{"schemaVersion":"1.0","revision":"fa961ab24277a91737c3","article":{"id":"scwiki-d14","topicId":"scwiki-topic-d14","code":"D14","slug":"kagome-superconductors","title":"Kagome superconductors","summary":"Connect kagome band geometry with material-specific superconducting evidence, separating charge order, Hall response, pressure conditions and pairing candidates.","aliases":["kagome superconductivity","kagome superconductors","kagome 超导","笼目超导"],"evidenceTypes":["experiment","theory","hypothesis"],"relatedCodes":["B13","H4","C7","C8","E1"],"editorialStatus":"scoped-check","contentState":"pilot","modifiedAt":"2026-10-19T17:39:26.273430+00:00","review":{"checkedAt":"2026-10-20","scope":"Selected Guo,OrtizCs and LiuCr author passages/figures, plus Liu final pressure criteria/methods/Figure3; Cheng author HTML methods/results; inherited CDW/TRSB/PDW audits; original abstracts with explicit limits; independent kagome band algebra. D14 follow-up: selected Kang author v2 band assignments, DFT and methods text, Figures 3–4 and Table S1; computed sublattice and measured dispersion evidence separated.","limitations":["Complete scientific acceptance remains open.","Abstract-only references do not establish full methods, orbital assignment or unique pairing mechanisms.","Final-version comparisons, supplements, pressure/current controls and raw-data acceptance remain open.","Nearest-neighbor spectra do not reproduce a material, superconducting gap equation or invariant."]},"provenance":{"repository":"JackZH26/jzis-superconductivity","commit":"0a7c9d6696804ec26aa12f8eed68b55c9b3c0fcf","path":"D_material_families/D14_kagome.md","sha256":"c100136570cc9f04734a03d9927f17258ffd122af7b503e1b7c6bec46dbf5df4","sourceId":"file-2c2008f2375478c5"},"sourceMap":[{"startLine":1,"endLine":148,"targetSections":["scope","mathematical-assumptions","experimental-criteria","limits-and-disputes","discovery-implications","related-topics"],"decision":"edited-with-scoped-evidence","note":"Preserve model/family/CDW/Hall/TRSB/PDW/pressure/Cr/Fe/Sc comparison topics. Correct source attribution, pressure criterion, symmetry inference and categorical diagnostic claims. Quantitative claims lacking checked methods excluded."}],"corrections":[{"id":"scwiki-d14-correction-1","description":"Conjoined CDW paper s41467-022-33995-2 is by Li et al., not Stahl et al. FeGe PRL129166401 is first-authored by Jia-Xin Yin, with Teng a coauthor.","sourceId":"source-80eda571fc6d710c","scope":"Correct pinned attribution; retain distinct CDW and FeGe evidence."},{"id":"scwiki-d14-correction-2","description":"CsCr3Sb5 6.4K is a resistive onset at4.2GPa, distinct from critical-field midpoint. Frieze charge-stripe symmetry and charge-order TRSB do not establish chiral superconductivity.","sourceId":"source-d0ee5c328ca326ee","scope":"Separate pressure, criterion and order-parameter evidence."},{"id":"scwiki-d14-correction-3","description":"Flat bands/VHS and four proposed diagnostics are not universal sufficient or necessary definitions of topological superconductivity. FeGe and ScV6Sn6 comparison studies are not superconductivity reports.","sourceId":"source-e9b1bdb7cb3c0ee4","scope":"Remove categorical mechanism and material inferences."},{"id":"scwiki-d14-correction-kang-scope","description":"Distinguish three band assignments, kz-dependent Fermi-level crossings, DFT-derived sublattice weights and photon/temperature conditions. The reported 20 meV charge-order gap is not a superconducting gap or pairing-symmetry measurement.","sourceId":"source-dbcbd572b05dcaa4","scope":"Selected original author-version spectroscopy/model evidence; no raw-data reproduction."}],"equationChecks":[{"targetSectionId":"mathematical-assumptions","tex":"E_\\pm=t[-1\\pm\\sqrt{4S-3}]","check":"1311 independent numerical spectra, Gamma/K/M degeneracies,2 saddle Hessians and3 same-sublattice hopping perturbations. No material fit or pairing/topology calculation."}],"references":[{"id":"source-1cd7f905ef6df6e1","doi":"10.1103/PhysRevB.80.113102","title":"Topological insulator on the kagome lattice","year":2009,"url":"https://doi.org/10.1103/PhysRevB.80.113102","publicationStatus":"journal-article","verification":{"scope":"selected-author-model-and-spectrum","checkedAt":"2026-10-19","evidenceUrl":"https://arxiv.org/pdf/0905.3385v2","note":"Author v2 and journal publication 25 September 2009. Selected pp1–2 read; p2 Hamiltonian/spectrum visually checked. Source uses nearest-neighbor vectors; article uses triangular Bravais vectors twice as long. Full SOC invariant calculation not reproduced."}},{"id":"source-96cec6968d3c379a","doi":"10.1103/PhysRevMaterials.3.094407","title":"New kagome prototype materials: discovery of KV3Sb5, RbV3Sb5 and CsV3Sb5","year":2019,"url":"https://doi.org/10.1103/PhysRevMaterials.3.094407","publicationStatus":"journal-article","verification":{"scope":"publisher-original-abstract","checkedAt":"2026-10-19","evidenceUrl":"https://journals.aps.org/prmaterials/abstract/10.1103/PhysRevMaterials.3.094407","note":"Published 16 September 2019. Original abstract establishes the layered family and anomalies; not a demonstration that all members are superconducting. Full methods and stoichiometry audit open."}},{"id":"source-d49026ec4f5a10a4","doi":"10.1103/PhysRevLett.125.247002","title":"CsV3Sb5: A Z2 Topological Kagome Metal with a Superconducting Ground State","year":2020,"url":"https://doi.org/10.1103/PhysRevLett.125.247002","publicationStatus":"journal-article","verification":{"scope":"selected-author-bulk-transition-and-ARPES-conditions","checkedAt":"2026-10-19","evidenceUrl":"https://arxiv.org/pdf/2011.06745v1","note":"Author v1 13 November 2020. Selected p2 methods/results and p3 Figure2 read; p3 visually checked. Magnetization, transport and heat capacity support about2.5K onset. 8mA probe current suppresses transport onset; limited base temperature prevents detailed gap analysis. Normal-state ARPES50–120K; predicted surface band above EF is not an occupied-band observation. Final/supplement/raw-data acceptance open."}},{"id":"source-1dbc07dbbbe19132","doi":"10.1103/PhysRevMaterials.5.034801","title":"Superconductivity in the Z2 kagome metal KV3Sb5","year":2021,"url":"https://doi.org/10.1103/PhysRevMaterials.5.034801","publicationStatus":"journal-article","verification":{"scope":"author-original-abstract-only","checkedAt":"2026-10-19","evidenceUrl":"https://arxiv.org/abs/2012.09097","note":"Original abstract checked for bulk superconducting membership, using magnetization, transport and heat capacity. Exact numerical criteria and full methods not audited here."}},{"id":"source-4027fb28ea284a9f","doi":"10.1088/0256-307X/38/3/037403","title":"Superconductivity and Normal-State Properties of Kagome Metal RbV3Sb5 Single Crystals","year":2021,"url":"https://doi.org/10.1088/0256-307X/38/3/037403","publicationStatus":"journal-article","verification":{"scope":"publisher-original-abstract-only","checkedAt":"2026-10-19","evidenceUrl":"https://cpl.iphy.ac.cn/article/doi/10.1088/0256-307X/38/3/037403","note":"Qiangwei Yin et al.; original publisher abstract checked for superconducting membership, higher-temperature anomalies and multiband Hall interpretation. No numerical transition criterion or full methods audit claimed."}},{"id":"source-7746049011a0e640","doi":"10.1103/PhysRevX.11.031026","title":"Three-Dimensional Charge Density Wave and Surface-Dependent Vortex-Core States in a Kagome Superconductor CsV3Sb5","year":2021,"url":"https://doi.org/10.1103/PhysRevX.11.031026","publicationStatus":"journal-article","verification":{"scope":"publisher-abstract-check","checkedAt":"2026-10-19","evidenceUrl":"https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.031026","note":"Published 2 August 2021. Surface step phase shift and suggested three-dimensional order checked at abstract scope; vortex-state identity and full STM data not independently established."}},{"id":"source-80eda571fc6d710c","doi":"10.1038/s41467-022-33995-2","title":"Discovery of conjoined charge density waves in the kagome superconductor CsV3Sb5","year":2022,"url":"https://doi.org/10.1038/s41467-022-33995-2","publicationStatus":"journal-article","verification":{"scope":"selected-publisher-web-passages-check","checkedAt":"2026-10-19","evidenceUrl":"https://www.nature.com/articles/s41467-022-33995-2","note":"Li et al., published 26 October 2022. Abstract, selected results and Figures 1–4 captions read as text; images and raw profiles not independently reviewed. Corrects the inherited attribution to Stahl. Measurements at 10 K and charge-order onsets are not superconducting Tc."}},{"id":"source-dbcbd572b05dcaa4","doi":"10.1038/s41567-021-01451-5","title":"Twofold van Hove singularity and origin of charge order in topological kagome superconductor CsV3Sb5","year":2022,"url":"https://doi.org/10.1038/s41567-021-01451-5","publicationStatus":"journal-article","verification":{"scope":"selected-author-band-assignments-figures-and-conditions","checkedAt":"2026-10-20","evidenceUrl":"https://arxiv.org/pdf/2105.01689v2","note":"Author v2, 6 November 2021. Selected pp. 4–9, Figures 3–4 (pp. 17–18), and Table S1 (p. 31) read; three pages visually inspected. Distinguishes the K2 saddle below the Fermi level from kz-dependent K1/K2-prime crossings, DFT sublattice weights from ARPES intensity, and the charge-order gap from a superconducting gap. Complete final-version comparison, supplement and raw-data fits remain unchecked."}},{"id":"source-646e363b41fcabb3","doi":"10.1126/sciadv.abb6003","title":"Giant, unconventional anomalous Hall effect in the metallic frustrated magnet candidate, KV3Sb5","year":2020,"url":"https://doi.org/10.1126/sciadv.abb6003","publicationStatus":"journal-article","verification":{"scope":"author-institution-abstract-only","checkedAt":"2026-10-19","evidenceUrl":"https://digitalcommons.usf.edu/phy_facpub/92/","note":"Yang et al.;31July2020. Institutional original abstract checked: anomalous Hall response without reported long-range magnetic order. No full ordinary-Hall subtraction or microscopic mechanism audit. Publisher retrieval failed; PMC/PubMed returned challenge pages, which were not treated as evidence."}},{"id":"source-59d803435c0df1ef","doi":"10.1103/PhysRevB.104.L041103","title":"Concurrence of anomalous Hall effect and charge density wave in a superconducting topological kagome metal","year":2021,"url":"https://doi.org/10.1103/PhysRevB.104.L041103","publicationStatus":"journal-article","verification":{"scope":"publisher-original-abstract-only","checkedAt":"2026-10-19","evidenceUrl":"https://journals.aps.org/prb/abstract/10.1103/PhysRevB.104.L041103","note":"Yu et al.;8July2021. AHE follows higher-temperature CDW and disappears with CDW suppression under pressure. Skew scattering and Berry-curvature interpretation is the authors explanation, not a measured superconducting order parameter. Full background subtraction and methods open."}},{"id":"source-484da7abcc165cd3","doi":"10.1038/s41586-021-04327-z","title":"Time-reversal symmetry-breaking charge order in a kagome superconductor","year":2022,"url":"https://doi.org/10.1038/s41586-021-04327-z","publicationStatus":"journal-article","verification":{"scope":"selected-author-manuscript-check","checkedAt":"2026-10-18","evidenceUrl":"https://arxiv.org/pdf/2106.13443v2","note":"Selected pp. 2–3 and 6 plus experimental-methods passages; Fig. 1 on p. 2 visually checked. December 2021 author version 2, published February 2022. Nuclear/electronic and charge/superconducting distinctions retained; full final-version/data review open."}},{"id":"source-057c43c86174f961","doi":"10.1038/s41586-021-03983-5","title":"Roton pair density wave in a strong-coupling kagome superconductor","year":2021,"url":"https://doi.org/10.1038/s41586-021-03983-5","publicationStatus":"journal-article","verification":{"scope":"selected-author-manuscript-check","checkedAt":"2026-10-18","evidenceUrl":"https://arxiv.org/pdf/2103.09188v2","note":"Selected pp. 3–7 and methods pp. 17–18; Fig. 3 on p. 14 visually checked. Author version 2 September 2021 has a different title and mistyped journal volume 559; publisher confirms Nature 599. Final-version/raw-data comparison open."}},{"id":"source-4fb5d6fb51bdb253","doi":"10.1103/PhysRevLett.126.247001","title":"Double Superconducting Dome and Triple Enhancement of Tc in the Kagome Superconductor CsV3Sb5 under High Pressure","year":2021,"url":"https://doi.org/10.1103/PhysRevLett.126.247001","publicationStatus":"journal-article","verification":{"scope":"publisher-original-abstract-only","checkedAt":"2026-10-19","evidenceUrl":"https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.126.247001","note":"Chen et al.;17June2021. Original abstract describes nonmonotonic superconductivity and charge order under pressure. Full pressure calibration, resistive criteria and mechanism assignment not checked here."}},{"id":"source-d0ee5c328ca326ee","doi":"10.1038/s41586-024-07761-x","title":"Superconductivity under pressure in a chromium-based kagome metal","year":2024,"url":"https://doi.org/10.1038/s41586-024-07761-x","publicationStatus":"journal-article","verification":{"scope":"selected-author-and-final-pressure-criteria","checkedAt":"2026-10-19","evidenceUrl":"https://arxiv.org/pdf/2309.13514v2","note":"Author v2 dated16March2024 has a different title; publisher title/date28August2024 checked independently. Selected pp6–7 results/Figure3 and p17 methods read; p7 visually checked. 6.4K is onset at4.2GPa; Hc2 criterion50%normal resistance; fitted14.34T not directly observed zero-temperature field. Cubic-anvil glycerol with room-temperature load calibration differs from lower-pressure piston-cell Daphne/Pb calibration. Final institutional PDF selected p4 results/Figure3 and pp7–8 pressure methods also checked; p4 visually inspected. Field direction explicitly uncertain, so no anisotropic Hc2 claim. Full extended-data/raw AC calibration and complete version comparison open."}},{"id":"source-c415e45e91e02c10","doi":"10.1038/s41567-026-03232-4","title":"Frieze charge stripes in a correlated kagome superconductor","year":2026,"url":"https://doi.org/10.1038/s41567-026-03232-4","publicationStatus":"journal-article","verification":{"scope":"selected-author-HTML-results-and-STM-methods","checkedAt":"2026-10-19","evidenceUrl":"https://arxiv.org/html/2510.06168v1","note":"Published2April2026;authorv1 7October2025. Selected Results, growth/STM methods and symmetry description read in author HTML. Cleaved Sb surface,4.5K base,50/45K modulation scales, mirror-glide symmetry precludes global handedness. No high-pressure superconducting order-parameter measurement in this STM study. Figure images, full simulation and final comparison open."}},{"id":"source-e9b1bdb7cb3c0ee4","doi":"10.1103/PhysRevLett.129.166401","title":"Discovery of Charge Order and Corresponding Edge State in Kagome Magnet FeGe","year":2022,"url":"https://doi.org/10.1103/PhysRevLett.129.166401","publicationStatus":"journal-article","verification":{"scope":"publisher-original-abstract-and-attribution","checkedAt":"2026-10-19","evidenceUrl":"https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.129.166401","note":"Published10October2022;first author Jia-Xin Yin, with Xiaokun Teng a coauthor. Original abstract:2x2 charge order, antiferromagnetic stacking and charge-order-gap edge state. It does not establish a superconducting transition or Majorana state. Full methods open."}},{"id":"source-ed0ebd2f956f2b5f","doi":"10.1103/PhysRevLett.129.216402","title":"Charge Density Wave in Kagome Lattice Intermetallic ScV6Sn6","year":2022,"url":"https://doi.org/10.1103/PhysRevLett.129.216402","publicationStatus":"journal-article","verification":{"scope":"publisher-original-abstract-only","checkedAt":"2026-10-19","evidenceUrl":"https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.129.216402","note":"Published18November2022. Arachchige et al.;92K first-order transition, x-ray/neutron lattice modulation. Charge-order comparison material, not superconductivity evidence. Full diffraction/supplement audit open."}}],"materialCases":[{"id":"scwiki-d14-material-1","recordType":"experiment","formula":"CsV3Sb5","sample":"Ortiz2020 crystals; bulk evidence from magnetic/transport/calorimetric anomalies; current-sensitive resistive onset","tcK":2.5,"reportedTemperatureK":2.5,"temperatureKind":"transition","temperatureNote":"Approximate superconducting onset; probe current affects resistive curve. Not a universal value.","pressureRegime":"ambient","pressureGPa":null,"equilibrium":"unknown","criterion":"onset","probe":"Transport, magnetization and heat capacity","sourceId":"source-d49026ec4f5a10a4","aliases":["cesium vanadium antimonide"]},{"id":"scwiki-d14-material-2","recordType":"experiment","formula":"CsCr3Sb5","sample":"Liu2024 cubic-anvil pressure experiment at4.2GPa","tcK":6.4,"reportedTemperatureK":6.4,"temperatureKind":"transition","temperatureNote":"Resistive onset; differs from50%normal-resistance critical-field criterion.","pressureRegime":"high","pressureGPa":{"min":4.2,"max":4.2},"equilibrium":"unknown","criterion":"onset","probe":"High-pressure resistivity","sourceId":"source-d0ee5c328ca326ee","aliases":["cesium chromium antimonide"]}],"claims":[{"id":"scwiki-d14-claim-scope-1","sectionId":"scope","statement":"Kagome geometry offers a useful starting point for studying flat bands, Dirac crossings, charge order and superconductivity. It does not guarantee that a flat band lies at the Fermi energy, that magnetic frustration produces a spin liquid, or that a material has a high transition temperature. This article separates superconducting AV3Sb5 compounds, pressure-induced superconductivity in CsCr3Sb5 and charge-ordered comparison materials. Normal-state topology and superconducting topology remain separate questions.","evidenceType":"hypothesis","sourceIds":["source-1cd7f905ef6df6e1","source-96cec6968d3c379a","source-d49026ec4f5a10a4","source-d0ee5c328ca326ee","source-e9b1bdb7cb3c0ee4","source-ed0ebd2f956f2b5f"],"conditions":"Keep composition, pressure, current, surface termination, temperature type and transition criterion separate. Normal-state geometry/order is not superconducting topology.","verificationScope":"Selected primary passages/figures and restricted band checks; full scientific acceptance remains open."},{"id":"scwiki-d14-claim-mathematical-assumptions-1","sectionId":"mathematical-assumptions","statement":"Take one spinless orbital on each of three sites $0,\\mathbf a_1/2,\\mathbf a_2/2$, with triangular Bravais vectors and $q_i=\\mathbf k\\cdot\\mathbf a_i$. For positive nearest-neighbor hopping $t$, a Bloch Hamiltonian is $H=-2t\\begin{pmatrix}0&c_1&c_2\\\\c_1&0&c_3\\\\c_2&c_3&0\\end{pmatrix}$, where $c_1=\\cos(q_1/2)$, $c_2=\\cos(q_2/2)$ and $c_3=\\cos[(q_2-q_1)/2]$. Its bands are $E_f=2t$ and $E_\\pm=t[-1\\pm\\sqrt{4S-3}]$, with $S=c_1^2+c_2^2+c_3^2$. The vectors in Guo and Franz's convention are nearest-neighbor vectors, half the Bravais vectors used here.","evidenceType":"theory","sourceIds":["source-1cd7f905ef6df6e1"],"conditions":"Keep composition, pressure, current, surface termination, temperature type and transition criterion separate. Normal-state geometry/order is not superconducting topology.","verificationScope":"Selected primary passages/figures and restricted band checks; full scientific acceptance remains open."},{"id":"scwiki-d14-claim-mathematical-assumptions-2","sectionId":"mathematical-assumptions","statement":"The model has a flat-band contact at Gamma, a Dirac crossing at K and dispersive-band saddles at M. Independent diagonalization checks 1,311 momentum/hopping combinations; numerical Hessians have opposite-sign curvatures at the two M-point saddles. Adding equal same-sublattice hopping shifts all bands by $\\delta(\\mathbf q)=-2u[\\cos q_1+\\cos q_2+\\cos(q_2-q_1)]$. The formerly flat branch then spans $9|u|$ between Gamma and K while the kagome geometry remains. These checks illustrate model sensitivity; they do not calculate a pairing interaction, a material transition temperature or a superconducting invariant.","evidenceType":"theory","sourceIds":["source-1cd7f905ef6df6e1"],"conditions":"Keep composition, pressure, current, surface termination, temperature type and transition criterion separate. Normal-state geometry/order is not superconducting topology.","verificationScope":"Selected primary passages/figures and restricted band checks; full scientific acceptance remains open."},{"id":"scwiki-d14-claim-mathematical-assumptions-3","sectionId":"mathematical-assumptions","statement":"Real compounds add orbital character, interlayer hopping and reconstruction. Kang's CsV3Sb5 author manuscript combines ARPES dispersions with DFT orbital and sublattice projections:\n\n| Band | Orbital and sublattice assignment | Energy and interpretation |\n| --- | --- | --- |\n| K1 | Mainly $d_{xy}/d_{x^2-y^2}$; p-type, predominantly one sublattice | Can cross $E_F$ as $k_z$ changes; higher-order saddle behavior |\n| K2 | Mainly $d_{xz}/d_{yz}$; p-type | Saddle reported at $-0.15\\pm0.03$ eV relative to $E_F$; remains below $E_F$ in the examined dispersion |\n| K2' | Mainly $d_{xz}/d_{yz}$; m-type, mixed sublattices | Can cross $E_F$ with $k_z$; opposite saddle concavity and stronger nesting |\n\nHere p/m means pure/mixed **sublattice character**, not a superconducting gap symmetry. The sublattice weights come from calculated Bloch functions; ARPES brightness alone does not measure them.\n\nFigure 3 uses 88 eV photons at 60 K. Figure 4 instead uses 95 eV photons at 35 and 95 K, with linear horizontal polarization in both datasets. Its reported approximately 20 meV feature is a **charge-order gap**, not a superconducting gap. Matrix elements change visibility across Brillouin zones. The displayed DFT analysis omits spin–orbit coupling; full reconstruction, spectral fitting and final-version comparisons remain unchecked here. These band constraints do not select the superconducting pairing symmetry.","evidenceType":"editorial-analysis","sourceIds":["source-dbcbd572b05dcaa4"],"conditions":"CsV3Sb5; author v2 Figure 3: 88 eV photons, linear horizontal polarization, 60 K. Figure 4: 95 eV photons, linear horizontal polarization, 35 and 95 K. Sublattice assignments are calculated; energies are relative to the Fermi level. The charge-order gap is not a superconducting gap.","verificationScope":"Selected author v2 pp. 4–9, Figure 3 (p. 17), Figure 4 (p. 18), and Table S1 (p. 31); three pages visually inspected. No raw-data refit, complete final-version comparison or determination of superconducting symmetry.","sourceRelationship":"context-for-editorial-analysis","derivationNote":"Editorial comparison of ARPES measurements and DFT projections from selected author v2 pp. 4–9, Figures 3–4 and Table S1. This table organizes measured and computed evidence; it is not a new orbital fit, DFT calculation or pairing derivation."},{"id":"scwiki-d14-claim-experimental-criteria-1","sectionId":"experimental-criteria","statement":"Ortiz's original family study identified K, Rb and Cs vanadium antimonides as layered kagome metals. The later CsV3Sb5 superconductivity paper combines magnetization, resistivity and heat capacity around a 2.5 K onset. Its transport onset is suppressed at an 8 mA probe current and returns toward the nominal value at lower current, illustrating why excitation belongs in the sample record. The heat-capacity temperature floor limits conclusions about the low-temperature gap. Subsequent K and Rb member reports should retain their own samples and criteria rather than being collapsed into a universal family transition range.","evidenceType":"experiment","sourceIds":["source-96cec6968d3c379a","source-d49026ec4f5a10a4","source-1dbc07dbbbe19132","source-4027fb28ea284a9f"],"conditions":"Keep composition, pressure, current, surface termination, temperature type and transition criterion separate. Normal-state geometry/order is not superconducting topology.","verificationScope":"Selected primary passages/figures and restricted band checks; full scientific acceptance remains open."},{"id":"scwiki-d14-claim-experimental-criteria-2","sectionId":"experimental-criteria","statement":"The same CsV3Sb5 work discusses a much higher-temperature anomaly and a normal-state topological band background. ARPES taken well above the superconducting transition and calculated surface states above the Fermi energy do not directly measure a superconducting gap invariant. Liang's three-dimensional CDW study and Li's conjoined-CDW study further emphasize stacking, temperature and surface dependence. Different modulation descriptions cannot be merged into one structure common to every sample or termination.","evidenceType":"experiment","sourceIds":["source-d49026ec4f5a10a4","source-7746049011a0e640","source-80eda571fc6d710c"],"conditions":"Keep composition, pressure, current, surface termination, temperature type and transition criterion separate. Normal-state geometry/order is not superconducting topology.","verificationScope":"Selected primary passages/figures and restricted band checks; full scientific acceptance remains open."},{"id":"scwiki-d14-claim-experimental-criteria-3","sectionId":"experimental-criteria","statement":"Yang reports anomalous Hall response in KV3Sb5; Yu connects anomalous Hall response in CsV3Sb5 to its higher-temperature charge-order regime. Neither result is a phase-sensitive measurement of superconducting chirality. Ordinary multiband transport, scattering and Berry-curvature contributions require separate analysis. Likewise, the checked Mielke muon study concerns time-reversal symmetry breaking associated with charge order. A signal emerging near that ordering scale cannot simply be reassigned to a superconducting $d+id$ state.","evidenceType":"experiment","sourceIds":["source-646e363b41fcabb3","source-59d803435c0df1ef","source-484da7abcc165cd3"],"conditions":"Keep composition, pressure, current, surface termination, temperature type and transition criterion separate. Normal-state geometry/order is not superconducting topology.","verificationScope":"Selected primary passages/figures and restricted band checks; full scientific acceptance remains open."},{"id":"scwiki-d14-claim-experimental-criteria-4","sectionId":"experimental-criteria","statement":"Chen's spatially resolved tunneling work proposes a roton pair-density-wave interpretation in CsV3Sb5. Pair-related modulations are significant evidence to investigate, but charge-order changes in local density of states, tunneling matrix elements and Josephson coupling remain relevant controls. Pressure studies also show nonmonotonic superconducting and charge-order scales. Two domes do not by themselves establish two pairing mechanisms: structure, bands, scattering and calibration can evolve together.","evidenceType":"experiment","sourceIds":["source-057c43c86174f961","source-4fb5d6fb51bdb253"],"conditions":"Keep composition, pressure, current, surface termination, temperature type and transition criterion separate. Normal-state geometry/order is not superconducting topology.","verificationScope":"Selected primary passages/figures and restricted band checks; full scientific acceptance remains open."},{"id":"scwiki-d14-claim-experimental-criteria-5","sectionId":"experimental-criteria","statement":"For CsCr3Sb5, Liu's author manuscript and selected final-paper results report a maximum resistive onset of 6.4 K at 4.2 GPa, with zero resistance and AC susceptibility supporting bulk superconductivity over a pressure interval. Its critical-field curves instead use half the normal resistance. The fitted zero-temperature field is therefore not an independently observed field boundary. The final text explicitly leaves the field direction uncertain, preventing an anisotropy claim. The cubic-anvil measurement uses glycerol and room-temperature load calibration; the lower-pressure piston-cell setup uses a different medium and calibration. These are high-pressure records, not ambient-pressure entries or universal chromium-family numbers.","evidenceType":"experiment","sourceIds":["source-d0ee5c328ca326ee"],"conditions":"Keep composition, pressure, current, surface termination, temperature type and transition criterion separate. Normal-state geometry/order is not superconducting topology.","verificationScope":"Selected primary passages/figures and restricted band checks; full scientific acceptance remains open."},{"id":"scwiki-d14-claim-experimental-criteria-6","sectionId":"experimental-criteria","statement":"Cheng's April 2026 paper adds a distinct charge-order result in CsCr3Sb5. The selected author text describes cleaved-surface STM with a 4.5 K base temperature and two higher-temperature modulation scales. Its stripe pattern breaks mirror symmetries while retaining a mirror-glide operation; opposite local textures do not define global handedness. Those surface images are not a high-pressure superconducting order-parameter measurement and cannot establish chiral superconductivity.","evidenceType":"experiment","sourceIds":["source-c415e45e91e02c10"],"conditions":"Keep composition, pressure, current, surface termination, temperature type and transition criterion separate. Normal-state geometry/order is not superconducting topology.","verificationScope":"Selected primary passages/figures and restricted band checks; full scientific acceptance remains open."},{"id":"scwiki-d14-claim-experimental-criteria-7","sectionId":"experimental-criteria","statement":"FeGe and ScV6Sn6 serve as comparisons. Yin's FeGe study reports charge order, magnetic stacking and an edge state within a charge-order energy gap; Arachchige's ScV6Sn6 work reports a lattice-modulated charge-order transition. Neither cited result establishes superconductivity. Absence of such evidence in these papers should not be rewritten as a timeless claim that either material can never superconduct under any preparation or pressure.","evidenceType":"experiment","sourceIds":["source-e9b1bdb7cb3c0ee4","source-ed0ebd2f956f2b5f"],"conditions":"Keep composition, pressure, current, surface termination, temperature type and transition criterion separate. Normal-state geometry/order is not superconducting topology.","verificationScope":"Selected primary passages/figures and restricted band checks; full scientific acceptance remains open."},{"id":"scwiki-d14-claim-limits-and-disputes-1","sectionId":"limits-and-disputes","statement":"Allowed pairing representations are candidates until tested against the actual superconducting state. Charge-order time-reversal breaking, a normal-state anomalous Hall signal, structural handedness, tunneling modulation and a zero-bias feature each address different questions. Phase-sensitive experiments, temperature-resolved symmetry probes, bulk gap constraints and boundary-state tests can provide complementary discrimination; they are not a universal checklist that defines every possible topological superconductor. Complete scientific acceptance remains open: several references retain abstract-only review, and final-version comparisons, supplements and raw-data analyses are unfinished.","evidenceType":"hypothesis","sourceIds":["source-d49026ec4f5a10a4","source-80eda571fc6d710c","source-59d803435c0df1ef","source-484da7abcc165cd3","source-057c43c86174f961","source-c415e45e91e02c10"],"conditions":"Keep composition, pressure, current, surface termination, temperature type and transition criterion separate. Normal-state geometry/order is not superconducting topology.","verificationScope":"Selected primary passages/figures and restricted band checks; full scientific acceptance remains open."},{"id":"scwiki-d14-claim-discovery-implications-1","sectionId":"discovery-implications","statement":"Record composition, pressure path, excitation, surface termination and the onset, midpoint, measured-zero and thermodynamic criteria separately. Compare measured band positions with a specified model before invoking flat-band enhancement. Test whether changing charge order also changes disorder, structure or carrier balance. The useful next experiment resolves competing interpretations on a characterized sample, rather than promoting a geometric label or an isolated transition number into a mechanism.","evidenceType":"hypothesis","sourceIds":["source-1cd7f905ef6df6e1","source-d49026ec4f5a10a4","source-dbcbd572b05dcaa4","source-4fb5d6fb51bdb253","source-d0ee5c328ca326ee"],"conditions":"Keep composition, pressure, current, surface termination, temperature type and transition criterion separate. Normal-state geometry/order is not superconducting topology.","verificationScope":"Selected primary passages/figures and restricted band checks; full scientific acceptance remains open."}],"body":"## Scope\n\nKagome geometry offers a useful starting point for studying flat bands, Dirac crossings, charge order and superconductivity. It does not guarantee that a flat band lies at the Fermi energy, that magnetic frustration produces a spin liquid, or that a material has a high transition temperature. This article separates superconducting AV3Sb5 compounds, pressure-induced superconductivity in CsCr3Sb5 and charge-ordered comparison materials. Normal-state topology and superconducting topology remain separate questions. [R1](#ref-source-1cd7f905ef6df6e1) [R2](#ref-source-96cec6968d3c379a) [R3](#ref-source-d49026ec4f5a10a4) [R14](#ref-source-d0ee5c328ca326ee) [R16](#ref-source-e9b1bdb7cb3c0ee4) [R17](#ref-source-ed0ebd2f956f2b5f)\n\n## Mathematical assumptions\n\nTake one spinless orbital on each of three sites $0,\\mathbf a_1/2,\\mathbf a_2/2$, with triangular Bravais vectors and $q_i=\\mathbf k\\cdot\\mathbf a_i$. For positive nearest-neighbor hopping $t$, a Bloch Hamiltonian is $H=-2t\\begin{pmatrix}0&c_1&c_2\\\\c_1&0&c_3\\\\c_2&c_3&0\\end{pmatrix}$, where $c_1=\\cos(q_1/2)$, $c_2=\\cos(q_2/2)$ and $c_3=\\cos[(q_2-q_1)/2]$. Its bands are $E_f=2t$ and $E_\\pm=t[-1\\pm\\sqrt{4S-3}]$, with $S=c_1^2+c_2^2+c_3^2$. The vectors in Guo and Franz's convention are nearest-neighbor vectors, half the Bravais vectors used here. [R1](#ref-source-1cd7f905ef6df6e1)\n\nThe model has a flat-band contact at Gamma, a Dirac crossing at K and dispersive-band saddles at M. Independent diagonalization checks 1,311 momentum/hopping combinations; numerical Hessians have opposite-sign curvatures at the two M-point saddles. Adding equal same-sublattice hopping shifts all bands by $\\delta(\\mathbf q)=-2u[\\cos q_1+\\cos q_2+\\cos(q_2-q_1)]$. The formerly flat branch then spans $9|u|$ between Gamma and K while the kagome geometry remains. These checks illustrate model sensitivity; they do not calculate a pairing interaction, a material transition temperature or a superconducting invariant. [R1](#ref-source-1cd7f905ef6df6e1)\n\nReal compounds add orbital character, interlayer hopping and reconstruction. Kang's CsV3Sb5 author manuscript combines ARPES dispersions with DFT orbital and sublattice projections:\n\n| Band | Orbital and sublattice assignment | Energy and interpretation |\n| --- | --- | --- |\n| K1 | Mainly $d_{xy}/d_{x^2-y^2}$; p-type, predominantly one sublattice | Can cross $E_F$ as $k_z$ changes; higher-order saddle behavior |\n| K2 | Mainly $d_{xz}/d_{yz}$; p-type | Saddle reported at $-0.15\\pm0.03$ eV relative to $E_F$; remains below $E_F$ in the examined dispersion |\n| K2' | Mainly $d_{xz}/d_{yz}$; m-type, mixed sublattices | Can cross $E_F$ with $k_z$; opposite saddle concavity and stronger nesting |\n\nHere p/m means pure/mixed **sublattice character**, not a superconducting gap symmetry. The sublattice weights come from calculated Bloch functions; ARPES brightness alone does not measure them.\n\nFigure 3 uses 88 eV photons at 60 K. Figure 4 instead uses 95 eV photons at 35 and 95 K, with linear horizontal polarization in both datasets. Its reported approximately 20 meV feature is a **charge-order gap**, not a superconducting gap. Matrix elements change visibility across Brillouin zones. The displayed DFT analysis omits spin–orbit coupling; full reconstruction, spectral fitting and final-version comparisons remain unchecked here. These band constraints do not select the superconducting pairing symmetry. [R8](#ref-source-dbcbd572b05dcaa4)\n\n## Experimental criteria\n\nOrtiz's original family study identified K, Rb and Cs vanadium antimonides as layered kagome metals. The later CsV3Sb5 superconductivity paper combines magnetization, resistivity and heat capacity around a 2.5 K onset. Its transport onset is suppressed at an 8 mA probe current and returns toward the nominal value at lower current, illustrating why excitation belongs in the sample record. The heat-capacity temperature floor limits conclusions about the low-temperature gap. Subsequent K and Rb member reports should retain their own samples and criteria rather than being collapsed into a universal family transition range. [R2](#ref-source-96cec6968d3c379a) [R3](#ref-source-d49026ec4f5a10a4) [R4](#ref-source-1dbc07dbbbe19132) [R5](#ref-source-4027fb28ea284a9f)\n\nThe same CsV3Sb5 work discusses a much higher-temperature anomaly and a normal-state topological band background. ARPES taken well above the superconducting transition and calculated surface states above the Fermi energy do not directly measure a superconducting gap invariant. Liang's three-dimensional CDW study and Li's conjoined-CDW study further emphasize stacking, temperature and surface dependence. Different modulation descriptions cannot be merged into one structure common to every sample or termination. [R3](#ref-source-d49026ec4f5a10a4) [R6](#ref-source-7746049011a0e640) [R7](#ref-source-80eda571fc6d710c)\n\nYang reports anomalous Hall response in KV3Sb5; Yu connects anomalous Hall response in CsV3Sb5 to its higher-temperature charge-order regime. Neither result is a phase-sensitive measurement of superconducting chirality. Ordinary multiband transport, scattering and Berry-curvature contributions require separate analysis. Likewise, the checked Mielke muon study concerns time-reversal symmetry breaking associated with charge order. A signal emerging near that ordering scale cannot simply be reassigned to a superconducting $d+id$ state. [R9](#ref-source-646e363b41fcabb3) [R10](#ref-source-59d803435c0df1ef) [R11](#ref-source-484da7abcc165cd3)\n\nChen's spatially resolved tunneling work proposes a roton pair-density-wave interpretation in CsV3Sb5. Pair-related modulations are significant evidence to investigate, but charge-order changes in local density of states, tunneling matrix elements and Josephson coupling remain relevant controls. Pressure studies also show nonmonotonic superconducting and charge-order scales. Two domes do not by themselves establish two pairing mechanisms: structure, bands, scattering and calibration can evolve together. [R12](#ref-source-057c43c86174f961) [R13](#ref-source-4fb5d6fb51bdb253)\n\nFor CsCr3Sb5, Liu's author manuscript and selected final-paper results report a maximum resistive onset of 6.4 K at 4.2 GPa, with zero resistance and AC susceptibility supporting bulk superconductivity over a pressure interval. Its critical-field curves instead use half the normal resistance. The fitted zero-temperature field is therefore not an independently observed field boundary. The final text explicitly leaves the field direction uncertain, preventing an anisotropy claim. The cubic-anvil measurement uses glycerol and room-temperature load calibration; the lower-pressure piston-cell setup uses a different medium and calibration. These are high-pressure records, not ambient-pressure entries or universal chromium-family numbers. [R14](#ref-source-d0ee5c328ca326ee)\n\nCheng's April 2026 paper adds a distinct charge-order result in CsCr3Sb5. The selected author text describes cleaved-surface STM with a 4.5 K base temperature and two higher-temperature modulation scales. Its stripe pattern breaks mirror symmetries while retaining a mirror-glide operation; opposite local textures do not define global handedness. Those surface images are not a high-pressure superconducting order-parameter measurement and cannot establish chiral superconductivity. [R15](#ref-source-c415e45e91e02c10)\n\nFeGe and ScV6Sn6 serve as comparisons. Yin's FeGe study reports charge order, magnetic stacking and an edge state within a charge-order energy gap; Arachchige's ScV6Sn6 work reports a lattice-modulated charge-order transition. Neither cited result establishes superconductivity. Absence of such evidence in these papers should not be rewritten as a timeless claim that either material can never superconduct under any preparation or pressure. [R16](#ref-source-e9b1bdb7cb3c0ee4) [R17](#ref-source-ed0ebd2f956f2b5f)\n\n## Limits and disputes\n\nAllowed pairing representations are candidates until tested against the actual superconducting state. Charge-order time-reversal breaking, a normal-state anomalous Hall signal, structural handedness, tunneling modulation and a zero-bias feature each address different questions. Phase-sensitive experiments, temperature-resolved symmetry probes, bulk gap constraints and boundary-state tests can provide complementary discrimination; they are not a universal checklist that defines every possible topological superconductor. Complete scientific acceptance remains open: several references retain abstract-only review, and final-version comparisons, supplements and raw-data analyses are unfinished. [R3](#ref-source-d49026ec4f5a10a4) [R7](#ref-source-80eda571fc6d710c) [R10](#ref-source-59d803435c0df1ef) [R11](#ref-source-484da7abcc165cd3) [R12](#ref-source-057c43c86174f961) [R15](#ref-source-c415e45e91e02c10)\n\n## Discovery implications\n\nRecord composition, pressure path, excitation, surface termination and the onset, midpoint, measured-zero and thermodynamic criteria separately. Compare measured band positions with a specified model before invoking flat-band enhancement. Test whether changing charge order also changes disorder, structure or carrier balance. The useful next experiment resolves competing interpretations on a characterized sample, rather than promoting a geometric label or an isolated transition number into a mechanism. [R1](#ref-source-1cd7f905ef6df6e1) [R3](#ref-source-d49026ec4f5a10a4) [R8](#ref-source-dbcbd572b05dcaa4) [R13](#ref-source-4fb5d6fb51bdb253) [R14](#ref-source-d0ee5c328ca326ee)\n\n## Related topics\n\n[Flat bands](/scwiki/flat-band-pairing), [Charge density waves](/scwiki/charge-density-waves), [Chiral pairing](/scwiki/chiral-pairing), [Pair density waves](/scwiki/pair-density-wave), and [Pressure tuning](/scwiki/pressure-tuning).","revision":"a6ded33868163826c2b6","sections":[{"id":"scope","title":"Scope","markdown":"## Scope\n\nKagome geometry offers a useful starting point for studying flat bands, Dirac crossings, charge order and superconductivity. It does not guarantee that a flat band lies at the Fermi energy, that magnetic frustration produces a spin liquid, or that a material has a high transition temperature. This article separates superconducting AV3Sb5 compounds, pressure-induced superconductivity in CsCr3Sb5 and charge-ordered comparison materials. Normal-state topology and superconducting topology remain separate questions. [R1](#ref-source-1cd7f905ef6df6e1) [R2](#ref-source-96cec6968d3c379a) [R3](#ref-source-d49026ec4f5a10a4) [R14](#ref-source-d0ee5c328ca326ee) [R16](#ref-source-e9b1bdb7cb3c0ee4) [R17](#ref-source-ed0ebd2f956f2b5f)"},{"id":"mathematical-assumptions","title":"Mathematical assumptions","markdown":"## Mathematical assumptions\n\nTake one spinless orbital on each of three sites $0,\\mathbf a_1/2,\\mathbf a_2/2$, with triangular Bravais vectors and $q_i=\\mathbf k\\cdot\\mathbf a_i$. For positive nearest-neighbor hopping $t$, a Bloch Hamiltonian is $H=-2t\\begin{pmatrix}0&c_1&c_2\\\\c_1&0&c_3\\\\c_2&c_3&0\\end{pmatrix}$, where $c_1=\\cos(q_1/2)$, $c_2=\\cos(q_2/2)$ and $c_3=\\cos[(q_2-q_1)/2]$. Its bands are $E_f=2t$ and $E_\\pm=t[-1\\pm\\sqrt{4S-3}]$, with $S=c_1^2+c_2^2+c_3^2$. The vectors in Guo and Franz's convention are nearest-neighbor vectors, half the Bravais vectors used here. [R1](#ref-source-1cd7f905ef6df6e1)\n\nThe model has a flat-band contact at Gamma, a Dirac crossing at K and dispersive-band saddles at M. Independent diagonalization checks 1,311 momentum/hopping combinations; numerical Hessians have opposite-sign curvatures at the two M-point saddles. Adding equal same-sublattice hopping shifts all bands by $\\delta(\\mathbf q)=-2u[\\cos q_1+\\cos q_2+\\cos(q_2-q_1)]$. The formerly flat branch then spans $9|u|$ between Gamma and K while the kagome geometry remains. These checks illustrate model sensitivity; they do not calculate a pairing interaction, a material transition temperature or a superconducting invariant. [R1](#ref-source-1cd7f905ef6df6e1)\n\nReal compounds add orbital character, interlayer hopping and reconstruction. Kang's CsV3Sb5 author manuscript combines ARPES dispersions with DFT orbital and sublattice projections:\n\n| Band | Orbital and sublattice assignment | Energy and interpretation |\n| --- | --- | --- |\n| K1 | Mainly $d_{xy}/d_{x^2-y^2}$; p-type, predominantly one sublattice | Can cross $E_F$ as $k_z$ changes; higher-order saddle behavior |\n| K2 | Mainly $d_{xz}/d_{yz}$; p-type | Saddle reported at $-0.15\\pm0.03$ eV relative to $E_F$; remains below $E_F$ in the examined dispersion |\n| K2' | Mainly $d_{xz}/d_{yz}$; m-type, mixed sublattices | Can cross $E_F$ with $k_z$; opposite saddle concavity and stronger nesting |\n\nHere p/m means pure/mixed **sublattice character**, not a superconducting gap symmetry. The sublattice weights come from calculated Bloch functions; ARPES brightness alone does not measure them.\n\nFigure 3 uses 88 eV photons at 60 K. Figure 4 instead uses 95 eV photons at 35 and 95 K, with linear horizontal polarization in both datasets. Its reported approximately 20 meV feature is a **charge-order gap**, not a superconducting gap. Matrix elements change visibility across Brillouin zones. The displayed DFT analysis omits spin–orbit coupling; full reconstruction, spectral fitting and final-version comparisons remain unchecked here. These band constraints do not select the superconducting pairing symmetry. [R8](#ref-source-dbcbd572b05dcaa4)"},{"id":"experimental-criteria","title":"Experimental criteria","markdown":"## Experimental criteria\n\nOrtiz's original family study identified K, Rb and Cs vanadium antimonides as layered kagome metals. The later CsV3Sb5 superconductivity paper combines magnetization, resistivity and heat capacity around a 2.5 K onset. Its transport onset is suppressed at an 8 mA probe current and returns toward the nominal value at lower current, illustrating why excitation belongs in the sample record. The heat-capacity temperature floor limits conclusions about the low-temperature gap. Subsequent K and Rb member reports should retain their own samples and criteria rather than being collapsed into a universal family transition range. [R2](#ref-source-96cec6968d3c379a) [R3](#ref-source-d49026ec4f5a10a4) [R4](#ref-source-1dbc07dbbbe19132) [R5](#ref-source-4027fb28ea284a9f)\n\nThe same CsV3Sb5 work discusses a much higher-temperature anomaly and a normal-state topological band background. ARPES taken well above the superconducting transition and calculated surface states above the Fermi energy do not directly measure a superconducting gap invariant. Liang's three-dimensional CDW study and Li's conjoined-CDW study further emphasize stacking, temperature and surface dependence. Different modulation descriptions cannot be merged into one structure common to every sample or termination. [R3](#ref-source-d49026ec4f5a10a4) [R6](#ref-source-7746049011a0e640) [R7](#ref-source-80eda571fc6d710c)\n\nYang reports anomalous Hall response in KV3Sb5; Yu connects anomalous Hall response in CsV3Sb5 to its higher-temperature charge-order regime. Neither result is a phase-sensitive measurement of superconducting chirality. Ordinary multiband transport, scattering and Berry-curvature contributions require separate analysis. Likewise, the checked Mielke muon study concerns time-reversal symmetry breaking associated with charge order. A signal emerging near that ordering scale cannot simply be reassigned to a superconducting $d+id$ state. [R9](#ref-source-646e363b41fcabb3) [R10](#ref-source-59d803435c0df1ef) [R11](#ref-source-484da7abcc165cd3)\n\nChen's spatially resolved tunneling work proposes a roton pair-density-wave interpretation in CsV3Sb5. Pair-related modulations are significant evidence to investigate, but charge-order changes in local density of states, tunneling matrix elements and Josephson coupling remain relevant controls. Pressure studies also show nonmonotonic superconducting and charge-order scales. Two domes do not by themselves establish two pairing mechanisms: structure, bands, scattering and calibration can evolve together. [R12](#ref-source-057c43c86174f961) [R13](#ref-source-4fb5d6fb51bdb253)\n\nFor CsCr3Sb5, Liu's author manuscript and selected final-paper results report a maximum resistive onset of 6.4 K at 4.2 GPa, with zero resistance and AC susceptibility supporting bulk superconductivity over a pressure interval. Its critical-field curves instead use half the normal resistance. The fitted zero-temperature field is therefore not an independently observed field boundary. The final text explicitly leaves the field direction uncertain, preventing an anisotropy claim. The cubic-anvil measurement uses glycerol and room-temperature load calibration; the lower-pressure piston-cell setup uses a different medium and calibration. These are high-pressure records, not ambient-pressure entries or universal chromium-family numbers. [R14](#ref-source-d0ee5c328ca326ee)\n\nCheng's April 2026 paper adds a distinct charge-order result in CsCr3Sb5. The selected author text describes cleaved-surface STM with a 4.5 K base temperature and two higher-temperature modulation scales. Its stripe pattern breaks mirror symmetries while retaining a mirror-glide operation; opposite local textures do not define global handedness. Those surface images are not a high-pressure superconducting order-parameter measurement and cannot establish chiral superconductivity. [R15](#ref-source-c415e45e91e02c10)\n\nFeGe and ScV6Sn6 serve as comparisons. Yin's FeGe study reports charge order, magnetic stacking and an edge state within a charge-order energy gap; Arachchige's ScV6Sn6 work reports a lattice-modulated charge-order transition. Neither cited result establishes superconductivity. Absence of such evidence in these papers should not be rewritten as a timeless claim that either material can never superconduct under any preparation or pressure. [R16](#ref-source-e9b1bdb7cb3c0ee4) [R17](#ref-source-ed0ebd2f956f2b5f)"},{"id":"limits-and-disputes","title":"Limits and disputes","markdown":"## Limits and disputes\n\nAllowed pairing representations are candidates until tested against the actual superconducting state. Charge-order time-reversal breaking, a normal-state anomalous Hall signal, structural handedness, tunneling modulation and a zero-bias feature each address different questions. Phase-sensitive experiments, temperature-resolved symmetry probes, bulk gap constraints and boundary-state tests can provide complementary discrimination; they are not a universal checklist that defines every possible topological superconductor. Complete scientific acceptance remains open: several references retain abstract-only review, and final-version comparisons, supplements and raw-data analyses are unfinished. [R3](#ref-source-d49026ec4f5a10a4) [R7](#ref-source-80eda571fc6d710c) [R10](#ref-source-59d803435c0df1ef) [R11](#ref-source-484da7abcc165cd3) [R12](#ref-source-057c43c86174f961) [R15](#ref-source-c415e45e91e02c10)"},{"id":"discovery-implications","title":"Discovery implications","markdown":"## Discovery implications\n\nRecord composition, pressure path, excitation, surface termination and the onset, midpoint, measured-zero and thermodynamic criteria separately. Compare measured band positions with a specified model before invoking flat-band enhancement. Test whether changing charge order also changes disorder, structure or carrier balance. The useful next experiment resolves competing interpretations on a characterized sample, rather than promoting a geometric label or an isolated transition number into a mechanism. [R1](#ref-source-1cd7f905ef6df6e1) [R3](#ref-source-d49026ec4f5a10a4) [R8](#ref-source-dbcbd572b05dcaa4) [R13](#ref-source-4fb5d6fb51bdb253) [R14](#ref-source-d0ee5c328ca326ee)"},{"id":"related-topics","title":"Related topics","markdown":"## Related topics\n\n[Flat bands](/scwiki/flat-band-pairing), [Charge density waves](/scwiki/charge-density-waves), [Chiral pairing](/scwiki/chiral-pairing), [Pair density waves](/scwiki/pair-density-wave), and [Pressure tuning](/scwiki/pressure-tuning)."},{"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| CsV3Sb5 (aliases: cesium vanadium antimonide); Ortiz2020 crystals; bulk evidence from magnetic/transport/calorimetric anomalies; current-sensitive resistive onset | 2.5 K; Approximate superconducting onset; probe current affects resistive curve. Not a universal value. | transition; onset | Transport, magnetization and heat capacity | ambient; unknown GPa | unknown | experiment; [source](#ref-source-d49026ec4f5a10a4) |\n| CsCr3Sb5 (aliases: cesium chromium antimonide); Liu2024 cubic-anvil pressure experiment at4.2GPa | 6.4 K; Resistive onset; differs from50%normal-resistance critical-field criterion. | transition; onset | High-pressure resistivity | high; 4.2 to 4.2 GPa | unknown | experiment; [source](#ref-source-d0ee5c328ca326ee) |"}],"markdown":"# Kagome superconductors\n\nConnect kagome band geometry with material-specific superconducting evidence, separating charge order, Hall response, pressure conditions and pairing candidates.\n\n## Scope\n\nKagome geometry offers a useful starting point for studying flat bands, Dirac crossings, charge order and superconductivity. It does not guarantee that a flat band lies at the Fermi energy, that magnetic frustration produces a spin liquid, or that a material has a high transition temperature. This article separates superconducting AV3Sb5 compounds, pressure-induced superconductivity in CsCr3Sb5 and charge-ordered comparison materials. Normal-state topology and superconducting topology remain separate questions. [R1](#ref-source-1cd7f905ef6df6e1) [R2](#ref-source-96cec6968d3c379a) [R3](#ref-source-d49026ec4f5a10a4) [R14](#ref-source-d0ee5c328ca326ee) [R16](#ref-source-e9b1bdb7cb3c0ee4) [R17](#ref-source-ed0ebd2f956f2b5f)\n\n## Mathematical assumptions\n\nTake one spinless orbital on each of three sites $0,\\mathbf a_1/2,\\mathbf a_2/2$, with triangular Bravais vectors and $q_i=\\mathbf k\\cdot\\mathbf a_i$. For positive nearest-neighbor hopping $t$, a Bloch Hamiltonian is $H=-2t\\begin{pmatrix}0&c_1&c_2\\\\c_1&0&c_3\\\\c_2&c_3&0\\end{pmatrix}$, where $c_1=\\cos(q_1/2)$, $c_2=\\cos(q_2/2)$ and $c_3=\\cos[(q_2-q_1)/2]$. Its bands are $E_f=2t$ and $E_\\pm=t[-1\\pm\\sqrt{4S-3}]$, with $S=c_1^2+c_2^2+c_3^2$. The vectors in Guo and Franz's convention are nearest-neighbor vectors, half the Bravais vectors used here. [R1](#ref-source-1cd7f905ef6df6e1)\n\nThe model has a flat-band contact at Gamma, a Dirac crossing at K and dispersive-band saddles at M. Independent diagonalization checks 1,311 momentum/hopping combinations; numerical Hessians have opposite-sign curvatures at the two M-point saddles. Adding equal same-sublattice hopping shifts all bands by $\\delta(\\mathbf q)=-2u[\\cos q_1+\\cos q_2+\\cos(q_2-q_1)]$. The formerly flat branch then spans $9|u|$ between Gamma and K while the kagome geometry remains. These checks illustrate model sensitivity; they do not calculate a pairing interaction, a material transition temperature or a superconducting invariant. [R1](#ref-source-1cd7f905ef6df6e1)\n\nReal compounds add orbital character, interlayer hopping and reconstruction. Kang's CsV3Sb5 author manuscript combines ARPES dispersions with DFT orbital and sublattice projections:\n\n| Band | Orbital and sublattice assignment | Energy and interpretation |\n| --- | --- | --- |\n| K1 | Mainly $d_{xy}/d_{x^2-y^2}$; p-type, predominantly one sublattice | Can cross $E_F$ as $k_z$ changes; higher-order saddle behavior |\n| K2 | Mainly $d_{xz}/d_{yz}$; p-type | Saddle reported at $-0.15\\pm0.03$ eV relative to $E_F$; remains below $E_F$ in the examined dispersion |\n| K2' | Mainly $d_{xz}/d_{yz}$; m-type, mixed sublattices | Can cross $E_F$ with $k_z$; opposite saddle concavity and stronger nesting |\n\nHere p/m means pure/mixed **sublattice character**, not a superconducting gap symmetry. The sublattice weights come from calculated Bloch functions; ARPES brightness alone does not measure them.\n\nFigure 3 uses 88 eV photons at 60 K. Figure 4 instead uses 95 eV photons at 35 and 95 K, with linear horizontal polarization in both datasets. Its reported approximately 20 meV feature is a **charge-order gap**, not a superconducting gap. Matrix elements change visibility across Brillouin zones. The displayed DFT analysis omits spin–orbit coupling; full reconstruction, spectral fitting and final-version comparisons remain unchecked here. These band constraints do not select the superconducting pairing symmetry. [R8](#ref-source-dbcbd572b05dcaa4)\n\n## Experimental criteria\n\nOrtiz's original family study identified K, Rb and Cs vanadium antimonides as layered kagome metals. The later CsV3Sb5 superconductivity paper combines magnetization, resistivity and heat capacity around a 2.5 K onset. Its transport onset is suppressed at an 8 mA probe current and returns toward the nominal value at lower current, illustrating why excitation belongs in the sample record. The heat-capacity temperature floor limits conclusions about the low-temperature gap. Subsequent K and Rb member reports should retain their own samples and criteria rather than being collapsed into a universal family transition range. [R2](#ref-source-96cec6968d3c379a) [R3](#ref-source-d49026ec4f5a10a4) [R4](#ref-source-1dbc07dbbbe19132) [R5](#ref-source-4027fb28ea284a9f)\n\nThe same CsV3Sb5 work discusses a much higher-temperature anomaly and a normal-state topological band background. ARPES taken well above the superconducting transition and calculated surface states above the Fermi energy do not directly measure a superconducting gap invariant. Liang's three-dimensional CDW study and Li's conjoined-CDW study further emphasize stacking, temperature and surface dependence. Different modulation descriptions cannot be merged into one structure common to every sample or termination. [R3](#ref-source-d49026ec4f5a10a4) [R6](#ref-source-7746049011a0e640) [R7](#ref-source-80eda571fc6d710c)\n\nYang reports anomalous Hall response in KV3Sb5; Yu connects anomalous Hall response in CsV3Sb5 to its higher-temperature charge-order regime. Neither result is a phase-sensitive measurement of superconducting chirality. Ordinary multiband transport, scattering and Berry-curvature contributions require separate analysis. Likewise, the checked Mielke muon study concerns time-reversal symmetry breaking associated with charge order. A signal emerging near that ordering scale cannot simply be reassigned to a superconducting $d+id$ state. [R9](#ref-source-646e363b41fcabb3) [R10](#ref-source-59d803435c0df1ef) [R11](#ref-source-484da7abcc165cd3)\n\nChen's spatially resolved tunneling work proposes a roton pair-density-wave interpretation in CsV3Sb5. Pair-related modulations are significant evidence to investigate, but charge-order changes in local density of states, tunneling matrix elements and Josephson coupling remain relevant controls. Pressure studies also show nonmonotonic superconducting and charge-order scales. Two domes do not by themselves establish two pairing mechanisms: structure, bands, scattering and calibration can evolve together. [R12](#ref-source-057c43c86174f961) [R13](#ref-source-4fb5d6fb51bdb253)\n\nFor CsCr3Sb5, Liu's author manuscript and selected final-paper results report a maximum resistive onset of 6.4 K at 4.2 GPa, with zero resistance and AC susceptibility supporting bulk superconductivity over a pressure interval. Its critical-field curves instead use half the normal resistance. The fitted zero-temperature field is therefore not an independently observed field boundary. The final text explicitly leaves the field direction uncertain, preventing an anisotropy claim. The cubic-anvil measurement uses glycerol and room-temperature load calibration; the lower-pressure piston-cell setup uses a different medium and calibration. These are high-pressure records, not ambient-pressure entries or universal chromium-family numbers. [R14](#ref-source-d0ee5c328ca326ee)\n\nCheng's April 2026 paper adds a distinct charge-order result in CsCr3Sb5. The selected author text describes cleaved-surface STM with a 4.5 K base temperature and two higher-temperature modulation scales. Its stripe pattern breaks mirror symmetries while retaining a mirror-glide operation; opposite local textures do not define global handedness. Those surface images are not a high-pressure superconducting order-parameter measurement and cannot establish chiral superconductivity. [R15](#ref-source-c415e45e91e02c10)\n\nFeGe and ScV6Sn6 serve as comparisons. Yin's FeGe study reports charge order, magnetic stacking and an edge state within a charge-order energy gap; Arachchige's ScV6Sn6 work reports a lattice-modulated charge-order transition. Neither cited result establishes superconductivity. Absence of such evidence in these papers should not be rewritten as a timeless claim that either material can never superconduct under any preparation or pressure. [R16](#ref-source-e9b1bdb7cb3c0ee4) [R17](#ref-source-ed0ebd2f956f2b5f)\n\n## Limits and disputes\n\nAllowed pairing representations are candidates until tested against the actual superconducting state. Charge-order time-reversal breaking, a normal-state anomalous Hall signal, structural handedness, tunneling modulation and a zero-bias feature each address different questions. Phase-sensitive experiments, temperature-resolved symmetry probes, bulk gap constraints and boundary-state tests can provide complementary discrimination; they are not a universal checklist that defines every possible topological superconductor. Complete scientific acceptance remains open: several references retain abstract-only review, and final-version comparisons, supplements and raw-data analyses are unfinished. [R3](#ref-source-d49026ec4f5a10a4) [R7](#ref-source-80eda571fc6d710c) [R10](#ref-source-59d803435c0df1ef) [R11](#ref-source-484da7abcc165cd3) [R12](#ref-source-057c43c86174f961) [R15](#ref-source-c415e45e91e02c10)\n\n## Discovery implications\n\nRecord composition, pressure path, excitation, surface termination and the onset, midpoint, measured-zero and thermodynamic criteria separately. Compare measured band positions with a specified model before invoking flat-band enhancement. Test whether changing charge order also changes disorder, structure or carrier balance. The useful next experiment resolves competing interpretations on a characterized sample, rather than promoting a geometric label or an isolated transition number into a mechanism. [R1](#ref-source-1cd7f905ef6df6e1) [R3](#ref-source-d49026ec4f5a10a4) [R8](#ref-source-dbcbd572b05dcaa4) [R13](#ref-source-4fb5d6fb51bdb253) [R14](#ref-source-d0ee5c328ca326ee)\n\n## Related topics\n\n[Flat bands](/scwiki/flat-band-pairing), [Charge density waves](/scwiki/charge-density-waves), [Chiral pairing](/scwiki/chiral-pairing), [Pair density waves](/scwiki/pair-density-wave), and [Pressure tuning](/scwiki/pressure-tuning).\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| CsV3Sb5 (aliases: cesium vanadium antimonide); Ortiz2020 crystals; bulk evidence from magnetic/transport/calorimetric anomalies; current-sensitive resistive onset | 2.5 K; Approximate superconducting onset; probe current affects resistive curve. Not a universal value. | transition; onset | Transport, magnetization and heat capacity | ambient; unknown GPa | unknown | experiment; [source](#ref-source-d49026ec4f5a10a4) |\n| CsCr3Sb5 (aliases: cesium chromium antimonide); Liu2024 cubic-anvil pressure experiment at4.2GPa | 6.4 K; Resistive onset; differs from50%normal-resistance critical-field criterion. | transition; onset | High-pressure resistivity | high; 4.2 to 4.2 GPa | unknown | experiment; [source](#ref-source-d0ee5c328ca326ee) |\n\n## Sources\n\n### Ref source-1cd7f905ef6df6e1\n\n[R1] Topological insulator on the kagome lattice (2009). [DOI 10.1103/PhysRevB.80.113102](https://doi.org/10.1103/PhysRevB.80.113102). Publication: journal-article. Check: selected-author-model-and-spectrum. Checked: 2026-10-19. Author v2 and journal publication 25 September 2009. Selected pp1–2 read; p2 Hamiltonian/spectrum visually checked. Source uses nearest-neighbor vectors; article uses triangular Bravais vectors twice as long. Full SOC invariant calculation not reproduced.\n### Ref source-96cec6968d3c379a\n\n[R2] New kagome prototype materials: discovery of KV3Sb5, RbV3Sb5 and CsV3Sb5 (2019). [DOI 10.1103/PhysRevMaterials.3.094407](https://doi.org/10.1103/PhysRevMaterials.3.094407). Publication: journal-article. Check: publisher-original-abstract. Checked: 2026-10-19. Published 16 September 2019. Original abstract establishes the layered family and anomalies; not a demonstration that all members are superconducting. Full methods and stoichiometry audit open.\n### Ref source-d49026ec4f5a10a4\n\n[R3] CsV3Sb5: A Z2 Topological Kagome Metal with a Superconducting Ground State (2020). [DOI 10.1103/PhysRevLett.125.247002](https://doi.org/10.1103/PhysRevLett.125.247002). Publication: journal-article. Check: selected-author-bulk-transition-and-ARPES-conditions. Checked: 2026-10-19. Author v1 13 November 2020. Selected p2 methods/results and p3 Figure2 read; p3 visually checked. Magnetization, transport and heat capacity support about2.5K onset. 8mA probe current suppresses transport onset; limited base temperature prevents detailed gap analysis. Normal-state ARPES50–120K; predicted surface band above EF is not an occupied-band observation. Final/supplement/raw-data acceptance open.\n### Ref source-1dbc07dbbbe19132\n\n[R4] Superconductivity in the Z2 kagome metal KV3Sb5 (2021). [DOI 10.1103/PhysRevMaterials.5.034801](https://doi.org/10.1103/PhysRevMaterials.5.034801). Publication: journal-article. Check: author-original-abstract-only. Checked: 2026-10-19. Original abstract checked for bulk superconducting membership, using magnetization, transport and heat capacity. Exact numerical criteria and full methods not audited here.\n### Ref source-4027fb28ea284a9f\n\n[R5] Superconductivity and Normal-State Properties of Kagome Metal RbV3Sb5 Single Crystals (2021). [DOI 10.1088/0256-307X/38/3/037403](https://doi.org/10.1088/0256-307X/38/3/037403). Publication: journal-article. Check: publisher-original-abstract-only. Checked: 2026-10-19. Qiangwei Yin et al.; original publisher abstract checked for superconducting membership, higher-temperature anomalies and multiband Hall interpretation. No numerical transition criterion or full methods audit claimed.\n### Ref source-7746049011a0e640\n\n[R6] Three-Dimensional Charge Density Wave and Surface-Dependent Vortex-Core States in a Kagome Superconductor CsV3Sb5 (2021). [DOI 10.1103/PhysRevX.11.031026](https://doi.org/10.1103/PhysRevX.11.031026). Publication: journal-article. Check: publisher-abstract-check. Checked: 2026-10-19. Published 2 August 2021. Surface step phase shift and suggested three-dimensional order checked at abstract scope; vortex-state identity and full STM data not independently established.\n### Ref source-80eda571fc6d710c\n\n[R7] Discovery of conjoined charge density waves in the kagome superconductor CsV3Sb5 (2022). [DOI 10.1038/s41467-022-33995-2](https://doi.org/10.1038/s41467-022-33995-2). Publication: journal-article. Check: selected-publisher-web-passages-check. Checked: 2026-10-19. Li et al., published 26 October 2022. Abstract, selected results and Figures 1–4 captions read as text; images and raw profiles not independently reviewed. Corrects the inherited attribution to Stahl. Measurements at 10 K and charge-order onsets are not superconducting Tc.\n### Ref source-dbcbd572b05dcaa4\n\n[R8] Twofold van Hove singularity and origin of charge order in topological kagome superconductor CsV3Sb5 (2022). [DOI 10.1038/s41567-021-01451-5](https://doi.org/10.1038/s41567-021-01451-5). Publication: journal-article. Check: selected-author-band-assignments-figures-and-conditions. Checked: 2026-10-20. Author v2, 6 November 2021. Selected pp. 4–9, Figures 3–4 (pp. 17–18), and Table S1 (p. 31) read; three pages visually inspected. Distinguishes the K2 saddle below the Fermi level from kz-dependent K1/K2-prime crossings, DFT sublattice weights from ARPES intensity, and the charge-order gap from a superconducting gap. Complete final-version comparison, supplement and raw-data fits remain unchecked.\n### Ref source-646e363b41fcabb3\n\n[R9] Giant, unconventional anomalous Hall effect in the metallic frustrated magnet candidate, KV3Sb5 (2020). [DOI 10.1126/sciadv.abb6003](https://doi.org/10.1126/sciadv.abb6003). Publication: journal-article. Check: author-institution-abstract-only. Checked: 2026-10-19. Yang et al.;31July2020. Institutional original abstract checked: anomalous Hall response without reported long-range magnetic order. No full ordinary-Hall subtraction or microscopic mechanism audit. Publisher retrieval failed; PMC/PubMed returned challenge pages, which were not treated as evidence.\n### Ref source-59d803435c0df1ef\n\n[R10] Concurrence of anomalous Hall effect and charge density wave in a superconducting topological kagome metal (2021). [DOI 10.1103/PhysRevB.104.L041103](https://doi.org/10.1103/PhysRevB.104.L041103). Publication: journal-article. Check: publisher-original-abstract-only. Checked: 2026-10-19. Yu et al.;8July2021. AHE follows higher-temperature CDW and disappears with CDW suppression under pressure. Skew scattering and Berry-curvature interpretation is the authors explanation, not a measured superconducting order parameter. Full background subtraction and methods open.\n### Ref source-484da7abcc165cd3\n\n[R11] Time-reversal symmetry-breaking charge order in a kagome superconductor (2022). [DOI 10.1038/s41586-021-04327-z](https://doi.org/10.1038/s41586-021-04327-z). Publication: journal-article. Check: selected-author-manuscript-check. Checked: 2026-10-18. Selected pp. 2–3 and 6 plus experimental-methods passages; Fig. 1 on p. 2 visually checked. December 2021 author version 2, published February 2022. Nuclear/electronic and charge/superconducting distinctions retained; full final-version/data review open.\n### Ref source-057c43c86174f961\n\n[R12] Roton pair density wave in a strong-coupling kagome superconductor (2021). [DOI 10.1038/s41586-021-03983-5](https://doi.org/10.1038/s41586-021-03983-5). Publication: journal-article. Check: selected-author-manuscript-check. Checked: 2026-10-18. Selected pp. 3–7 and methods pp. 17–18; Fig. 3 on p. 14 visually checked. Author version 2 September 2021 has a different title and mistyped journal volume 559; publisher confirms Nature 599. Final-version/raw-data comparison open.\n### Ref source-4fb5d6fb51bdb253\n\n[R13] Double Superconducting Dome and Triple Enhancement of Tc in the Kagome Superconductor CsV3Sb5 under High Pressure (2021). [DOI 10.1103/PhysRevLett.126.247001](https://doi.org/10.1103/PhysRevLett.126.247001). Publication: journal-article. Check: publisher-original-abstract-only. Checked: 2026-10-19. Chen et al.;17June2021. Original abstract describes nonmonotonic superconductivity and charge order under pressure. Full pressure calibration, resistive criteria and mechanism assignment not checked here.\n### Ref source-d0ee5c328ca326ee\n\n[R14] Superconductivity under pressure in a chromium-based kagome metal (2024). [DOI 10.1038/s41586-024-07761-x](https://doi.org/10.1038/s41586-024-07761-x). Publication: journal-article. Check: selected-author-and-final-pressure-criteria. Checked: 2026-10-19. Author v2 dated16March2024 has a different title; publisher title/date28August2024 checked independently. Selected pp6–7 results/Figure3 and p17 methods read; p7 visually checked. 6.4K is onset at4.2GPa; Hc2 criterion50%normal resistance; fitted14.34T not directly observed zero-temperature field. Cubic-anvil glycerol with room-temperature load calibration differs from lower-pressure piston-cell Daphne/Pb calibration. Final institutional PDF selected p4 results/Figure3 and pp7–8 pressure methods also checked; p4 visually inspected. Field direction explicitly uncertain, so no anisotropic Hc2 claim. Full extended-data/raw AC calibration and complete version comparison open.\n### Ref source-c415e45e91e02c10\n\n[R15] Frieze charge stripes in a correlated kagome superconductor (2026). [DOI 10.1038/s41567-026-03232-4](https://doi.org/10.1038/s41567-026-03232-4). Publication: journal-article. Check: selected-author-HTML-results-and-STM-methods. Checked: 2026-10-19. Published2April2026;authorv1 7October2025. Selected Results, growth/STM methods and symmetry description read in author HTML. Cleaved Sb surface,4.5K base,50/45K modulation scales, mirror-glide symmetry precludes global handedness. No high-pressure superconducting order-parameter measurement in this STM study. Figure images, full simulation and final comparison open.\n### Ref source-e9b1bdb7cb3c0ee4\n\n[R16] Discovery of Charge Order and Corresponding Edge State in Kagome Magnet FeGe (2022). [DOI 10.1103/PhysRevLett.129.166401](https://doi.org/10.1103/PhysRevLett.129.166401). Publication: journal-article. Check: publisher-original-abstract-and-attribution. Checked: 2026-10-19. Published10October2022;first author Jia-Xin Yin, with Xiaokun Teng a coauthor. Original abstract:2x2 charge order, antiferromagnetic stacking and charge-order-gap edge state. It does not establish a superconducting transition or Majorana state. Full methods open.\n### Ref source-ed0ebd2f956f2b5f\n\n[R17] Charge Density Wave in Kagome Lattice Intermetallic ScV6Sn6 (2022). [DOI 10.1103/PhysRevLett.129.216402](https://doi.org/10.1103/PhysRevLett.129.216402). Publication: journal-article. Check: publisher-original-abstract-only. Checked: 2026-10-19. Published18November2022. Arachchige et al.;92K first-order transition, x-ray/neutron lattice modulation. Charge-order comparison material, not superconductivity evidence. Full diffraction/supplement audit open.\n\n## Claim evidence and conditions\n\n### scwiki-d14-claim-scope-1\n\nKagome geometry offers a useful starting point for studying flat bands, Dirac crossings, charge order and superconductivity. It does not guarantee that a flat band lies at the Fermi energy, that magnetic frustration produces a spin liquid, or that a material has a high transition temperature. This article separates superconducting AV3Sb5 compounds, pressure-induced superconductivity in CsCr3Sb5 and charge-ordered comparison materials. Normal-state topology and superconducting topology remain separate questions.\n\nEvidence: hypothesis. Sources: source-1cd7f905ef6df6e1, source-96cec6968d3c379a, source-d49026ec4f5a10a4, source-d0ee5c328ca326ee, source-e9b1bdb7cb3c0ee4, source-ed0ebd2f956f2b5f.\n\nConditions: Keep composition, pressure, current, surface termination, temperature type and transition criterion separate. Normal-state geometry/order is not superconducting topology.\n\nVerification scope: Selected primary passages/figures and restricted band checks; full scientific acceptance remains open.\n\n### scwiki-d14-claim-mathematical-assumptions-1\n\nTake one spinless orbital on each of three sites $0,\\mathbf a_1/2,\\mathbf a_2/2$, with triangular Bravais vectors and $q_i=\\mathbf k\\cdot\\mathbf a_i$. For positive nearest-neighbor hopping $t$, a Bloch Hamiltonian is $H=-2t\\begin{pmatrix}0&c_1&c_2\\\\c_1&0&c_3\\\\c_2&c_3&0\\end{pmatrix}$, where $c_1=\\cos(q_1/2)$, $c_2=\\cos(q_2/2)$ and $c_3=\\cos[(q_2-q_1)/2]$. Its bands are $E_f=2t$ and $E_\\pm=t[-1\\pm\\sqrt{4S-3}]$, with $S=c_1^2+c_2^2+c_3^2$. The vectors in Guo and Franz's convention are nearest-neighbor vectors, half the Bravais vectors used here.\n\nEvidence: theory. Sources: source-1cd7f905ef6df6e1.\n\nConditions: Keep composition, pressure, current, surface termination, temperature type and transition criterion separate. Normal-state geometry/order is not superconducting topology.\n\nVerification scope: Selected primary passages/figures and restricted band checks; full scientific acceptance remains open.\n\n### scwiki-d14-claim-mathematical-assumptions-2\n\nThe model has a flat-band contact at Gamma, a Dirac crossing at K and dispersive-band saddles at M. Independent diagonalization checks 1,311 momentum/hopping combinations; numerical Hessians have opposite-sign curvatures at the two M-point saddles. Adding equal same-sublattice hopping shifts all bands by $\\delta(\\mathbf q)=-2u[\\cos q_1+\\cos q_2+\\cos(q_2-q_1)]$. The formerly flat branch then spans $9|u|$ between Gamma and K while the kagome geometry remains. These checks illustrate model sensitivity; they do not calculate a pairing interaction, a material transition temperature or a superconducting invariant.\n\nEvidence: theory. Sources: source-1cd7f905ef6df6e1.\n\nConditions: Keep composition, pressure, current, surface termination, temperature type and transition criterion separate. Normal-state geometry/order is not superconducting topology.\n\nVerification scope: Selected primary passages/figures and restricted band checks; full scientific acceptance remains open.\n\n### scwiki-d14-claim-mathematical-assumptions-3\n\nReal compounds add orbital character, interlayer hopping and reconstruction. Kang's CsV3Sb5 author manuscript combines ARPES dispersions with DFT orbital and sublattice projections:\n\n| Band | Orbital and sublattice assignment | Energy and interpretation |\n| --- | --- | --- |\n| K1 | Mainly $d_{xy}/d_{x^2-y^2}$; p-type, predominantly one sublattice | Can cross $E_F$ as $k_z$ changes; higher-order saddle behavior |\n| K2 | Mainly $d_{xz}/d_{yz}$; p-type | Saddle reported at $-0.15\\pm0.03$ eV relative to $E_F$; remains below $E_F$ in the examined dispersion |\n| K2' | Mainly $d_{xz}/d_{yz}$; m-type, mixed sublattices | Can cross $E_F$ with $k_z$; opposite saddle concavity and stronger nesting |\n\nHere p/m means pure/mixed **sublattice character**, not a superconducting gap symmetry. The sublattice weights come from calculated Bloch functions; ARPES brightness alone does not measure them.\n\nFigure 3 uses 88 eV photons at 60 K. Figure 4 instead uses 95 eV photons at 35 and 95 K, with linear horizontal polarization in both datasets. Its reported approximately 20 meV feature is a **charge-order gap**, not a superconducting gap. Matrix elements change visibility across Brillouin zones. The displayed DFT analysis omits spin–orbit coupling; full reconstruction, spectral fitting and final-version comparisons remain unchecked here. These band constraints do not select the superconducting pairing symmetry.\n\nEvidence: editorial-analysis. Sources: source-dbcbd572b05dcaa4.\n\nSource relationship: context-for-editorial-analysis. Editorial comparison of ARPES measurements and DFT projections from selected author v2 pp. 4–9, Figures 3–4 and Table S1. This table organizes measured and computed evidence; it is not a new orbital fit, DFT calculation or pairing derivation.\n\nConditions: CsV3Sb5; author v2 Figure 3: 88 eV photons, linear horizontal polarization, 60 K. Figure 4: 95 eV photons, linear horizontal polarization, 35 and 95 K. Sublattice assignments are calculated; energies are relative to the Fermi level. The charge-order gap is not a superconducting gap.\n\nVerification scope: Selected author v2 pp. 4–9, Figure 3 (p. 17), Figure 4 (p. 18), and Table S1 (p. 31); three pages visually inspected. No raw-data refit, complete final-version comparison or determination of superconducting symmetry.\n\n### scwiki-d14-claim-experimental-criteria-1\n\nOrtiz's original family study identified K, Rb and Cs vanadium antimonides as layered kagome metals. The later CsV3Sb5 superconductivity paper combines magnetization, resistivity and heat capacity around a 2.5 K onset. Its transport onset is suppressed at an 8 mA probe current and returns toward the nominal value at lower current, illustrating why excitation belongs in the sample record. The heat-capacity temperature floor limits conclusions about the low-temperature gap. Subsequent K and Rb member reports should retain their own samples and criteria rather than being collapsed into a universal family transition range.\n\nEvidence: experiment. Sources: source-96cec6968d3c379a, source-d49026ec4f5a10a4, source-1dbc07dbbbe19132, source-4027fb28ea284a9f.\n\nConditions: Keep composition, pressure, current, surface termination, temperature type and transition criterion separate. Normal-state geometry/order is not superconducting topology.\n\nVerification scope: Selected primary passages/figures and restricted band checks; full scientific acceptance remains open.\n\n### scwiki-d14-claim-experimental-criteria-2\n\nThe same CsV3Sb5 work discusses a much higher-temperature anomaly and a normal-state topological band background. ARPES taken well above the superconducting transition and calculated surface states above the Fermi energy do not directly measure a superconducting gap invariant. Liang's three-dimensional CDW study and Li's conjoined-CDW study further emphasize stacking, temperature and surface dependence. Different modulation descriptions cannot be merged into one structure common to every sample or termination.\n\nEvidence: experiment. Sources: source-d49026ec4f5a10a4, source-7746049011a0e640, source-80eda571fc6d710c.\n\nConditions: Keep composition, pressure, current, surface termination, temperature type and transition criterion separate. Normal-state geometry/order is not superconducting topology.\n\nVerification scope: Selected primary passages/figures and restricted band checks; full scientific acceptance remains open.\n\n### scwiki-d14-claim-experimental-criteria-3\n\nYang reports anomalous Hall response in KV3Sb5; Yu connects anomalous Hall response in CsV3Sb5 to its higher-temperature charge-order regime. Neither result is a phase-sensitive measurement of superconducting chirality. Ordinary multiband transport, scattering and Berry-curvature contributions require separate analysis. Likewise, the checked Mielke muon study concerns time-reversal symmetry breaking associated with charge order. A signal emerging near that ordering scale cannot simply be reassigned to a superconducting $d+id$ state.\n\nEvidence: experiment. Sources: source-646e363b41fcabb3, source-59d803435c0df1ef, source-484da7abcc165cd3.\n\nConditions: Keep composition, pressure, current, surface termination, temperature type and transition criterion separate. Normal-state geometry/order is not superconducting topology.\n\nVerification scope: Selected primary passages/figures and restricted band checks; full scientific acceptance remains open.\n\n### scwiki-d14-claim-experimental-criteria-4\n\nChen's spatially resolved tunneling work proposes a roton pair-density-wave interpretation in CsV3Sb5. Pair-related modulations are significant evidence to investigate, but charge-order changes in local density of states, tunneling matrix elements and Josephson coupling remain relevant controls. Pressure studies also show nonmonotonic superconducting and charge-order scales. Two domes do not by themselves establish two pairing mechanisms: structure, bands, scattering and calibration can evolve together.\n\nEvidence: experiment. Sources: source-057c43c86174f961, source-4fb5d6fb51bdb253.\n\nConditions: Keep composition, pressure, current, surface termination, temperature type and transition criterion separate. Normal-state geometry/order is not superconducting topology.\n\nVerification scope: Selected primary passages/figures and restricted band checks; full scientific acceptance remains open.\n\n### scwiki-d14-claim-experimental-criteria-5\n\nFor CsCr3Sb5, Liu's author manuscript and selected final-paper results report a maximum resistive onset of 6.4 K at 4.2 GPa, with zero resistance and AC susceptibility supporting bulk superconductivity over a pressure interval. Its critical-field curves instead use half the normal resistance. The fitted zero-temperature field is therefore not an independently observed field boundary. The final text explicitly leaves the field direction uncertain, preventing an anisotropy claim. The cubic-anvil measurement uses glycerol and room-temperature load calibration; the lower-pressure piston-cell setup uses a different medium and calibration. These are high-pressure records, not ambient-pressure entries or universal chromium-family numbers.\n\nEvidence: experiment. Sources: source-d0ee5c328ca326ee.\n\nConditions: Keep composition, pressure, current, surface termination, temperature type and transition criterion separate. Normal-state geometry/order is not superconducting topology.\n\nVerification scope: Selected primary passages/figures and restricted band checks; full scientific acceptance remains open.\n\n### scwiki-d14-claim-experimental-criteria-6\n\nCheng's April 2026 paper adds a distinct charge-order result in CsCr3Sb5. The selected author text describes cleaved-surface STM with a 4.5 K base temperature and two higher-temperature modulation scales. Its stripe pattern breaks mirror symmetries while retaining a mirror-glide operation; opposite local textures do not define global handedness. Those surface images are not a high-pressure superconducting order-parameter measurement and cannot establish chiral superconductivity.\n\nEvidence: experiment. Sources: source-c415e45e91e02c10.\n\nConditions: Keep composition, pressure, current, surface termination, temperature type and transition criterion separate. Normal-state geometry/order is not superconducting topology.\n\nVerification scope: Selected primary passages/figures and restricted band checks; full scientific acceptance remains open.\n\n### scwiki-d14-claim-experimental-criteria-7\n\nFeGe and ScV6Sn6 serve as comparisons. Yin's FeGe study reports charge order, magnetic stacking and an edge state within a charge-order energy gap; Arachchige's ScV6Sn6 work reports a lattice-modulated charge-order transition. Neither cited result establishes superconductivity. Absence of such evidence in these papers should not be rewritten as a timeless claim that either material can never superconduct under any preparation or pressure.\n\nEvidence: experiment. Sources: source-e9b1bdb7cb3c0ee4, source-ed0ebd2f956f2b5f.\n\nConditions: Keep composition, pressure, current, surface termination, temperature type and transition criterion separate. Normal-state geometry/order is not superconducting topology.\n\nVerification scope: Selected primary passages/figures and restricted band checks; full scientific acceptance remains open.\n\n### scwiki-d14-claim-limits-and-disputes-1\n\nAllowed pairing representations are candidates until tested against the actual superconducting state. Charge-order time-reversal breaking, a normal-state anomalous Hall signal, structural handedness, tunneling modulation and a zero-bias feature each address different questions. Phase-sensitive experiments, temperature-resolved symmetry probes, bulk gap constraints and boundary-state tests can provide complementary discrimination; they are not a universal checklist that defines every possible topological superconductor. Complete scientific acceptance remains open: several references retain abstract-only review, and final-version comparisons, supplements and raw-data analyses are unfinished.\n\nEvidence: hypothesis. Sources: source-d49026ec4f5a10a4, source-80eda571fc6d710c, source-59d803435c0df1ef, source-484da7abcc165cd3, source-057c43c86174f961, source-c415e45e91e02c10.\n\nConditions: Keep composition, pressure, current, surface termination, temperature type and transition criterion separate. Normal-state geometry/order is not superconducting topology.\n\nVerification scope: Selected primary passages/figures and restricted band checks; full scientific acceptance remains open.\n\n### scwiki-d14-claim-discovery-implications-1\n\nRecord composition, pressure path, excitation, surface termination and the onset, midpoint, measured-zero and thermodynamic criteria separately. Compare measured band positions with a specified model before invoking flat-band enhancement. Test whether changing charge order also changes disorder, structure or carrier balance. The useful next experiment resolves competing interpretations on a characterized sample, rather than promoting a geometric label or an isolated transition number into a mechanism.\n\nEvidence: hypothesis. Sources: source-1cd7f905ef6df6e1, source-d49026ec4f5a10a4, source-dbcbd572b05dcaa4, source-4fb5d6fb51bdb253, source-d0ee5c328ca326ee.\n\nConditions: Keep composition, pressure, current, surface termination, temperature type and transition criterion separate. Normal-state geometry/order is not superconducting topology.\n\nVerification scope: Selected primary passages/figures and restricted band checks; full scientific acceptance remains open.\n\n## Revision and review\n\nArticle ID: scwiki-d14. Revision: a6ded33868163826c2b6. Updated: 2026-10-19T17:39:26.273430+00:00.\n\nReview scope: Selected Guo,OrtizCs and LiuCr author passages/figures, plus Liu final pressure criteria/methods/Figure3; Cheng author HTML methods/results; inherited CDW/TRSB/PDW audits; original abstracts with explicit limits; independent kagome band algebra. D14 follow-up: selected Kang author v2 band assignments, DFT and methods text, Figures 3–4 and Table S1; computed sublattice and measured dispersion evidence separated.\n\n- Complete scientific acceptance remains open.\n- Abstract-only references do not establish full methods, orbital assignment or unique pairing mechanisms.\n- Final-version comparisons, supplements, pressure/current controls and raw-data acceptance remain open.\n- Nearest-neighbor spectra do not reproduce a material, superconducting gap equation or invariant.\n\nSource: [D_material_families/D14_kagome.md](https://github.com/JackZH26/jzis-superconductivity/blob/0a7c9d6696804ec26aa12f8eed68b55c9b3c0fcf/D_material_families/D14_kagome.md), commit 0a7c9d6696804ec26aa12f8eed68b55c9b3c0fcf, SHA-256 c100136570cc9f04734a03d9927f17258ffd122af7b503e1b7c6bec46dbf5df4.\n","wordCount":1139}}