resistance and contactless proximity-detector measurements. Tilting away from the b axis revealed an extended high-field region. The experiment reached approximately 73 T; extrapolated persistence beyond that field is not a measured upper boundary. Its multicomponent triplet interpretation remains a model conclusion. Supplementary sample details, heating corrections and the deposited raw data have not been independently reanalyzed here.

Evidence: experiment. Sources: source-0c4d7cebb12a0d5b.

Conditions: Material, sample, pressure, field direction and probe-specific conditions; model amplitudes and operating temperatures are not measured transition temperatures.

Verification scope: Selected primary passages and bounded algebra; full scientific acceptance and original-data reproduction remain open.

### scwiki-d8-claim-discovery-implications-2

The 2026 transverse-fluctuation study measured the normal state at 4 K; superconducting phase boundaries at 300 mK were comparisons with earlier work. Neither temperature is a newly measured transition temperature in that experiment. Discovery records should retain the sample, pressure, field direction, probe and criterion, then compare mechanisms across compatible conditions. The goal is to identify informative constraints, not rank unrelated temperatures or convert candidate topology into an established engineering capability.

Evidence: experiment. Sources: source-15cfc4a2f9587af0.

Conditions: Material, sample, pressure, field direction and probe-specific conditions; model amplitudes and operating temperatures are not measured transition temperatures.

Verification scope: Selected primary passages and bounded algebra; full scientific acceptance and original-data reproduction remain open.

## Revision and review

Article ID: scwiki-d8. Revision: 184da41a895f3705f5b0. Updated: 2026-10-19T16:38:16.196320+00:00.

Review scope: Selected CeCu2Si2 and CeCoIn5 methods, nuclear subtraction, proposed gap model and UTe2 pulsed-field passages; previously scoped uranium evidence and independent bounded algebra. Follow-up separates Pang sample/probe criteria, fitting window, assumed penetration-depth scale and model-inference limits.

- Full scientific acceptance and raw-data reproduction remain open.
- Author manuscripts are version-labelled; complete final-version comparisons remain open.
- Several magnetic-mechanism references remain abstract or selected-passage checks.
- No pairing symmetry, topological classification or device performance is certified by these checks.

Source: [D_material_families/D8_heavy_fermion.md](https://github.com/JackZH26/jzis-superconductivity/blob/0a7c9d6696804ec26aa12f8eed68b55c9b3c0fcf/D_material_families/D8_heavy_fermion.md), commit 0a7c9d6696804ec26aa12f8eed68b55c9b3c0fcf, SHA-256 d389474b7d40c91c84b51b5d175bd0038239b825f4dccf53353b4097d02e1d4f.