{"schemaVersion":"1.0","revision":"fa961ab24277a91737c3","article":{"id":"scwiki-a10","topicId":"scwiki-topic-a10","code":"A10","slug":"quasiparticle-interference","title":"Quasiparticle interference: momentum structure and phase limits","summary":"Read Fourier-transform tunneling maps with their scattering, sampling and phase assumptions. Distinguish measured modulation from inferred bands, gap sign and competing order.","aliases":["QPI","BQPI","FT-STM","quasiparticle scattering","octet model","phase resolved tunneling"],"evidenceTypes":["theory","experiment","hypothesis"],"relatedCodes":["A5","A9","D3","D4","B12","C2"],"editorialStatus":"scoped-check","contentState":"pilot","modifiedAt":"2026-10-18T22:51:56.579986+00:00","review":{"checkedAt":"2026-10-19","scope":"Selected Hoffman, Wang–Lee and Sprau author-manuscript passages; bibliographic identity corrections; independent finite-model and Fourier calculations.","limitations":["Scoped passage checks are not complete scientific acceptance or experimental replication.","McElroy and the vortex-core paper remain bibliographic pointers; earlier manuscript checks do not certify final-version equivalence.","FeSe sign inference retains defect, phase origin, band and model assumptions; no universal pairing state assigned.","Measurement temperatures are not transition temperatures; no Tc values are extracted here.","The displayed spin-resolved, finite-lattice response specializes the source framework; its local synthetic checks do not reproduce the complete published calculation."]},"provenance":{"repository":"JackZH26/jzis-superconductivity","commit":"0a7c9d6696804ec26aa12f8eed68b55c9b3c0fcf","path":"A_phenomenology/A10_quasiparticle_interference.md","sha256":"f82bb31e8b35f847536cf493b8d0267c022f124c0f86e664d386e583d72e590e","sourceId":"file-d9367783139c3905"},"sourceMap":[{"startLine":1,"endLine":11,"targetSections":["scope","mathematical-assumptions"],"decision":"edited-with-scoped-evidence","note":"Probe and matrix-element limits preserved; Fourier conventions made explicit."},{"startLine":12,"endLine":17,"targetSections":["experimental-criteria","limits-and-disputes"],"decision":"edited-with-scoped-evidence","note":"Cuprate examples retained with corrected Hoffman attribution and octet boundary."},{"startLine":18,"endLine":21,"targetSections":["experimental-criteria","mathematical-assumptions"],"decision":"edited-with-scoped-evidence","note":"Phase-sensitive FeSe protocol tied to selected manuscript passages."},{"startLine":22,"endLine":27,"targetSections":["limits-and-disputes"],"decision":"edited-with-scoped-evidence","note":"QPI/static-order distinction qualified; neither dispersion nor its absence is unique."},{"startLine":28,"endLine":36,"targetSections":["experimental-criteria","limits-and-disputes"],"decision":"edited-with-scoped-evidence","note":"Reporting and sampling criteria retained."},{"startLine":37,"endLine":46,"targetSections":["limits-and-disputes","discovery-implications","related-topics"],"decision":"edited-with-scoped-evidence","note":"Source identities traced; McElroy corrected and original vortex source retained."}],"references":[{"id":"source-e8e6ef56da103435","doi":"10.1126/science.1072640","title":"Imaging Quasiparticle Interference in Bi2Sr2CaCu2O8+delta","year":2002,"url":"https://doi.org/10.1126/science.1072640","publicationStatus":"journal-article","verification":{"scope":"author-manuscript-scoped-check","checkedAt":"2026-10-18","evidenceUrl":"https://arxiv.org/pdf/cond-mat/0209276v1","note":"Selected pp. 2–6: elastic scattering, 4.2 K conductance maps and dispersing peaks. Raw maps and final-version differences not reanalyzed."}},{"id":"source-6e0b3a25ead07f3c","doi":"10.1103/PhysRevB.67.020511","title":"Quasiparticle scattering interference in high-temperature superconductors","year":2003,"url":"https://doi.org/10.1103/PhysRevB.67.020511","publicationStatus":"journal-article","verification":{"scope":"author-manuscript-scoped-check","checkedAt":"2026-10-19","evidenceUrl":"https://arxiv.org/pdf/cond-mat/0205118v3","note":"Author v3 dated 20 August 2002, associated journal 2003. Selected pp. 1-2; p. 1 Eq. (1) pixels rechecked for both Nambu diagonal blocks, p. 2 previously viewed for off-shell/coherence-factor limits. Site spin-resolved block and discrete normalization are explicit local conventions. Full published calculation and final-version comparison remain open."}},{"id":"source-230ea3ac9496dc90","doi":"10.1038/nature01496","title":"Relating atomic-scale electronic phenomena to wave-like quasiparticle states in superconducting Bi2Sr2CaCu2O8+delta","year":2003,"url":"https://doi.org/10.1038/nature01496","publicationStatus":"journal-article","verification":{"scope":"publisher-metadata-scoped-check","checkedAt":"2026-10-18","evidenceUrl":"https://www.nature.com/articles/nature01496","note":"Publisher title/authors/pages and Crossref identity checked; full text/data not audited. Replaces inherited unrelated biology DOI nature02269."}},{"id":"source-2f227038c5cf73a9","doi":"10.1126/science.aal1575","title":"Discovery of orbital-selective Cooper pairing in FeSe","year":2017,"url":"https://doi.org/10.1126/science.aal1575","publicationStatus":"journal-article","verification":{"scope":"author-manuscript-scoped-check","checkedAt":"2026-10-18","evidenceUrl":"https://arxiv.org/pdf/1611.02134v2","note":"Selected manuscript p. 7 and pp. 10–11 plus supplementary section VII (PDF pp. 36–37): 280 mK, defect-centered phase, interband region and controls. Full FeSe model/data and final-version comparison not reproduced."}},{"id":"source-353efd52d3443260","doi":"10.1126/science.1066974","title":"A Four Unit Cell Periodic Pattern of Quasi-Particle States Surrounding Vortex Cores in Bi2Sr2CaCu2O8+delta","year":2002,"url":"https://doi.org/10.1126/science.1066974","publicationStatus":"journal-article","verification":{"scope":"crossref-metadata-only","checkedAt":"2026-10-18","evidenceUrl":"https://api.crossref.org/works/10.1126/science.1066974","note":"Distinct vortex-core paper retained to document inherited attribution mismatch; no detailed vortex experiment audited here."}}],"claims":[{"id":"scwiki-a10-claim-scope-1","sectionId":"scope","statement":"Quasiparticle interference (QPI) uses spatial variations in scanning tunneling conductance to constrain electronic states and scattering. Elastic scattering can connect states of equal energy with momentum transfer $\\mathbf q=\\mathbf k'-\\mathbf k$. A Fourier peak is a feature of a measured response, not a direct photograph of a Fermi surface or a uniquely identified order parameter. Keep the tunneling matrix element, defect channel and preprocessing attached to every interpretation.","evidenceType":"theory","sourceIds":["source-6e0b3a25ead07f3c"],"conditions":"Conditional retarded Green-function/DFT and ideal coherence-factor models; finite synthetic calculations are not fits to cuprates or FeSe.","verificationScope":"Selected source locations are stated in references; independent Fourier/resolvent checks apply only to the explicit ideal models."},{"id":"scwiki-a10-claim-scope-2","sectionId":"scope","statement":"In a weak-tunneling description with a sufficiently smooth tip spectrum and matrix element, low-temperature differential conductance can approximate a sample's local density of states. Thermal and instrumental convolution, spatially varying set points and orbital sensitivity can change that relation. A conductance map and an ideal local-density-of-states calculation should not be treated as interchangeable without testing these assumptions.","evidenceType":"theory","sourceIds":["source-6e0b3a25ead07f3c"],"conditions":"Conditional retarded Green-function/DFT and ideal coherence-factor models; finite synthetic calculations are not fits to cuprates or FeSe.","verificationScope":"Selected source locations are stated in references; independent Fourier/resolvent checks apply only to the explicit ideal models."},{"id":"scwiki-a10-claim-mathematical-assumptions-1","sectionId":"mathematical-assumptions","statement":"With the convention $\\tilde g(\\mathbf q,E)=\\sum_{\\mathbf r}e^{-i\\mathbf q\\cdot\\mathbf r}g(\\mathbf r,E)$, a translated pattern obeys","evidenceType":"theory","sourceIds":["source-6e0b3a25ead07f3c"],"conditions":"Conditional retarded Green-function/DFT and ideal coherence-factor models; finite synthetic calculations are not fits to cuprates or FeSe.","verificationScope":"Selected source locations are stated in references; independent Fourier/resolvent checks apply only to the explicit ideal models.","sourceRelationship":"context-for-local-derivation","derivationNote":"Local discrete-Fourier definition and translation/conjugation identities; exact algebra and sampled periodic examples. Wang–Lee supplies scattering context, not a separate experiment supporting the chosen convention."},{"id":"scwiki-a10-claim-mathematical-assumptions-2","sectionId":"mathematical-assumptions","statement":"$$g'(\\mathbf r,E)=g(\\mathbf r-\\mathbf r_0,E),\\qquad\\tilde g'=e^{-i\\mathbf q\\cdot\\mathbf r_0}\\tilde g.$$","evidenceType":"theory","sourceIds":["source-6e0b3a25ead07f3c"],"conditions":"Conditional retarded Green-function/DFT and ideal coherence-factor models; finite synthetic calculations are not fits to cuprates or FeSe.","verificationScope":"Selected source locations are stated in references; independent Fourier/resolvent checks apply only to the explicit ideal models.","sourceRelationship":"context-for-local-derivation","derivationNote":"Local discrete-Fourier definition and translation/conjugation identities; exact algebra and sampled periodic examples. Wang–Lee supplies scattering context, not a separate experiment supporting the chosen convention."},{"id":"scwiki-a10-claim-mathematical-assumptions-3","sectionId":"mathematical-assumptions","statement":"Its Fourier magnitude is unchanged, while its real and imaginary parts generally change. A real map satisfies $\\tilde g(-\\mathbf q)=\\tilde g(\\mathbf q)^*$. Independent discrete-transform checks verify both identities, an exactly sampled cosine and sampling aliases. Finite cropping can also change amplitudes; the exact translation identity assumes the whole pattern or periodic data, not two differently cropped fields.","evidenceType":"theory","sourceIds":["source-6e0b3a25ead07f3c"],"conditions":"Conditional retarded Green-function/DFT and ideal coherence-factor models; finite synthetic calculations are not fits to cuprates or FeSe.","verificationScope":"Selected source locations are stated in references; independent Fourier/resolvent checks apply only to the explicit ideal models.","sourceRelationship":"context-for-local-derivation","derivationNote":"Local discrete-Fourier definition and translation/conjugation identities; exact algebra and sampled periodic examples. Wang–Lee supplies scattering context, not a separate experiment supporting the chosen convention."},{"id":"scwiki-a10-claim-mathematical-assumptions-4","sectionId":"mathematical-assumptions","statement":"For a periodic lattice with $N$ sites and one static, local defect at the origin, define an ideal electron-block response","evidenceType":"theory","sourceIds":["source-6e0b3a25ead07f3c"],"conditions":"Conditional retarded Green-function/DFT and ideal coherence-factor models; finite synthetic calculations are not fits to cuprates or FeSe.","verificationScope":"Selected source locations are stated in references; independent Fourier/resolvent checks apply only to the explicit ideal models.","sourceRelationship":"mixed-source-and-local-derivation","derivationNote":"Wang–Lee author v3 p. 1 Eq. (1) supplies the scattering-response framework with both Nambu diagonal blocks. This entry locally specializes to one spin-resolved electron block, N-site normalization and a static local defect; T follows from T=V+Vg0T when the inverse exists. Six finite-model resolvent comparisons check these conventions, not material data."},{"id":"scwiki-a10-claim-mathematical-assumptions-5","sectionId":"mathematical-assumptions","statement":"$$\\Lambda(\\mathbf q,E)=\\frac{1}{N}\\sum_{\\mathbf k}[G_0(\\mathbf k,E)\\,T(E)\\,G_0(\\mathbf k-\\mathbf q,E)]_{11}.$$","evidenceType":"theory","sourceIds":["source-6e0b3a25ead07f3c"],"conditions":"Conditional retarded Green-function/DFT and ideal coherence-factor models; finite synthetic calculations are not fits to cuprates or FeSe.","verificationScope":"Selected source locations are stated in references; independent Fourier/resolvent checks apply only to the explicit ideal models.","sourceRelationship":"mixed-source-and-local-derivation","derivationNote":"Wang–Lee author v3 p. 1 Eq. (1) supplies the scattering-response framework with both Nambu diagonal blocks. This entry locally specializes to one spin-resolved electron block, N-site normalization and a static local defect; T follows from T=V+Vg0T when the inverse exists. Six finite-model resolvent comparisons check these conventions, not material data."},{"id":"scwiki-a10-claim-mathematical-assumptions-6","sectionId":"mathematical-assumptions","statement":"Here $G_0$ is a retarded Nambu Green function and $T=[1-Vg_0]^{-1}V$, with $g_0=N^{-1}\\sum_{\\mathbf k}G_0$. The Fourier transform of the spin-resolved electron density-of-states change is","evidenceType":"theory","sourceIds":["source-6e0b3a25ead07f3c"],"conditions":"Conditional retarded Green-function/DFT and ideal coherence-factor models; finite synthetic calculations are not fits to cuprates or FeSe.","verificationScope":"Selected source locations are stated in references; independent Fourier/resolvent checks apply only to the explicit ideal models.","sourceRelationship":"mixed-source-and-local-derivation","derivationNote":"Wang–Lee author v3 p. 1 Eq. (1) supplies the scattering-response framework with both Nambu diagonal blocks. This entry locally specializes to one spin-resolved electron block, N-site normalization and a static local defect; T follows from T=V+Vg0T when the inverse exists. Six finite-model resolvent comparisons check these conventions, not material data."},{"id":"scwiki-a10-claim-mathematical-assumptions-7","sectionId":"mathematical-assumptions","statement":"$$\\delta\\tilde\\rho(\\mathbf q,E)=-\\frac{\\Lambda(\\mathbf q,E)-\\Lambda(-\\mathbf q,E)^*}{2\\pi i}.$$","evidenceType":"theory","sourceIds":["source-6e0b3a25ead07f3c"],"conditions":"Conditional retarded Green-function/DFT and ideal coherence-factor models; finite synthetic calculations are not fits to cuprates or FeSe.","verificationScope":"Selected source locations are stated in references; independent Fourier/resolvent checks apply only to the explicit ideal models.","sourceRelationship":"mixed-source-and-local-derivation","derivationNote":"Wang–Lee author v3 p. 1 Eq. (1) supplies the scattering-response framework with both Nambu diagonal blocks. This entry locally specializes to one spin-resolved electron block, N-site normalization and a static local defect; T follows from T=V+Vg0T when the inverse exists. Six finite-model resolvent comparisons check these conventions, not material data."},{"id":"scwiki-a10-claim-mathematical-assumptions-8","sectionId":"mathematical-assumptions","statement":"Taking just $-\\operatorname{Im}\\Lambda(\\mathbf q)/\\pi$ is insufficient for a general complex Fourier map. It becomes valid with the additional even-in-momentum response condition. Six independent checks compare full real-space resolvent inversion with the scattering expression on a ten-site, fixed-gap model; displaced defects expose the lost phase. This is a normalization and response check, not a cuprate or FeSe simulation. The selected Wang–Lee manuscript supplies the broader scattering framework and explicitly discusses off-shell and matrix-element limits. Its Eq. (1) includes both Nambu diagonal blocks; the expression here uses an explicitly spin-resolved electron block and a discrete lattice normalization. These local conventions and their checks are not a verbatim reproduction of the full source formula.","evidenceType":"theory","sourceIds":["source-6e0b3a25ead07f3c"],"conditions":"Conditional retarded Green-function/DFT and ideal coherence-factor models; finite synthetic calculations are not fits to cuprates or FeSe.","verificationScope":"Selected source locations are stated in references; independent Fourier/resolvent checks apply only to the explicit ideal models.","sourceRelationship":"mixed-source-and-local-derivation","derivationNote":"Source v3 pp. 1-2 supports the scattering framework and off-shell/matrix-element caution. The complex-Fourier conjugation argument and six fixed-gap finite-model checks are local; source Eq. (1) and this spin-resolved form are explicitly distinguished."},{"id":"scwiki-a10-claim-mathematical-assumptions-9","sectionId":"mathematical-assumptions","statement":"A joint-density-of-states construction counts candidate equal-energy connections but omits scattering amplitudes and coherence factors. In an ideal equal-magnitude, real-gap Fermi-surface limit, scalar and magnetic Born amplitudes contain $uu'-vv'$ and $uu'+vv'$. Setting $u=u'=1/\\sqrt2$ and $v=\\operatorname{sgn}(\\Delta)/\\sqrt2$ interchanges their zero/nonzero weights when the relative gap sign changes. This conditional example explains sensitivity to the impurity channel; it does not identify a real defect from one bright peak.","evidenceType":"theory","sourceIds":["source-6e0b3a25ead07f3c"],"conditions":"Conditional retarded Green-function/DFT and ideal coherence-factor models; finite synthetic calculations are not fits to cuprates or FeSe.","verificationScope":"Selected source locations are stated in references; independent Fourier/resolvent checks apply only to the explicit ideal models.","sourceRelationship":"mixed-source-and-local-derivation","derivationNote":"Source v3 p. 2 gives scalar/magnetic coherence-factor dependence. The equal-magnitude, real-gap, xi=0 weights are a local ideal-limit evaluation, not identification of an experimental defect."},{"id":"scwiki-a10-claim-experimental-criteria-1","sectionId":"experimental-criteria","statement":"Hoffman and colleagues' dispersing-QPI manuscript reports Bi2212 conductance imaging at 4.2 K. Selected pages describe two peak families with opposite energy trends and doping-dependent dispersion, interpreted against photoemission information. Its Science DOI ends in **1072640**. The inherited DOI ending in **1066974** instead identifies their distinct vortex-core modulation paper; these are not interchangeable evidence.","evidenceType":"experiment","sourceIds":["source-e8e6ef56da103435","source-353efd52d3443260"],"conditions":"Bi2212 conductance imaging at 4.2 K; selected earlier manuscript only, raw data not reanalyzed.","verificationScope":"Selected source locations are stated in references; independent Fourier/resolvent checks apply only to the explicit ideal models."},{"id":"scwiki-a10-claim-experimental-criteria-2","sectionId":"experimental-criteria","statement":"Sprau and colleagues' FeSe manuscript reports imaging at 280 mK. The relative-sign analysis uses the real parts at opposite energies, isolates an interband momentum region and places the Fourier origin at a defect. Selected supplementary passages vary the integration area and repeat the analysis on additional impurities. The reported sign inference is conditional on their scattering model and band assignment; it is not an inference from the absolute Fourier intensity alone.","evidenceType":"experiment","sourceIds":["source-2f227038c5cf73a9"],"conditions":"FeSe conductance imaging at 280 mK; selected manuscript model-dependent relative-sign inference, not a universal iron-based result.","verificationScope":"Selected source locations are stated in references; independent Fourier/resolvent checks apply only to the explicit ideal models."},{"id":"scwiki-a10-claim-experimental-criteria-3","sectionId":"experimental-criteria","statement":"Report field of view, pixel spacing, spatial drift correction, bias grid, temperature, excitation amplitude, tip condition, set-point protocol and defect selection. Preserve both raw and processed maps. State whether a displayed quantity is a complex transform, its real part, magnitude, power or a ratio: these operations retain different information. Explain normalization, windowing, background removal, symmetrization and peak uncertainties.","evidenceType":"hypothesis","sourceIds":["source-6e0b3a25ead07f3c"],"conditions":"Editorial inference/reporting boundaries; no unique pairing mechanism or static order assigned.","verificationScope":"Selected source locations are stated in references; independent Fourier/resolvent checks apply only to the explicit ideal models."},{"id":"scwiki-a10-claim-limits-and-disputes-1","sectionId":"limits-and-disputes","statement":"For $N_x$ equally spaced pixels of spacing $a_x$, the periodic-transform length is $L_x=N_xa_x$ and angular-wavevector bin spacing is $2\\pi/L_x$; the Nyquist bound is $\\pi/a_x$. Using cycles per length removes the $2\\pi$ factors. Zero padding interpolates the transform but does not create a larger measured field. A window trades spectral leakage against peak width, so bin spacing alone is not an experimental uncertainty or guaranteed resolving power.","evidenceType":"theory","sourceIds":["source-6e0b3a25ead07f3c"],"conditions":"Conditional retarded Green-function/DFT and ideal coherence-factor models; finite synthetic calculations are not fits to cuprates or FeSe.","verificationScope":"Selected source locations are stated in references; independent Fourier/resolvent checks apply only to the explicit ideal models."},{"id":"scwiki-a10-claim-limits-and-disputes-2","sectionId":"limits-and-disputes","statement":"Energy dispersion supports a scattering interpretation only together with band, defect and temperature/field controls. Weak dispersion over a limited window does not by itself prove charge order; Bragg, structural, moire and electronic features can overlap. Conversely, an order and QPI may coexist. The cuprate octet geometry must not be imposed on arbitrary multiband spectra.","evidenceType":"hypothesis","sourceIds":["source-6e0b3a25ead07f3c"],"conditions":"Editorial inference/reporting boundaries; no unique pairing mechanism or static order assigned.","verificationScope":"Selected source locations are stated in references; independent Fourier/resolvent checks apply only to the explicit ideal models."},{"id":"scwiki-a10-claim-limits-and-disputes-3","sectionId":"limits-and-disputes","statement":"The McElroy reference in the pinned chapter used an unrelated biology DOI, **nature02269**. The correct QPI paper is **nature01496**; its publisher identity is checked here, while its detailed data remain outside this entry's review. The original source is preserved and the replacement recorded.","evidenceType":"hypothesis","sourceIds":["source-230ea3ac9496dc90"],"conditions":"Editorial inference/reporting boundaries; no unique pairing mechanism or static order assigned.","verificationScope":"Selected source locations are stated in references; independent Fourier/resolvent checks apply only to the explicit ideal models."},{"id":"scwiki-a10-claim-discovery-implications-1","sectionId":"discovery-implications","statement":"Use QPI to compare explicit candidate electronic and scattering models against multiple observables. A useful claim states which alternatives the data discriminate, which are still compatible, and how uncertainty in defect identity or preprocessing changes the result. Combine gap-magnitude constraints with independent bulk and phase-sensitive evidence before assigning a pairing state or mechanism.","evidenceType":"hypothesis","sourceIds":["source-6e0b3a25ead07f3c"],"conditions":"Editorial inference/reporting boundaries; no unique pairing mechanism or static order assigned.","verificationScope":"Selected source locations are stated in references; independent Fourier/resolvent checks apply only to the explicit ideal models."}],"corrections":[{"id":"scwiki-a10-correction-1","description":"Replaced unrelated nature02269 with McElroy QPI DOI nature01496; retained the pinned source unchanged.","sourceId":"source-230ea3ac9496dc90","scope":"Source identity correction, not a correction to either paper."},{"id":"scwiki-a10-correction-2","description":"Distinguished dispersing-QPI science.1072640 from vortex-core modulation science.1066974; both identities remain traceable.","sourceId":"source-e8e6ef56da103435","scope":"Correct attribution to the experiment described."}],"equationChecks":[{"targetSectionId":"mathematical-assumptions","tex":"\\delta\\tilde\\rho(q)=-[\\Lambda(q)-\\Lambda(-q)^*]/(2\\pi i)","check":"Six full finite BdG resolvent versus T-matrix comparisons, including displaced-defect counterexamples to naive imaginary-part Fourier formula."},{"targetSectionId":"mathematical-assumptions","tex":"\\tilde g\\prime=e^{-iqr_0}\\tilde g","check":"Discrete phase translation, magnitude invariance, Hermitian symmetry, sampled cosine and alias checks; ideal coherence-factor sign/channel weights."}],"materialCases":[{"id":"scwiki-a10-material-1","formula":"Bi2Sr2CaCu2O8+delta","sample":"Hoffman Bi2212 crystals; selected imaging passages","recordType":"experiment","tcK":null,"reportedTemperatureK":4.2,"temperatureKind":"spectroscopic-gap","temperatureNote":"Measurement temperature, not a transition Tc","criterion":"qpi-conductance-map","pressureRegime":"unknown","pressureGPa":null,"equilibrium":"unknown","probe":"Differential tunneling conductance maps; 4.2 K, cryogenic cleavage and Fourier peak tracking","sourceId":"source-e8e6ef56da103435","aliases":["cuprate","cuprates"]},{"id":"scwiki-a10-material-2","formula":"FeSe","sample":"Sprau bulk FeSe; selected manuscript and defect analysis","recordType":"experiment","tcK":null,"reportedTemperatureK":0.28,"temperatureKind":"spectroscopic-gap","temperatureNote":"Measurement temperature, not a transition Tc","criterion":"qpi-conductance-map","pressureRegime":"unknown","pressureGPa":null,"equilibrium":"unknown","probe":"280 mK conductance maps; defect-centered Fourier phase and selected interband integration region","sourceId":"source-2f227038c5cf73a9","aliases":["iron-based","iron based superconductors"]}],"body":"## Scope\n\nQuasiparticle interference (QPI) uses spatial variations in scanning tunneling conductance to constrain electronic states and scattering. Elastic scattering can connect states of equal energy with momentum transfer $\\mathbf q=\\mathbf k'-\\mathbf k$. A Fourier peak is a feature of a measured response, not a direct photograph of a Fermi surface or a uniquely identified order parameter. Keep the tunneling matrix element, defect channel and preprocessing attached to every interpretation.\n\nIn a weak-tunneling description with a sufficiently smooth tip spectrum and matrix element, low-temperature differential conductance can approximate a sample's local density of states. Thermal and instrumental convolution, spatially varying set points and orbital sensitivity can change that relation. A conductance map and an ideal local-density-of-states calculation should not be treated as interchangeable without testing these assumptions.\n\n## Mathematical assumptions\n\nWith the convention $\\tilde g(\\mathbf q,E)=\\sum_{\\mathbf r}e^{-i\\mathbf q\\cdot\\mathbf r}g(\\mathbf r,E)$, a translated pattern obeys\n\n$$g'(\\mathbf r,E)=g(\\mathbf r-\\mathbf r_0,E),\\qquad\\tilde g'=e^{-i\\mathbf q\\cdot\\mathbf r_0}\\tilde g.$$\n\nIts Fourier magnitude is unchanged, while its real and imaginary parts generally change. A real map satisfies $\\tilde g(-\\mathbf q)=\\tilde g(\\mathbf q)^*$. Independent discrete-transform checks verify both identities, an exactly sampled cosine and sampling aliases. Finite cropping can also change amplitudes; the exact translation identity assumes the whole pattern or periodic data, not two differently cropped fields.\n\nFor a periodic lattice with $N$ sites and one static, local defect at the origin, define an ideal electron-block response\n\n$$\\Lambda(\\mathbf q,E)=\\frac{1}{N}\\sum_{\\mathbf k}[G_0(\\mathbf k,E)\\,T(E)\\,G_0(\\mathbf k-\\mathbf q,E)]_{11}.$$\n\nHere $G_0$ is a retarded Nambu Green function and $T=[1-Vg_0]^{-1}V$, with $g_0=N^{-1}\\sum_{\\mathbf k}G_0$. The Fourier transform of the spin-resolved electron density-of-states change is\n\n$$\\delta\\tilde\\rho(\\mathbf q,E)=-\\frac{\\Lambda(\\mathbf q,E)-\\Lambda(-\\mathbf q,E)^*}{2\\pi i}.$$\n\nTaking just $-\\operatorname{Im}\\Lambda(\\mathbf q)/\\pi$ is insufficient for a general complex Fourier map. It becomes valid with the additional even-in-momentum response condition. Six independent checks compare full real-space resolvent inversion with the scattering expression on a ten-site, fixed-gap model; displaced defects expose the lost phase. This is a normalization and response check, not a cuprate or FeSe simulation. The selected Wang–Lee manuscript supplies the broader scattering framework and explicitly discusses off-shell and matrix-element limits. Its Eq. (1) includes both Nambu diagonal blocks; the expression here uses an explicitly spin-resolved electron block and a discrete lattice normalization. These local conventions and their checks are not a verbatim reproduction of the full source formula. [R2](#ref-source-6e0b3a25ead07f3c)\n\nA joint-density-of-states construction counts candidate equal-energy connections but omits scattering amplitudes and coherence factors. In an ideal equal-magnitude, real-gap Fermi-surface limit, scalar and magnetic Born amplitudes contain $uu'-vv'$ and $uu'+vv'$. Setting $u=u'=1/\\sqrt2$ and $v=\\operatorname{sgn}(\\Delta)/\\sqrt2$ interchanges their zero/nonzero weights when the relative gap sign changes. This conditional example explains sensitivity to the impurity channel; it does not identify a real defect from one bright peak. [R2](#ref-source-6e0b3a25ead07f3c)\n\n## Experimental criteria\n\nHoffman and colleagues' dispersing-QPI manuscript reports Bi2212 conductance imaging at 4.2 K. Selected pages describe two peak families with opposite energy trends and doping-dependent dispersion, interpreted against photoemission information. Its Science DOI ends in **1072640**. The inherited DOI ending in **1066974** instead identifies their distinct vortex-core modulation paper; these are not interchangeable evidence. [R1](#ref-source-e8e6ef56da103435) [R5](#ref-source-353efd52d3443260)\n\nSprau and colleagues' FeSe manuscript reports imaging at 280 mK. The relative-sign analysis uses the real parts at opposite energies, isolates an interband momentum region and places the Fourier origin at a defect. Selected supplementary passages vary the integration area and repeat the analysis on additional impurities. The reported sign inference is conditional on their scattering model and band assignment; it is not an inference from the absolute Fourier intensity alone. [R4](#ref-source-2f227038c5cf73a9)\n\nReport field of view, pixel spacing, spatial drift correction, bias grid, temperature, excitation amplitude, tip condition, set-point protocol and defect selection. Preserve both raw and processed maps. State whether a displayed quantity is a complex transform, its real part, magnitude, power or a ratio: these operations retain different information. Explain normalization, windowing, background removal, symmetrization and peak uncertainties.\n\n## Limits and disputes\n\nFor $N_x$ equally spaced pixels of spacing $a_x$, the periodic-transform length is $L_x=N_xa_x$ and angular-wavevector bin spacing is $2\\pi/L_x$; the Nyquist bound is $\\pi/a_x$. Using cycles per length removes the $2\\pi$ factors. Zero padding interpolates the transform but does not create a larger measured field. A window trades spectral leakage against peak width, so bin spacing alone is not an experimental uncertainty or guaranteed resolving power.\n\nEnergy dispersion supports a scattering interpretation only together with band, defect and temperature/field controls. Weak dispersion over a limited window does not by itself prove charge order; Bragg, structural, moire and electronic features can overlap. Conversely, an order and QPI may coexist. The cuprate octet geometry must not be imposed on arbitrary multiband spectra.\n\nThe McElroy reference in the pinned chapter used an unrelated biology DOI, **nature02269**. The correct QPI paper is **nature01496**; its publisher identity is checked here, while its detailed data remain outside this entry's review. The original source is preserved and the replacement recorded. [R3](#ref-source-230ea3ac9496dc90)\n\n## Discovery implications\n\nUse QPI to compare explicit candidate electronic and scattering models against multiple observables. A useful claim states which alternatives the data discriminate, which are still compatible, and how uncertainty in defect identity or preprocessing changes the result. Combine gap-magnitude constraints with independent bulk and phase-sensitive evidence before assigning a pairing state or mechanism.\n\n## Related topics\n\nContinue with [superconducting gaps](/scwiki/superconducting-gap), [Andreev reflection](/scwiki/andreev-reflection), [cuprates](/scwiki/cuprates), [iron-based superconductors](/scwiki/iron-based-superconductors), [multiband pairing](/scwiki/multiband-pairing), and [s± pairing](/scwiki/s-plus-minus).","revision":"36f6dcca4941c8e9d9f7","sections":[{"id":"scope","title":"Scope","markdown":"## Scope\n\nQuasiparticle interference (QPI) uses spatial variations in scanning tunneling conductance to constrain electronic states and scattering. Elastic scattering can connect states of equal energy with momentum transfer $\\mathbf q=\\mathbf k'-\\mathbf k$. A Fourier peak is a feature of a measured response, not a direct photograph of a Fermi surface or a uniquely identified order parameter. Keep the tunneling matrix element, defect channel and preprocessing attached to every interpretation.\n\nIn a weak-tunneling description with a sufficiently smooth tip spectrum and matrix element, low-temperature differential conductance can approximate a sample's local density of states. Thermal and instrumental convolution, spatially varying set points and orbital sensitivity can change that relation. A conductance map and an ideal local-density-of-states calculation should not be treated as interchangeable without testing these assumptions."},{"id":"mathematical-assumptions","title":"Mathematical assumptions","markdown":"## Mathematical assumptions\n\nWith the convention $\\tilde g(\\mathbf q,E)=\\sum_{\\mathbf r}e^{-i\\mathbf q\\cdot\\mathbf r}g(\\mathbf r,E)$, a translated pattern obeys\n\n$$g'(\\mathbf r,E)=g(\\mathbf r-\\mathbf r_0,E),\\qquad\\tilde g'=e^{-i\\mathbf q\\cdot\\mathbf r_0}\\tilde g.$$\n\nIts Fourier magnitude is unchanged, while its real and imaginary parts generally change. A real map satisfies $\\tilde g(-\\mathbf q)=\\tilde g(\\mathbf q)^*$. Independent discrete-transform checks verify both identities, an exactly sampled cosine and sampling aliases. Finite cropping can also change amplitudes; the exact translation identity assumes the whole pattern or periodic data, not two differently cropped fields.\n\nFor a periodic lattice with $N$ sites and one static, local defect at the origin, define an ideal electron-block response\n\n$$\\Lambda(\\mathbf q,E)=\\frac{1}{N}\\sum_{\\mathbf k}[G_0(\\mathbf k,E)\\,T(E)\\,G_0(\\mathbf k-\\mathbf q,E)]_{11}.$$\n\nHere $G_0$ is a retarded Nambu Green function and $T=[1-Vg_0]^{-1}V$, with $g_0=N^{-1}\\sum_{\\mathbf k}G_0$. The Fourier transform of the spin-resolved electron density-of-states change is\n\n$$\\delta\\tilde\\rho(\\mathbf q,E)=-\\frac{\\Lambda(\\mathbf q,E)-\\Lambda(-\\mathbf q,E)^*}{2\\pi i}.$$\n\nTaking just $-\\operatorname{Im}\\Lambda(\\mathbf q)/\\pi$ is insufficient for a general complex Fourier map. It becomes valid with the additional even-in-momentum response condition. Six independent checks compare full real-space resolvent inversion with the scattering expression on a ten-site, fixed-gap model; displaced defects expose the lost phase. This is a normalization and response check, not a cuprate or FeSe simulation. The selected Wang–Lee manuscript supplies the broader scattering framework and explicitly discusses off-shell and matrix-element limits. Its Eq. (1) includes both Nambu diagonal blocks; the expression here uses an explicitly spin-resolved electron block and a discrete lattice normalization. These local conventions and their checks are not a verbatim reproduction of the full source formula. [R2](#ref-source-6e0b3a25ead07f3c)\n\nA joint-density-of-states construction counts candidate equal-energy connections but omits scattering amplitudes and coherence factors. In an ideal equal-magnitude, real-gap Fermi-surface limit, scalar and magnetic Born amplitudes contain $uu'-vv'$ and $uu'+vv'$. Setting $u=u'=1/\\sqrt2$ and $v=\\operatorname{sgn}(\\Delta)/\\sqrt2$ interchanges their zero/nonzero weights when the relative gap sign changes. This conditional example explains sensitivity to the impurity channel; it does not identify a real defect from one bright peak. [R2](#ref-source-6e0b3a25ead07f3c)"},{"id":"experimental-criteria","title":"Experimental criteria","markdown":"## Experimental criteria\n\nHoffman and colleagues' dispersing-QPI manuscript reports Bi2212 conductance imaging at 4.2 K. Selected pages describe two peak families with opposite energy trends and doping-dependent dispersion, interpreted against photoemission information. Its Science DOI ends in **1072640**. The inherited DOI ending in **1066974** instead identifies their distinct vortex-core modulation paper; these are not interchangeable evidence. [R1](#ref-source-e8e6ef56da103435) [R5](#ref-source-353efd52d3443260)\n\nSprau and colleagues' FeSe manuscript reports imaging at 280 mK. The relative-sign analysis uses the real parts at opposite energies, isolates an interband momentum region and places the Fourier origin at a defect. Selected supplementary passages vary the integration area and repeat the analysis on additional impurities. The reported sign inference is conditional on their scattering model and band assignment; it is not an inference from the absolute Fourier intensity alone. [R4](#ref-source-2f227038c5cf73a9)\n\nReport field of view, pixel spacing, spatial drift correction, bias grid, temperature, excitation amplitude, tip condition, set-point protocol and defect selection. Preserve both raw and processed maps. State whether a displayed quantity is a complex transform, its real part, magnitude, power or a ratio: these operations retain different information. Explain normalization, windowing, background removal, symmetrization and peak uncertainties."},{"id":"limits-and-disputes","title":"Limits and disputes","markdown":"## Limits and disputes\n\nFor $N_x$ equally spaced pixels of spacing $a_x$, the periodic-transform length is $L_x=N_xa_x$ and angular-wavevector bin spacing is $2\\pi/L_x$; the Nyquist bound is $\\pi/a_x$. Using cycles per length removes the $2\\pi$ factors. Zero padding interpolates the transform but does not create a larger measured field. A window trades spectral leakage against peak width, so bin spacing alone is not an experimental uncertainty or guaranteed resolving power.\n\nEnergy dispersion supports a scattering interpretation only together with band, defect and temperature/field controls. Weak dispersion over a limited window does not by itself prove charge order; Bragg, structural, moire and electronic features can overlap. Conversely, an order and QPI may coexist. The cuprate octet geometry must not be imposed on arbitrary multiband spectra.\n\nThe McElroy reference in the pinned chapter used an unrelated biology DOI, **nature02269**. The correct QPI paper is **nature01496**; its publisher identity is checked here, while its detailed data remain outside this entry's review. The original source is preserved and the replacement recorded. [R3](#ref-source-230ea3ac9496dc90)"},{"id":"discovery-implications","title":"Discovery implications","markdown":"## Discovery implications\n\nUse QPI to compare explicit candidate electronic and scattering models against multiple observables. A useful claim states which alternatives the data discriminate, which are still compatible, and how uncertainty in defect identity or preprocessing changes the result. Combine gap-magnitude constraints with independent bulk and phase-sensitive evidence before assigning a pairing state or mechanism."},{"id":"related-topics","title":"Related topics","markdown":"## Related topics\n\nContinue with [superconducting gaps](/scwiki/superconducting-gap), [Andreev reflection](/scwiki/andreev-reflection), [cuprates](/scwiki/cuprates), [iron-based superconductors](/scwiki/iron-based-superconductors), [multiband pairing](/scwiki/multiband-pairing), and [s± pairing](/scwiki/s-plus-minus)."},{"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| Bi2Sr2CaCu2O8+delta (aliases: cuprate, cuprates); Hoffman Bi2212 crystals; selected imaging passages | 4.2 K; Measurement temperature, not a transition Tc | spectroscopic-gap; qpi-conductance-map | Differential tunneling conductance maps; 4.2 K, cryogenic cleavage and Fourier peak tracking | unknown; unknown GPa | unknown | experiment; [source](#ref-source-e8e6ef56da103435) |\n| FeSe (aliases: iron-based, iron based superconductors); Sprau bulk FeSe; selected manuscript and defect analysis | 0.28 K; Measurement temperature, not a transition Tc | spectroscopic-gap; qpi-conductance-map | 280 mK conductance maps; defect-centered Fourier phase and selected interband integration region | unknown; unknown GPa | unknown | experiment; [source](#ref-source-2f227038c5cf73a9) |"}],"markdown":"# Quasiparticle interference: momentum structure and phase limits\n\nRead Fourier-transform tunneling maps with their scattering, sampling and phase assumptions. Distinguish measured modulation from inferred bands, gap sign and competing order.\n\n## Scope\n\nQuasiparticle interference (QPI) uses spatial variations in scanning tunneling conductance to constrain electronic states and scattering. Elastic scattering can connect states of equal energy with momentum transfer $\\mathbf q=\\mathbf k'-\\mathbf k$. A Fourier peak is a feature of a measured response, not a direct photograph of a Fermi surface or a uniquely identified order parameter. Keep the tunneling matrix element, defect channel and preprocessing attached to every interpretation.\n\nIn a weak-tunneling description with a sufficiently smooth tip spectrum and matrix element, low-temperature differential conductance can approximate a sample's local density of states. Thermal and instrumental convolution, spatially varying set points and orbital sensitivity can change that relation. A conductance map and an ideal local-density-of-states calculation should not be treated as interchangeable without testing these assumptions.\n\n## Mathematical assumptions\n\nWith the convention $\\tilde g(\\mathbf q,E)=\\sum_{\\mathbf r}e^{-i\\mathbf q\\cdot\\mathbf r}g(\\mathbf r,E)$, a translated pattern obeys\n\n$$g'(\\mathbf r,E)=g(\\mathbf r-\\mathbf r_0,E),\\qquad\\tilde g'=e^{-i\\mathbf q\\cdot\\mathbf r_0}\\tilde g.$$\n\nIts Fourier magnitude is unchanged, while its real and imaginary parts generally change. A real map satisfies $\\tilde g(-\\mathbf q)=\\tilde g(\\mathbf q)^*$. Independent discrete-transform checks verify both identities, an exactly sampled cosine and sampling aliases. Finite cropping can also change amplitudes; the exact translation identity assumes the whole pattern or periodic data, not two differently cropped fields.\n\nFor a periodic lattice with $N$ sites and one static, local defect at the origin, define an ideal electron-block response\n\n$$\\Lambda(\\mathbf q,E)=\\frac{1}{N}\\sum_{\\mathbf k}[G_0(\\mathbf k,E)\\,T(E)\\,G_0(\\mathbf k-\\mathbf q,E)]_{11}.$$\n\nHere $G_0$ is a retarded Nambu Green function and $T=[1-Vg_0]^{-1}V$, with $g_0=N^{-1}\\sum_{\\mathbf k}G_0$. The Fourier transform of the spin-resolved electron density-of-states change is\n\n$$\\delta\\tilde\\rho(\\mathbf q,E)=-\\frac{\\Lambda(\\mathbf q,E)-\\Lambda(-\\mathbf q,E)^*}{2\\pi i}.$$\n\nTaking just $-\\operatorname{Im}\\Lambda(\\mathbf q)/\\pi$ is insufficient for a general complex Fourier map. It becomes valid with the additional even-in-momentum response condition. Six independent checks compare full real-space resolvent inversion with the scattering expression on a ten-site, fixed-gap model; displaced defects expose the lost phase. This is a normalization and response check, not a cuprate or FeSe simulation. The selected Wang–Lee manuscript supplies the broader scattering framework and explicitly discusses off-shell and matrix-element limits. Its Eq. (1) includes both Nambu diagonal blocks; the expression here uses an explicitly spin-resolved electron block and a discrete lattice normalization. These local conventions and their checks are not a verbatim reproduction of the full source formula. [R2](#ref-source-6e0b3a25ead07f3c)\n\nA joint-density-of-states construction counts candidate equal-energy connections but omits scattering amplitudes and coherence factors. In an ideal equal-magnitude, real-gap Fermi-surface limit, scalar and magnetic Born amplitudes contain $uu'-vv'$ and $uu'+vv'$. Setting $u=u'=1/\\sqrt2$ and $v=\\operatorname{sgn}(\\Delta)/\\sqrt2$ interchanges their zero/nonzero weights when the relative gap sign changes. This conditional example explains sensitivity to the impurity channel; it does not identify a real defect from one bright peak. [R2](#ref-source-6e0b3a25ead07f3c)\n\n## Experimental criteria\n\nHoffman and colleagues' dispersing-QPI manuscript reports Bi2212 conductance imaging at 4.2 K. Selected pages describe two peak families with opposite energy trends and doping-dependent dispersion, interpreted against photoemission information. Its Science DOI ends in **1072640**. The inherited DOI ending in **1066974** instead identifies their distinct vortex-core modulation paper; these are not interchangeable evidence. [R1](#ref-source-e8e6ef56da103435) [R5](#ref-source-353efd52d3443260)\n\nSprau and colleagues' FeSe manuscript reports imaging at 280 mK. The relative-sign analysis uses the real parts at opposite energies, isolates an interband momentum region and places the Fourier origin at a defect. Selected supplementary passages vary the integration area and repeat the analysis on additional impurities. The reported sign inference is conditional on their scattering model and band assignment; it is not an inference from the absolute Fourier intensity alone. [R4](#ref-source-2f227038c5cf73a9)\n\nReport field of view, pixel spacing, spatial drift correction, bias grid, temperature, excitation amplitude, tip condition, set-point protocol and defect selection. Preserve both raw and processed maps. State whether a displayed quantity is a complex transform, its real part, magnitude, power or a ratio: these operations retain different information. Explain normalization, windowing, background removal, symmetrization and peak uncertainties.\n\n## Limits and disputes\n\nFor $N_x$ equally spaced pixels of spacing $a_x$, the periodic-transform length is $L_x=N_xa_x$ and angular-wavevector bin spacing is $2\\pi/L_x$; the Nyquist bound is $\\pi/a_x$. Using cycles per length removes the $2\\pi$ factors. Zero padding interpolates the transform but does not create a larger measured field. A window trades spectral leakage against peak width, so bin spacing alone is not an experimental uncertainty or guaranteed resolving power.\n\nEnergy dispersion supports a scattering interpretation only together with band, defect and temperature/field controls. Weak dispersion over a limited window does not by itself prove charge order; Bragg, structural, moire and electronic features can overlap. Conversely, an order and QPI may coexist. The cuprate octet geometry must not be imposed on arbitrary multiband spectra.\n\nThe McElroy reference in the pinned chapter used an unrelated biology DOI, **nature02269**. The correct QPI paper is **nature01496**; its publisher identity is checked here, while its detailed data remain outside this entry's review. The original source is preserved and the replacement recorded. [R3](#ref-source-230ea3ac9496dc90)\n\n## Discovery implications\n\nUse QPI to compare explicit candidate electronic and scattering models against multiple observables. A useful claim states which alternatives the data discriminate, which are still compatible, and how uncertainty in defect identity or preprocessing changes the result. Combine gap-magnitude constraints with independent bulk and phase-sensitive evidence before assigning a pairing state or mechanism.\n\n## Related topics\n\nContinue with [superconducting gaps](/scwiki/superconducting-gap), [Andreev reflection](/scwiki/andreev-reflection), [cuprates](/scwiki/cuprates), [iron-based superconductors](/scwiki/iron-based-superconductors), [multiband pairing](/scwiki/multiband-pairing), and [s± pairing](/scwiki/s-plus-minus).\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| Bi2Sr2CaCu2O8+delta (aliases: cuprate, cuprates); Hoffman Bi2212 crystals; selected imaging passages | 4.2 K; Measurement temperature, not a transition Tc | spectroscopic-gap; qpi-conductance-map | Differential tunneling conductance maps; 4.2 K, cryogenic cleavage and Fourier peak tracking | unknown; unknown GPa | unknown | experiment; [source](#ref-source-e8e6ef56da103435) |\n| FeSe (aliases: iron-based, iron based superconductors); Sprau bulk FeSe; selected manuscript and defect analysis | 0.28 K; Measurement temperature, not a transition Tc | spectroscopic-gap; qpi-conductance-map | 280 mK conductance maps; defect-centered Fourier phase and selected interband integration region | unknown; unknown GPa | unknown | experiment; [source](#ref-source-2f227038c5cf73a9) |\n\n## Sources\n\n### Ref source-e8e6ef56da103435\n\n[R1] Imaging Quasiparticle Interference in Bi2Sr2CaCu2O8+delta (2002). [DOI 10.1126/science.1072640](https://doi.org/10.1126/science.1072640). Publication: journal-article. Check: author-manuscript-scoped-check. Checked: 2026-10-18. Selected pp. 2–6: elastic scattering, 4.2 K conductance maps and dispersing peaks. Raw maps and final-version differences not reanalyzed.\n### Ref source-6e0b3a25ead07f3c\n\n[R2] Quasiparticle scattering interference in high-temperature superconductors (2003). [DOI 10.1103/PhysRevB.67.020511](https://doi.org/10.1103/PhysRevB.67.020511). Publication: journal-article. Check: author-manuscript-scoped-check. Checked: 2026-10-19. Author v3 dated 20 August 2002, associated journal 2003. Selected pp. 1-2; p. 1 Eq. (1) pixels rechecked for both Nambu diagonal blocks, p. 2 previously viewed for off-shell/coherence-factor limits. Site spin-resolved block and discrete normalization are explicit local conventions. Full published calculation and final-version comparison remain open.\n### Ref source-230ea3ac9496dc90\n\n[R3] Relating atomic-scale electronic phenomena to wave-like quasiparticle states in superconducting Bi2Sr2CaCu2O8+delta (2003). [DOI 10.1038/nature01496](https://doi.org/10.1038/nature01496). Publication: journal-article. Check: publisher-metadata-scoped-check. Checked: 2026-10-18. Publisher title/authors/pages and Crossref identity checked; full text/data not audited. Replaces inherited unrelated biology DOI nature02269.\n### Ref source-2f227038c5cf73a9\n\n[R4] Discovery of orbital-selective Cooper pairing in FeSe (2017). [DOI 10.1126/science.aal1575](https://doi.org/10.1126/science.aal1575). Publication: journal-article. Check: author-manuscript-scoped-check. Checked: 2026-10-18. Selected manuscript p. 7 and pp. 10–11 plus supplementary section VII (PDF pp. 36–37): 280 mK, defect-centered phase, interband region and controls. Full FeSe model/data and final-version comparison not reproduced.\n### Ref source-353efd52d3443260\n\n[R5] A Four Unit Cell Periodic Pattern of Quasi-Particle States Surrounding Vortex Cores in Bi2Sr2CaCu2O8+delta (2002). [DOI 10.1126/science.1066974](https://doi.org/10.1126/science.1066974). Publication: journal-article. Check: crossref-metadata-only. Checked: 2026-10-18. Distinct vortex-core paper retained to document inherited attribution mismatch; no detailed vortex experiment audited here.\n\n## Claim evidence and conditions\n\n### scwiki-a10-claim-scope-1\n\nQuasiparticle interference (QPI) uses spatial variations in scanning tunneling conductance to constrain electronic states and scattering. Elastic scattering can connect states of equal energy with momentum transfer $\\mathbf q=\\mathbf k'-\\mathbf k$. A Fourier peak is a feature of a measured response, not a direct photograph of a Fermi surface or a uniquely identified order parameter. Keep the tunneling matrix element, defect channel and preprocessing attached to every interpretation.\n\nEvidence: theory. Sources: source-6e0b3a25ead07f3c.\n\nConditions: Conditional retarded Green-function/DFT and ideal coherence-factor models; finite synthetic calculations are not fits to cuprates or FeSe.\n\nVerification scope: Selected source locations are stated in references; independent Fourier/resolvent checks apply only to the explicit ideal models.\n\n### scwiki-a10-claim-scope-2\n\nIn a weak-tunneling description with a sufficiently smooth tip spectrum and matrix element, low-temperature differential conductance can approximate a sample's local density of states. Thermal and instrumental convolution, spatially varying set points and orbital sensitivity can change that relation. A conductance map and an ideal local-density-of-states calculation should not be treated as interchangeable without testing these assumptions.\n\nEvidence: theory. Sources: source-6e0b3a25ead07f3c.\n\nConditions: Conditional retarded Green-function/DFT and ideal coherence-factor models; finite synthetic calculations are not fits to cuprates or FeSe.\n\nVerification scope: Selected source locations are stated in references; independent Fourier/resolvent checks apply only to the explicit ideal models.\n\n### scwiki-a10-claim-mathematical-assumptions-1\n\nWith the convention $\\tilde g(\\mathbf q,E)=\\sum_{\\mathbf r}e^{-i\\mathbf q\\cdot\\mathbf r}g(\\mathbf r,E)$, a translated pattern obeys\n\nEvidence: theory. Sources: source-6e0b3a25ead07f3c.\n\nSource relationship: context-for-local-derivation. Local discrete-Fourier definition and translation/conjugation identities; exact algebra and sampled periodic examples. Wang–Lee supplies scattering context, not a separate experiment supporting the chosen convention.\n\nConditions: Conditional retarded Green-function/DFT and ideal coherence-factor models; finite synthetic calculations are not fits to cuprates or FeSe.\n\nVerification scope: Selected source locations are stated in references; independent Fourier/resolvent checks apply only to the explicit ideal models.\n\n### scwiki-a10-claim-mathematical-assumptions-2\n\n$$g'(\\mathbf r,E)=g(\\mathbf r-\\mathbf r_0,E),\\qquad\\tilde g'=e^{-i\\mathbf q\\cdot\\mathbf r_0}\\tilde g.$$\n\nEvidence: theory. Sources: source-6e0b3a25ead07f3c.\n\nSource relationship: context-for-local-derivation. Local discrete-Fourier definition and translation/conjugation identities; exact algebra and sampled periodic examples. Wang–Lee supplies scattering context, not a separate experiment supporting the chosen convention.\n\nConditions: Conditional retarded Green-function/DFT and ideal coherence-factor models; finite synthetic calculations are not fits to cuprates or FeSe.\n\nVerification scope: Selected source locations are stated in references; independent Fourier/resolvent checks apply only to the explicit ideal models.\n\n### scwiki-a10-claim-mathematical-assumptions-3\n\nIts Fourier magnitude is unchanged, while its real and imaginary parts generally change. A real map satisfies $\\tilde g(-\\mathbf q)=\\tilde g(\\mathbf q)^*$. Independent discrete-transform checks verify both identities, an exactly sampled cosine and sampling aliases. Finite cropping can also change amplitudes; the exact translation identity assumes the whole pattern or periodic data, not two differently cropped fields.\n\nEvidence: theory. Sources: source-6e0b3a25ead07f3c.\n\nSource relationship: context-for-local-derivation. Local discrete-Fourier definition and translation/conjugation identities; exact algebra and sampled periodic examples. Wang–Lee supplies scattering context, not a separate experiment supporting the chosen convention.\n\nConditions: Conditional retarded Green-function/DFT and ideal coherence-factor models; finite synthetic calculations are not fits to cuprates or FeSe.\n\nVerification scope: Selected source locations are stated in references; independent Fourier/resolvent checks apply only to the explicit ideal models.\n\n### scwiki-a10-claim-mathematical-assumptions-4\n\nFor a periodic lattice with $N$ sites and one static, local defect at the origin, define an ideal electron-block response\n\nEvidence: theory. Sources: source-6e0b3a25ead07f3c.\n\nSource relationship: mixed-source-and-local-derivation. Wang–Lee author v3 p. 1 Eq. (1) supplies the scattering-response framework with both Nambu diagonal blocks. This entry locally specializes to one spin-resolved electron block, N-site normalization and a static local defect; T follows from T=V+Vg0T when the inverse exists. Six finite-model resolvent comparisons check these conventions, not material data.\n\nConditions: Conditional retarded Green-function/DFT and ideal coherence-factor models; finite synthetic calculations are not fits to cuprates or FeSe.\n\nVerification scope: Selected source locations are stated in references; independent Fourier/resolvent checks apply only to the explicit ideal models.\n\n### scwiki-a10-claim-mathematical-assumptions-5\n\n$$\\Lambda(\\mathbf q,E)=\\frac{1}{N}\\sum_{\\mathbf k}[G_0(\\mathbf k,E)\\,T(E)\\,G_0(\\mathbf k-\\mathbf q,E)]_{11}.$$\n\nEvidence: theory. Sources: source-6e0b3a25ead07f3c.\n\nSource relationship: mixed-source-and-local-derivation. Wang–Lee author v3 p. 1 Eq. (1) supplies the scattering-response framework with both Nambu diagonal blocks. This entry locally specializes to one spin-resolved electron block, N-site normalization and a static local defect; T follows from T=V+Vg0T when the inverse exists. Six finite-model resolvent comparisons check these conventions, not material data.\n\nConditions: Conditional retarded Green-function/DFT and ideal coherence-factor models; finite synthetic calculations are not fits to cuprates or FeSe.\n\nVerification scope: Selected source locations are stated in references; independent Fourier/resolvent checks apply only to the explicit ideal models.\n\n### scwiki-a10-claim-mathematical-assumptions-6\n\nHere $G_0$ is a retarded Nambu Green function and $T=[1-Vg_0]^{-1}V$, with $g_0=N^{-1}\\sum_{\\mathbf k}G_0$. The Fourier transform of the spin-resolved electron density-of-states change is\n\nEvidence: theory. Sources: source-6e0b3a25ead07f3c.\n\nSource relationship: mixed-source-and-local-derivation. Wang–Lee author v3 p. 1 Eq. (1) supplies the scattering-response framework with both Nambu diagonal blocks. This entry locally specializes to one spin-resolved electron block, N-site normalization and a static local defect; T follows from T=V+Vg0T when the inverse exists. Six finite-model resolvent comparisons check these conventions, not material data.\n\nConditions: Conditional retarded Green-function/DFT and ideal coherence-factor models; finite synthetic calculations are not fits to cuprates or FeSe.\n\nVerification scope: Selected source locations are stated in references; independent Fourier/resolvent checks apply only to the explicit ideal models.\n\n### scwiki-a10-claim-mathematical-assumptions-7\n\n$$\\delta\\tilde\\rho(\\mathbf q,E)=-\\frac{\\Lambda(\\mathbf q,E)-\\Lambda(-\\mathbf q,E)^*}{2\\pi i}.$$\n\nEvidence: theory. Sources: source-6e0b3a25ead07f3c.\n\nSource relationship: mixed-source-and-local-derivation. Wang–Lee author v3 p. 1 Eq. (1) supplies the scattering-response framework with both Nambu diagonal blocks. This entry locally specializes to one spin-resolved electron block, N-site normalization and a static local defect; T follows from T=V+Vg0T when the inverse exists. Six finite-model resolvent comparisons check these conventions, not material data.\n\nConditions: Conditional retarded Green-function/DFT and ideal coherence-factor models; finite synthetic calculations are not fits to cuprates or FeSe.\n\nVerification scope: Selected source locations are stated in references; independent Fourier/resolvent checks apply only to the explicit ideal models.\n\n### scwiki-a10-claim-mathematical-assumptions-8\n\nTaking just $-\\operatorname{Im}\\Lambda(\\mathbf q)/\\pi$ is insufficient for a general complex Fourier map. It becomes valid with the additional even-in-momentum response condition. Six independent checks compare full real-space resolvent inversion with the scattering expression on a ten-site, fixed-gap model; displaced defects expose the lost phase. This is a normalization and response check, not a cuprate or FeSe simulation. The selected Wang–Lee manuscript supplies the broader scattering framework and explicitly discusses off-shell and matrix-element limits. Its Eq. (1) includes both Nambu diagonal blocks; the expression here uses an explicitly spin-resolved electron block and a discrete lattice normalization. These local conventions and their checks are not a verbatim reproduction of the full source formula.\n\nEvidence: theory. Sources: source-6e0b3a25ead07f3c.\n\nSource relationship: mixed-source-and-local-derivation. Source v3 pp. 1-2 supports the scattering framework and off-shell/matrix-element caution. The complex-Fourier conjugation argument and six fixed-gap finite-model checks are local; source Eq. (1) and this spin-resolved form are explicitly distinguished.\n\nConditions: Conditional retarded Green-function/DFT and ideal coherence-factor models; finite synthetic calculations are not fits to cuprates or FeSe.\n\nVerification scope: Selected source locations are stated in references; independent Fourier/resolvent checks apply only to the explicit ideal models.\n\n### scwiki-a10-claim-mathematical-assumptions-9\n\nA joint-density-of-states construction counts candidate equal-energy connections but omits scattering amplitudes and coherence factors. In an ideal equal-magnitude, real-gap Fermi-surface limit, scalar and magnetic Born amplitudes contain $uu'-vv'$ and $uu'+vv'$. Setting $u=u'=1/\\sqrt2$ and $v=\\operatorname{sgn}(\\Delta)/\\sqrt2$ interchanges their zero/nonzero weights when the relative gap sign changes. This conditional example explains sensitivity to the impurity channel; it does not identify a real defect from one bright peak.\n\nEvidence: theory. Sources: source-6e0b3a25ead07f3c.\n\nSource relationship: mixed-source-and-local-derivation. Source v3 p. 2 gives scalar/magnetic coherence-factor dependence. The equal-magnitude, real-gap, xi=0 weights are a local ideal-limit evaluation, not identification of an experimental defect.\n\nConditions: Conditional retarded Green-function/DFT and ideal coherence-factor models; finite synthetic calculations are not fits to cuprates or FeSe.\n\nVerification scope: Selected source locations are stated in references; independent Fourier/resolvent checks apply only to the explicit ideal models.\n\n### scwiki-a10-claim-experimental-criteria-1\n\nHoffman and colleagues' dispersing-QPI manuscript reports Bi2212 conductance imaging at 4.2 K. Selected pages describe two peak families with opposite energy trends and doping-dependent dispersion, interpreted against photoemission information. Its Science DOI ends in **1072640**. The inherited DOI ending in **1066974** instead identifies their distinct vortex-core modulation paper; these are not interchangeable evidence.\n\nEvidence: experiment. Sources: source-e8e6ef56da103435, source-353efd52d3443260.\n\nConditions: Bi2212 conductance imaging at 4.2 K; selected earlier manuscript only, raw data not reanalyzed.\n\nVerification scope: Selected source locations are stated in references; independent Fourier/resolvent checks apply only to the explicit ideal models.\n\n### scwiki-a10-claim-experimental-criteria-2\n\nSprau and colleagues' FeSe manuscript reports imaging at 280 mK. The relative-sign analysis uses the real parts at opposite energies, isolates an interband momentum region and places the Fourier origin at a defect. Selected supplementary passages vary the integration area and repeat the analysis on additional impurities. The reported sign inference is conditional on their scattering model and band assignment; it is not an inference from the absolute Fourier intensity alone.\n\nEvidence: experiment. Sources: source-2f227038c5cf73a9.\n\nConditions: FeSe conductance imaging at 280 mK; selected manuscript model-dependent relative-sign inference, not a universal iron-based result.\n\nVerification scope: Selected source locations are stated in references; independent Fourier/resolvent checks apply only to the explicit ideal models.\n\n### scwiki-a10-claim-experimental-criteria-3\n\nReport field of view, pixel spacing, spatial drift correction, bias grid, temperature, excitation amplitude, tip condition, set-point protocol and defect selection. Preserve both raw and processed maps. State whether a displayed quantity is a complex transform, its real part, magnitude, power or a ratio: these operations retain different information. Explain normalization, windowing, background removal, symmetrization and peak uncertainties.\n\nEvidence: hypothesis. Sources: source-6e0b3a25ead07f3c.\n\nConditions: Editorial inference/reporting boundaries; no unique pairing mechanism or static order assigned.\n\nVerification scope: Selected source locations are stated in references; independent Fourier/resolvent checks apply only to the explicit ideal models.\n\n### scwiki-a10-claim-limits-and-disputes-1\n\nFor $N_x$ equally spaced pixels of spacing $a_x$, the periodic-transform length is $L_x=N_xa_x$ and angular-wavevector bin spacing is $2\\pi/L_x$; the Nyquist bound is $\\pi/a_x$. Using cycles per length removes the $2\\pi$ factors. Zero padding interpolates the transform but does not create a larger measured field. A window trades spectral leakage against peak width, so bin spacing alone is not an experimental uncertainty or guaranteed resolving power.\n\nEvidence: theory. Sources: source-6e0b3a25ead07f3c.\n\nConditions: Conditional retarded Green-function/DFT and ideal coherence-factor models; finite synthetic calculations are not fits to cuprates or FeSe.\n\nVerification scope: Selected source locations are stated in references; independent Fourier/resolvent checks apply only to the explicit ideal models.\n\n### scwiki-a10-claim-limits-and-disputes-2\n\nEnergy dispersion supports a scattering interpretation only together with band, defect and temperature/field controls. Weak dispersion over a limited window does not by itself prove charge order; Bragg, structural, moire and electronic features can overlap. Conversely, an order and QPI may coexist. The cuprate octet geometry must not be imposed on arbitrary multiband spectra.\n\nEvidence: hypothesis. Sources: source-6e0b3a25ead07f3c.\n\nConditions: Editorial inference/reporting boundaries; no unique pairing mechanism or static order assigned.\n\nVerification scope: Selected source locations are stated in references; independent Fourier/resolvent checks apply only to the explicit ideal models.\n\n### scwiki-a10-claim-limits-and-disputes-3\n\nThe McElroy reference in the pinned chapter used an unrelated biology DOI, **nature02269**. The correct QPI paper is **nature01496**; its publisher identity is checked here, while its detailed data remain outside this entry's review. The original source is preserved and the replacement recorded.\n\nEvidence: hypothesis. Sources: source-230ea3ac9496dc90.\n\nConditions: Editorial inference/reporting boundaries; no unique pairing mechanism or static order assigned.\n\nVerification scope: Selected source locations are stated in references; independent Fourier/resolvent checks apply only to the explicit ideal models.\n\n### scwiki-a10-claim-discovery-implications-1\n\nUse QPI to compare explicit candidate electronic and scattering models against multiple observables. A useful claim states which alternatives the data discriminate, which are still compatible, and how uncertainty in defect identity or preprocessing changes the result. Combine gap-magnitude constraints with independent bulk and phase-sensitive evidence before assigning a pairing state or mechanism.\n\nEvidence: hypothesis. Sources: source-6e0b3a25ead07f3c.\n\nConditions: Editorial inference/reporting boundaries; no unique pairing mechanism or static order assigned.\n\nVerification scope: Selected source locations are stated in references; independent Fourier/resolvent checks apply only to the explicit ideal models.\n\n## Revision and review\n\nArticle ID: scwiki-a10. Revision: 36f6dcca4941c8e9d9f7. Updated: 2026-10-18T22:51:56.579986+00:00.\n\nReview scope: Selected Hoffman, Wang–Lee and Sprau author-manuscript passages; bibliographic identity corrections; independent finite-model and Fourier calculations.\n\n- Scoped passage checks are not complete scientific acceptance or experimental replication.\n- McElroy and the vortex-core paper remain bibliographic pointers; earlier manuscript checks do not certify final-version equivalence.\n- FeSe sign inference retains defect, phase origin, band and model assumptions; no universal pairing state assigned.\n- Measurement temperatures are not transition temperatures; no Tc values are extracted here.\n- The displayed spin-resolved, finite-lattice response specializes the source framework; its local synthetic checks do not reproduce the complete published calculation.\n\nSource: [A_phenomenology/A10_quasiparticle_interference.md](https://github.com/JackZH26/jzis-superconductivity/blob/0a7c9d6696804ec26aa12f8eed68b55c9b3c0fcf/A_phenomenology/A10_quasiparticle_interference.md), commit 0a7c9d6696804ec26aa12f8eed68b55c9b3c0fcf, SHA-256 f82bb31e8b35f847536cf493b8d0267c022f124c0f86e664d386e583d72e590e.\n","wordCount":869}}