{"schemaVersion":"1.0","revision":"fa961ab24277a91737c3","article":{"id":"scwiki-h4","topicId":"scwiki-topic-h4","code":"H4","slug":"charge-density-waves","title":"Charge-density waves: observations, competition and reconstruction","summary":"Read charge-order evidence with its material, wave vector, dimensionality and resolution limits; distinguish competition from a pairing mechanism.","aliases":["charge density wave","charge-density waves","CDW","电荷密度波"],"evidenceTypes":["experiment","theory","hypothesis"],"relatedCodes":["H3","B6","C8"],"editorialStatus":"scoped-check","contentState":"pilot","modifiedAt":"2026-10-18T16:48:09.729599+00:00","review":{"checkedAt":"2026-10-19","scope":"Selected Gerber author methods and diffraction figures; Chang final methods, table and figures; primary kagome abstracts and Li publisher passages; inherited scoped B6/C8 evidence; independent correlation and Gaussian-width checks.","limitations":["Complete scientific acceptance remains open.","Complete source-version, raw-data, supplementary calibration and competing-structure reviews remain open.","Selected abstracts do not establish a unique CDW mechanism, PDW or superconducting chirality.","Line-shape examples are models, not reanalyses of experimental profiles."]},"provenance":{"repository":"JackZH26/jzis-superconductivity","commit":"0a7c9d6696804ec26aa12f8eed68b55c9b3c0fcf","path":"H_anomalous_normal_state/H4_CDW.md","sha256":"cb5476fe2c7c2dea8b709ea989ffbb124b785c4437edb20dafaac852188af6b4","sourceId":"file-89e072ebf9e09927"},"sourceMap":[{"startLine":1,"endLine":123,"targetSections":["scope","mathematical-assumptions","experimental-criteria","limits-and-disputes","discovery-implications","related-topics"],"decision":"edited-with-scoped-evidence","note":"Pinned chapter retained. Corrected reference attribution, separated resolution treatments and probe limits. Original audit labels do not prove full acceptance."}],"corrections":[{"id":"scwiki-h4-correction-1","description":"The conjoined-CDW paper with DOI 10.1038/s41467-022-33995-2 is by Li and colleagues. Stahl's temperature-dependent stacking paper is DOI 10.1103/PhysRevB.105.195136.","sourceId":"source-80eda571fc6d710c","scope":"Correct inherited author-to-DOI attribution; preserve distinct structures and study conditions."}],"equationChecks":[{"targetSectionId":"mathematical-assumptions","tex":"S(q)=(1-r^2)/(1+r^2-2r\\cos q)","check":"30 lattice Fourier sums and 9 Gaussian variance corrections independently checked; B6 static free-energy illustration retained with explicit quartic convention. No diffraction fit reproduced."}],"references":[{"id":"source-b33aab72ae697f3a","doi":"10.1038/375561a0","title":"Evidence for stripe correlations of spins and holes in copper oxide superconductors","year":1995,"url":"https://doi.org/10.1038/375561a0","publicationStatus":"journal-article","verification":{"scope":"publisher-abstract-check","checkedAt":"2026-10-18","evidenceUrl":"https://www.nature.com/articles/375561a0","note":"Publisher abstract and identity checked: 15 June 1995, Nd-substituted compound x=0.12, neutron diffraction. Full paper and data not reviewed."}},{"id":"source-9ae65971bc3eb5b8","doi":"10.1126/science.1223532","title":"Long-Range Incommensurate Charge Fluctuations in (Y,Nd)Ba2Cu3O6+x","year":2012,"url":"https://doi.org/10.1126/science.1223532","publicationStatus":"journal-article","verification":{"scope":"author-manuscript-scoped-check","checkedAt":"2026-10-18","evidenceUrl":"https://arxiv.org/pdf/1207.0915v1","note":"Ghiringhelli et al. selected PDF pp.4–6,20–21: resonance/polarization,130meV resolution, author20meV bound and competition. Bound is not a resolved mode. Final-version and raw-data review open."}},{"id":"source-c4a9d4e1b52d95bb","doi":"10.1038/nphys2456","title":"Direct observation of competition between superconductivity and charge density wave order in YBa2Cu3O6.67","year":2012,"url":"https://doi.org/10.1038/nphys2456","publicationStatus":"journal-article","verification":{"scope":"author-manuscript-scoped-check","checkedAt":"2026-10-18","evidenceUrl":"https://arxiv.org/pdf/1206.4333v2","note":"Chang et al. selected pp.1–2: detwinned ortho-VIII crystal,100keV,up to17T,67K versus135K; zero-field CDW and field enhancement below Tc. Transition criterion/raw data not fully audited; no sample Tc record created."}},{"id":"source-d9477b85392d03f9","doi":"10.1126/science.aac6257","title":"Three-dimensional charge density wave order in YBa2Cu3O6.67 at high magnetic fields","year":2015,"url":"https://doi.org/10.1126/science.aac6257","publicationStatus":"journal-article","verification":{"scope":"selected-author-methods-and-figure-check","checkedAt":"2026-10-19","evidenceUrl":"https://arxiv.org/pdf/1506.07910v1","note":"Author v1 selected pp. 4, 10, 13 read; Figures 2 and 3 on pp. 9–10 visually checked. Gaussian correlation lengths are uncorrected lower bounds. Final-version comparison and raw-data reproduction remain open."}},{"id":"source-b89f6bcf54acb4d8","doi":"10.1038/ncomms11494","title":"Magnetic field controlled charge density wave coupling in underdoped YBa2Cu3O6+x","year":2016,"url":"https://doi.org/10.1038/ncomms11494","publicationStatus":"journal-article","verification":{"scope":"selected-final-methods-table-and-figure-check","checkedAt":"2026-10-19","evidenceUrl":"https://www.nature.com/articles/ncomms11494.pdf","note":"Published 5 May 2016. Selected pp. 3, 5–6 read; Figures 4–5 on p. 5 and Table 1/methods on p. 6 visually checked. Resolution-corrected Gaussian widths, 16.9 T limit and absolute temperature uncertainty distinguished. Complete raw-profile and stacking-model reproduction remain open."}},{"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-d773a884dacbd7c9","doi":"10.1103/PhysRevB.105.195136","title":"Temperature-driven reorganization of electronic order in CsV3Sb5","year":2022,"url":"https://doi.org/10.1103/PhysRevB.105.195136","publicationStatus":"journal-article","verification":{"scope":"publisher-abstract-and-identity-check","checkedAt":"2026-10-19","evidenceUrl":"https://journals.aps.org/prb/abstract/10.1103/PhysRevB.105.195136","note":"Stahl et al., published 24 May 2022. Abstract reports temperature-dependent stacking and a null diffraction response up to 10 T. Full refinements not reviewed; distinguish this DOI from Li et al. conjoined-CDW work."}},{"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-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":"accepted-manuscript-abstract-check","checkedAt":"2026-10-19","evidenceUrl":"https://www.dora.lib4ri.ch/psi/islandora/object/psi:40892/datastream/PDF2/Mielke_III-2022-Time-reversal_symmetry-breaking_charge_order_in-(accepted_version).pdf","note":"Accepted manuscript opening abstract read: KV3Sb5 muon field-width enhancement below charge ordering. Full background calibration, magnetic interpretation and superconducting gap fits remain 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-74169f2f9bc31219","doi":"10.1103/PhysRevLett.75.4650","title":"Singular Quasiparticle Scattering in the Proximity of Charge Instabilities","year":1995,"url":"https://doi.org/10.1103/PhysRevLett.75.4650","publicationStatus":"journal-article","verification":{"scope":"publisher-abstract-scoped-check","checkedAt":"2026-10-18","evidenceUrl":"https://link.aps.org/doi/10.1103/PhysRevLett.75.4650","note":"Castellani–Di Castro–Grilli abstract: infinite-U Hubbard–Holstein model and long-range Coulomb change from zero to finite wave vector. Full calculation not read or reproduced."}}],"materialCases":[{"recordType":"experiment","tcK":null,"temperatureKind":"measurement","pressureRegime":"ambient","pressureGPa":null,"equilibrium":"unknown","id":"scwiki-h4-material-1","formula":"YBa2Cu3O6.67","sample":"Gerber high-field YBCO6.67 diffraction series","reportedTemperatureK":10,"temperatureNote":"Diffraction at 10 K; not superconducting Tc.","criterion":"diffraction-measurement","probe":"Pulsed-field X-ray diffraction","sourceId":"source-d9477b85392d03f9","aliases":["YBCO"]},{"recordType":"experiment","tcK":null,"temperatureKind":"measurement","pressureRegime":"ambient","pressureGPa":null,"equilibrium":"unknown","id":"scwiki-h4-material-2","formula":"CsV3Sb5","sample":"Li resonant scattering specimen at ambient pressure","reportedTemperatureK":10,"temperatureNote":"Resonant scattering at 10 K; not superconducting Tc.","criterion":"REXS-measurement","probe":"Sb L1-edge resonant elastic X-ray scattering","sourceId":"source-80eda571fc6d710c","aliases":["CsV3Sb5"]},{"recordType":"experiment","tcK":null,"temperatureKind":"measurement","pressureRegime":"high","pressureGPa":{"min":1,"max":1},"equilibrium":"unknown","id":"scwiki-h4-material-3","formula":"CsV3Sb5","sample":"Li high-pressure diffraction at 1 GPa","reportedTemperatureK":61,"temperatureNote":"Diffraction comparison temperature; separates charge-order peaks and is not superconducting Tc.","criterion":"diffraction-measurement","probe":"High-pressure X-ray diffraction","sourceId":"source-80eda571fc6d710c","aliases":["CsV3Sb5"]}],"claims":[{"id":"scwiki-h4-claim-scope-1","sectionId":"scope","statement":"A charge-density wave (CDW) modulates the electronic density at a finite wave vector, often together with atomic displacements. Cuprates and kagome compounds exhibit several distinct charge-order patterns. Their coexistence or competition with superconductivity depends on composition, temperature, field, pressure and the probe's spatial and temporal resolution. Neither a density modulation nor a nearby superconducting dome identifies the pairing interaction.","evidenceType":"hypothesis","sourceIds":["source-9ae65971bc3eb5b8","source-c4a9d4e1b52d95bb","source-80eda571fc6d710c","source-74169f2f9bc31219"],"conditions":"Retain specimen, wave vector units, field, pressure, probe, source version and resolution correction. Charge-order and measurement temperatures are not superconducting Tc.","verificationScope":"Selected primary evidence and independent correlation models; full scientific acceptance remains open."},{"id":"scwiki-h4-claim-scope-2","sectionId":"scope","statement":"This page addresses observations and their interpretation. Pair-density waves instead modulate the superconducting pair field; spin-density waves modulate magnetization. Charge order, structural chirality, broken time-reversal symmetry and superconducting chirality are different claims. The retained source chapter's citation of Stahl for the conjoined-CDW paper is corrected: that paper is by Li and colleagues; Stahl's temperature-dependent stacking study has a different DOI.","evidenceType":"hypothesis","sourceIds":["source-d773a884dacbd7c9","source-80eda571fc6d710c","source-484da7abcc165cd3","source-057c43c86174f961"],"conditions":"Retain specimen, wave vector units, field, pressure, probe, source version and resolution correction. Charge-order and measurement temperatures are not superconducting Tc.","verificationScope":"Selected primary evidence and independent correlation models; full scientific acceptance remains open."},{"id":"scwiki-h4-claim-mathematical-assumptions-1","sectionId":"mathematical-assumptions","statement":"A single-component modulation can be written as $\\rho(\\mathbf r)=\\rho_0+\\operatorname{Re}[\\rho_{\\mathbf Q}e^{i\\mathbf Q\\cdot\\mathbf r}]$. Peak position identifies periodicity, while width constrains correlations under a stated line-shape model. For the illustrative lattice correlation $C(n)=r^{|n|}$, with $r=e^{-1/\\xi}$ and $\\xi$ in lattice spacings, the Fourier sum is $S(q)=(1-r^2)/(1+r^2-2r\\cos q)$. Here $q$ is dimensionless radians per spacing, measured from the ordering wave vector. Finite $\\xi$ produces a finite-width peak; observing that peak does not establish infinite-range order. This is an independent correlation model, not a fit to the cited specimens.","evidenceType":"theory","sourceIds":["source-d9477b85392d03f9","source-b89f6bcf54acb4d8"],"conditions":"Retain specimen, wave vector units, field, pressure, probe, source version and resolution correction. Charge-order and measurement temperatures are not superconducting Tc.","verificationScope":"Selected primary evidence and independent correlation models; full scientific acceptance remains open."},{"id":"scwiki-h4-claim-mathematical-assumptions-2","sectionId":"mathematical-assumptions","statement":"Correlation lengths also depend on resolution and conventions. If both intrinsic and instrumental profiles are Gaussian, $\\sigma_{\\rm obs}^2=\\sigma_{\\rm int}^2+\\sigma_R^2$. The convention $\\xi=1/\\sigma_{\\rm int}$ then requires momentum widths in inverse-length units. Reciprocal-lattice widths need the appropriate lattice conversion. Uncorrected $1/\\sigma_{\\rm obs}$ is a lower bound within this model. Gaussian standard deviations, Lorentzian half-widths and full widths are not interchangeable; a resolution-limited peak yields a bound rather than a precisely measured divergence.","evidenceType":"theory","sourceIds":["source-d9477b85392d03f9","source-b89f6bcf54acb4d8"],"conditions":"Retain specimen, wave vector units, field, pressure, probe, source version and resolution correction. Charge-order and measurement temperatures are not superconducting Tc.","verificationScope":"Selected primary evidence and independent correlation models; full scientific acceptance remains open."},{"id":"scwiki-h4-claim-mathematical-assumptions-3","sectionId":"mathematical-assumptions","statement":"A phenomenological free energy $F=a_s|\\Delta|^2+b_s|\\Delta|^4+a_c|\\rho_{\\mathbf Q}|^2+b_c|\\rho_{\\mathbf Q}|^4+g|\\Delta|^2|\\rho_{\\mathbf Q}|^2$ illustrates static competition when $g>0$. With positive quartic coefficients, a stable interior coexistence minimum additionally requires $4b_sb_c-g^2>0$ and positive equilibrium squared amplitudes. Competition alone neither guarantees coexistence nor determines the frequency-dependent pairing kernel. Charge fluctuations could contribute to an effective interaction in a specified microscopic model without making every observed CDW a pairing mechanism.","evidenceType":"theory","sourceIds":["source-c4a9d4e1b52d95bb","source-74169f2f9bc31219"],"conditions":"Retain specimen, wave vector units, field, pressure, probe, source version and resolution correction. Charge-order and measurement temperatures are not superconducting Tc.","verificationScope":"Selected primary evidence and independent correlation models; full scientific acceptance remains open."},{"id":"scwiki-h4-claim-experimental-criteria-1","sectionId":"experimental-criteria","statement":"Tranquada's historical neutron result concerns Nd-substituted La1.6−xNd0.4SrxCuO4 at $x=0.12$. Its static stripe evidence and suppressed superconductivity should not be assigned indiscriminately to every one-eighth-doped cuprate. Ghiringhelli's resonant X-ray study adds an element-sensitive charge response in underdoped YBCO. The selected author text uses 130 meV instrumental resolution and argues for a much smaller energy bound; that bound is not a separately resolved sharp collective mode.","evidenceType":"experiment","sourceIds":["source-b33aab72ae697f3a","source-9ae65971bc3eb5b8"],"conditions":"Retain specimen, wave vector units, field, pressure, probe, source version and resolution correction. Charge-order and measurement temperatures are not superconducting Tc.","verificationScope":"Selected primary evidence and independent correlation models; full scientific acceptance remains open."},{"id":"scwiki-h4-claim-experimental-criteria-2","sectionId":"experimental-criteria","statement":"Chang's 2012 experiment on detwinned ortho-VIII YBa2Cu3O6.67 finds charge-order intensity suppressed on entering the superconducting regime and enhanced by magnetic field below it. Those controlled changes support competition in this specimen. They do not isolate every field-induced change in vortices or electronic structure, and do not identify a unique microscopic interaction.","evidenceType":"experiment","sourceIds":["source-c4a9d4e1b52d95bb"],"conditions":"Retain specimen, wave vector units, field, pressure, probe, source version and resolution correction. Charge-order and measurement temperatures are not superconducting Tc.","verificationScope":"Selected primary evidence and independent correlation models; full scientific acceptance remains open."},{"id":"scwiki-h4-claim-experimental-criteria-3","sectionId":"experimental-criteria","statement":"Gerber's high-field diffraction shows additional interlayer-correlated order developing above about 15 T at 10 K. The author Figure 3 separates peaks near integer and half-integer out-of-plane coordinates and extracts Gaussian widths. Its reported lengths are explicitly uncorrected for resolution. Chang's 2016 study instead reports resolution-corrected widths: for YBCO6.67, the c-axis scale reaches about four lattice periods within the measured field range. Finite three-dimensional correlations must remain distinct from unlimited long-range coherence. These analyses cannot be combined by silently treating corrected and uncorrected widths as equivalent.","evidenceType":"experiment","sourceIds":["source-d9477b85392d03f9","source-b89f6bcf54acb4d8"],"conditions":"Retain specimen, wave vector units, field, pressure, probe, source version and resolution correction. Charge-order and measurement temperatures are not superconducting Tc.","verificationScope":"Selected primary evidence and independent correlation models; full scientific acceptance remains open."},{"id":"scwiki-h4-claim-experimental-criteria-4","sectionId":"experimental-criteria","statement":"Kagome studies probe different structures and surfaces. Liang's STM step-edge phase shift suggests $2\\times2\\times2$ order. Stahl's bulk diffraction reports a low-temperature $2\\times2\\times2$ structure changing to $2\\times2\\times4$ near 60 K on warming; its null response to fields up to 10 T does not rule out broken time-reversal symmetry. Li's separate CsV3Sb5 study resolves conjoined $2\\times2\\times1$ and $2\\times2\\times2$ charge-order responses, with distinct resonant behavior and a roughly 4 K onset separation at 1 GPa. That separation concerns charge order, not two superconducting transitions.","evidenceType":"experiment","sourceIds":["source-7746049011a0e640","source-d773a884dacbd7c9","source-80eda571fc6d710c"],"conditions":"Retain specimen, wave vector units, field, pressure, probe, source version and resolution correction. Charge-order and measurement temperatures are not superconducting Tc.","verificationScope":"Selected primary evidence and independent correlation models; full scientific acceptance remains open."},{"id":"scwiki-h4-claim-limits-and-disputes-1","sectionId":"limits-and-disputes","statement":"A scattering superlattice peak needs electronic, structural and instrumental interpretation; it is not by itself proof of an exclusively electronic instability. STM conductance modulations must be compared across bias, surface termination and bulk probes. Li's surface modulation and bulk-null comparison illustrates why a surface pattern cannot automatically be promoted to a universal bulk phase. The present review does not independently reproduce those sensitivity limits or resolve every reported stacking structure.","evidenceType":"hypothesis","sourceIds":["source-7746049011a0e640","source-80eda571fc6d710c"],"conditions":"Retain specimen, wave vector units, field, pressure, probe, source version and resolution correction. Charge-order and measurement temperatures are not superconducting Tc.","verificationScope":"Selected primary evidence and independent correlation models; full scientific acceptance remains open."},{"id":"scwiki-h4-claim-limits-and-disputes-2","sectionId":"limits-and-disputes","statement":"Mielke's accepted-manuscript abstract reports enhanced internal-field widths in KV3Sb5 below charge ordering, interpreted as time-reversal symmetry breaking. This is a normal-state charge-order claim, not a direct determination of chiral superconducting pairing. Chen's spatially modulated tunnelling signatures motivate a kagome PDW interpretation, but interpretation of the pair field requires additional evidence beyond ordinary charge contrast. Material identity, probe coupling and the superconducting transition must remain explicit.","evidenceType":"hypothesis","sourceIds":["source-484da7abcc165cd3","source-057c43c86174f961"],"conditions":"Retain specimen, wave vector units, field, pressure, probe, source version and resolution correction. Charge-order and measurement temperatures are not superconducting Tc.","verificationScope":"Selected primary evidence and independent correlation models; full scientific acceptance remains open."},{"id":"scwiki-h4-claim-limits-and-disputes-3","sectionId":"limits-and-disputes","statement":"Complete scientific acceptance remains open. Selected methods and figures, historical abstracts and independent line-shape checks do not replace full source-version comparisons, raw diffraction reproduction, all supplementary calibrations or competing-structure assessment. A Hall anomaly, a Fermi-surface pocket or a charge onset below a pseudogap scale cannot alone specify which charge structure causes reconstruction or whether it mediates pairing.","evidenceType":"hypothesis","sourceIds":["source-c4a9d4e1b52d95bb","source-d9477b85392d03f9","source-b89f6bcf54acb4d8"],"conditions":"Retain specimen, wave vector units, field, pressure, probe, source version and resolution correction. Charge-order and measurement temperatures are not superconducting Tc.","verificationScope":"Selected primary evidence and independent correlation models; full scientific acceptance remains open."},{"id":"scwiki-h4-claim-discovery-implications-1","sectionId":"discovery-implications","statement":"Preserve the measured wave vector and reciprocal units, sample composition, oxygen order, field direction, pressure medium, line shape and resolution treatment. Compare competing-order amplitudes on characterized specimens and distinguish a static order parameter from dynamic spectral weight. Useful predictions should connect a particular charge structure to a testable electronic reconstruction and superconducting response, including results that could falsify the proposed connection.","evidenceType":"hypothesis","sourceIds":["source-9ae65971bc3eb5b8","source-c4a9d4e1b52d95bb","source-b89f6bcf54acb4d8","source-74169f2f9bc31219"],"conditions":"Retain specimen, wave vector units, field, pressure, probe, source version and resolution correction. Charge-order and measurement temperatures are not superconducting Tc.","verificationScope":"Selected primary evidence and independent correlation models; full scientific acceptance remains open."}],"body":"## Scope\n\nA charge-density wave (CDW) modulates the electronic density at a finite wave vector, often together with atomic displacements. Cuprates and kagome compounds exhibit several distinct charge-order patterns. Their coexistence or competition with superconductivity depends on composition, temperature, field, pressure and the probe's spatial and temporal resolution. Neither a density modulation nor a nearby superconducting dome identifies the pairing interaction. [R2](#ref-source-9ae65971bc3eb5b8) [R3](#ref-source-c4a9d4e1b52d95bb) [R8](#ref-source-80eda571fc6d710c) [R11](#ref-source-74169f2f9bc31219)\n\nThis page addresses observations and their interpretation. Pair-density waves instead modulate the superconducting pair field; spin-density waves modulate magnetization. Charge order, structural chirality, broken time-reversal symmetry and superconducting chirality are different claims. The retained source chapter's citation of Stahl for the conjoined-CDW paper is corrected: that paper is by Li and colleagues; Stahl's temperature-dependent stacking study has a different DOI. [R7](#ref-source-d773a884dacbd7c9) [R8](#ref-source-80eda571fc6d710c) [R9](#ref-source-484da7abcc165cd3) [R10](#ref-source-057c43c86174f961)\n\n## Mathematical assumptions\n\nA single-component modulation can be written as $\\rho(\\mathbf r)=\\rho_0+\\operatorname{Re}[\\rho_{\\mathbf Q}e^{i\\mathbf Q\\cdot\\mathbf r}]$. Peak position identifies periodicity, while width constrains correlations under a stated line-shape model. For the illustrative lattice correlation $C(n)=r^{|n|}$, with $r=e^{-1/\\xi}$ and $\\xi$ in lattice spacings, the Fourier sum is $S(q)=(1-r^2)/(1+r^2-2r\\cos q)$. Here $q$ is dimensionless radians per spacing, measured from the ordering wave vector. Finite $\\xi$ produces a finite-width peak; observing that peak does not establish infinite-range order. This is an independent correlation model, not a fit to the cited specimens. [R4](#ref-source-d9477b85392d03f9) [R5](#ref-source-b89f6bcf54acb4d8)\n\nCorrelation lengths also depend on resolution and conventions. If both intrinsic and instrumental profiles are Gaussian, $\\sigma_{\\rm obs}^2=\\sigma_{\\rm int}^2+\\sigma_R^2$. The convention $\\xi=1/\\sigma_{\\rm int}$ then requires momentum widths in inverse-length units. Reciprocal-lattice widths need the appropriate lattice conversion. Uncorrected $1/\\sigma_{\\rm obs}$ is a lower bound within this model. Gaussian standard deviations, Lorentzian half-widths and full widths are not interchangeable; a resolution-limited peak yields a bound rather than a precisely measured divergence. [R4](#ref-source-d9477b85392d03f9) [R5](#ref-source-b89f6bcf54acb4d8)\n\nA phenomenological free energy $F=a_s|\\Delta|^2+b_s|\\Delta|^4+a_c|\\rho_{\\mathbf Q}|^2+b_c|\\rho_{\\mathbf Q}|^4+g|\\Delta|^2|\\rho_{\\mathbf Q}|^2$ illustrates static competition when $g>0$. With positive quartic coefficients, a stable interior coexistence minimum additionally requires $4b_sb_c-g^2>0$ and positive equilibrium squared amplitudes. Competition alone neither guarantees coexistence nor determines the frequency-dependent pairing kernel. Charge fluctuations could contribute to an effective interaction in a specified microscopic model without making every observed CDW a pairing mechanism. [R3](#ref-source-c4a9d4e1b52d95bb) [R11](#ref-source-74169f2f9bc31219)\n\n## Experimental criteria\n\nTranquada's historical neutron result concerns Nd-substituted La1.6−xNd0.4SrxCuO4 at $x=0.12$. Its static stripe evidence and suppressed superconductivity should not be assigned indiscriminately to every one-eighth-doped cuprate. Ghiringhelli's resonant X-ray study adds an element-sensitive charge response in underdoped YBCO. The selected author text uses 130 meV instrumental resolution and argues for a much smaller energy bound; that bound is not a separately resolved sharp collective mode. [R1](#ref-source-b33aab72ae697f3a) [R2](#ref-source-9ae65971bc3eb5b8)\n\nChang's 2012 experiment on detwinned ortho-VIII YBa2Cu3O6.67 finds charge-order intensity suppressed on entering the superconducting regime and enhanced by magnetic field below it. Those controlled changes support competition in this specimen. They do not isolate every field-induced change in vortices or electronic structure, and do not identify a unique microscopic interaction. [R3](#ref-source-c4a9d4e1b52d95bb)\n\nGerber's high-field diffraction shows additional interlayer-correlated order developing above about 15 T at 10 K. The author Figure 3 separates peaks near integer and half-integer out-of-plane coordinates and extracts Gaussian widths. Its reported lengths are explicitly uncorrected for resolution. Chang's 2016 study instead reports resolution-corrected widths: for YBCO6.67, the c-axis scale reaches about four lattice periods within the measured field range. Finite three-dimensional correlations must remain distinct from unlimited long-range coherence. These analyses cannot be combined by silently treating corrected and uncorrected widths as equivalent. [R4](#ref-source-d9477b85392d03f9) [R5](#ref-source-b89f6bcf54acb4d8)\n\nKagome studies probe different structures and surfaces. Liang's STM step-edge phase shift suggests $2\\times2\\times2$ order. Stahl's bulk diffraction reports a low-temperature $2\\times2\\times2$ structure changing to $2\\times2\\times4$ near 60 K on warming; its null response to fields up to 10 T does not rule out broken time-reversal symmetry. Li's separate CsV3Sb5 study resolves conjoined $2\\times2\\times1$ and $2\\times2\\times2$ charge-order responses, with distinct resonant behavior and a roughly 4 K onset separation at 1 GPa. That separation concerns charge order, not two superconducting transitions. [R6](#ref-source-7746049011a0e640) [R7](#ref-source-d773a884dacbd7c9) [R8](#ref-source-80eda571fc6d710c)\n\n## Limits and disputes\n\nA scattering superlattice peak needs electronic, structural and instrumental interpretation; it is not by itself proof of an exclusively electronic instability. STM conductance modulations must be compared across bias, surface termination and bulk probes. Li's surface modulation and bulk-null comparison illustrates why a surface pattern cannot automatically be promoted to a universal bulk phase. The present review does not independently reproduce those sensitivity limits or resolve every reported stacking structure. [R6](#ref-source-7746049011a0e640) [R8](#ref-source-80eda571fc6d710c)\n\nMielke's accepted-manuscript abstract reports enhanced internal-field widths in KV3Sb5 below charge ordering, interpreted as time-reversal symmetry breaking. This is a normal-state charge-order claim, not a direct determination of chiral superconducting pairing. Chen's spatially modulated tunnelling signatures motivate a kagome PDW interpretation, but interpretation of the pair field requires additional evidence beyond ordinary charge contrast. Material identity, probe coupling and the superconducting transition must remain explicit. [R9](#ref-source-484da7abcc165cd3) [R10](#ref-source-057c43c86174f961)\n\nComplete scientific acceptance remains open. Selected methods and figures, historical abstracts and independent line-shape checks do not replace full source-version comparisons, raw diffraction reproduction, all supplementary calibrations or competing-structure assessment. A Hall anomaly, a Fermi-surface pocket or a charge onset below a pseudogap scale cannot alone specify which charge structure causes reconstruction or whether it mediates pairing. [R3](#ref-source-c4a9d4e1b52d95bb) [R4](#ref-source-d9477b85392d03f9) [R5](#ref-source-b89f6bcf54acb4d8)\n\n## Discovery implications\n\nPreserve the measured wave vector and reciprocal units, sample composition, oxygen order, field direction, pressure medium, line shape and resolution treatment. Compare competing-order amplitudes on characterized specimens and distinguish a static order parameter from dynamic spectral weight. Useful predictions should connect a particular charge structure to a testable electronic reconstruction and superconducting response, including results that could falsify the proposed connection. [R2](#ref-source-9ae65971bc3eb5b8) [R3](#ref-source-c4a9d4e1b52d95bb) [R5](#ref-source-b89f6bcf54acb4d8) [R11](#ref-source-74169f2f9bc31219)\n\n## Related topics\n\n[Pseudogap](/scwiki/pseudogap), [Charge-fluctuation pairing](/scwiki/charge-fluctuation-pairing), and [Pair-density waves](/scwiki/pair-density-wave).","revision":"092d1a01d0e22c7c3549","sections":[{"id":"scope","title":"Scope","markdown":"## Scope\n\nA charge-density wave (CDW) modulates the electronic density at a finite wave vector, often together with atomic displacements. Cuprates and kagome compounds exhibit several distinct charge-order patterns. Their coexistence or competition with superconductivity depends on composition, temperature, field, pressure and the probe's spatial and temporal resolution. Neither a density modulation nor a nearby superconducting dome identifies the pairing interaction. [R2](#ref-source-9ae65971bc3eb5b8) [R3](#ref-source-c4a9d4e1b52d95bb) [R8](#ref-source-80eda571fc6d710c) [R11](#ref-source-74169f2f9bc31219)\n\nThis page addresses observations and their interpretation. Pair-density waves instead modulate the superconducting pair field; spin-density waves modulate magnetization. Charge order, structural chirality, broken time-reversal symmetry and superconducting chirality are different claims. The retained source chapter's citation of Stahl for the conjoined-CDW paper is corrected: that paper is by Li and colleagues; Stahl's temperature-dependent stacking study has a different DOI. [R7](#ref-source-d773a884dacbd7c9) [R8](#ref-source-80eda571fc6d710c) [R9](#ref-source-484da7abcc165cd3) [R10](#ref-source-057c43c86174f961)"},{"id":"mathematical-assumptions","title":"Mathematical assumptions","markdown":"## Mathematical assumptions\n\nA single-component modulation can be written as $\\rho(\\mathbf r)=\\rho_0+\\operatorname{Re}[\\rho_{\\mathbf Q}e^{i\\mathbf Q\\cdot\\mathbf r}]$. Peak position identifies periodicity, while width constrains correlations under a stated line-shape model. For the illustrative lattice correlation $C(n)=r^{|n|}$, with $r=e^{-1/\\xi}$ and $\\xi$ in lattice spacings, the Fourier sum is $S(q)=(1-r^2)/(1+r^2-2r\\cos q)$. Here $q$ is dimensionless radians per spacing, measured from the ordering wave vector. Finite $\\xi$ produces a finite-width peak; observing that peak does not establish infinite-range order. This is an independent correlation model, not a fit to the cited specimens. [R4](#ref-source-d9477b85392d03f9) [R5](#ref-source-b89f6bcf54acb4d8)\n\nCorrelation lengths also depend on resolution and conventions. If both intrinsic and instrumental profiles are Gaussian, $\\sigma_{\\rm obs}^2=\\sigma_{\\rm int}^2+\\sigma_R^2$. The convention $\\xi=1/\\sigma_{\\rm int}$ then requires momentum widths in inverse-length units. Reciprocal-lattice widths need the appropriate lattice conversion. Uncorrected $1/\\sigma_{\\rm obs}$ is a lower bound within this model. Gaussian standard deviations, Lorentzian half-widths and full widths are not interchangeable; a resolution-limited peak yields a bound rather than a precisely measured divergence. [R4](#ref-source-d9477b85392d03f9) [R5](#ref-source-b89f6bcf54acb4d8)\n\nA phenomenological free energy $F=a_s|\\Delta|^2+b_s|\\Delta|^4+a_c|\\rho_{\\mathbf Q}|^2+b_c|\\rho_{\\mathbf Q}|^4+g|\\Delta|^2|\\rho_{\\mathbf Q}|^2$ illustrates static competition when $g>0$. With positive quartic coefficients, a stable interior coexistence minimum additionally requires $4b_sb_c-g^2>0$ and positive equilibrium squared amplitudes. Competition alone neither guarantees coexistence nor determines the frequency-dependent pairing kernel. Charge fluctuations could contribute to an effective interaction in a specified microscopic model without making every observed CDW a pairing mechanism. [R3](#ref-source-c4a9d4e1b52d95bb) [R11](#ref-source-74169f2f9bc31219)"},{"id":"experimental-criteria","title":"Experimental criteria","markdown":"## Experimental criteria\n\nTranquada's historical neutron result concerns Nd-substituted La1.6−xNd0.4SrxCuO4 at $x=0.12$. Its static stripe evidence and suppressed superconductivity should not be assigned indiscriminately to every one-eighth-doped cuprate. Ghiringhelli's resonant X-ray study adds an element-sensitive charge response in underdoped YBCO. The selected author text uses 130 meV instrumental resolution and argues for a much smaller energy bound; that bound is not a separately resolved sharp collective mode. [R1](#ref-source-b33aab72ae697f3a) [R2](#ref-source-9ae65971bc3eb5b8)\n\nChang's 2012 experiment on detwinned ortho-VIII YBa2Cu3O6.67 finds charge-order intensity suppressed on entering the superconducting regime and enhanced by magnetic field below it. Those controlled changes support competition in this specimen. They do not isolate every field-induced change in vortices or electronic structure, and do not identify a unique microscopic interaction. [R3](#ref-source-c4a9d4e1b52d95bb)\n\nGerber's high-field diffraction shows additional interlayer-correlated order developing above about 15 T at 10 K. The author Figure 3 separates peaks near integer and half-integer out-of-plane coordinates and extracts Gaussian widths. Its reported lengths are explicitly uncorrected for resolution. Chang's 2016 study instead reports resolution-corrected widths: for YBCO6.67, the c-axis scale reaches about four lattice periods within the measured field range. Finite three-dimensional correlations must remain distinct from unlimited long-range coherence. These analyses cannot be combined by silently treating corrected and uncorrected widths as equivalent. [R4](#ref-source-d9477b85392d03f9) [R5](#ref-source-b89f6bcf54acb4d8)\n\nKagome studies probe different structures and surfaces. Liang's STM step-edge phase shift suggests $2\\times2\\times2$ order. Stahl's bulk diffraction reports a low-temperature $2\\times2\\times2$ structure changing to $2\\times2\\times4$ near 60 K on warming; its null response to fields up to 10 T does not rule out broken time-reversal symmetry. Li's separate CsV3Sb5 study resolves conjoined $2\\times2\\times1$ and $2\\times2\\times2$ charge-order responses, with distinct resonant behavior and a roughly 4 K onset separation at 1 GPa. That separation concerns charge order, not two superconducting transitions. [R6](#ref-source-7746049011a0e640) [R7](#ref-source-d773a884dacbd7c9) [R8](#ref-source-80eda571fc6d710c)"},{"id":"limits-and-disputes","title":"Limits and disputes","markdown":"## Limits and disputes\n\nA scattering superlattice peak needs electronic, structural and instrumental interpretation; it is not by itself proof of an exclusively electronic instability. STM conductance modulations must be compared across bias, surface termination and bulk probes. Li's surface modulation and bulk-null comparison illustrates why a surface pattern cannot automatically be promoted to a universal bulk phase. The present review does not independently reproduce those sensitivity limits or resolve every reported stacking structure. [R6](#ref-source-7746049011a0e640) [R8](#ref-source-80eda571fc6d710c)\n\nMielke's accepted-manuscript abstract reports enhanced internal-field widths in KV3Sb5 below charge ordering, interpreted as time-reversal symmetry breaking. This is a normal-state charge-order claim, not a direct determination of chiral superconducting pairing. Chen's spatially modulated tunnelling signatures motivate a kagome PDW interpretation, but interpretation of the pair field requires additional evidence beyond ordinary charge contrast. Material identity, probe coupling and the superconducting transition must remain explicit. [R9](#ref-source-484da7abcc165cd3) [R10](#ref-source-057c43c86174f961)\n\nComplete scientific acceptance remains open. Selected methods and figures, historical abstracts and independent line-shape checks do not replace full source-version comparisons, raw diffraction reproduction, all supplementary calibrations or competing-structure assessment. A Hall anomaly, a Fermi-surface pocket or a charge onset below a pseudogap scale cannot alone specify which charge structure causes reconstruction or whether it mediates pairing. [R3](#ref-source-c4a9d4e1b52d95bb) [R4](#ref-source-d9477b85392d03f9) [R5](#ref-source-b89f6bcf54acb4d8)"},{"id":"discovery-implications","title":"Discovery implications","markdown":"## Discovery implications\n\nPreserve the measured wave vector and reciprocal units, sample composition, oxygen order, field direction, pressure medium, line shape and resolution treatment. Compare competing-order amplitudes on characterized specimens and distinguish a static order parameter from dynamic spectral weight. Useful predictions should connect a particular charge structure to a testable electronic reconstruction and superconducting response, including results that could falsify the proposed connection. [R2](#ref-source-9ae65971bc3eb5b8) [R3](#ref-source-c4a9d4e1b52d95bb) [R5](#ref-source-b89f6bcf54acb4d8) [R11](#ref-source-74169f2f9bc31219)"},{"id":"related-topics","title":"Related topics","markdown":"## Related topics\n\n[Pseudogap](/scwiki/pseudogap), [Charge-fluctuation pairing](/scwiki/charge-fluctuation-pairing), and [Pair-density waves](/scwiki/pair-density-wave)."},{"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| YBa2Cu3O6.67 (aliases: YBCO); Gerber high-field YBCO6.67 diffraction series | 10 K; Diffraction at 10 K; not superconducting Tc. | measurement; diffraction-measurement | Pulsed-field X-ray diffraction | ambient; unknown GPa | unknown | experiment; [source](#ref-source-d9477b85392d03f9) |\n| CsV3Sb5 (aliases: CsV3Sb5); Li resonant scattering specimen at ambient pressure | 10 K; Resonant scattering at 10 K; not superconducting Tc. | measurement; REXS-measurement | Sb L1-edge resonant elastic X-ray scattering | ambient; unknown GPa | unknown | experiment; [source](#ref-source-80eda571fc6d710c) |\n| CsV3Sb5 (aliases: CsV3Sb5); Li high-pressure diffraction at 1 GPa | 61 K; Diffraction comparison temperature; separates charge-order peaks and is not superconducting Tc. | measurement; diffraction-measurement | High-pressure X-ray diffraction | high; 1 to 1 GPa | unknown | experiment; [source](#ref-source-80eda571fc6d710c) |"}],"markdown":"# Charge-density waves: observations, competition and reconstruction\n\nRead charge-order evidence with its material, wave vector, dimensionality and resolution limits; distinguish competition from a pairing mechanism.\n\n## Scope\n\nA charge-density wave (CDW) modulates the electronic density at a finite wave vector, often together with atomic displacements. Cuprates and kagome compounds exhibit several distinct charge-order patterns. Their coexistence or competition with superconductivity depends on composition, temperature, field, pressure and the probe's spatial and temporal resolution. Neither a density modulation nor a nearby superconducting dome identifies the pairing interaction. [R2](#ref-source-9ae65971bc3eb5b8) [R3](#ref-source-c4a9d4e1b52d95bb) [R8](#ref-source-80eda571fc6d710c) [R11](#ref-source-74169f2f9bc31219)\n\nThis page addresses observations and their interpretation. Pair-density waves instead modulate the superconducting pair field; spin-density waves modulate magnetization. Charge order, structural chirality, broken time-reversal symmetry and superconducting chirality are different claims. The retained source chapter's citation of Stahl for the conjoined-CDW paper is corrected: that paper is by Li and colleagues; Stahl's temperature-dependent stacking study has a different DOI. [R7](#ref-source-d773a884dacbd7c9) [R8](#ref-source-80eda571fc6d710c) [R9](#ref-source-484da7abcc165cd3) [R10](#ref-source-057c43c86174f961)\n\n## Mathematical assumptions\n\nA single-component modulation can be written as $\\rho(\\mathbf r)=\\rho_0+\\operatorname{Re}[\\rho_{\\mathbf Q}e^{i\\mathbf Q\\cdot\\mathbf r}]$. Peak position identifies periodicity, while width constrains correlations under a stated line-shape model. For the illustrative lattice correlation $C(n)=r^{|n|}$, with $r=e^{-1/\\xi}$ and $\\xi$ in lattice spacings, the Fourier sum is $S(q)=(1-r^2)/(1+r^2-2r\\cos q)$. Here $q$ is dimensionless radians per spacing, measured from the ordering wave vector. Finite $\\xi$ produces a finite-width peak; observing that peak does not establish infinite-range order. This is an independent correlation model, not a fit to the cited specimens. [R4](#ref-source-d9477b85392d03f9) [R5](#ref-source-b89f6bcf54acb4d8)\n\nCorrelation lengths also depend on resolution and conventions. If both intrinsic and instrumental profiles are Gaussian, $\\sigma_{\\rm obs}^2=\\sigma_{\\rm int}^2+\\sigma_R^2$. The convention $\\xi=1/\\sigma_{\\rm int}$ then requires momentum widths in inverse-length units. Reciprocal-lattice widths need the appropriate lattice conversion. Uncorrected $1/\\sigma_{\\rm obs}$ is a lower bound within this model. Gaussian standard deviations, Lorentzian half-widths and full widths are not interchangeable; a resolution-limited peak yields a bound rather than a precisely measured divergence. [R4](#ref-source-d9477b85392d03f9) [R5](#ref-source-b89f6bcf54acb4d8)\n\nA phenomenological free energy $F=a_s|\\Delta|^2+b_s|\\Delta|^4+a_c|\\rho_{\\mathbf Q}|^2+b_c|\\rho_{\\mathbf Q}|^4+g|\\Delta|^2|\\rho_{\\mathbf Q}|^2$ illustrates static competition when $g>0$. With positive quartic coefficients, a stable interior coexistence minimum additionally requires $4b_sb_c-g^2>0$ and positive equilibrium squared amplitudes. Competition alone neither guarantees coexistence nor determines the frequency-dependent pairing kernel. Charge fluctuations could contribute to an effective interaction in a specified microscopic model without making every observed CDW a pairing mechanism. [R3](#ref-source-c4a9d4e1b52d95bb) [R11](#ref-source-74169f2f9bc31219)\n\n## Experimental criteria\n\nTranquada's historical neutron result concerns Nd-substituted La1.6−xNd0.4SrxCuO4 at $x=0.12$. Its static stripe evidence and suppressed superconductivity should not be assigned indiscriminately to every one-eighth-doped cuprate. Ghiringhelli's resonant X-ray study adds an element-sensitive charge response in underdoped YBCO. The selected author text uses 130 meV instrumental resolution and argues for a much smaller energy bound; that bound is not a separately resolved sharp collective mode. [R1](#ref-source-b33aab72ae697f3a) [R2](#ref-source-9ae65971bc3eb5b8)\n\nChang's 2012 experiment on detwinned ortho-VIII YBa2Cu3O6.67 finds charge-order intensity suppressed on entering the superconducting regime and enhanced by magnetic field below it. Those controlled changes support competition in this specimen. They do not isolate every field-induced change in vortices or electronic structure, and do not identify a unique microscopic interaction. [R3](#ref-source-c4a9d4e1b52d95bb)\n\nGerber's high-field diffraction shows additional interlayer-correlated order developing above about 15 T at 10 K. The author Figure 3 separates peaks near integer and half-integer out-of-plane coordinates and extracts Gaussian widths. Its reported lengths are explicitly uncorrected for resolution. Chang's 2016 study instead reports resolution-corrected widths: for YBCO6.67, the c-axis scale reaches about four lattice periods within the measured field range. Finite three-dimensional correlations must remain distinct from unlimited long-range coherence. These analyses cannot be combined by silently treating corrected and uncorrected widths as equivalent. [R4](#ref-source-d9477b85392d03f9) [R5](#ref-source-b89f6bcf54acb4d8)\n\nKagome studies probe different structures and surfaces. Liang's STM step-edge phase shift suggests $2\\times2\\times2$ order. Stahl's bulk diffraction reports a low-temperature $2\\times2\\times2$ structure changing to $2\\times2\\times4$ near 60 K on warming; its null response to fields up to 10 T does not rule out broken time-reversal symmetry. Li's separate CsV3Sb5 study resolves conjoined $2\\times2\\times1$ and $2\\times2\\times2$ charge-order responses, with distinct resonant behavior and a roughly 4 K onset separation at 1 GPa. That separation concerns charge order, not two superconducting transitions. [R6](#ref-source-7746049011a0e640) [R7](#ref-source-d773a884dacbd7c9) [R8](#ref-source-80eda571fc6d710c)\n\n## Limits and disputes\n\nA scattering superlattice peak needs electronic, structural and instrumental interpretation; it is not by itself proof of an exclusively electronic instability. STM conductance modulations must be compared across bias, surface termination and bulk probes. Li's surface modulation and bulk-null comparison illustrates why a surface pattern cannot automatically be promoted to a universal bulk phase. The present review does not independently reproduce those sensitivity limits or resolve every reported stacking structure. [R6](#ref-source-7746049011a0e640) [R8](#ref-source-80eda571fc6d710c)\n\nMielke's accepted-manuscript abstract reports enhanced internal-field widths in KV3Sb5 below charge ordering, interpreted as time-reversal symmetry breaking. This is a normal-state charge-order claim, not a direct determination of chiral superconducting pairing. Chen's spatially modulated tunnelling signatures motivate a kagome PDW interpretation, but interpretation of the pair field requires additional evidence beyond ordinary charge contrast. Material identity, probe coupling and the superconducting transition must remain explicit. [R9](#ref-source-484da7abcc165cd3) [R10](#ref-source-057c43c86174f961)\n\nComplete scientific acceptance remains open. Selected methods and figures, historical abstracts and independent line-shape checks do not replace full source-version comparisons, raw diffraction reproduction, all supplementary calibrations or competing-structure assessment. A Hall anomaly, a Fermi-surface pocket or a charge onset below a pseudogap scale cannot alone specify which charge structure causes reconstruction or whether it mediates pairing. [R3](#ref-source-c4a9d4e1b52d95bb) [R4](#ref-source-d9477b85392d03f9) [R5](#ref-source-b89f6bcf54acb4d8)\n\n## Discovery implications\n\nPreserve the measured wave vector and reciprocal units, sample composition, oxygen order, field direction, pressure medium, line shape and resolution treatment. Compare competing-order amplitudes on characterized specimens and distinguish a static order parameter from dynamic spectral weight. Useful predictions should connect a particular charge structure to a testable electronic reconstruction and superconducting response, including results that could falsify the proposed connection. [R2](#ref-source-9ae65971bc3eb5b8) [R3](#ref-source-c4a9d4e1b52d95bb) [R5](#ref-source-b89f6bcf54acb4d8) [R11](#ref-source-74169f2f9bc31219)\n\n## Related topics\n\n[Pseudogap](/scwiki/pseudogap), [Charge-fluctuation pairing](/scwiki/charge-fluctuation-pairing), and [Pair-density waves](/scwiki/pair-density-wave).\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| YBa2Cu3O6.67 (aliases: YBCO); Gerber high-field YBCO6.67 diffraction series | 10 K; Diffraction at 10 K; not superconducting Tc. | measurement; diffraction-measurement | Pulsed-field X-ray diffraction | ambient; unknown GPa | unknown | experiment; [source](#ref-source-d9477b85392d03f9) |\n| CsV3Sb5 (aliases: CsV3Sb5); Li resonant scattering specimen at ambient pressure | 10 K; Resonant scattering at 10 K; not superconducting Tc. | measurement; REXS-measurement | Sb L1-edge resonant elastic X-ray scattering | ambient; unknown GPa | unknown | experiment; [source](#ref-source-80eda571fc6d710c) |\n| CsV3Sb5 (aliases: CsV3Sb5); Li high-pressure diffraction at 1 GPa | 61 K; Diffraction comparison temperature; separates charge-order peaks and is not superconducting Tc. | measurement; diffraction-measurement | High-pressure X-ray diffraction | high; 1 to 1 GPa | unknown | experiment; [source](#ref-source-80eda571fc6d710c) |\n\n## Sources\n\n### Ref source-b33aab72ae697f3a\n\n[R1] Evidence for stripe correlations of spins and holes in copper oxide superconductors (1995). [DOI 10.1038/375561a0](https://doi.org/10.1038/375561a0). Publication: journal-article. Check: publisher-abstract-check. Checked: 2026-10-18. Publisher abstract and identity checked: 15 June 1995, Nd-substituted compound x=0.12, neutron diffraction. Full paper and data not reviewed.\n### Ref source-9ae65971bc3eb5b8\n\n[R2] Long-Range Incommensurate Charge Fluctuations in (Y,Nd)Ba2Cu3O6+x (2012). [DOI 10.1126/science.1223532](https://doi.org/10.1126/science.1223532). Publication: journal-article. Check: author-manuscript-scoped-check. Checked: 2026-10-18. Ghiringhelli et al. selected PDF pp.4–6,20–21: resonance/polarization,130meV resolution, author20meV bound and competition. Bound is not a resolved mode. Final-version and raw-data review open.\n### Ref source-c4a9d4e1b52d95bb\n\n[R3] Direct observation of competition between superconductivity and charge density wave order in YBa2Cu3O6.67 (2012). [DOI 10.1038/nphys2456](https://doi.org/10.1038/nphys2456). Publication: journal-article. Check: author-manuscript-scoped-check. Checked: 2026-10-18. Chang et al. selected pp.1–2: detwinned ortho-VIII crystal,100keV,up to17T,67K versus135K; zero-field CDW and field enhancement below Tc. Transition criterion/raw data not fully audited; no sample Tc record created.\n### Ref source-d9477b85392d03f9\n\n[R4] Three-dimensional charge density wave order in YBa2Cu3O6.67 at high magnetic fields (2015). [DOI 10.1126/science.aac6257](https://doi.org/10.1126/science.aac6257). Publication: journal-article. Check: selected-author-methods-and-figure-check. Checked: 2026-10-19. Author v1 selected pp. 4, 10, 13 read; Figures 2 and 3 on pp. 9–10 visually checked. Gaussian correlation lengths are uncorrected lower bounds. Final-version comparison and raw-data reproduction remain open.\n### Ref source-b89f6bcf54acb4d8\n\n[R5] Magnetic field controlled charge density wave coupling in underdoped YBa2Cu3O6+x (2016). [DOI 10.1038/ncomms11494](https://doi.org/10.1038/ncomms11494). Publication: journal-article. Check: selected-final-methods-table-and-figure-check. Checked: 2026-10-19. Published 5 May 2016. Selected pp. 3, 5–6 read; Figures 4–5 on p. 5 and Table 1/methods on p. 6 visually checked. Resolution-corrected Gaussian widths, 16.9 T limit and absolute temperature uncertainty distinguished. Complete raw-profile and stacking-model reproduction remain open.\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-d773a884dacbd7c9\n\n[R7] Temperature-driven reorganization of electronic order in CsV3Sb5 (2022). [DOI 10.1103/PhysRevB.105.195136](https://doi.org/10.1103/PhysRevB.105.195136). Publication: journal-article. Check: publisher-abstract-and-identity-check. Checked: 2026-10-19. Stahl et al., published 24 May 2022. Abstract reports temperature-dependent stacking and a null diffraction response up to 10 T. Full refinements not reviewed; distinguish this DOI from Li et al. conjoined-CDW work.\n### Ref source-80eda571fc6d710c\n\n[R8] 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-484da7abcc165cd3\n\n[R9] 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: accepted-manuscript-abstract-check. Checked: 2026-10-19. Accepted manuscript opening abstract read: KV3Sb5 muon field-width enhancement below charge ordering. Full background calibration, magnetic interpretation and superconducting gap fits remain open.\n### Ref source-057c43c86174f961\n\n[R10] 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-74169f2f9bc31219\n\n[R11] Singular Quasiparticle Scattering in the Proximity of Charge Instabilities (1995). [DOI 10.1103/PhysRevLett.75.4650](https://doi.org/10.1103/PhysRevLett.75.4650). Publication: journal-article. Check: publisher-abstract-scoped-check. Checked: 2026-10-18. Castellani–Di Castro–Grilli abstract: infinite-U Hubbard–Holstein model and long-range Coulomb change from zero to finite wave vector. Full calculation not read or reproduced.\n\n## Claim evidence and conditions\n\n### scwiki-h4-claim-scope-1\n\nA charge-density wave (CDW) modulates the electronic density at a finite wave vector, often together with atomic displacements. Cuprates and kagome compounds exhibit several distinct charge-order patterns. Their coexistence or competition with superconductivity depends on composition, temperature, field, pressure and the probe's spatial and temporal resolution. Neither a density modulation nor a nearby superconducting dome identifies the pairing interaction.\n\nEvidence: hypothesis. Sources: source-9ae65971bc3eb5b8, source-c4a9d4e1b52d95bb, source-80eda571fc6d710c, source-74169f2f9bc31219.\n\nConditions: Retain specimen, wave vector units, field, pressure, probe, source version and resolution correction. Charge-order and measurement temperatures are not superconducting Tc.\n\nVerification scope: Selected primary evidence and independent correlation models; full scientific acceptance remains open.\n\n### scwiki-h4-claim-scope-2\n\nThis page addresses observations and their interpretation. Pair-density waves instead modulate the superconducting pair field; spin-density waves modulate magnetization. Charge order, structural chirality, broken time-reversal symmetry and superconducting chirality are different claims. The retained source chapter's citation of Stahl for the conjoined-CDW paper is corrected: that paper is by Li and colleagues; Stahl's temperature-dependent stacking study has a different DOI.\n\nEvidence: hypothesis. Sources: source-d773a884dacbd7c9, source-80eda571fc6d710c, source-484da7abcc165cd3, source-057c43c86174f961.\n\nConditions: Retain specimen, wave vector units, field, pressure, probe, source version and resolution correction. Charge-order and measurement temperatures are not superconducting Tc.\n\nVerification scope: Selected primary evidence and independent correlation models; full scientific acceptance remains open.\n\n### scwiki-h4-claim-mathematical-assumptions-1\n\nA single-component modulation can be written as $\\rho(\\mathbf r)=\\rho_0+\\operatorname{Re}[\\rho_{\\mathbf Q}e^{i\\mathbf Q\\cdot\\mathbf r}]$. Peak position identifies periodicity, while width constrains correlations under a stated line-shape model. For the illustrative lattice correlation $C(n)=r^{|n|}$, with $r=e^{-1/\\xi}$ and $\\xi$ in lattice spacings, the Fourier sum is $S(q)=(1-r^2)/(1+r^2-2r\\cos q)$. Here $q$ is dimensionless radians per spacing, measured from the ordering wave vector. Finite $\\xi$ produces a finite-width peak; observing that peak does not establish infinite-range order. This is an independent correlation model, not a fit to the cited specimens.\n\nEvidence: theory. Sources: source-d9477b85392d03f9, source-b89f6bcf54acb4d8.\n\nConditions: Retain specimen, wave vector units, field, pressure, probe, source version and resolution correction. Charge-order and measurement temperatures are not superconducting Tc.\n\nVerification scope: Selected primary evidence and independent correlation models; full scientific acceptance remains open.\n\n### scwiki-h4-claim-mathematical-assumptions-2\n\nCorrelation lengths also depend on resolution and conventions. If both intrinsic and instrumental profiles are Gaussian, $\\sigma_{\\rm obs}^2=\\sigma_{\\rm int}^2+\\sigma_R^2$. The convention $\\xi=1/\\sigma_{\\rm int}$ then requires momentum widths in inverse-length units. Reciprocal-lattice widths need the appropriate lattice conversion. Uncorrected $1/\\sigma_{\\rm obs}$ is a lower bound within this model. Gaussian standard deviations, Lorentzian half-widths and full widths are not interchangeable; a resolution-limited peak yields a bound rather than a precisely measured divergence.\n\nEvidence: theory. Sources: source-d9477b85392d03f9, source-b89f6bcf54acb4d8.\n\nConditions: Retain specimen, wave vector units, field, pressure, probe, source version and resolution correction. Charge-order and measurement temperatures are not superconducting Tc.\n\nVerification scope: Selected primary evidence and independent correlation models; full scientific acceptance remains open.\n\n### scwiki-h4-claim-mathematical-assumptions-3\n\nA phenomenological free energy $F=a_s|\\Delta|^2+b_s|\\Delta|^4+a_c|\\rho_{\\mathbf Q}|^2+b_c|\\rho_{\\mathbf Q}|^4+g|\\Delta|^2|\\rho_{\\mathbf Q}|^2$ illustrates static competition when $g>0$. With positive quartic coefficients, a stable interior coexistence minimum additionally requires $4b_sb_c-g^2>0$ and positive equilibrium squared amplitudes. Competition alone neither guarantees coexistence nor determines the frequency-dependent pairing kernel. Charge fluctuations could contribute to an effective interaction in a specified microscopic model without making every observed CDW a pairing mechanism.\n\nEvidence: theory. Sources: source-c4a9d4e1b52d95bb, source-74169f2f9bc31219.\n\nConditions: Retain specimen, wave vector units, field, pressure, probe, source version and resolution correction. Charge-order and measurement temperatures are not superconducting Tc.\n\nVerification scope: Selected primary evidence and independent correlation models; full scientific acceptance remains open.\n\n### scwiki-h4-claim-experimental-criteria-1\n\nTranquada's historical neutron result concerns Nd-substituted La1.6−xNd0.4SrxCuO4 at $x=0.12$. Its static stripe evidence and suppressed superconductivity should not be assigned indiscriminately to every one-eighth-doped cuprate. Ghiringhelli's resonant X-ray study adds an element-sensitive charge response in underdoped YBCO. The selected author text uses 130 meV instrumental resolution and argues for a much smaller energy bound; that bound is not a separately resolved sharp collective mode.\n\nEvidence: experiment. Sources: source-b33aab72ae697f3a, source-9ae65971bc3eb5b8.\n\nConditions: Retain specimen, wave vector units, field, pressure, probe, source version and resolution correction. Charge-order and measurement temperatures are not superconducting Tc.\n\nVerification scope: Selected primary evidence and independent correlation models; full scientific acceptance remains open.\n\n### scwiki-h4-claim-experimental-criteria-2\n\nChang's 2012 experiment on detwinned ortho-VIII YBa2Cu3O6.67 finds charge-order intensity suppressed on entering the superconducting regime and enhanced by magnetic field below it. Those controlled changes support competition in this specimen. They do not isolate every field-induced change in vortices or electronic structure, and do not identify a unique microscopic interaction.\n\nEvidence: experiment. Sources: source-c4a9d4e1b52d95bb.\n\nConditions: Retain specimen, wave vector units, field, pressure, probe, source version and resolution correction. Charge-order and measurement temperatures are not superconducting Tc.\n\nVerification scope: Selected primary evidence and independent correlation models; full scientific acceptance remains open.\n\n### scwiki-h4-claim-experimental-criteria-3\n\nGerber's high-field diffraction shows additional interlayer-correlated order developing above about 15 T at 10 K. The author Figure 3 separates peaks near integer and half-integer out-of-plane coordinates and extracts Gaussian widths. Its reported lengths are explicitly uncorrected for resolution. Chang's 2016 study instead reports resolution-corrected widths: for YBCO6.67, the c-axis scale reaches about four lattice periods within the measured field range. Finite three-dimensional correlations must remain distinct from unlimited long-range coherence. These analyses cannot be combined by silently treating corrected and uncorrected widths as equivalent.\n\nEvidence: experiment. Sources: source-d9477b85392d03f9, source-b89f6bcf54acb4d8.\n\nConditions: Retain specimen, wave vector units, field, pressure, probe, source version and resolution correction. Charge-order and measurement temperatures are not superconducting Tc.\n\nVerification scope: Selected primary evidence and independent correlation models; full scientific acceptance remains open.\n\n### scwiki-h4-claim-experimental-criteria-4\n\nKagome studies probe different structures and surfaces. Liang's STM step-edge phase shift suggests $2\\times2\\times2$ order. Stahl's bulk diffraction reports a low-temperature $2\\times2\\times2$ structure changing to $2\\times2\\times4$ near 60 K on warming; its null response to fields up to 10 T does not rule out broken time-reversal symmetry. Li's separate CsV3Sb5 study resolves conjoined $2\\times2\\times1$ and $2\\times2\\times2$ charge-order responses, with distinct resonant behavior and a roughly 4 K onset separation at 1 GPa. That separation concerns charge order, not two superconducting transitions.\n\nEvidence: experiment. Sources: source-7746049011a0e640, source-d773a884dacbd7c9, source-80eda571fc6d710c.\n\nConditions: Retain specimen, wave vector units, field, pressure, probe, source version and resolution correction. Charge-order and measurement temperatures are not superconducting Tc.\n\nVerification scope: Selected primary evidence and independent correlation models; full scientific acceptance remains open.\n\n### scwiki-h4-claim-limits-and-disputes-1\n\nA scattering superlattice peak needs electronic, structural and instrumental interpretation; it is not by itself proof of an exclusively electronic instability. STM conductance modulations must be compared across bias, surface termination and bulk probes. Li's surface modulation and bulk-null comparison illustrates why a surface pattern cannot automatically be promoted to a universal bulk phase. The present review does not independently reproduce those sensitivity limits or resolve every reported stacking structure.\n\nEvidence: hypothesis. Sources: source-7746049011a0e640, source-80eda571fc6d710c.\n\nConditions: Retain specimen, wave vector units, field, pressure, probe, source version and resolution correction. Charge-order and measurement temperatures are not superconducting Tc.\n\nVerification scope: Selected primary evidence and independent correlation models; full scientific acceptance remains open.\n\n### scwiki-h4-claim-limits-and-disputes-2\n\nMielke's accepted-manuscript abstract reports enhanced internal-field widths in KV3Sb5 below charge ordering, interpreted as time-reversal symmetry breaking. This is a normal-state charge-order claim, not a direct determination of chiral superconducting pairing. Chen's spatially modulated tunnelling signatures motivate a kagome PDW interpretation, but interpretation of the pair field requires additional evidence beyond ordinary charge contrast. Material identity, probe coupling and the superconducting transition must remain explicit.\n\nEvidence: hypothesis. Sources: source-484da7abcc165cd3, source-057c43c86174f961.\n\nConditions: Retain specimen, wave vector units, field, pressure, probe, source version and resolution correction. Charge-order and measurement temperatures are not superconducting Tc.\n\nVerification scope: Selected primary evidence and independent correlation models; full scientific acceptance remains open.\n\n### scwiki-h4-claim-limits-and-disputes-3\n\nComplete scientific acceptance remains open. Selected methods and figures, historical abstracts and independent line-shape checks do not replace full source-version comparisons, raw diffraction reproduction, all supplementary calibrations or competing-structure assessment. A Hall anomaly, a Fermi-surface pocket or a charge onset below a pseudogap scale cannot alone specify which charge structure causes reconstruction or whether it mediates pairing.\n\nEvidence: hypothesis. Sources: source-c4a9d4e1b52d95bb, source-d9477b85392d03f9, source-b89f6bcf54acb4d8.\n\nConditions: Retain specimen, wave vector units, field, pressure, probe, source version and resolution correction. Charge-order and measurement temperatures are not superconducting Tc.\n\nVerification scope: Selected primary evidence and independent correlation models; full scientific acceptance remains open.\n\n### scwiki-h4-claim-discovery-implications-1\n\nPreserve the measured wave vector and reciprocal units, sample composition, oxygen order, field direction, pressure medium, line shape and resolution treatment. Compare competing-order amplitudes on characterized specimens and distinguish a static order parameter from dynamic spectral weight. Useful predictions should connect a particular charge structure to a testable electronic reconstruction and superconducting response, including results that could falsify the proposed connection.\n\nEvidence: hypothesis. Sources: source-9ae65971bc3eb5b8, source-c4a9d4e1b52d95bb, source-b89f6bcf54acb4d8, source-74169f2f9bc31219.\n\nConditions: Retain specimen, wave vector units, field, pressure, probe, source version and resolution correction. Charge-order and measurement temperatures are not superconducting Tc.\n\nVerification scope: Selected primary evidence and independent correlation models; full scientific acceptance remains open.\n\n## Revision and review\n\nArticle ID: scwiki-h4. Revision: 092d1a01d0e22c7c3549. Updated: 2026-10-18T16:48:09.729599+00:00.\n\nReview scope: Selected Gerber author methods and diffraction figures; Chang final methods, table and figures; primary kagome abstracts and Li publisher passages; inherited scoped B6/C8 evidence; independent correlation and Gaussian-width checks.\n\n- Complete scientific acceptance remains open.\n- Complete source-version, raw-data, supplementary calibration and competing-structure reviews remain open.\n- Selected abstracts do not establish a unique CDW mechanism, PDW or superconducting chirality.\n- Line-shape examples are models, not reanalyses of experimental profiles.\n\nSource: [H_anomalous_normal_state/H4_CDW.md](https://github.com/JackZH26/jzis-superconductivity/blob/0a7c9d6696804ec26aa12f8eed68b55c9b3c0fcf/H_anomalous_normal_state/H4_CDW.md), commit 0a7c9d6696804ec26aa12f8eed68b55c9b3c0fcf, SHA-256 cb5476fe2c7c2dea8b709ea989ffbb124b785c4437edb20dafaac852188af6b4.\n","wordCount":926}}