# Kagome superconductors

Connect kagome band geometry with material-specific superconducting evidence, separating charge order, Hall response, pressure conditions and pairing candidates.

## Scope

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. [R1](#ref-source-1cd7f905ef6df6e1) [R2](#ref-source-96cec6968d3c379a) [R3](#ref-source-d49026ec4f5a10a4) [R14](#ref-source-d0ee5c328ca326ee) [R16](#ref-source-e9b1bdb7cb3c0ee4) [R17](#ref-source-ed0ebd2f956f2b5f)

## Mathematical assumptions

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. [R1](#ref-source-1cd7f905ef6df6e1)

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. [R1](#ref-source-1cd7f905ef6df6e1)

Real compounds add orbital character, interlayer hopping and reconstruction. Kang's CsV3Sb5 author manuscript combines ARPES dispersions with DFT orbital and sublattice projections:

| Band | Orbital and sublattice assignment | Energy and interpretation |
| --- | --- | --- |
| 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 |
| 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 |
| K2' | Mainly $d_{xz}/d_{yz}$; m-type, mixed sublattices | Can cross $E_F$ with $k_z$; opposite saddle concavity and stronger nesting |

Here 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.

Figure 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)

## Experimental criteria

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. [R2](#ref-source-96cec6968d3c379a) [R3](#ref-source-d49026ec4f5a10a4) [R4](#ref-source-1dbc07dbbbe19132) [R5](#ref-source-4027fb28ea284a9f)

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. [R3](#ref-source-d49026ec4f5a10a4) [R6](#ref-source-7746049011a0e640) [R7](#ref-source-80eda571fc6d710c)

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. [R9](#ref-source-646e363b41fcabb3) [R10](#ref-source-59d803435c0df1ef) [R11](#ref-source-484da7abcc165cd3)

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. [R12](#ref-source-057c43c86174f961) [R13](#ref-source-4fb5d6fb51bdb253)

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. [R14](#ref-source-d0ee5c328ca326ee)

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. [R15](#ref-source-c415e45e91e02c10)

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. [R16](#ref-source-e9b1bdb7cb3c0ee4) [R17](#ref-source-ed0ebd2f956f2b5f)

## Limits and disputes

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. [R3](#ref-source-d49026ec4f5a10a4) [R7](#ref-source-80eda571fc6d710c) [R10](#ref-source-59d803435c0df1ef) [R11](#ref-source-484da7abcc165cd3) [R12](#ref-source-057c43c86174f961) [R15](#ref-source-c415e45e91e02c10)

## Discovery implications

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. [R1](#ref-source-1cd7f905ef6df6e1) [R3](#ref-source-d49026ec4f5a10a4) [R8](#ref-source-dbcbd572b05dcaa4) [R13](#ref-source-4fb5d6fb51bdb253) [R14](#ref-source-d0ee5c328ca326ee)

## Related topics

[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).

## Material cases

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

| Material and sample | Reported temperature | Criterion | Probe | Pressure | State | Evidence |
|---|---|---|---|---|---|---|
| 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) |
| 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) |

## Sources

### Ref source-1cd7f905ef6df6e1

[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.
### Ref source-96cec6968d3c379a

[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.
### Ref source-d49026ec4f5a10a4

[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.
### Ref source-1dbc07dbbbe19132

[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.
### Ref source-4027fb28ea284a9f

[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.
### Ref source-7746049011a0e640

[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.
### Ref source-80eda571fc6d710c

[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.
### Ref source-dbcbd572b05dcaa4

[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.
### Ref source-646e363b41fcabb3

[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.
### Ref source-59d803435c0df1ef

[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.
### Ref source-484da7abcc165cd3

[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.
### Ref source-057c43c86174f961

[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.
### Ref source-4fb5d6fb51bdb253

[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.
### Ref source-d0ee5c328ca326ee

[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.
### Ref source-c415e45e91e02c10

[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.
### Ref source-e9b1bdb7cb3c0ee4

[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.
### Ref source-ed0ebd2f956f2b5f

[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.

## Claim evidence and conditions

### scwiki-d14-claim-scope-1

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.

Evidence: hypothesis. Sources: 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.

Verification scope: Selected primary passages/figures and restricted band checks; full scientific acceptance remains open.

### scwiki-d14-claim-mathematical-assumptions-1

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.

Evidence: theory. Sources: source-1cd7f905ef6df6e1.

Conditions: Keep composition, pressure, current, surface termination, temperature type and transition criterion separate. Normal-state geometry/order is not superconducting topology.

Verification scope: Selected primary passages/figures and restricted band checks; full scientific acceptance remains open.

### scwiki-d14-claim-mathematical-assumptions-2

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.

Evidence: theory. Sources: source-1cd7f905ef6df6e1.

Conditions: Keep composition, pressure, current, surface termination, temperature type and transition criterion separate. Normal-state geometry/order is not superconducting topology.

Verification scope: Selected primary passages/figures and restricted band checks; full scientific acceptance remains open.

### scwiki-d14-claim-mathematical-assumptions-3

Real compounds add orbital character, interlayer hopping and reconstruction. Kang's CsV3Sb5 author manuscript combines ARPES dispersions with DFT orbital and sublattice projections:

| Band | Orbital and sublattice assignment | Energy and interpretation |
| --- | --- | --- |
| 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 |
| 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 |
| K2' | Mainly $d_{xz}/d_{yz}$; m-type, mixed sublattices | Can cross $E_F$ with $k_z$; opposite saddle concavity and stronger nesting |

Here 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.

Figure 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.

Evidence: editorial-analysis. Sources: source-dbcbd572b05dcaa4.

Source 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.

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.

Verification 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.

### scwiki-d14-claim-experimental-criteria-1

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.

Evidence: experiment. Sources: 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.

Verification scope: Selected primary passages/figures and restricted band checks; full scientific acceptance remains open.

### scwiki-d14-claim-experimental-criteria-2

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.

Evidence: experiment. Sources: 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.

Verification scope: Selected primary passages/figures and restricted band checks; full scientific acceptance remains open.

### scwiki-d14-claim-experimental-criteria-3

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.

Evidence: experiment. Sources: 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.

Verification scope: Selected primary passages/figures and restricted band checks; full scientific acceptance remains open.

### scwiki-d14-claim-experimental-criteria-4

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.

Evidence: experiment. Sources: 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.

Verification scope: Selected primary passages/figures and restricted band checks; full scientific acceptance remains open.

### scwiki-d14-claim-experimental-criteria-5

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.

Evidence: experiment. Sources: source-d0ee5c328ca326ee.

Conditions: Keep composition, pressure, current, surface termination, temperature type and transition criterion separate. Normal-state geometry/order is not superconducting topology.

Verification scope: Selected primary passages/figures and restricted band checks; full scientific acceptance remains open.

### scwiki-d14-claim-experimental-criteria-6

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.

Evidence: experiment. Sources: source-c415e45e91e02c10.

Conditions: Keep composition, pressure, current, surface termination, temperature type and transition criterion separate. Normal-state geometry/order is not superconducting topology.

Verification scope: Selected primary passages/figures and restricted band checks; full scientific acceptance remains open.

### scwiki-d14-claim-experimental-criteria-7

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.

Evidence: experiment. Sources: 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.

Verification scope: Selected primary passages/figures and restricted band checks; full scientific acceptance remains open.

### scwiki-d14-claim-limits-and-disputes-1

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.

Evidence: hypothesis. Sources: 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.

Verification scope: Selected primary passages/figures and restricted band checks; full scientific acceptance remains open.

### scwiki-d14-claim-discovery-implications-1

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.

Evidence: hypothesis. Sources: 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.

Verification scope: Selected primary passages/figures and restricted band checks; full scientific acceptance remains open.

## Revision and review

Article ID: scwiki-d14. Revision: a6ded33868163826c2b6. Updated: 2026-10-19T17:39:26.273430+00:00.

Review 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.

- 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.

Source: [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.