{"schemaVersion":"1.0","revision":"fa961ab24277a91737c3","article":{"id":"scwiki-d1","topicId":"scwiki-topic-d1","code":"D1","slug":"elemental-superconductors","title":"Elemental superconductors: benchmarks, phases and pressure","summary":"Compare elemental systems without confusing chemical identity, crystal phase, measured transitions and theoretical estimates.","aliases":["elemental superconductors","mercury","lead","niobium","scandium","lithium","calcium","compressed iron","monatomic superconductors"],"evidenceTypes":["theory","experiment","prediction"],"relatedCodes":["A4","A5","A6","B1","B2"],"editorialStatus":"scoped-check","contentState":"pilot","modifiedAt":"2026-10-19T15:22:41.346250+00:00","review":{"checkedAt":"2026-10-19","scope":"Selected Onnes lecture scan, Rowell normalization conditions, Sc published methods/table and Nb contextual methods; explicitly limited Li/Fe/Ca/2026 theory checks. Independent isotope derivatives, printed-parameter estimates and SI field-length check. Follow-up: Rowell1970 published barrier/normal-reference text and Marsiglio v1 coupling/inversion passages re-read;13 local thermal-convolution and transmission controls. Other source checks not repeated.","limitations":["Full scientific acceptance and raw-data/convergence reviews remain open.","Original mercury isotope datasets and lead inversion are metadata-level references only; original1911 scan not obtained.","Ca comment identity recorded but its argument and reconciliation remain unread.","2026 Sc theory is abstract-only; numerical consistency does not reproduce DFT or establish bulk magnetic evidence."]},"provenance":{"repository":"JackZH26/jzis-superconductivity","commit":"0a7c9d6696804ec26aa12f8eed68b55c9b3c0fcf","path":"D_material_families/D1_elemental_metals.md","sha256":"09606dedbf321b1f5b231ea0c8061a0ab7adda20be151994b8b459ab34257fbe","sourceId":"file-caeb99b1a050e5f2"},"sourceMap":[{"startLine":1,"endLine":64,"targetSections":["scope","mathematical-assumptions","experimental-criteria","limits-and-disputes","discovery-implications","related-topics"],"decision":"edited-with-scoped-evidence","note":"All pinned lines retained in source repository; conditional theory and named phase/probe examples expanded with explicit review boundaries."}],"references":[{"id":"source-d36e5a81b57e823f","doi":null,"title":"Investigations into the properties of substances at low temperatures (Nobel lecture, 11 December 1913; later notes included)","year":1913,"url":"https://www.nevis.columbia.edu/~haas/documents/physics_nobel_lectures/physics01-21-2.pdf","publicationStatus":"technical-report","verification":{"scope":"selected-primary-lecture-scan-check","checkedAt":"2026-10-18","evidenceUrl":"https://www.nevis.columbia.edu/~haas/documents/physics_nobel_lectures/physics01-21-2.pdf","note":"Selected printed pp.330–336 (PDF pp.76–82), mercury apparatus/resolution and current threshold. PDF pp.79–80 visually checked. Later 1914 addendum distinguished; original 1911 communication scan remains unavailable."}},{"id":"source-eff5a2a1c455e7f6","doi":"10.1103/PhysRev.78.477","title":"Isotope Effect in the Superconductivity of Mercury","year":1950,"url":"https://doi.org/10.1103/PhysRev.78.477","publicationStatus":"journal-article","verification":{"scope":"publisher-metadata-only","checkedAt":"2026-10-18","evidenceUrl":"https://journals.aps.org/pr/abstract/10.1103/PhysRev.78.477","note":"Title, author and publication date checked. Original full text unavailable at attempted endpoint; no mercury isotope exponent or dataset certified."}},{"id":"source-e8a489943f13c9f8","doi":"10.1103/PhysRev.78.487","title":"Superconductivity of Isotopes of Mercury","year":1950,"url":"https://doi.org/10.1103/PhysRev.78.487","publicationStatus":"journal-article","verification":{"scope":"publisher-metadata-only","checkedAt":"2026-10-18","evidenceUrl":"https://journals.aps.org/pr/abstract/10.1103/PhysRev.78.487","note":"Title, authors and publication date checked. Original full text unavailable at attempted endpoint; no mercury isotope exponent or dataset certified."}},{"id":"source-b66885f8fdc58181","doi":"10.1103/PhysRevLett.14.108","title":"Lead Phonon Spectrum Calculated from Superconducting Density of States","year":1965,"url":"https://doi.org/10.1103/PhysRevLett.14.108","publicationStatus":"journal-article","verification":{"scope":"publisher-metadata-only","checkedAt":"2026-10-19","evidenceUrl":"https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.14.108","note":"Publisher title, DOI and25January1965 date rechecked. Content requires subscription; original spectrum/inversion not obtained or reproduced."}},{"id":"source-aa8182fe7a3d8d0c","doi":"10.1103/PhysRev.167.331","title":"Transition Temperature of Strong-Coupled Superconductors","year":1968,"url":"https://doi.org/10.1103/PhysRev.167.331","publicationStatus":"journal-article","verification":{"scope":"primary-abstract-scoped-check","checkedAt":"2026-10-18","evidenceUrl":"https://journals.aps.org/pr/abstract/10.1103/PhysRev.167.331","note":"Publisher abstract: strong-coupling calculations and empirical parameters. Full original formula fit and dataset not reviewed."}},{"id":"source-0620df96ebbf2a66","doi":"10.1103/PhysRevB.12.905","title":"Transition temperature of strong-coupled superconductors reanalyzed","year":1975,"url":"https://doi.org/10.1103/PhysRevB.12.905","publicationStatus":"journal-article","verification":{"scope":"primary-abstract-scoped-check","checkedAt":"2026-10-18","evidenceUrl":"https://journals.aps.org/prb/abstract/10.1103/PhysRevB.12.905","note":"Publisher abstract: modified prefactor, spectral moment/shape corrections and large-coupling limits within Eliashberg theory. Full derivation and Pb-Bi data not reanalyzed."}},{"id":"source-27b24b231ced1ec3","doi":"10.6028/jres.074A.046","title":"Tunneling Measurements of Superconducting Quasi-Particle Density of States and Calculation of Phonon Spectra","year":1970,"url":"https://doi.org/10.6028/jres.074A.046","publicationStatus":"journal-article","verification":{"scope":"selected-published-text-check","checkedAt":"2026-10-19","evidenceUrl":"https://nvlpubs.nist.gov/nistpubs/jres/74A/jresv74An4p559_A1b.pdf","note":"Re-read published pp.560-561 barrier/current discussion and p.565 section5 plus oxide-excitation warning. Publication July-August1970 differs from1969 receipt. Text-only this round. Normal-reference requirements do not constitute a modern finite-temperature response fit; added SIN convolution is local."}},{"id":"source-cc7115129638a171","doi":"10.1038/nature01098","title":"Superconductivity in compressed lithium at 20 K","year":2002,"url":"https://doi.org/10.1038/nature01098","publicationStatus":"journal-article","verification":{"scope":"publisher-abstract-and-caption-check","checkedAt":"2026-10-18","evidenceUrl":"https://www.nature.com/articles/nature01098","note":"Published10 October2002. Selected abstract/figure captions only; full phase/probe/raw data review open."}},{"id":"source-61e8b60fcacfb53b","doi":"10.1038/nature05820","title":"Superconductivity in lithium below 0.4 millikelvin at ambient pressure","year":2007,"url":"https://doi.org/10.1038/nature05820","publicationStatus":"journal-article","verification":{"scope":"publisher-indexed-abstract-and-caption-check","checkedAt":"2026-10-18","evidenceUrl":"https://www.nature.com/articles/nature05820","note":"Published10 May2007; indexed abstract and Meissner figure caption checked. Direct page retrieval later redirected to sign-in; full methods not reviewed. 0.4mK=.0004K."}},{"id":"source-dc73a11d591aebd0","doi":"10.1103/PhysRevResearch.5.043248","title":"Superconductivity up to 37.6 K in compressed scandium","year":2023,"url":"https://doi.org/10.1103/PhysRevResearch.5.043248","publicationStatus":"journal-article","verification":{"scope":"selected-published-text-and-table-check","checkedAt":"2026-10-18","evidenceUrl":"https://harvest.aps.org/v2/journals/articles/10.1103/PhysRevResearch.5.043248/fulltext","note":"Published15 December2023. Selected pp.1–4 and TableI; pp.2/4 visually checked. Six formula estimates checked with input-rounding bounds; no raw-data, DFT or full supplement reproduction."}},{"id":"source-bc42a3144ddb335e","doi":"10.1103/PhysRevB.83.220512","title":"Superconducting state of Ca-VII below a critical temperature of 29 K at a pressure of 216 GPa","year":2011,"url":"https://doi.org/10.1103/PhysRevB.83.220512","publicationStatus":"journal-article","verification":{"scope":"publisher-abstract-and-selected-methods-check","checkedAt":"2026-10-18","evidenceUrl":"https://harvest.aps.org/v2/journals/articles/10.1103/PhysRevB.83.220512/fulltext","note":"Published22 June2011. Abstract and selected first-page methods via web text. Full comment10.1103/PhysRevB.84.216501 reconciliation remains open; no independent curve analysis."}},{"id":"source-c563fd6be7dd9167","doi":"10.1103/PhysRevB.84.216501","title":"Comment on “Superconducting state of Ca-VII below a critical temperature of 29 K at a pressure of 216 GPa”","year":2011,"url":"https://doi.org/10.1103/PhysRevB.84.216501","publicationStatus":"journal-article","verification":{"scope":"crossref-registration-metadata-only","checkedAt":"2026-10-18","evidenceUrl":"https://api.crossref.org/works/10.1103/PhysRevB.84.216501","note":"Crossref primary registration confirms M. Andersson and 6 December 2011 publication. Full comment unavailable; its argument and reconciliation remain unreviewed."}},{"id":"source-7301d50108f9de56","doi":"10.1038/35085536","title":"Superconductivity in the non-magnetic state of iron under pressure","year":2001,"url":"https://doi.org/10.1038/35085536","publicationStatus":"journal-article","verification":{"scope":"primary-abstract-via-PubMed","checkedAt":"2026-10-18","evidenceUrl":"https://pubmed.ncbi.nlm.nih.gov/11460158/","note":"Published19 July2001. Abstract only: resistance and Meissner report below2K under15–30GPa. Full methods and pairing analysis not reviewed."}},{"id":"source-29962a8944db57fa","doi":"10.1103/v5j2-9bv6","title":"Electronic mechanism of pressure-enhanced superconductivity in scandium","year":2026,"url":"https://doi.org/10.1103/v5j2-9bv6","publicationStatus":"journal-article","verification":{"scope":"publisher-abstract-check","checkedAt":"2026-10-18","evidenceUrl":"https://journals.aps.org/prb/abstract/10.1103/v5j2-9bv6","note":"Published8 September2026, distinct from issue1 September. Band broadening and overlap linked to electron–phonon coupling; full text subscription required, no calculation reproduced."}},{"id":"source-835031575efae07a","doi":"10.1103/PhysRevAccelBeams.27.062001","title":"Field, frequency, and temperature dependencies of the surface resistance of nitrogen diffused niobium superconducting radio frequency cavities","year":2024,"url":"https://doi.org/10.1103/PhysRevAccelBeams.27.062001","publicationStatus":"journal-article","verification":{"scope":"selected-published-background-methods-check","checkedAt":"2026-10-18","evidenceUrl":"https://journals.aps.org/prab/pdf/10.1103/PhysRevAccelBeams.27.062001","note":"Published12 June2024. Selected pp.1–2: high-purity Nb cavity surface treatments and approximate9.25K cooldown reference. Used only as contextual Nb scale, not pristine-element dataset or acceptance of all cavity models."}},{"id":"source-d56b04dc0b32c796","doi":"10.1016/j.aop.2020.168102","title":"Eliashberg Theory: a short review","year":2020,"url":"https://doi.org/10.1016/j.aop.2020.168102","publicationStatus":"journal-article","verification":{"scope":"author-review-scoped-check","checkedAt":"2026-10-19","evidenceUrl":"https://arxiv.org/pdf/1911.05065v1","note":"Follow-up author v1 text: PDFp.3 coupling-frequency dependence and PDFp.5 subsection A inversion discussion/Eq.21; current is measured and alpha2F inferred using Eliashberg equations. Prior selected model benchmark check retained; no full final-version comparison or original lead inversion rerun."}},{"id":"source-ba10e800a1246bf6","doi":"10.1103/PhysRev.108.1175","title":"Theory of Superconductivity","year":1957,"url":"https://doi.org/10.1103/PhysRev.108.1175","publicationStatus":"journal-article","verification":{"scope":"primary-full-text-scoped-check","checkedAt":"2026-10-18","evidenceUrl":"https://journals.aps.org/pr/pdf/10.1103/PhysRev.108.1175","note":"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."}}],"claims":[{"id":"scwiki-d1-claim-scope-1","sectionId":"scope","statement":"An elemental superconductor contains one chemical element, but that label does not specify its crystal structure, bands, coupling strength or pressure history. Elemental systems provide useful benchmarks for electron–phonon theory; they do not all reduce to one weak-coupling model. Niobium's approximately 9.2 K transition is a useful conventional scale, not a ceiling on elemental superconductivity or a certified value for every sample.","evidenceType":"theory","sourceIds":["source-aa8182fe7a3d8d0c","source-835031575efae07a"],"conditions":"Element, phase and sample conditions; historical lecture dates separated.","verificationScope":"Named primary passages and bounded independent examples only; complete scientific acceptance open."},{"id":"scwiki-d1-claim-scope-2","sectionId":"scope","statement":"The mercury discovery is associated with Onnes's 1911 report. His later Nobel lecture describes the abrupt resistance decrease near 4.2 K, explicitly qualified by measurement accuracy, and a current threshold above which voltage reappeared. The lecture scan includes subsequent notes and a 1914 addendum; those later observations should not be dated to 1911. It is a firsthand account, not a substitute for a modern magnetic-volume or heat-capacity measurement.","evidenceType":"theory","sourceIds":["source-d36e5a81b57e823f"],"conditions":"Element, phase and sample conditions; historical lecture dates separated.","verificationScope":"Named primary passages and bounded independent examples only; complete scientific acceptance open."},{"id":"scwiki-d1-claim-mathematical-assumptions-1","sectionId":"mathematical-assumptions","statement":"The isotope coefficient is $\\alpha=-d\\ln T_c/d\\ln M$. If harmonic frequencies scale as $M^{-1/2}$ while the dimensionless pairing parameters remain fixed, the corresponding transition scale has $\\alpha=1/2$. This is a conditional model statement, not a value certified here for the original mercury datasets. Maxwell and Reynolds are retained as the historical experimental sources; their full datasets still require direct review. An isotope substitution may also change structure or anharmonic motion, so a measured coefficient must retain its sample and phase conditions.","evidenceType":"theory","sourceIds":["source-eff5a2a1c455e7f6","source-e8a489943f13c9f8","source-0620df96ebbf2a66"],"conditions":"Finite imposed isotope model and printed-parameter formula check; no DFT, stability or experimental replication.","verificationScope":"Named primary passages and bounded independent examples only; complete scientific acceptance open."},{"id":"scwiki-d1-claim-mathematical-assumptions-2","sectionId":"mathematical-assumptions","statement":"The weak-coupling isotropic BCS benchmark is $2\\Delta(0)/(k_BT_c)\\simeq3.53$. Lead is a strong-coupling benchmark, so that number is not a compulsory fit to its tunneling spectrum. Retardation makes the gap energy dependent; a full gap alone does not establish its sign structure or the microscopic pairing interaction.","evidenceType":"theory","sourceIds":["source-d56b04dc0b32c796","source-ba10e800a1246bf6"],"conditions":"Finite imposed isotope model and printed-parameter formula check; no DFT, stability or experimental replication.","verificationScope":"Named primary passages and bounded independent examples only; complete scientific acceptance open."},{"id":"scwiki-d1-claim-mathematical-assumptions-3","sectionId":"mathematical-assumptions","statement":"For an illustrative McMillan-type estimate, write $T_c=(\\omega_{\\log}/1.2)\\exp[-A/D]$, with $A=1.04(1+\\lambda)$ and $D=\\lambda-\\mu^*(1+0.62\\lambda)>0$, taking $\\omega_{\\log}$ in kelvin. If $\\mu^*=\\mu/[1+\\mu\\ln(E_{\\mathrm{el}}/\\omega_{\\log})]$, with the two cutoff scales in the same units, fixed $\\lambda,\\mu,E_{\\mathrm{el}}$ give $\\alpha=\\tfrac12[1-A(1+0.62\\lambda)(\\mu^*)^2/D^2]$. Three finite-difference mass substitutions independently confirm this derivative and its difference from the fixed-$\\mu^*$ limit. These examples are not mercury fits. The estimate omits the full Allen–Dynes shape factors and is not a universal upper bound.","evidenceType":"theory","sourceIds":["source-aa8182fe7a3d8d0c","source-0620df96ebbf2a66","source-d56b04dc0b32c796"],"conditions":"Finite imposed isotope model and printed-parameter formula check; no DFT, stability or experimental replication.","verificationScope":"Named primary passages and bounded independent examples only; complete scientific acceptance open."},{"id":"scwiki-d1-claim-mathematical-assumptions-4","sectionId":"mathematical-assumptions","statement":"In the Sc paper's Table I, six printed estimates are consistent with the input rounding intervals. Sc-IV printed inputs yield 21.37/18.72 K, versus listed 21.5/18.8 K; exact reproduction needs unrounded inputs. Sc-V at 260 GPa gives 30.07/26.38 K for $\\mu^*=0.10/0.13$. These are calculations, not the measured 37.6 K onset at a different pressure. The reported extrapolated $B_{c2}(0)=21.3$ T implies $\\xi=\\sqrt{\\Phi_0/(2\\pi B_{c2})}=39.31$ angstrom; this checks units, not the extrapolation model.","evidenceType":"theory","sourceIds":["source-dc73a11d591aebd0"],"conditions":"Finite imposed isotope model and printed-parameter formula check; no DFT, stability or experimental replication.","verificationScope":"Named primary passages and bounded independent examples only; complete scientific acceptance open."},{"id":"scwiki-d1-claim-experimental-criteria-1","sectionId":"experimental-criteria","statement":"Tunneling conductance needs an appropriate normal reference. Rowell's 1970 account requires tunneling-dominated current and a barrier that stays effectively unchanged across the superconducting transition. Record how the normal reference was obtained, including its temperature and field; division alone does not remove a changed barrier or an unrelated parallel current. Oxide and interface excitations need not be electrode density-of-states features. The 1965 McMillan–Rowell paper is retained as the historical lead inversion reference; its original quantitative inversion has not been rerun here. The coupling-weighted spectrum $\\alpha^2F$ is inferred using an Eliashberg model, not read directly from conductance or identified with the bare phonon density of states.\n\nFor a local illustration of thermal convolution, assume weak elastic superconductor–insulator–normal-metal (SIN) tunneling, flat normal-electrode and normal-reference densities, a constant tunneling matrix element, and a sample spectrum unchanged by bias. At a common electron temperature, $G(V)/G_N=\\int_{-\\infty}^{\\infty}n_s(E)[-f'(E-eV)]\\,dE$, where $n_s$ is the dimensionless sample density and $f$ the Fermi function. The kernel is $[4k_BT\\cosh^2((E-eV)/(2k_BT))]^{-1}$. Finite temperature averages the spectrum; it does not return $n_s(eV)$ point by point. A hard-gap toy density, zero for $|E|<\\Delta$ and one outside, gives $G(0)/G_N=2/[1+\\exp(\\Delta/k_BT)]>0$ despite zero density at zero energy. Nine current-derivative checks, three hard-gap checks and a changed-transmission control verify this local example. It omits coherence peaks and intrinsic temperature dependence. A superconducting counterelectrode, a bias-dependent barrier, momentum-selective tunneling or extra broadening requires the corresponding response model. These checks neither invert an experimental spectrum nor determine a material's pairing mechanism.","evidenceType":"experiment","sourceIds":["source-b66885f8fdc58181","source-27b24b231ced1ec3","source-d56b04dc0b32c796"],"conditions":"Normal-reference provenance, temperature and field retained; tunneling-dominated current and unchanged barrier required. Local thermal formula additionally assumes weak elastic SIN tunneling, flat normal densities, constant matrix element, common electron temperature and no bias-dependent sample spectrum. No material spectrum, pairing mechanism or alpha2F inversion inferred.","verificationScope":"Rowell published text p.565 and barrier discussion, Marsiglio v1 selected coupling/inversion passages and1965 publisher identity checked;13 local cases passed. Original lead inversion, full source comparisons and independent scientific review remain open.","sourceRelationship":"mixed-source-and-local-derivation","derivationNote":"Rowell1970 supplies normalization and barrier conditions; Marsiglio author review explains model-dependent inversion and coupling-weighted alpha2F. McMillan-Rowell1965 is metadata-level historical context only. Thermal convolution, hard-gap conductance and transmission controls are local calculations, not source data reproduction."},{"id":"scwiki-d1-claim-experimental-criteria-2","sectionId":"experimental-criteria","statement":"Lithium illustrates why conditions cannot be dropped from a material label. Shimizu and colleagues reported compressed Li reaching about 20 K at 48 GPa in 2002; Tuoriniemi and colleagues reported an ambient-pressure transition around 0.4 mK in 2007, with a Meissner-state figure. The latter is 0.0004 K, not 0.4 K. These source checks cover abstracts and selected captions; they do not establish an entire phase diagram or independently validate the underlying data.","evidenceType":"experiment","sourceIds":["source-cc7115129638a171","source-61e8b60fcacfb53b"],"conditions":"Keep named source, phase, pressure and measurement criteria; abstract-only and inaccessible-comment scopes explicit.","verificationScope":"Named primary passages and bounded independent examples only; complete scientific acceptance open."},{"id":"scwiki-d1-claim-experimental-criteria-3","sectionId":"experimental-criteria","statement":"Wang and colleagues reported Sc onset at 37.6 K and 243 GPa, distinct from the plotted 37.3 K at 244 GPa. Four-probe warming measurements used diamond Raman pressure calibration; onset means departure from the normal-state line. Field/current suppression supports the transport assignment, but no Meissner measurement was supplied. Phase boundaries were inferred from transition trends and compared with earlier diffraction. Applied fields reached 9 T; 21.3 T is an extrapolation.","evidenceType":"experiment","sourceIds":["source-dc73a11d591aebd0"],"conditions":"Keep named source, phase, pressure and measurement criteria; abstract-only and inaccessible-comment scopes explicit.","verificationScope":"Named primary passages and bounded independent examples only; complete scientific acceptance open."},{"id":"scwiki-d1-claim-experimental-criteria-4","sectionId":"experimental-criteria","statement":"Sakata and colleagues reported Ca-VII near 29 K at 216 GPa. Their selected methods describe room-temperature diffraction and transport; a room-temperature structure measurement does not automatically determine the low-temperature phase. An Andersson comment is part of the source trail, but its contents have not yet been obtained in this review. The reported result remains attributed to its authors, with that reconciliation open.","evidenceType":"experiment","sourceIds":["source-bc42a3144ddb335e","source-c563fd6be7dd9167"],"conditions":"Keep named source, phase, pressure and measurement criteria; abstract-only and inaccessible-comment scopes explicit.","verificationScope":"Named primary passages and bounded independent examples only; complete scientific acceptance open."},{"id":"scwiki-d1-claim-experimental-criteria-5","sectionId":"experimental-criteria","statement":"Iron is another warning against classification by ambient behavior. Shimizu and colleagues reported a resistance drop and Meissner signal below 2 K under 15–30 GPa in the non-magnetic state. This abstract-level evidence does not identify the pairing interaction or justify transferring a simple weak-coupling description from an unrelated element. Magnetic history, structure and purity need their own assessment.","evidenceType":"experiment","sourceIds":["source-7301d50108f9de56"],"conditions":"Keep named source, phase, pressure and measurement criteria; abstract-only and inaccessible-comment scopes explicit.","verificationScope":"Named primary passages and bounded independent examples only; complete scientific acceptance open."},{"id":"scwiki-d1-claim-limits-and-disputes-1","sectionId":"limits-and-disputes","statement":"A finite resistive transition, instrument-limited zero resistance, field suppression, magnetic shielding and a bulk thermodynamic anomaly answer different questions. Compare them on the same sample or explain why samples differ. Report the thermometer, onset/midpoint/zero criterion, pressure calibration, pressure medium, compression path and structural measurement temperature. Missing information stays unknown rather than being inferred from the chemical formula.","evidenceType":"theory","sourceIds":["source-d36e5a81b57e823f","source-cc7115129638a171","source-dc73a11d591aebd0","source-bc42a3144ddb335e"],"conditions":"Probe-specific inference; no unsupported bulk-volume, mechanism or world-record certification.","verificationScope":"Named primary passages and bounded independent examples only; complete scientific acceptance open."},{"id":"scwiki-d1-claim-limits-and-disputes-2","sectionId":"limits-and-disputes","statement":"The September 2026 Sc theory paper connects compression, increasing overlap of 3d orbitals and band broadening to stronger electron–phonon coupling. Its phrase “electronic mechanism” does not mean a demonstrated nonphonon pairing glue. This page has checked the publisher abstract only: no new experimental transition, full calculation or universal elemental record is inferred from that description. Historical “highest” claims must be dated to the publication and its comparison set.","evidenceType":"theory","sourceIds":["source-29962a8944db57fa"],"conditions":"Probe-specific inference; no unsupported bulk-volume, mechanism or world-record certification.","verificationScope":"Named primary passages and bounded independent examples only; complete scientific acceptance open."},{"id":"scwiki-d1-claim-discovery-implications-1","sectionId":"discovery-implications","statement":"Treat an element as a collection of phase-specific test cases. Useful screening combines a dynamically and thermodynamically plausible structure, electron–phonon matrix elements, electronic energy scales and a stated Coulomb treatment, then asks which experimental observable could falsify the prediction. Agreement with one transition temperature does not validate the whole spectral function, numerical convergence or phase assignment. Keep calculated values separate from experimental transition records and preserve negative or incomplete evidence.","evidenceType":"theory","sourceIds":["source-aa8182fe7a3d8d0c","source-0620df96ebbf2a66","source-d56b04dc0b32c796"],"conditions":"Screening logic only; full scientific acceptance remains open.","verificationScope":"Named primary passages and bounded independent examples only; complete scientific acceptance open."}],"corrections":[{"id":"scwiki-d1-correction-1","description":"Separated historical dates, conditional isotope scaling, transition criteria and model estimates; contemporary Sc evidence added without a current-record claim.","sourceId":"source-dc73a11d591aebd0","scope":"Evidence conditions and scope, not a change to pinned source bytes."}],"equationChecks":[{"targetSectionId":"mathematical-assumptions","tex":"\\alpha=-d\\ln T_c/d\\ln M","check":"Three finite-difference mass substitutions against analytic derivative, plus three fixed-mu-star limits."},{"targetSectionId":"mathematical-assumptions","tex":"T_c=(\\omega_{\\log}/1.2)\\exp[-A/D]","check":"Six Sc TableI estimates and input rounding intervals; two exact rounding mismatches explicitly retained."},{"targetSectionId":"mathematical-assumptions","tex":"\\xi=\\sqrt{\\Phi_0/(2\\pi B_{c2})}","check":"SI conversion from extrapolated21.3T gives39.31angstrom; no field fit replicated."}],"materialCases":[{"id":"scwiki-d1-material-1","formula":"Sc","sample":"Wang2023 compressed Sc; maximum reported onset","recordType":"experiment","reportedTemperatureK":37.6,"tcK":37.6,"temperatureKind":"transition","temperatureNote":"Authors report onset at243GPa; magnetic-volume validation not supplied.","criterion":"resistive-onset","pressureRegime":"high","pressureGPa":{"min":243,"max":243},"equilibrium":"unknown","probe":"Four-probe warming resistance; diamond Raman pressure; field/current follow-up","sourceId":"source-dc73a11d591aebd0"},{"id":"scwiki-d1-material-2","formula":"Sc","sample":"Sc-V TableI at260GPa, mu*=.10","recordType":"prediction","reportedTemperatureK":30.1,"tcK":null,"temperatureKind":"transition","temperatureNote":"Printed model estimate; not an experimental transition record.","criterion":"calculated-transition","pressureRegime":"high","pressureGPa":{"min":260,"max":260},"equilibrium":"unknown","probe":"Electron–phonon calculation plus modified McMillan estimate; no DFT reproduction","sourceId":"source-dc73a11d591aebd0"},{"id":"scwiki-d1-material-3","formula":"Li","sample":"Tuoriniemi2007 ambient natural lithium","recordType":"experiment","reportedTemperatureK":0.0004,"tcK":0.0004,"temperatureKind":"transition","temperatureNote":"Abstract-level report of0.4mK; not0.4K; full methods review pending.","criterion":"reported-magnetic-transition","pressureRegime":"ambient","pressureGPa":null,"equilibrium":"unknown","probe":"Meissner-state figure caption and publisher abstract","sourceId":"source-61e8b60fcacfb53b"}],"body":"## Scope\n\nAn elemental superconductor contains one chemical element, but that label does not specify its crystal structure, bands, coupling strength or pressure history. Elemental systems provide useful benchmarks for electron–phonon theory; they do not all reduce to one weak-coupling model. Niobium's approximately 9.2 K transition is a useful conventional scale, not a ceiling on elemental superconductivity or a certified value for every sample. [R5](#ref-source-aa8182fe7a3d8d0c) [R15](#ref-source-835031575efae07a)\n\nThe mercury discovery is associated with Onnes's 1911 report. His later Nobel lecture describes the abrupt resistance decrease near 4.2 K, explicitly qualified by measurement accuracy, and a current threshold above which voltage reappeared. The lecture scan includes subsequent notes and a 1914 addendum; those later observations should not be dated to 1911. It is a firsthand account, not a substitute for a modern magnetic-volume or heat-capacity measurement. [R1](#ref-source-d36e5a81b57e823f)\n\n## Mathematical assumptions\n\nThe isotope coefficient is $\\alpha=-d\\ln T_c/d\\ln M$. If harmonic frequencies scale as $M^{-1/2}$ while the dimensionless pairing parameters remain fixed, the corresponding transition scale has $\\alpha=1/2$. This is a conditional model statement, not a value certified here for the original mercury datasets. Maxwell and Reynolds are retained as the historical experimental sources; their full datasets still require direct review. An isotope substitution may also change structure or anharmonic motion, so a measured coefficient must retain its sample and phase conditions. [R2](#ref-source-eff5a2a1c455e7f6) [R3](#ref-source-e8a489943f13c9f8) [R6](#ref-source-0620df96ebbf2a66)\n\nThe weak-coupling isotropic BCS benchmark is $2\\Delta(0)/(k_BT_c)\\simeq3.53$. Lead is a strong-coupling benchmark, so that number is not a compulsory fit to its tunneling spectrum. Retardation makes the gap energy dependent; a full gap alone does not establish its sign structure or the microscopic pairing interaction. [R16](#ref-source-d56b04dc0b32c796) [R17](#ref-source-ba10e800a1246bf6)\n\nFor an illustrative McMillan-type estimate, write $T_c=(\\omega_{\\log}/1.2)\\exp[-A/D]$, with $A=1.04(1+\\lambda)$ and $D=\\lambda-\\mu^*(1+0.62\\lambda)>0$, taking $\\omega_{\\log}$ in kelvin. If $\\mu^*=\\mu/[1+\\mu\\ln(E_{\\mathrm{el}}/\\omega_{\\log})]$, with the two cutoff scales in the same units, fixed $\\lambda,\\mu,E_{\\mathrm{el}}$ give $\\alpha=\\tfrac12[1-A(1+0.62\\lambda)(\\mu^*)^2/D^2]$. Three finite-difference mass substitutions independently confirm this derivative and its difference from the fixed-$\\mu^*$ limit. These examples are not mercury fits. The estimate omits the full Allen–Dynes shape factors and is not a universal upper bound. [R5](#ref-source-aa8182fe7a3d8d0c) [R6](#ref-source-0620df96ebbf2a66) [R16](#ref-source-d56b04dc0b32c796)\n\nIn the Sc paper's Table I, six printed estimates are consistent with the input rounding intervals. Sc-IV printed inputs yield 21.37/18.72 K, versus listed 21.5/18.8 K; exact reproduction needs unrounded inputs. Sc-V at 260 GPa gives 30.07/26.38 K for $\\mu^*=0.10/0.13$. These are calculations, not the measured 37.6 K onset at a different pressure. The reported extrapolated $B_{c2}(0)=21.3$ T implies $\\xi=\\sqrt{\\Phi_0/(2\\pi B_{c2})}=39.31$ angstrom; this checks units, not the extrapolation model. [R10](#ref-source-dc73a11d591aebd0)\n\n## Experimental criteria\n\nTunneling conductance needs an appropriate normal reference. Rowell's 1970 account requires tunneling-dominated current and a barrier that stays effectively unchanged across the superconducting transition. Record how the normal reference was obtained, including its temperature and field; division alone does not remove a changed barrier or an unrelated parallel current. Oxide and interface excitations need not be electrode density-of-states features. The 1965 McMillan–Rowell paper is retained as the historical lead inversion reference; its original quantitative inversion has not been rerun here. The coupling-weighted spectrum $\\alpha^2F$ is inferred using an Eliashberg model, not read directly from conductance or identified with the bare phonon density of states.\n\nFor a local illustration of thermal convolution, assume weak elastic superconductor–insulator–normal-metal (SIN) tunneling, flat normal-electrode and normal-reference densities, a constant tunneling matrix element, and a sample spectrum unchanged by bias. At a common electron temperature, $G(V)/G_N=\\int_{-\\infty}^{\\infty}n_s(E)[-f'(E-eV)]\\,dE$, where $n_s$ is the dimensionless sample density and $f$ the Fermi function. The kernel is $[4k_BT\\cosh^2((E-eV)/(2k_BT))]^{-1}$. Finite temperature averages the spectrum; it does not return $n_s(eV)$ point by point. A hard-gap toy density, zero for $|E|<\\Delta$ and one outside, gives $G(0)/G_N=2/[1+\\exp(\\Delta/k_BT)]>0$ despite zero density at zero energy. Nine current-derivative checks, three hard-gap checks and a changed-transmission control verify this local example. It omits coherence peaks and intrinsic temperature dependence. A superconducting counterelectrode, a bias-dependent barrier, momentum-selective tunneling or extra broadening requires the corresponding response model. These checks neither invert an experimental spectrum nor determine a material's pairing mechanism. [R4](#ref-source-b66885f8fdc58181) [R7](#ref-source-27b24b231ced1ec3) [R16](#ref-source-d56b04dc0b32c796)\n\nLithium illustrates why conditions cannot be dropped from a material label. Shimizu and colleagues reported compressed Li reaching about 20 K at 48 GPa in 2002; Tuoriniemi and colleagues reported an ambient-pressure transition around 0.4 mK in 2007, with a Meissner-state figure. The latter is 0.0004 K, not 0.4 K. These source checks cover abstracts and selected captions; they do not establish an entire phase diagram or independently validate the underlying data. [R8](#ref-source-cc7115129638a171) [R9](#ref-source-61e8b60fcacfb53b)\n\nWang and colleagues reported Sc onset at 37.6 K and 243 GPa, distinct from the plotted 37.3 K at 244 GPa. Four-probe warming measurements used diamond Raman pressure calibration; onset means departure from the normal-state line. Field/current suppression supports the transport assignment, but no Meissner measurement was supplied. Phase boundaries were inferred from transition trends and compared with earlier diffraction. Applied fields reached 9 T; 21.3 T is an extrapolation. [R10](#ref-source-dc73a11d591aebd0)\n\nSakata and colleagues reported Ca-VII near 29 K at 216 GPa. Their selected methods describe room-temperature diffraction and transport; a room-temperature structure measurement does not automatically determine the low-temperature phase. An Andersson comment is part of the source trail, but its contents have not yet been obtained in this review. The reported result remains attributed to its authors, with that reconciliation open. [R11](#ref-source-bc42a3144ddb335e) [R12](#ref-source-c563fd6be7dd9167)\n\nIron is another warning against classification by ambient behavior. Shimizu and colleagues reported a resistance drop and Meissner signal below 2 K under 15–30 GPa in the non-magnetic state. This abstract-level evidence does not identify the pairing interaction or justify transferring a simple weak-coupling description from an unrelated element. Magnetic history, structure and purity need their own assessment. [R13](#ref-source-7301d50108f9de56)\n\n## Limits and disputes\n\nA finite resistive transition, instrument-limited zero resistance, field suppression, magnetic shielding and a bulk thermodynamic anomaly answer different questions. Compare them on the same sample or explain why samples differ. Report the thermometer, onset/midpoint/zero criterion, pressure calibration, pressure medium, compression path and structural measurement temperature. Missing information stays unknown rather than being inferred from the chemical formula. [R1](#ref-source-d36e5a81b57e823f) [R8](#ref-source-cc7115129638a171) [R10](#ref-source-dc73a11d591aebd0) [R11](#ref-source-bc42a3144ddb335e)\n\nThe September 2026 Sc theory paper connects compression, increasing overlap of 3d orbitals and band broadening to stronger electron–phonon coupling. Its phrase “electronic mechanism” does not mean a demonstrated nonphonon pairing glue. This page has checked the publisher abstract only: no new experimental transition, full calculation or universal elemental record is inferred from that description. Historical “highest” claims must be dated to the publication and its comparison set. [R14](#ref-source-29962a8944db57fa)\n\n## Discovery implications\n\nTreat an element as a collection of phase-specific test cases. Useful screening combines a dynamically and thermodynamically plausible structure, electron–phonon matrix elements, electronic energy scales and a stated Coulomb treatment, then asks which experimental observable could falsify the prediction. Agreement with one transition temperature does not validate the whole spectral function, numerical convergence or phase assignment. Keep calculated values separate from experimental transition records and preserve negative or incomplete evidence. [R5](#ref-source-aa8182fe7a3d8d0c) [R6](#ref-source-0620df96ebbf2a66) [R16](#ref-source-d56b04dc0b32c796)\n\n## Related topics\n\nContinue with [isotope effects](/scwiki/isotope-effect), [BCS theory](/scwiki/bcs-weak-coupling), [Eliashberg theory](/scwiki/eliashberg-strong-coupling), [superconducting gaps](/scwiki/superconducting-gap) and [critical fields](/scwiki/critical-fields).","revision":"82aea111e522f015b7f7","sections":[{"id":"scope","title":"Scope","markdown":"## Scope\n\nAn elemental superconductor contains one chemical element, but that label does not specify its crystal structure, bands, coupling strength or pressure history. Elemental systems provide useful benchmarks for electron–phonon theory; they do not all reduce to one weak-coupling model. Niobium's approximately 9.2 K transition is a useful conventional scale, not a ceiling on elemental superconductivity or a certified value for every sample. [R5](#ref-source-aa8182fe7a3d8d0c) [R15](#ref-source-835031575efae07a)\n\nThe mercury discovery is associated with Onnes's 1911 report. His later Nobel lecture describes the abrupt resistance decrease near 4.2 K, explicitly qualified by measurement accuracy, and a current threshold above which voltage reappeared. The lecture scan includes subsequent notes and a 1914 addendum; those later observations should not be dated to 1911. It is a firsthand account, not a substitute for a modern magnetic-volume or heat-capacity measurement. [R1](#ref-source-d36e5a81b57e823f)"},{"id":"mathematical-assumptions","title":"Mathematical assumptions","markdown":"## Mathematical assumptions\n\nThe isotope coefficient is $\\alpha=-d\\ln T_c/d\\ln M$. If harmonic frequencies scale as $M^{-1/2}$ while the dimensionless pairing parameters remain fixed, the corresponding transition scale has $\\alpha=1/2$. This is a conditional model statement, not a value certified here for the original mercury datasets. Maxwell and Reynolds are retained as the historical experimental sources; their full datasets still require direct review. An isotope substitution may also change structure or anharmonic motion, so a measured coefficient must retain its sample and phase conditions. [R2](#ref-source-eff5a2a1c455e7f6) [R3](#ref-source-e8a489943f13c9f8) [R6](#ref-source-0620df96ebbf2a66)\n\nThe weak-coupling isotropic BCS benchmark is $2\\Delta(0)/(k_BT_c)\\simeq3.53$. Lead is a strong-coupling benchmark, so that number is not a compulsory fit to its tunneling spectrum. Retardation makes the gap energy dependent; a full gap alone does not establish its sign structure or the microscopic pairing interaction. [R16](#ref-source-d56b04dc0b32c796) [R17](#ref-source-ba10e800a1246bf6)\n\nFor an illustrative McMillan-type estimate, write $T_c=(\\omega_{\\log}/1.2)\\exp[-A/D]$, with $A=1.04(1+\\lambda)$ and $D=\\lambda-\\mu^*(1+0.62\\lambda)>0$, taking $\\omega_{\\log}$ in kelvin. If $\\mu^*=\\mu/[1+\\mu\\ln(E_{\\mathrm{el}}/\\omega_{\\log})]$, with the two cutoff scales in the same units, fixed $\\lambda,\\mu,E_{\\mathrm{el}}$ give $\\alpha=\\tfrac12[1-A(1+0.62\\lambda)(\\mu^*)^2/D^2]$. Three finite-difference mass substitutions independently confirm this derivative and its difference from the fixed-$\\mu^*$ limit. These examples are not mercury fits. The estimate omits the full Allen–Dynes shape factors and is not a universal upper bound. [R5](#ref-source-aa8182fe7a3d8d0c) [R6](#ref-source-0620df96ebbf2a66) [R16](#ref-source-d56b04dc0b32c796)\n\nIn the Sc paper's Table I, six printed estimates are consistent with the input rounding intervals. Sc-IV printed inputs yield 21.37/18.72 K, versus listed 21.5/18.8 K; exact reproduction needs unrounded inputs. Sc-V at 260 GPa gives 30.07/26.38 K for $\\mu^*=0.10/0.13$. These are calculations, not the measured 37.6 K onset at a different pressure. The reported extrapolated $B_{c2}(0)=21.3$ T implies $\\xi=\\sqrt{\\Phi_0/(2\\pi B_{c2})}=39.31$ angstrom; this checks units, not the extrapolation model. [R10](#ref-source-dc73a11d591aebd0)"},{"id":"experimental-criteria","title":"Experimental criteria","markdown":"## Experimental criteria\n\nTunneling conductance needs an appropriate normal reference. Rowell's 1970 account requires tunneling-dominated current and a barrier that stays effectively unchanged across the superconducting transition. Record how the normal reference was obtained, including its temperature and field; division alone does not remove a changed barrier or an unrelated parallel current. Oxide and interface excitations need not be electrode density-of-states features. The 1965 McMillan–Rowell paper is retained as the historical lead inversion reference; its original quantitative inversion has not been rerun here. The coupling-weighted spectrum $\\alpha^2F$ is inferred using an Eliashberg model, not read directly from conductance or identified with the bare phonon density of states.\n\nFor a local illustration of thermal convolution, assume weak elastic superconductor–insulator–normal-metal (SIN) tunneling, flat normal-electrode and normal-reference densities, a constant tunneling matrix element, and a sample spectrum unchanged by bias. At a common electron temperature, $G(V)/G_N=\\int_{-\\infty}^{\\infty}n_s(E)[-f'(E-eV)]\\,dE$, where $n_s$ is the dimensionless sample density and $f$ the Fermi function. The kernel is $[4k_BT\\cosh^2((E-eV)/(2k_BT))]^{-1}$. Finite temperature averages the spectrum; it does not return $n_s(eV)$ point by point. A hard-gap toy density, zero for $|E|<\\Delta$ and one outside, gives $G(0)/G_N=2/[1+\\exp(\\Delta/k_BT)]>0$ despite zero density at zero energy. Nine current-derivative checks, three hard-gap checks and a changed-transmission control verify this local example. It omits coherence peaks and intrinsic temperature dependence. A superconducting counterelectrode, a bias-dependent barrier, momentum-selective tunneling or extra broadening requires the corresponding response model. These checks neither invert an experimental spectrum nor determine a material's pairing mechanism. [R4](#ref-source-b66885f8fdc58181) [R7](#ref-source-27b24b231ced1ec3) [R16](#ref-source-d56b04dc0b32c796)\n\nLithium illustrates why conditions cannot be dropped from a material label. Shimizu and colleagues reported compressed Li reaching about 20 K at 48 GPa in 2002; Tuoriniemi and colleagues reported an ambient-pressure transition around 0.4 mK in 2007, with a Meissner-state figure. The latter is 0.0004 K, not 0.4 K. These source checks cover abstracts and selected captions; they do not establish an entire phase diagram or independently validate the underlying data. [R8](#ref-source-cc7115129638a171) [R9](#ref-source-61e8b60fcacfb53b)\n\nWang and colleagues reported Sc onset at 37.6 K and 243 GPa, distinct from the plotted 37.3 K at 244 GPa. Four-probe warming measurements used diamond Raman pressure calibration; onset means departure from the normal-state line. Field/current suppression supports the transport assignment, but no Meissner measurement was supplied. Phase boundaries were inferred from transition trends and compared with earlier diffraction. Applied fields reached 9 T; 21.3 T is an extrapolation. [R10](#ref-source-dc73a11d591aebd0)\n\nSakata and colleagues reported Ca-VII near 29 K at 216 GPa. Their selected methods describe room-temperature diffraction and transport; a room-temperature structure measurement does not automatically determine the low-temperature phase. An Andersson comment is part of the source trail, but its contents have not yet been obtained in this review. The reported result remains attributed to its authors, with that reconciliation open. [R11](#ref-source-bc42a3144ddb335e) [R12](#ref-source-c563fd6be7dd9167)\n\nIron is another warning against classification by ambient behavior. Shimizu and colleagues reported a resistance drop and Meissner signal below 2 K under 15–30 GPa in the non-magnetic state. This abstract-level evidence does not identify the pairing interaction or justify transferring a simple weak-coupling description from an unrelated element. Magnetic history, structure and purity need their own assessment. [R13](#ref-source-7301d50108f9de56)"},{"id":"limits-and-disputes","title":"Limits and disputes","markdown":"## Limits and disputes\n\nA finite resistive transition, instrument-limited zero resistance, field suppression, magnetic shielding and a bulk thermodynamic anomaly answer different questions. Compare them on the same sample or explain why samples differ. Report the thermometer, onset/midpoint/zero criterion, pressure calibration, pressure medium, compression path and structural measurement temperature. Missing information stays unknown rather than being inferred from the chemical formula. [R1](#ref-source-d36e5a81b57e823f) [R8](#ref-source-cc7115129638a171) [R10](#ref-source-dc73a11d591aebd0) [R11](#ref-source-bc42a3144ddb335e)\n\nThe September 2026 Sc theory paper connects compression, increasing overlap of 3d orbitals and band broadening to stronger electron–phonon coupling. Its phrase “electronic mechanism” does not mean a demonstrated nonphonon pairing glue. This page has checked the publisher abstract only: no new experimental transition, full calculation or universal elemental record is inferred from that description. Historical “highest” claims must be dated to the publication and its comparison set. [R14](#ref-source-29962a8944db57fa)"},{"id":"discovery-implications","title":"Discovery implications","markdown":"## Discovery implications\n\nTreat an element as a collection of phase-specific test cases. Useful screening combines a dynamically and thermodynamically plausible structure, electron–phonon matrix elements, electronic energy scales and a stated Coulomb treatment, then asks which experimental observable could falsify the prediction. Agreement with one transition temperature does not validate the whole spectral function, numerical convergence or phase assignment. Keep calculated values separate from experimental transition records and preserve negative or incomplete evidence. [R5](#ref-source-aa8182fe7a3d8d0c) [R6](#ref-source-0620df96ebbf2a66) [R16](#ref-source-d56b04dc0b32c796)"},{"id":"related-topics","title":"Related topics","markdown":"## Related topics\n\nContinue with [isotope effects](/scwiki/isotope-effect), [BCS theory](/scwiki/bcs-weak-coupling), [Eliashberg theory](/scwiki/eliashberg-strong-coupling), [superconducting gaps](/scwiki/superconducting-gap) and [critical fields](/scwiki/critical-fields)."},{"id":"material-cases","title":"Material cases","markdown":"## Material cases\n\nValues describe individual reports, not a ranking. Unknown means the checked source did not supply the field at this review scope.\n\n| Material and sample | Reported temperature | Criterion | Probe | Pressure | State | Evidence |\n|---|---|---|---|---|---|---|\n| Sc; Wang2023 compressed Sc; maximum reported onset | 37.6 K; Authors report onset at243GPa; magnetic-volume validation not supplied. | transition; resistive-onset | Four-probe warming resistance; diamond Raman pressure; field/current follow-up | high; 243 to 243 GPa | unknown | experiment; [source](#ref-source-dc73a11d591aebd0) |\n| Sc; Sc-V TableI at260GPa, mu*=.10 | 30.1 K; Printed model estimate; not an experimental transition record. | transition; calculated-transition | Electron–phonon calculation plus modified McMillan estimate; no DFT reproduction | high; 260 to 260 GPa | unknown | prediction; [source](#ref-source-dc73a11d591aebd0) |\n| Li; Tuoriniemi2007 ambient natural lithium | 0.0004 K; Abstract-level report of0.4mK; not0.4K; full methods review pending. | transition; reported-magnetic-transition | Meissner-state figure caption and publisher abstract | ambient; unknown GPa | unknown | experiment; [source](#ref-source-61e8b60fcacfb53b) |"}],"markdown":"# Elemental superconductors: benchmarks, phases and pressure\n\nCompare elemental systems without confusing chemical identity, crystal phase, measured transitions and theoretical estimates.\n\n## Scope\n\nAn elemental superconductor contains one chemical element, but that label does not specify its crystal structure, bands, coupling strength or pressure history. Elemental systems provide useful benchmarks for electron–phonon theory; they do not all reduce to one weak-coupling model. Niobium's approximately 9.2 K transition is a useful conventional scale, not a ceiling on elemental superconductivity or a certified value for every sample. [R5](#ref-source-aa8182fe7a3d8d0c) [R15](#ref-source-835031575efae07a)\n\nThe mercury discovery is associated with Onnes's 1911 report. His later Nobel lecture describes the abrupt resistance decrease near 4.2 K, explicitly qualified by measurement accuracy, and a current threshold above which voltage reappeared. The lecture scan includes subsequent notes and a 1914 addendum; those later observations should not be dated to 1911. It is a firsthand account, not a substitute for a modern magnetic-volume or heat-capacity measurement. [R1](#ref-source-d36e5a81b57e823f)\n\n## Mathematical assumptions\n\nThe isotope coefficient is $\\alpha=-d\\ln T_c/d\\ln M$. If harmonic frequencies scale as $M^{-1/2}$ while the dimensionless pairing parameters remain fixed, the corresponding transition scale has $\\alpha=1/2$. This is a conditional model statement, not a value certified here for the original mercury datasets. Maxwell and Reynolds are retained as the historical experimental sources; their full datasets still require direct review. An isotope substitution may also change structure or anharmonic motion, so a measured coefficient must retain its sample and phase conditions. [R2](#ref-source-eff5a2a1c455e7f6) [R3](#ref-source-e8a489943f13c9f8) [R6](#ref-source-0620df96ebbf2a66)\n\nThe weak-coupling isotropic BCS benchmark is $2\\Delta(0)/(k_BT_c)\\simeq3.53$. Lead is a strong-coupling benchmark, so that number is not a compulsory fit to its tunneling spectrum. Retardation makes the gap energy dependent; a full gap alone does not establish its sign structure or the microscopic pairing interaction. [R16](#ref-source-d56b04dc0b32c796) [R17](#ref-source-ba10e800a1246bf6)\n\nFor an illustrative McMillan-type estimate, write $T_c=(\\omega_{\\log}/1.2)\\exp[-A/D]$, with $A=1.04(1+\\lambda)$ and $D=\\lambda-\\mu^*(1+0.62\\lambda)>0$, taking $\\omega_{\\log}$ in kelvin. If $\\mu^*=\\mu/[1+\\mu\\ln(E_{\\mathrm{el}}/\\omega_{\\log})]$, with the two cutoff scales in the same units, fixed $\\lambda,\\mu,E_{\\mathrm{el}}$ give $\\alpha=\\tfrac12[1-A(1+0.62\\lambda)(\\mu^*)^2/D^2]$. Three finite-difference mass substitutions independently confirm this derivative and its difference from the fixed-$\\mu^*$ limit. These examples are not mercury fits. The estimate omits the full Allen–Dynes shape factors and is not a universal upper bound. [R5](#ref-source-aa8182fe7a3d8d0c) [R6](#ref-source-0620df96ebbf2a66) [R16](#ref-source-d56b04dc0b32c796)\n\nIn the Sc paper's Table I, six printed estimates are consistent with the input rounding intervals. Sc-IV printed inputs yield 21.37/18.72 K, versus listed 21.5/18.8 K; exact reproduction needs unrounded inputs. Sc-V at 260 GPa gives 30.07/26.38 K for $\\mu^*=0.10/0.13$. These are calculations, not the measured 37.6 K onset at a different pressure. The reported extrapolated $B_{c2}(0)=21.3$ T implies $\\xi=\\sqrt{\\Phi_0/(2\\pi B_{c2})}=39.31$ angstrom; this checks units, not the extrapolation model. [R10](#ref-source-dc73a11d591aebd0)\n\n## Experimental criteria\n\nTunneling conductance needs an appropriate normal reference. Rowell's 1970 account requires tunneling-dominated current and a barrier that stays effectively unchanged across the superconducting transition. Record how the normal reference was obtained, including its temperature and field; division alone does not remove a changed barrier or an unrelated parallel current. Oxide and interface excitations need not be electrode density-of-states features. The 1965 McMillan–Rowell paper is retained as the historical lead inversion reference; its original quantitative inversion has not been rerun here. The coupling-weighted spectrum $\\alpha^2F$ is inferred using an Eliashberg model, not read directly from conductance or identified with the bare phonon density of states.\n\nFor a local illustration of thermal convolution, assume weak elastic superconductor–insulator–normal-metal (SIN) tunneling, flat normal-electrode and normal-reference densities, a constant tunneling matrix element, and a sample spectrum unchanged by bias. At a common electron temperature, $G(V)/G_N=\\int_{-\\infty}^{\\infty}n_s(E)[-f'(E-eV)]\\,dE$, where $n_s$ is the dimensionless sample density and $f$ the Fermi function. The kernel is $[4k_BT\\cosh^2((E-eV)/(2k_BT))]^{-1}$. Finite temperature averages the spectrum; it does not return $n_s(eV)$ point by point. A hard-gap toy density, zero for $|E|<\\Delta$ and one outside, gives $G(0)/G_N=2/[1+\\exp(\\Delta/k_BT)]>0$ despite zero density at zero energy. Nine current-derivative checks, three hard-gap checks and a changed-transmission control verify this local example. It omits coherence peaks and intrinsic temperature dependence. A superconducting counterelectrode, a bias-dependent barrier, momentum-selective tunneling or extra broadening requires the corresponding response model. These checks neither invert an experimental spectrum nor determine a material's pairing mechanism. [R4](#ref-source-b66885f8fdc58181) [R7](#ref-source-27b24b231ced1ec3) [R16](#ref-source-d56b04dc0b32c796)\n\nLithium illustrates why conditions cannot be dropped from a material label. Shimizu and colleagues reported compressed Li reaching about 20 K at 48 GPa in 2002; Tuoriniemi and colleagues reported an ambient-pressure transition around 0.4 mK in 2007, with a Meissner-state figure. The latter is 0.0004 K, not 0.4 K. These source checks cover abstracts and selected captions; they do not establish an entire phase diagram or independently validate the underlying data. [R8](#ref-source-cc7115129638a171) [R9](#ref-source-61e8b60fcacfb53b)\n\nWang and colleagues reported Sc onset at 37.6 K and 243 GPa, distinct from the plotted 37.3 K at 244 GPa. Four-probe warming measurements used diamond Raman pressure calibration; onset means departure from the normal-state line. Field/current suppression supports the transport assignment, but no Meissner measurement was supplied. Phase boundaries were inferred from transition trends and compared with earlier diffraction. Applied fields reached 9 T; 21.3 T is an extrapolation. [R10](#ref-source-dc73a11d591aebd0)\n\nSakata and colleagues reported Ca-VII near 29 K at 216 GPa. Their selected methods describe room-temperature diffraction and transport; a room-temperature structure measurement does not automatically determine the low-temperature phase. An Andersson comment is part of the source trail, but its contents have not yet been obtained in this review. The reported result remains attributed to its authors, with that reconciliation open. [R11](#ref-source-bc42a3144ddb335e) [R12](#ref-source-c563fd6be7dd9167)\n\nIron is another warning against classification by ambient behavior. Shimizu and colleagues reported a resistance drop and Meissner signal below 2 K under 15–30 GPa in the non-magnetic state. This abstract-level evidence does not identify the pairing interaction or justify transferring a simple weak-coupling description from an unrelated element. Magnetic history, structure and purity need their own assessment. [R13](#ref-source-7301d50108f9de56)\n\n## Limits and disputes\n\nA finite resistive transition, instrument-limited zero resistance, field suppression, magnetic shielding and a bulk thermodynamic anomaly answer different questions. Compare them on the same sample or explain why samples differ. Report the thermometer, onset/midpoint/zero criterion, pressure calibration, pressure medium, compression path and structural measurement temperature. Missing information stays unknown rather than being inferred from the chemical formula. [R1](#ref-source-d36e5a81b57e823f) [R8](#ref-source-cc7115129638a171) [R10](#ref-source-dc73a11d591aebd0) [R11](#ref-source-bc42a3144ddb335e)\n\nThe September 2026 Sc theory paper connects compression, increasing overlap of 3d orbitals and band broadening to stronger electron–phonon coupling. Its phrase “electronic mechanism” does not mean a demonstrated nonphonon pairing glue. This page has checked the publisher abstract only: no new experimental transition, full calculation or universal elemental record is inferred from that description. Historical “highest” claims must be dated to the publication and its comparison set. [R14](#ref-source-29962a8944db57fa)\n\n## Discovery implications\n\nTreat an element as a collection of phase-specific test cases. Useful screening combines a dynamically and thermodynamically plausible structure, electron–phonon matrix elements, electronic energy scales and a stated Coulomb treatment, then asks which experimental observable could falsify the prediction. Agreement with one transition temperature does not validate the whole spectral function, numerical convergence or phase assignment. Keep calculated values separate from experimental transition records and preserve negative or incomplete evidence. [R5](#ref-source-aa8182fe7a3d8d0c) [R6](#ref-source-0620df96ebbf2a66) [R16](#ref-source-d56b04dc0b32c796)\n\n## Related topics\n\nContinue with [isotope effects](/scwiki/isotope-effect), [BCS theory](/scwiki/bcs-weak-coupling), [Eliashberg theory](/scwiki/eliashberg-strong-coupling), [superconducting gaps](/scwiki/superconducting-gap) and [critical fields](/scwiki/critical-fields).\n\n## Material cases\n\nValues describe individual reports, not a ranking. Unknown means the checked source did not supply the field at this review scope.\n\n| Material and sample | Reported temperature | Criterion | Probe | Pressure | State | Evidence |\n|---|---|---|---|---|---|---|\n| Sc; Wang2023 compressed Sc; maximum reported onset | 37.6 K; Authors report onset at243GPa; magnetic-volume validation not supplied. | transition; resistive-onset | Four-probe warming resistance; diamond Raman pressure; field/current follow-up | high; 243 to 243 GPa | unknown | experiment; [source](#ref-source-dc73a11d591aebd0) |\n| Sc; Sc-V TableI at260GPa, mu*=.10 | 30.1 K; Printed model estimate; not an experimental transition record. | transition; calculated-transition | Electron–phonon calculation plus modified McMillan estimate; no DFT reproduction | high; 260 to 260 GPa | unknown | prediction; [source](#ref-source-dc73a11d591aebd0) |\n| Li; Tuoriniemi2007 ambient natural lithium | 0.0004 K; Abstract-level report of0.4mK; not0.4K; full methods review pending. | transition; reported-magnetic-transition | Meissner-state figure caption and publisher abstract | ambient; unknown GPa | unknown | experiment; [source](#ref-source-61e8b60fcacfb53b) |\n\n## Sources\n\n### Ref source-d36e5a81b57e823f\n\n[R1] Investigations into the properties of substances at low temperatures (Nobel lecture, 11 December 1913; later notes included) (1913). [Source publication](https://www.nevis.columbia.edu/~haas/documents/physics_nobel_lectures/physics01-21-2.pdf). Publication: technical-report. Check: selected-primary-lecture-scan-check. Checked: 2026-10-18. Selected printed pp.330–336 (PDF pp.76–82), mercury apparatus/resolution and current threshold. PDF pp.79–80 visually checked. Later 1914 addendum distinguished; original 1911 communication scan remains unavailable.\n### Ref source-eff5a2a1c455e7f6\n\n[R2] Isotope Effect in the Superconductivity of Mercury (1950). [DOI 10.1103/PhysRev.78.477](https://doi.org/10.1103/PhysRev.78.477). Publication: journal-article. Check: publisher-metadata-only. Checked: 2026-10-18. Title, author and publication date checked. Original full text unavailable at attempted endpoint; no mercury isotope exponent or dataset certified.\n### Ref source-e8a489943f13c9f8\n\n[R3] Superconductivity of Isotopes of Mercury (1950). [DOI 10.1103/PhysRev.78.487](https://doi.org/10.1103/PhysRev.78.487). Publication: journal-article. Check: publisher-metadata-only. Checked: 2026-10-18. Title, authors and publication date checked. Original full text unavailable at attempted endpoint; no mercury isotope exponent or dataset certified.\n### Ref source-b66885f8fdc58181\n\n[R4] Lead Phonon Spectrum Calculated from Superconducting Density of States (1965). [DOI 10.1103/PhysRevLett.14.108](https://doi.org/10.1103/PhysRevLett.14.108). Publication: journal-article. Check: publisher-metadata-only. Checked: 2026-10-19. Publisher title, DOI and25January1965 date rechecked. Content requires subscription; original spectrum/inversion not obtained or reproduced.\n### Ref source-aa8182fe7a3d8d0c\n\n[R5] Transition Temperature of Strong-Coupled Superconductors (1968). [DOI 10.1103/PhysRev.167.331](https://doi.org/10.1103/PhysRev.167.331). Publication: journal-article. Check: primary-abstract-scoped-check. Checked: 2026-10-18. Publisher abstract: strong-coupling calculations and empirical parameters. Full original formula fit and dataset not reviewed.\n### Ref source-0620df96ebbf2a66\n\n[R6] Transition temperature of strong-coupled superconductors reanalyzed (1975). [DOI 10.1103/PhysRevB.12.905](https://doi.org/10.1103/PhysRevB.12.905). Publication: journal-article. Check: primary-abstract-scoped-check. Checked: 2026-10-18. Publisher abstract: modified prefactor, spectral moment/shape corrections and large-coupling limits within Eliashberg theory. Full derivation and Pb-Bi data not reanalyzed.\n### Ref source-27b24b231ced1ec3\n\n[R7] Tunneling Measurements of Superconducting Quasi-Particle Density of States and Calculation of Phonon Spectra (1970). [DOI 10.6028/jres.074A.046](https://doi.org/10.6028/jres.074A.046). Publication: journal-article. Check: selected-published-text-check. Checked: 2026-10-19. Re-read published pp.560-561 barrier/current discussion and p.565 section5 plus oxide-excitation warning. Publication July-August1970 differs from1969 receipt. Text-only this round. Normal-reference requirements do not constitute a modern finite-temperature response fit; added SIN convolution is local.\n### Ref source-cc7115129638a171\n\n[R8] Superconductivity in compressed lithium at 20 K (2002). [DOI 10.1038/nature01098](https://doi.org/10.1038/nature01098). Publication: journal-article. Check: publisher-abstract-and-caption-check. Checked: 2026-10-18. Published10 October2002. Selected abstract/figure captions only; full phase/probe/raw data review open.\n### Ref source-61e8b60fcacfb53b\n\n[R9] Superconductivity in lithium below 0.4 millikelvin at ambient pressure (2007). [DOI 10.1038/nature05820](https://doi.org/10.1038/nature05820). Publication: journal-article. Check: publisher-indexed-abstract-and-caption-check. Checked: 2026-10-18. Published10 May2007; indexed abstract and Meissner figure caption checked. Direct page retrieval later redirected to sign-in; full methods not reviewed. 0.4mK=.0004K.\n### Ref source-dc73a11d591aebd0\n\n[R10] Superconductivity up to 37.6 K in compressed scandium (2023). [DOI 10.1103/PhysRevResearch.5.043248](https://doi.org/10.1103/PhysRevResearch.5.043248). Publication: journal-article. Check: selected-published-text-and-table-check. Checked: 2026-10-18. Published15 December2023. Selected pp.1–4 and TableI; pp.2/4 visually checked. Six formula estimates checked with input-rounding bounds; no raw-data, DFT or full supplement reproduction.\n### Ref source-bc42a3144ddb335e\n\n[R11] Superconducting state of Ca-VII below a critical temperature of 29 K at a pressure of 216 GPa (2011). [DOI 10.1103/PhysRevB.83.220512](https://doi.org/10.1103/PhysRevB.83.220512). Publication: journal-article. Check: publisher-abstract-and-selected-methods-check. Checked: 2026-10-18. Published22 June2011. Abstract and selected first-page methods via web text. Full comment10.1103/PhysRevB.84.216501 reconciliation remains open; no independent curve analysis.\n### Ref source-c563fd6be7dd9167\n\n[R12] Comment on “Superconducting state of Ca-VII below a critical temperature of 29 K at a pressure of 216 GPa” (2011). [DOI 10.1103/PhysRevB.84.216501](https://doi.org/10.1103/PhysRevB.84.216501). Publication: journal-article. Check: crossref-registration-metadata-only. Checked: 2026-10-18. Crossref primary registration confirms M. Andersson and 6 December 2011 publication. Full comment unavailable; its argument and reconciliation remain unreviewed.\n### Ref source-7301d50108f9de56\n\n[R13] Superconductivity in the non-magnetic state of iron under pressure (2001). [DOI 10.1038/35085536](https://doi.org/10.1038/35085536). Publication: journal-article. Check: primary-abstract-via-PubMed. Checked: 2026-10-18. Published19 July2001. Abstract only: resistance and Meissner report below2K under15–30GPa. Full methods and pairing analysis not reviewed.\n### Ref source-29962a8944db57fa\n\n[R14] Electronic mechanism of pressure-enhanced superconductivity in scandium (2026). [DOI 10.1103/v5j2-9bv6](https://doi.org/10.1103/v5j2-9bv6). Publication: journal-article. Check: publisher-abstract-check. Checked: 2026-10-18. Published8 September2026, distinct from issue1 September. Band broadening and overlap linked to electron–phonon coupling; full text subscription required, no calculation reproduced.\n### Ref source-835031575efae07a\n\n[R15] Field, frequency, and temperature dependencies of the surface resistance of nitrogen diffused niobium superconducting radio frequency cavities (2024). [DOI 10.1103/PhysRevAccelBeams.27.062001](https://doi.org/10.1103/PhysRevAccelBeams.27.062001). Publication: journal-article. Check: selected-published-background-methods-check. Checked: 2026-10-18. Published12 June2024. Selected pp.1–2: high-purity Nb cavity surface treatments and approximate9.25K cooldown reference. Used only as contextual Nb scale, not pristine-element dataset or acceptance of all cavity models.\n### Ref source-d56b04dc0b32c796\n\n[R16] Eliashberg Theory: a short review (2020). [DOI 10.1016/j.aop.2020.168102](https://doi.org/10.1016/j.aop.2020.168102). Publication: journal-article. Check: author-review-scoped-check. Checked: 2026-10-19. Follow-up author v1 text: PDFp.3 coupling-frequency dependence and PDFp.5 subsection A inversion discussion/Eq.21; current is measured and alpha2F inferred using Eliashberg equations. Prior selected model benchmark check retained; no full final-version comparison or original lead inversion rerun.\n### Ref source-ba10e800a1246bf6\n\n[R17] 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.\n\n## Claim evidence and conditions\n\n### scwiki-d1-claim-scope-1\n\nAn elemental superconductor contains one chemical element, but that label does not specify its crystal structure, bands, coupling strength or pressure history. Elemental systems provide useful benchmarks for electron–phonon theory; they do not all reduce to one weak-coupling model. Niobium's approximately 9.2 K transition is a useful conventional scale, not a ceiling on elemental superconductivity or a certified value for every sample.\n\nEvidence: theory. Sources: source-aa8182fe7a3d8d0c, source-835031575efae07a.\n\nConditions: Element, phase and sample conditions; historical lecture dates separated.\n\nVerification scope: Named primary passages and bounded independent examples only; complete scientific acceptance open.\n\n### scwiki-d1-claim-scope-2\n\nThe mercury discovery is associated with Onnes's 1911 report. His later Nobel lecture describes the abrupt resistance decrease near 4.2 K, explicitly qualified by measurement accuracy, and a current threshold above which voltage reappeared. The lecture scan includes subsequent notes and a 1914 addendum; those later observations should not be dated to 1911. It is a firsthand account, not a substitute for a modern magnetic-volume or heat-capacity measurement.\n\nEvidence: theory. Sources: source-d36e5a81b57e823f.\n\nConditions: Element, phase and sample conditions; historical lecture dates separated.\n\nVerification scope: Named primary passages and bounded independent examples only; complete scientific acceptance open.\n\n### scwiki-d1-claim-mathematical-assumptions-1\n\nThe isotope coefficient is $\\alpha=-d\\ln T_c/d\\ln M$. If harmonic frequencies scale as $M^{-1/2}$ while the dimensionless pairing parameters remain fixed, the corresponding transition scale has $\\alpha=1/2$. This is a conditional model statement, not a value certified here for the original mercury datasets. Maxwell and Reynolds are retained as the historical experimental sources; their full datasets still require direct review. An isotope substitution may also change structure or anharmonic motion, so a measured coefficient must retain its sample and phase conditions.\n\nEvidence: theory. Sources: source-eff5a2a1c455e7f6, source-e8a489943f13c9f8, source-0620df96ebbf2a66.\n\nConditions: Finite imposed isotope model and printed-parameter formula check; no DFT, stability or experimental replication.\n\nVerification scope: Named primary passages and bounded independent examples only; complete scientific acceptance open.\n\n### scwiki-d1-claim-mathematical-assumptions-2\n\nThe weak-coupling isotropic BCS benchmark is $2\\Delta(0)/(k_BT_c)\\simeq3.53$. Lead is a strong-coupling benchmark, so that number is not a compulsory fit to its tunneling spectrum. Retardation makes the gap energy dependent; a full gap alone does not establish its sign structure or the microscopic pairing interaction.\n\nEvidence: theory. Sources: source-d56b04dc0b32c796, source-ba10e800a1246bf6.\n\nConditions: Finite imposed isotope model and printed-parameter formula check; no DFT, stability or experimental replication.\n\nVerification scope: Named primary passages and bounded independent examples only; complete scientific acceptance open.\n\n### scwiki-d1-claim-mathematical-assumptions-3\n\nFor an illustrative McMillan-type estimate, write $T_c=(\\omega_{\\log}/1.2)\\exp[-A/D]$, with $A=1.04(1+\\lambda)$ and $D=\\lambda-\\mu^*(1+0.62\\lambda)>0$, taking $\\omega_{\\log}$ in kelvin. If $\\mu^*=\\mu/[1+\\mu\\ln(E_{\\mathrm{el}}/\\omega_{\\log})]$, with the two cutoff scales in the same units, fixed $\\lambda,\\mu,E_{\\mathrm{el}}$ give $\\alpha=\\tfrac12[1-A(1+0.62\\lambda)(\\mu^*)^2/D^2]$. Three finite-difference mass substitutions independently confirm this derivative and its difference from the fixed-$\\mu^*$ limit. These examples are not mercury fits. The estimate omits the full Allen–Dynes shape factors and is not a universal upper bound.\n\nEvidence: theory. Sources: source-aa8182fe7a3d8d0c, source-0620df96ebbf2a66, source-d56b04dc0b32c796.\n\nConditions: Finite imposed isotope model and printed-parameter formula check; no DFT, stability or experimental replication.\n\nVerification scope: Named primary passages and bounded independent examples only; complete scientific acceptance open.\n\n### scwiki-d1-claim-mathematical-assumptions-4\n\nIn the Sc paper's Table I, six printed estimates are consistent with the input rounding intervals. Sc-IV printed inputs yield 21.37/18.72 K, versus listed 21.5/18.8 K; exact reproduction needs unrounded inputs. Sc-V at 260 GPa gives 30.07/26.38 K for $\\mu^*=0.10/0.13$. These are calculations, not the measured 37.6 K onset at a different pressure. The reported extrapolated $B_{c2}(0)=21.3$ T implies $\\xi=\\sqrt{\\Phi_0/(2\\pi B_{c2})}=39.31$ angstrom; this checks units, not the extrapolation model.\n\nEvidence: theory. Sources: source-dc73a11d591aebd0.\n\nConditions: Finite imposed isotope model and printed-parameter formula check; no DFT, stability or experimental replication.\n\nVerification scope: Named primary passages and bounded independent examples only; complete scientific acceptance open.\n\n### scwiki-d1-claim-experimental-criteria-1\n\nTunneling conductance needs an appropriate normal reference. Rowell's 1970 account requires tunneling-dominated current and a barrier that stays effectively unchanged across the superconducting transition. Record how the normal reference was obtained, including its temperature and field; division alone does not remove a changed barrier or an unrelated parallel current. Oxide and interface excitations need not be electrode density-of-states features. The 1965 McMillan–Rowell paper is retained as the historical lead inversion reference; its original quantitative inversion has not been rerun here. The coupling-weighted spectrum $\\alpha^2F$ is inferred using an Eliashberg model, not read directly from conductance or identified with the bare phonon density of states.\n\nFor a local illustration of thermal convolution, assume weak elastic superconductor–insulator–normal-metal (SIN) tunneling, flat normal-electrode and normal-reference densities, a constant tunneling matrix element, and a sample spectrum unchanged by bias. At a common electron temperature, $G(V)/G_N=\\int_{-\\infty}^{\\infty}n_s(E)[-f'(E-eV)]\\,dE$, where $n_s$ is the dimensionless sample density and $f$ the Fermi function. The kernel is $[4k_BT\\cosh^2((E-eV)/(2k_BT))]^{-1}$. Finite temperature averages the spectrum; it does not return $n_s(eV)$ point by point. A hard-gap toy density, zero for $|E|<\\Delta$ and one outside, gives $G(0)/G_N=2/[1+\\exp(\\Delta/k_BT)]>0$ despite zero density at zero energy. Nine current-derivative checks, three hard-gap checks and a changed-transmission control verify this local example. It omits coherence peaks and intrinsic temperature dependence. A superconducting counterelectrode, a bias-dependent barrier, momentum-selective tunneling or extra broadening requires the corresponding response model. These checks neither invert an experimental spectrum nor determine a material's pairing mechanism.\n\nEvidence: experiment. Sources: source-b66885f8fdc58181, source-27b24b231ced1ec3, source-d56b04dc0b32c796.\n\nSource relationship: mixed-source-and-local-derivation. Rowell1970 supplies normalization and barrier conditions; Marsiglio author review explains model-dependent inversion and coupling-weighted alpha2F. McMillan-Rowell1965 is metadata-level historical context only. Thermal convolution, hard-gap conductance and transmission controls are local calculations, not source data reproduction.\n\nConditions: Normal-reference provenance, temperature and field retained; tunneling-dominated current and unchanged barrier required. Local thermal formula additionally assumes weak elastic SIN tunneling, flat normal densities, constant matrix element, common electron temperature and no bias-dependent sample spectrum. No material spectrum, pairing mechanism or alpha2F inversion inferred.\n\nVerification scope: Rowell published text p.565 and barrier discussion, Marsiglio v1 selected coupling/inversion passages and1965 publisher identity checked;13 local cases passed. Original lead inversion, full source comparisons and independent scientific review remain open.\n\n### scwiki-d1-claim-experimental-criteria-2\n\nLithium illustrates why conditions cannot be dropped from a material label. Shimizu and colleagues reported compressed Li reaching about 20 K at 48 GPa in 2002; Tuoriniemi and colleagues reported an ambient-pressure transition around 0.4 mK in 2007, with a Meissner-state figure. The latter is 0.0004 K, not 0.4 K. These source checks cover abstracts and selected captions; they do not establish an entire phase diagram or independently validate the underlying data.\n\nEvidence: experiment. Sources: source-cc7115129638a171, source-61e8b60fcacfb53b.\n\nConditions: Keep named source, phase, pressure and measurement criteria; abstract-only and inaccessible-comment scopes explicit.\n\nVerification scope: Named primary passages and bounded independent examples only; complete scientific acceptance open.\n\n### scwiki-d1-claim-experimental-criteria-3\n\nWang and colleagues reported Sc onset at 37.6 K and 243 GPa, distinct from the plotted 37.3 K at 244 GPa. Four-probe warming measurements used diamond Raman pressure calibration; onset means departure from the normal-state line. Field/current suppression supports the transport assignment, but no Meissner measurement was supplied. Phase boundaries were inferred from transition trends and compared with earlier diffraction. Applied fields reached 9 T; 21.3 T is an extrapolation.\n\nEvidence: experiment. Sources: source-dc73a11d591aebd0.\n\nConditions: Keep named source, phase, pressure and measurement criteria; abstract-only and inaccessible-comment scopes explicit.\n\nVerification scope: Named primary passages and bounded independent examples only; complete scientific acceptance open.\n\n### scwiki-d1-claim-experimental-criteria-4\n\nSakata and colleagues reported Ca-VII near 29 K at 216 GPa. Their selected methods describe room-temperature diffraction and transport; a room-temperature structure measurement does not automatically determine the low-temperature phase. An Andersson comment is part of the source trail, but its contents have not yet been obtained in this review. The reported result remains attributed to its authors, with that reconciliation open.\n\nEvidence: experiment. Sources: source-bc42a3144ddb335e, source-c563fd6be7dd9167.\n\nConditions: Keep named source, phase, pressure and measurement criteria; abstract-only and inaccessible-comment scopes explicit.\n\nVerification scope: Named primary passages and bounded independent examples only; complete scientific acceptance open.\n\n### scwiki-d1-claim-experimental-criteria-5\n\nIron is another warning against classification by ambient behavior. Shimizu and colleagues reported a resistance drop and Meissner signal below 2 K under 15–30 GPa in the non-magnetic state. This abstract-level evidence does not identify the pairing interaction or justify transferring a simple weak-coupling description from an unrelated element. Magnetic history, structure and purity need their own assessment.\n\nEvidence: experiment. Sources: source-7301d50108f9de56.\n\nConditions: Keep named source, phase, pressure and measurement criteria; abstract-only and inaccessible-comment scopes explicit.\n\nVerification scope: Named primary passages and bounded independent examples only; complete scientific acceptance open.\n\n### scwiki-d1-claim-limits-and-disputes-1\n\nA finite resistive transition, instrument-limited zero resistance, field suppression, magnetic shielding and a bulk thermodynamic anomaly answer different questions. Compare them on the same sample or explain why samples differ. Report the thermometer, onset/midpoint/zero criterion, pressure calibration, pressure medium, compression path and structural measurement temperature. Missing information stays unknown rather than being inferred from the chemical formula.\n\nEvidence: theory. Sources: source-d36e5a81b57e823f, source-cc7115129638a171, source-dc73a11d591aebd0, source-bc42a3144ddb335e.\n\nConditions: Probe-specific inference; no unsupported bulk-volume, mechanism or world-record certification.\n\nVerification scope: Named primary passages and bounded independent examples only; complete scientific acceptance open.\n\n### scwiki-d1-claim-limits-and-disputes-2\n\nThe September 2026 Sc theory paper connects compression, increasing overlap of 3d orbitals and band broadening to stronger electron–phonon coupling. Its phrase “electronic mechanism” does not mean a demonstrated nonphonon pairing glue. This page has checked the publisher abstract only: no new experimental transition, full calculation or universal elemental record is inferred from that description. Historical “highest” claims must be dated to the publication and its comparison set.\n\nEvidence: theory. Sources: source-29962a8944db57fa.\n\nConditions: Probe-specific inference; no unsupported bulk-volume, mechanism or world-record certification.\n\nVerification scope: Named primary passages and bounded independent examples only; complete scientific acceptance open.\n\n### scwiki-d1-claim-discovery-implications-1\n\nTreat an element as a collection of phase-specific test cases. Useful screening combines a dynamically and thermodynamically plausible structure, electron–phonon matrix elements, electronic energy scales and a stated Coulomb treatment, then asks which experimental observable could falsify the prediction. Agreement with one transition temperature does not validate the whole spectral function, numerical convergence or phase assignment. Keep calculated values separate from experimental transition records and preserve negative or incomplete evidence.\n\nEvidence: theory. Sources: source-aa8182fe7a3d8d0c, source-0620df96ebbf2a66, source-d56b04dc0b32c796.\n\nConditions: Screening logic only; full scientific acceptance remains open.\n\nVerification scope: Named primary passages and bounded independent examples only; complete scientific acceptance open.\n\n## Revision and review\n\nArticle ID: scwiki-d1. Revision: 82aea111e522f015b7f7. Updated: 2026-10-19T15:22:41.346250+00:00.\n\nReview scope: Selected Onnes lecture scan, Rowell normalization conditions, Sc published methods/table and Nb contextual methods; explicitly limited Li/Fe/Ca/2026 theory checks. Independent isotope derivatives, printed-parameter estimates and SI field-length check. Follow-up: Rowell1970 published barrier/normal-reference text and Marsiglio v1 coupling/inversion passages re-read;13 local thermal-convolution and transmission controls. Other source checks not repeated.\n\n- Full scientific acceptance and raw-data/convergence reviews remain open.\n- Original mercury isotope datasets and lead inversion are metadata-level references only; original1911 scan not obtained.\n- Ca comment identity recorded but its argument and reconciliation remain unread.\n- 2026 Sc theory is abstract-only; numerical consistency does not reproduce DFT or establish bulk magnetic evidence.\n\nSource: [D_material_families/D1_elemental_metals.md](https://github.com/JackZH26/jzis-superconductivity/blob/0a7c9d6696804ec26aa12f8eed68b55c9b3c0fcf/D_material_families/D1_elemental_metals.md), commit 0a7c9d6696804ec26aa12f8eed68b55c9b3c0fcf, SHA-256 09606dedbf321b1f5b231ea0c8061a0ab7adda20be151994b8b459ab34257fbe.\n","wordCount":1145}}