{"schemaVersion":"1.0","revision":"fa961ab24277a91737c3","article":{"id":"scwiki-h9","topicId":"scwiki-topic-h9","code":"H9","slug":"hall-coefficient-sign-reversal","title":"Hall-coefficient sign reversal: carriers, mobility and evidence","summary":"Separate a Hall sign change from a Hall-number inference, account for multiband mobility and anomalous terms, and retain each experiment's normal-state boundary.","aliases":["Hall coefficient sign reversal","Hall number","ordinary Hall effect","霍尔系数变号","霍尔数"],"evidenceTypes":["experiment","theory","hypothesis"],"relatedCodes":["H8","H7","G3"],"editorialStatus":"scoped-check","contentState":"pilot","modifiedAt":"2026-10-18T17:26:39.189322+00:00","review":{"checkedAt":"2026-10-19","scope":"Selected Tsukada,Mun,Iida,Badoux author methods/results and figures; Ong final first page; Brouet primary abstract; inherited anomalous-Hall and Yang scopes; independent two-band tensor checks.","limitations":["Complete scientific acceptance remains open.","Complete final-version comparison, supplementary controls, calibration and raw-data reproduction remain open.","Brouet is abstract-scoped; Ong complete derivation and anomalous-Hall review not fully checked.","Mun/Iida apparent author-version composition typos are recorded but not silently repaired or used."]},"provenance":{"repository":"JackZH26/jzis-superconductivity","commit":"0a7c9d6696804ec26aa12f8eed68b55c9b3c0fcf","path":"H_anomalous_normal_state/H9_Hall_sign_reversal.md","sha256":"34e045c73f1a28ec7177001c5fcf0edbced1a63d2ce2f2c8c5e6722f4ed19613","sourceId":"file-02b313a904214e63"},"sourceMap":[{"startLine":1,"endLine":199,"targetSections":["scope","mathematical-assumptions","experimental-criteria","limits-and-disputes","discovery-implications","related-topics"],"decision":"edited-with-scoped-evidence","note":"Preserve five material comparisons, correct onset/zero-resistance wording, distinguish Hall sign/number and normal-state criteria, and retain incomplete primary-review limits."}],"corrections":[{"id":"scwiki-h9-correction-1","description":"Tsukada x=0.32 film shows no zero resistance but a reported resistive onset; categorical absence of all superconducting evidence is too strong.","sourceId":"source-7acbaed4e62141d9","scope":"Preserve onset versus zero-resistance distinction and sample-specific oxygen uncertainty."},{"id":"scwiki-h9-correction-2","description":"Iida effective Hall number uses absolute RH; Badoux pseudogap Hall-number change is not a mandatory Hall-sign reversal.","sourceId":"source-362cf0fd861683c3","scope":"Retain signed transverse response versus inferred positive Hall number; normal-state and transition criteria."}],"equationChecks":[{"targetSectionId":"mathematical-assumptions","tex":"R_H=(n_h\\mu_h^2-n_e\\mu_e^2)/[e(n_h\\mu_h+n_e\\mu_e)^2]","check":"16 weak-field tensor inversions, fixed-density sign crossover,6 uncompensated and3 compensated high-field cases,4 identical DC/Hall parameter sets with distinct MR, and even-leakage/odd-AHE antisymmetrization passed. No experimental fitting."}],"references":[{"id":"source-7acbaed4e62141d9","doi":"10.1103/PhysRevB.74.134508","title":"Negative Hall coefficients of heavily overdoped La2-xSrxCuO4","year":2006,"url":"https://doi.org/10.1103/PhysRevB.74.134508","publicationStatus":"journal-article","verification":{"scope":"selected-author-methods-and-figure-check","checkedAt":"2026-10-19","evidenceUrl":"https://arxiv.org/pdf/cond-mat/0605720v2","note":"Author v2,25August2006: selected pp1–6 andp10caption read;p11Figure2 visually checked. Tensile-strained epitaxial films on SrTiO3(100); Hall sweeps ±1T forx.08–.22 and ±6T forx.24–.40. Atx.32 no zero resistance but onset is reported, possibly from oxygen inhomogeneity. Final comparison/raw data remain open."}},{"id":"source-8c3b378d8802f683","doi":"10.1103/PhysRevLett.105.087001","title":"Significant reduction of electronic correlations upon isovalent Ru substitution of BaFe2As2","year":2010,"url":"https://doi.org/10.1103/PhysRevLett.105.087001","publicationStatus":"journal-article","verification":{"scope":"publisher-abstract-check","checkedAt":"2026-10-19","evidenceUrl":"https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.105.087001","note":"Publisher abstract checked: Ba(Fe0.65Ru0.35)2As2 electron/hole pockets and temperature-dependent Hall sign. Full sample/transport methods not read; no precise sign-change temperature extracted."}},{"id":"source-e24f6678715b4917","doi":"10.1103/PhysRevB.80.054517","title":"Thermoelectric power and Hall coefficient measurements on Ba(Fe1-xTMx)2As2 (TM=Co and Cu)","year":2009,"url":"https://doi.org/10.1103/PhysRevB.80.054517","publicationStatus":"journal-article","verification":{"scope":"selected-author-methods-and-figure-check","checkedAt":"2026-10-19","evidenceUrl":"https://arxiv.org/pdf/0906.1548v2","note":"Author v2,7August2009: selected pp1–6 read;p15Figure5 visually checked. WDS compositions, FeAs-flux crystals; AC four-wire Hall, field alongc, polarity reversed;25KFigure5 and90kOe temperature series. Exfoliation geometry uncertainty noted. p4 printed x>=0.38 conflicts with nearby0.038 scale: final-version comparison pending, numeric threshold not adopted."}},{"id":"source-362cf0fd861683c3","doi":"10.1038/srep28390","title":"Hall-plot of the phase diagram for Ba(Fe1-xCox)2As2","year":2016,"url":"https://doi.org/10.1038/srep28390","publicationStatus":"journal-article","verification":{"scope":"selected-author-methods-and-figure-check","checkedAt":"2026-10-19","evidenceUrl":"https://arxiv.org/pdf/1606.02865v2","note":"Author v2,10June2016; published22June2016. Selected p7Hall analysis, pp9–10methods,p18supplement Tc definition read; pp4Figure2 and9methods visually checked. Hall measured9T;14T belongs to separate MR/available field range. nH=V/(4e|RH|) perFe is positive by definition. p9prints0.74±0.017 for nominal0.08, an unresolved apparent typo; no measured concentration imported."}},{"id":"source-fae77f2c38d4cf72","doi":"10.1038/nature16983","title":"Change of carrier density at the pseudogap critical point of a cuprate superconductor","year":2016,"url":"https://doi.org/10.1038/nature16983","publicationStatus":"journal-article","verification":{"scope":"selected-author-methods-and-figure-check","checkedAt":"2026-10-19","evidenceUrl":"https://arxiv.org/pdf/1511.08162v1","note":"Author v1,25November2015: selected pp1–5,pp28–29methods/errors read;p11Figure2 visually checked. Pulses to88T; normal-state coverage at least40K, lower-temperature p=.16 limit explicit. Figure2 uses vortex melting Hvs, not Hc2. Absolute geometry error up to15percent distinct from relative temperature uncertainty. Published online22February2016. Final/supplement/raw analysis incomplete."}},{"id":"source-7faba5d556864a32","doi":"10.1103/RevModPhys.82.1539","title":"Anomalous Hall effect","year":2010,"url":"https://doi.org/10.1103/RevModPhys.82.1539","publicationStatus":"journal-article","verification":{"scope":"review-abstract-background-check","checkedAt":"2026-10-19","evidenceUrl":"https://arxiv.org/abs/0904.4154","note":"Author review abstract checked; intrinsic Berry curvature and extrinsic scattering mechanisms. Background only, not a complete primary experimental audit."}},{"id":"source-fd33407c49db2caf","doi":"10.1103/PhysRevB.43.193","title":"Geometric interpretation of the weak-field Hall conductivity in two-dimensional metals with arbitrary Fermi surface","year":1991,"url":"https://doi.org/10.1103/PhysRevB.43.193","publicationStatus":"journal-article","verification":{"scope":"selected-final-first-page-check","checkedAt":"2026-10-19","evidenceUrl":"https://scalettar.physics.ucdavis.edu/p298/HallGeometryOng.pdf","note":"Printedp193 scanned final page visually checked: abstract,introduction and startSectionII. Weak-field Boltzmann regime, mean-free-path curve l=v tau and Fermi-surface curvature; magnetic skew scattering and magnetic breakdown excluded. Complete geometric derivation not read."}},{"id":"source-3504ee9027165d0a","doi":"10.1038/s41586-026-10547-y","title":"Field re-entrant superconductivity in Eu-doped infinite-layer nickelates","year":2026,"url":"https://doi.org/10.1038/s41586-026-10547-y","publicationStatus":"journal-article","verification":{"scope":"selected-author-text-and-figures","checkedAt":"2026-10-18","evidenceUrl":"https://arxiv.org/pdf/2508.14666v3","note":"Published23April2026; read authorv3 dated25April2026, selectedpp2–8, captionsp12, methodsp13–14; Fig2p19/Fig3p20 visually checked. Full final equivalence, calibration and all raw data remain open."}}],"materialCases":[{"id":"scwiki-h9-material-1","recordType":"experiment","formula":"La2-xSrxCuO4","sample":"Tsukada epitaxial LSCO films on SrTiO3; room-temperature doping series","tcK":null,"reportedTemperatureK":300,"temperatureKind":"measurement","temperatureNote":"Hall measurement temperature, not a superconducting transition temperature.","pressureRegime":"ambient","pressureGPa":null,"equilibrium":"unknown","criterion":"normal-state-hall-measurement","probe":"Transverse transport with applied field","sourceId":"source-7acbaed4e62141d9","aliases":["LSCO","La2-xSrxCuO4"]},{"id":"scwiki-h9-material-2","recordType":"experiment","formula":"Ba(Fe1-xCox)2As2","sample":"Mun WDS-characterized Co-substituted crystals; Figure5","tcK":null,"reportedTemperatureK":25,"temperatureKind":"measurement","temperatureNote":"Hall measurement temperature, not a superconducting transition temperature.","pressureRegime":"ambient","pressureGPa":null,"equilibrium":"unknown","criterion":"normal-state-hall-measurement","probe":"Transverse transport with applied field","sourceId":"source-e24f6678715b4917","aliases":["Co-doped Ba122","Ba(Fe1-xCox)2As2"]}],"claims":[{"id":"scwiki-h9-claim-scope-1","sectionId":"scope","statement":"A Hall-coefficient sign reversal is a change in the sign of the transverse response under a declared wiring and field convention. It is distinct from a change in Hall magnitude, a peak, or an inferred Hall number. Electron and hole contributions can exchange transport weight without either Fermi-surface pocket disappearing. Neither a sign change nor a Hall anomaly by itself proves superconductivity, a Lifshitz transition or a particular pairing mechanism.","evidenceType":"hypothesis","sourceIds":["source-7acbaed4e62141d9","source-8c3b378d8802f683","source-e24f6678715b4917","source-fae77f2c38d4cf72"],"conditions":"Retain sign convention, field and temperature, normal-state criterion, composition/strain, tensor model, geometry and source version. Hall number and sign are distinct.","verificationScope":"Selected primary text/figures and independent Drude tensor checks; full scientific acceptance remains open."},{"id":"scwiki-h9-claim-scope-2","sectionId":"scope","statement":"Here $E_y=R_HJ_xB_z$ defines the sign. The elementary single-band Drude values are $R_H=-1/(n_e e)$ for electrons and $R_H=1/(n_h e)$ for holes, with $e>0$. These density interpretations require restrictive assumptions. Even a single crystalline band can have a complicated Hall response because Fermi-surface curvature and a momentum-dependent mean free path affect the weak-field conductivity. A temperature-dependent Hall coefficient is therefore not sufficient evidence for multiple bands.","evidenceType":"hypothesis","sourceIds":["source-fd33407c49db2caf"],"conditions":"Retain sign convention, field and temperature, normal-state criterion, composition/strain, tensor model, geometry and source version. Hall number and sign are distinct.","verificationScope":"Selected primary text/figures and independent Drude tensor checks; full scientific acceptance remains open."},{"id":"scwiki-h9-claim-mathematical-assumptions-1","sectionId":"mathematical-assumptions","statement":"For independent isotropic electron and hole Drude channels with positive mobilities and $\\mu_i B\\ll1$, $R_H=(n_h\\mu_h^2-n_e\\mu_e^2)/[e(n_h\\mu_h+n_e\\mu_e)^2]$. The sign changes when the mobility-squared weights cross. Fixed carrier densities can therefore produce a reversal as the mobility ratio varies. At zero field $\\sigma_0=e(n_h\\mu_h+n_e\\mu_e)$; even simultaneous values of $\\sigma_0$ and weak-field $R_H$ do not uniquely determine four density/mobility parameters. Independent tensor-inversion checks illustrate this degeneracy without fitting a material.","evidenceType":"theory","sourceIds":["source-362cf0fd861683c3","source-fd33407c49db2caf"],"conditions":"Retain sign convention, field and temperature, normal-state criterion, composition/strain, tensor model, geometry and source version. Hall number and sign are distinct.","verificationScope":"Selected primary text/figures and independent Drude tensor checks; full scientific acceptance remains open."},{"id":"scwiki-h9-claim-mathematical-assumptions-2","sectionId":"mathematical-assumptions","statement":"Beyond weak field, add conductivity tensors and invert the sum. In the same classical model, when both $\\mu_iB\\gg1$ and $n_h\\ne n_e$, the asymptotic slope is $\\rho_{yx}/B\\to1/[e(n_h-n_e)]$. Exact compensation is a different limit: for $n_h=n_e=n$, $\\rho_{yx}/B=(\\mu_h-\\mu_e)/[en(\\mu_h+\\mu_e)]$ at all fields in this model. A large laboratory field alone establishes neither of these asymptotic conditions. Quantum effects, coupled scattering and reconstructed bands may require a different model.","evidenceType":"theory","sourceIds":["source-362cf0fd861683c3","source-fd33407c49db2caf"],"conditions":"Retain sign convention, field and temperature, normal-state criterion, composition/strain, tensor model, geometry and source version. Hall number and sign are distinct.","verificationScope":"Selected primary text/figures and independent Drude tensor checks; full scientific acceptance remains open."},{"id":"scwiki-h9-claim-mathematical-assumptions-3","sectionId":"mathematical-assumptions","statement":"Ordinary and anomalous contributions must also be distinguished. A schematic $\\rho_{yx}=R_0B+\\rho_{yx}^{A}$ is not a universal fit, and an anomalous term need not be proportional to magnetization with a constant coefficient. Intrinsic Berry curvature, skew scattering and side jump are distinct mechanisms. Field antisymmetrization, $[\\rho_{yx}(B)-\\rho_{yx}(-B)]/2$, removes even longitudinal contact leakage but retains an odd anomalous Hall contribution. It does not isolate ordinary Hall transport by itself.","evidenceType":"theory","sourceIds":["source-7faba5d556864a32"],"conditions":"Retain sign convention, field and temperature, normal-state criterion, composition/strain, tensor model, geometry and source version. Hall number and sign are distinct.","verificationScope":"Selected primary text/figures and independent Drude tensor checks; full scientific acceptance remains open."},{"id":"scwiki-h9-claim-experimental-criteria-1","sectionId":"experimental-criteria","statement":"Tsukada and Ono studied epitaxial La2−xSrxCuO4 films on SrTiO3 with residual tensile strain. Their room-temperature Hall coefficient changes from positive to negative between x=0.28 and x=0.32. The heavily overdoped samples used field sweeps to ±6 T. This is a sample-series result at 300 K, not a universal cuprate doping boundary. The x=0.32 film lacks zero resistance but has a reported resistive onset, which the authors discuss in relation to possible oxygen inhomogeneity. Describing it simply as having no superconducting evidence would erase that distinction.","evidenceType":"experiment","sourceIds":["source-7acbaed4e62141d9"],"conditions":"Retain sign convention, field and temperature, normal-state criterion, composition/strain, tensor model, geometry and source version. Hall number and sign are distinct.","verificationScope":"Selected primary text/figures and independent Drude tensor checks; full scientific acceptance remains open."},{"id":"scwiki-h9-claim-experimental-criteria-2","sectionId":"experimental-criteria","statement":"Brouet's Ba(Fe0.65Ru0.35)2As2 study reports a temperature-dependent Hall sign together with electron and hole pockets. The checked primary abstract supports that limited statement; complete transport methods and a precise reversal temperature remain unreviewed here. Mun's Co- and Cu-substituted BaFe2As2 crystals provide a separate comparison: thermopower and Hall changes occur at comparable added-electron counts, but the Cu comparison does not show the corresponding resistive superconductivity. These Hall anomalies are not a superconductivity criterion or a universal sign-change threshold.","evidenceType":"experiment","sourceIds":["source-8c3b378d8802f683","source-e24f6678715b4917"],"conditions":"Retain sign convention, field and temperature, normal-state criterion, composition/strain, tensor model, geometry and source version. Hall number and sign are distinct.","verificationScope":"Selected primary text/figures and independent Drude tensor checks; full scientific acceptance remains open."},{"id":"scwiki-h9-claim-experimental-criteria-3","sectionId":"experimental-criteria","statement":"Mun's experiment measured composition by wavelength-dispersive spectroscopy and applied the Hall field along the crystal c axis, reversing field polarity to reduce contact offsets. Its 25 K comparison is a measurement temperature, not a transition temperature. Sample exfoliation can alter geometric factors, so normalized trends and absolute Hall magnitudes carry different uncertainties. Co/Cu substitution fraction and inferred added-electron count are also different horizontal axes.","evidenceType":"experiment","sourceIds":["source-e24f6678715b4917"],"conditions":"Retain sign convention, field and temperature, normal-state criterion, composition/strain, tensor model, geometry and source version. Hall number and sign are distinct.","verificationScope":"Selected primary text/figures and independent Drude tensor checks; full scientific acceptance remains open."},{"id":"scwiki-h9-claim-experimental-criteria-4","sectionId":"experimental-criteria","statement":"Iida's strained Ba(Fe1−xCox)2As2 films used MgO and CaF2 substrates and Hall measurements at 9 T. Their effective Hall number $n_H=V/(4e|R_H|)$, with unit-cell volume $V$, is positive by construction and expressed per Fe. It discards the Hall sign and is not a direct count of all mobile carriers in a multiband metal. The reported phase-diagram alignment concerns the studied strained films and selected bulk comparisons. The superconducting temperature uses a resistive onset criterion, rather than silently substituting zero resistance or magnetic shielding.","evidenceType":"experiment","sourceIds":["source-362cf0fd861683c3"],"conditions":"Retain sign convention, field and temperature, normal-state criterion, composition/strain, tensor model, geometry and source version. Hall number and sign are distinct.","verificationScope":"Selected primary text/figures and independent Drude tensor checks; full scientific acceptance remains open."},{"id":"scwiki-h9-claim-experimental-criteria-5","sectionId":"experimental-criteria","statement":"Badoux's YBa2Cu3Oy experiment distinguishes a charge-order reconstruction endpoint near p=0.16 from a pseudogap endpoint near p=0.19. The Hall-number interpretation changes from approximately 1+p toward p; this is not evidence for a mandatory Hall-sign reversal at the latter point. Pulsed fields reached 88 T, with a 50 K, 80 T cross-sample comparison. The author manuscript establishes normal-state access down to at least 40 K and explicitly leaves the lower-temperature p=0.16 behavior unresolved. Its vortex-melting field is not automatically the upper critical field.","evidenceType":"experiment","sourceIds":["source-fae77f2c38d4cf72"],"conditions":"Retain sign convention, field and temperature, normal-state criterion, composition/strain, tensor model, geometry and source version. Hall number and sign are distinct.","verificationScope":"Selected primary text/figures and independent Drude tensor checks; full scientific acceptance remains open."},{"id":"scwiki-h9-claim-limits-and-disputes-1","sectionId":"limits-and-disputes","statement":"Normal-state extraction needs more than a high-field label. Retain temperature, current, field direction, hysteresis branch and the independently justified superconducting boundary; vortex motion and magnetic contributions can contaminate a transverse signal. Yang's field-induced superconductivity study is a boundary example, not a source of an ordinary-Hall reversal field. Its superconducting phase-diagram scales must not be relabeled as Hall or anomalous-Hall thresholds.","evidenceType":"hypothesis","sourceIds":["source-fae77f2c38d4cf72","source-7faba5d556864a32","source-3504ee9027165d0a"],"conditions":"Retain sign convention, field and temperature, normal-state criterion, composition/strain, tensor model, geometry and source version. Hall number and sign are distinct.","verificationScope":"Selected primary text/figures and independent Drude tensor checks; full scientific acceptance remains open."},{"id":"scwiki-h9-claim-limits-and-disputes-2","sectionId":"limits-and-disputes","statement":"Complete scientific acceptance remains open. Most experimental checks here cover selected author-manuscript methods, results and figures, not complete final articles or raw-data reproduction. Brouet remains abstract-scoped; Ong's full geometric derivation and the anomalous-Hall review remain incompletely read. Apparent numeric typographical inconsistencies in the Mun and Iida author versions require final-version comparison; those uncertain composition values are not adopted. The independent Drude checks establish model algebra, not a unique interpretation of any experimental Hall curve.","evidenceType":"hypothesis","sourceIds":["source-7acbaed4e62141d9","source-8c3b378d8802f683","source-e24f6678715b4917","source-362cf0fd861683c3","source-fae77f2c38d4cf72","source-7faba5d556864a32","source-fd33407c49db2caf"],"conditions":"Retain sign convention, field and temperature, normal-state criterion, composition/strain, tensor model, geometry and source version. Hall number and sign are distinct.","verificationScope":"Selected primary text/figures and independent Drude tensor checks; full scientific acceptance remains open."},{"id":"scwiki-h9-claim-discovery-implications-1","sectionId":"discovery-implications","statement":"Treat a sign change as a prompt to test competing transport explanations. Combine field-dependent longitudinal and transverse resistivity, magnetoresistance, magnetic characterization and independent Fermi-surface information. Compare constrained models and retain geometry, strain, oxygen content and uncertainty. A mobility crossover, reconstructed Fermi surface and anomalous contribution can produce different predictions beyond a single Hall slope; a defensible conclusion specifies which alternatives the measurements actually exclude.","evidenceType":"hypothesis","sourceIds":["source-7acbaed4e62141d9","source-8c3b378d8802f683","source-362cf0fd861683c3","source-fae77f2c38d4cf72","source-fd33407c49db2caf"],"conditions":"Retain sign convention, field and temperature, normal-state criterion, composition/strain, tensor model, geometry and source version. Hall number and sign are distinct.","verificationScope":"Selected primary text/figures and independent Drude tensor checks; full scientific acceptance remains open."}],"body":"## Scope\n\nA Hall-coefficient sign reversal is a change in the sign of the transverse response under a declared wiring and field convention. It is distinct from a change in Hall magnitude, a peak, or an inferred Hall number. Electron and hole contributions can exchange transport weight without either Fermi-surface pocket disappearing. Neither a sign change nor a Hall anomaly by itself proves superconductivity, a Lifshitz transition or a particular pairing mechanism. [R1](#ref-source-7acbaed4e62141d9) [R2](#ref-source-8c3b378d8802f683) [R3](#ref-source-e24f6678715b4917) [R5](#ref-source-fae77f2c38d4cf72)\n\nHere $E_y=R_HJ_xB_z$ defines the sign. The elementary single-band Drude values are $R_H=-1/(n_e e)$ for electrons and $R_H=1/(n_h e)$ for holes, with $e>0$. These density interpretations require restrictive assumptions. Even a single crystalline band can have a complicated Hall response because Fermi-surface curvature and a momentum-dependent mean free path affect the weak-field conductivity. A temperature-dependent Hall coefficient is therefore not sufficient evidence for multiple bands. [R7](#ref-source-fd33407c49db2caf)\n\n## Mathematical assumptions\n\nFor independent isotropic electron and hole Drude channels with positive mobilities and $\\mu_i B\\ll1$, $R_H=(n_h\\mu_h^2-n_e\\mu_e^2)/[e(n_h\\mu_h+n_e\\mu_e)^2]$. The sign changes when the mobility-squared weights cross. Fixed carrier densities can therefore produce a reversal as the mobility ratio varies. At zero field $\\sigma_0=e(n_h\\mu_h+n_e\\mu_e)$; even simultaneous values of $\\sigma_0$ and weak-field $R_H$ do not uniquely determine four density/mobility parameters. Independent tensor-inversion checks illustrate this degeneracy without fitting a material. [R4](#ref-source-362cf0fd861683c3) [R7](#ref-source-fd33407c49db2caf)\n\nBeyond weak field, add conductivity tensors and invert the sum. In the same classical model, when both $\\mu_iB\\gg1$ and $n_h\\ne n_e$, the asymptotic slope is $\\rho_{yx}/B\\to1/[e(n_h-n_e)]$. Exact compensation is a different limit: for $n_h=n_e=n$, $\\rho_{yx}/B=(\\mu_h-\\mu_e)/[en(\\mu_h+\\mu_e)]$ at all fields in this model. A large laboratory field alone establishes neither of these asymptotic conditions. Quantum effects, coupled scattering and reconstructed bands may require a different model. [R4](#ref-source-362cf0fd861683c3) [R7](#ref-source-fd33407c49db2caf)\n\nOrdinary and anomalous contributions must also be distinguished. A schematic $\\rho_{yx}=R_0B+\\rho_{yx}^{A}$ is not a universal fit, and an anomalous term need not be proportional to magnetization with a constant coefficient. Intrinsic Berry curvature, skew scattering and side jump are distinct mechanisms. Field antisymmetrization, $[\\rho_{yx}(B)-\\rho_{yx}(-B)]/2$, removes even longitudinal contact leakage but retains an odd anomalous Hall contribution. It does not isolate ordinary Hall transport by itself. [R6](#ref-source-7faba5d556864a32)\n\n## Experimental criteria\n\nTsukada and Ono studied epitaxial La2−xSrxCuO4 films on SrTiO3 with residual tensile strain. Their room-temperature Hall coefficient changes from positive to negative between x=0.28 and x=0.32. The heavily overdoped samples used field sweeps to ±6 T. This is a sample-series result at 300 K, not a universal cuprate doping boundary. The x=0.32 film lacks zero resistance but has a reported resistive onset, which the authors discuss in relation to possible oxygen inhomogeneity. Describing it simply as having no superconducting evidence would erase that distinction. [R1](#ref-source-7acbaed4e62141d9)\n\nBrouet's Ba(Fe0.65Ru0.35)2As2 study reports a temperature-dependent Hall sign together with electron and hole pockets. The checked primary abstract supports that limited statement; complete transport methods and a precise reversal temperature remain unreviewed here. Mun's Co- and Cu-substituted BaFe2As2 crystals provide a separate comparison: thermopower and Hall changes occur at comparable added-electron counts, but the Cu comparison does not show the corresponding resistive superconductivity. These Hall anomalies are not a superconductivity criterion or a universal sign-change threshold. [R2](#ref-source-8c3b378d8802f683) [R3](#ref-source-e24f6678715b4917)\n\nMun's experiment measured composition by wavelength-dispersive spectroscopy and applied the Hall field along the crystal c axis, reversing field polarity to reduce contact offsets. Its 25 K comparison is a measurement temperature, not a transition temperature. Sample exfoliation can alter geometric factors, so normalized trends and absolute Hall magnitudes carry different uncertainties. Co/Cu substitution fraction and inferred added-electron count are also different horizontal axes. [R3](#ref-source-e24f6678715b4917)\n\nIida's strained Ba(Fe1−xCox)2As2 films used MgO and CaF2 substrates and Hall measurements at 9 T. Their effective Hall number $n_H=V/(4e|R_H|)$, with unit-cell volume $V$, is positive by construction and expressed per Fe. It discards the Hall sign and is not a direct count of all mobile carriers in a multiband metal. The reported phase-diagram alignment concerns the studied strained films and selected bulk comparisons. The superconducting temperature uses a resistive onset criterion, rather than silently substituting zero resistance or magnetic shielding. [R4](#ref-source-362cf0fd861683c3)\n\nBadoux's YBa2Cu3Oy experiment distinguishes a charge-order reconstruction endpoint near p=0.16 from a pseudogap endpoint near p=0.19. The Hall-number interpretation changes from approximately 1+p toward p; this is not evidence for a mandatory Hall-sign reversal at the latter point. Pulsed fields reached 88 T, with a 50 K, 80 T cross-sample comparison. The author manuscript establishes normal-state access down to at least 40 K and explicitly leaves the lower-temperature p=0.16 behavior unresolved. Its vortex-melting field is not automatically the upper critical field. [R5](#ref-source-fae77f2c38d4cf72)\n\n## Limits and disputes\n\nNormal-state extraction needs more than a high-field label. Retain temperature, current, field direction, hysteresis branch and the independently justified superconducting boundary; vortex motion and magnetic contributions can contaminate a transverse signal. Yang's field-induced superconductivity study is a boundary example, not a source of an ordinary-Hall reversal field. Its superconducting phase-diagram scales must not be relabeled as Hall or anomalous-Hall thresholds. [R5](#ref-source-fae77f2c38d4cf72) [R6](#ref-source-7faba5d556864a32) [R8](#ref-source-3504ee9027165d0a)\n\nComplete scientific acceptance remains open. Most experimental checks here cover selected author-manuscript methods, results and figures, not complete final articles or raw-data reproduction. Brouet remains abstract-scoped; Ong's full geometric derivation and the anomalous-Hall review remain incompletely read. Apparent numeric typographical inconsistencies in the Mun and Iida author versions require final-version comparison; those uncertain composition values are not adopted. The independent Drude checks establish model algebra, not a unique interpretation of any experimental Hall curve. [R1](#ref-source-7acbaed4e62141d9) [R2](#ref-source-8c3b378d8802f683) [R3](#ref-source-e24f6678715b4917) [R4](#ref-source-362cf0fd861683c3) [R5](#ref-source-fae77f2c38d4cf72) [R6](#ref-source-7faba5d556864a32) [R7](#ref-source-fd33407c49db2caf)\n\n## Discovery implications\n\nTreat a sign change as a prompt to test competing transport explanations. Combine field-dependent longitudinal and transverse resistivity, magnetoresistance, magnetic characterization and independent Fermi-surface information. Compare constrained models and retain geometry, strain, oxygen content and uncertainty. A mobility crossover, reconstructed Fermi surface and anomalous contribution can produce different predictions beyond a single Hall slope; a defensible conclusion specifies which alternatives the measurements actually exclude. [R1](#ref-source-7acbaed4e62141d9) [R2](#ref-source-8c3b378d8802f683) [R4](#ref-source-362cf0fd861683c3) [R5](#ref-source-fae77f2c38d4cf72) [R7](#ref-source-fd33407c49db2caf)\n\n## Related topics\n\n[Parallel conduction channels](/scwiki/parallel-conduction-channels), [Nonlinear Hall effect](/scwiki/nonlinear-hall-effect), and [Field-induced superconductivity](/scwiki/field-induced-superconductivity).","revision":"85ed19f928fa45dc6c34","sections":[{"id":"scope","title":"Scope","markdown":"## Scope\n\nA Hall-coefficient sign reversal is a change in the sign of the transverse response under a declared wiring and field convention. It is distinct from a change in Hall magnitude, a peak, or an inferred Hall number. Electron and hole contributions can exchange transport weight without either Fermi-surface pocket disappearing. Neither a sign change nor a Hall anomaly by itself proves superconductivity, a Lifshitz transition or a particular pairing mechanism. [R1](#ref-source-7acbaed4e62141d9) [R2](#ref-source-8c3b378d8802f683) [R3](#ref-source-e24f6678715b4917) [R5](#ref-source-fae77f2c38d4cf72)\n\nHere $E_y=R_HJ_xB_z$ defines the sign. The elementary single-band Drude values are $R_H=-1/(n_e e)$ for electrons and $R_H=1/(n_h e)$ for holes, with $e>0$. These density interpretations require restrictive assumptions. Even a single crystalline band can have a complicated Hall response because Fermi-surface curvature and a momentum-dependent mean free path affect the weak-field conductivity. A temperature-dependent Hall coefficient is therefore not sufficient evidence for multiple bands. [R7](#ref-source-fd33407c49db2caf)"},{"id":"mathematical-assumptions","title":"Mathematical assumptions","markdown":"## Mathematical assumptions\n\nFor independent isotropic electron and hole Drude channels with positive mobilities and $\\mu_i B\\ll1$, $R_H=(n_h\\mu_h^2-n_e\\mu_e^2)/[e(n_h\\mu_h+n_e\\mu_e)^2]$. The sign changes when the mobility-squared weights cross. Fixed carrier densities can therefore produce a reversal as the mobility ratio varies. At zero field $\\sigma_0=e(n_h\\mu_h+n_e\\mu_e)$; even simultaneous values of $\\sigma_0$ and weak-field $R_H$ do not uniquely determine four density/mobility parameters. Independent tensor-inversion checks illustrate this degeneracy without fitting a material. [R4](#ref-source-362cf0fd861683c3) [R7](#ref-source-fd33407c49db2caf)\n\nBeyond weak field, add conductivity tensors and invert the sum. In the same classical model, when both $\\mu_iB\\gg1$ and $n_h\\ne n_e$, the asymptotic slope is $\\rho_{yx}/B\\to1/[e(n_h-n_e)]$. Exact compensation is a different limit: for $n_h=n_e=n$, $\\rho_{yx}/B=(\\mu_h-\\mu_e)/[en(\\mu_h+\\mu_e)]$ at all fields in this model. A large laboratory field alone establishes neither of these asymptotic conditions. Quantum effects, coupled scattering and reconstructed bands may require a different model. [R4](#ref-source-362cf0fd861683c3) [R7](#ref-source-fd33407c49db2caf)\n\nOrdinary and anomalous contributions must also be distinguished. A schematic $\\rho_{yx}=R_0B+\\rho_{yx}^{A}$ is not a universal fit, and an anomalous term need not be proportional to magnetization with a constant coefficient. Intrinsic Berry curvature, skew scattering and side jump are distinct mechanisms. Field antisymmetrization, $[\\rho_{yx}(B)-\\rho_{yx}(-B)]/2$, removes even longitudinal contact leakage but retains an odd anomalous Hall contribution. It does not isolate ordinary Hall transport by itself. [R6](#ref-source-7faba5d556864a32)"},{"id":"experimental-criteria","title":"Experimental criteria","markdown":"## Experimental criteria\n\nTsukada and Ono studied epitaxial La2−xSrxCuO4 films on SrTiO3 with residual tensile strain. Their room-temperature Hall coefficient changes from positive to negative between x=0.28 and x=0.32. The heavily overdoped samples used field sweeps to ±6 T. This is a sample-series result at 300 K, not a universal cuprate doping boundary. The x=0.32 film lacks zero resistance but has a reported resistive onset, which the authors discuss in relation to possible oxygen inhomogeneity. Describing it simply as having no superconducting evidence would erase that distinction. [R1](#ref-source-7acbaed4e62141d9)\n\nBrouet's Ba(Fe0.65Ru0.35)2As2 study reports a temperature-dependent Hall sign together with electron and hole pockets. The checked primary abstract supports that limited statement; complete transport methods and a precise reversal temperature remain unreviewed here. Mun's Co- and Cu-substituted BaFe2As2 crystals provide a separate comparison: thermopower and Hall changes occur at comparable added-electron counts, but the Cu comparison does not show the corresponding resistive superconductivity. These Hall anomalies are not a superconductivity criterion or a universal sign-change threshold. [R2](#ref-source-8c3b378d8802f683) [R3](#ref-source-e24f6678715b4917)\n\nMun's experiment measured composition by wavelength-dispersive spectroscopy and applied the Hall field along the crystal c axis, reversing field polarity to reduce contact offsets. Its 25 K comparison is a measurement temperature, not a transition temperature. Sample exfoliation can alter geometric factors, so normalized trends and absolute Hall magnitudes carry different uncertainties. Co/Cu substitution fraction and inferred added-electron count are also different horizontal axes. [R3](#ref-source-e24f6678715b4917)\n\nIida's strained Ba(Fe1−xCox)2As2 films used MgO and CaF2 substrates and Hall measurements at 9 T. Their effective Hall number $n_H=V/(4e|R_H|)$, with unit-cell volume $V$, is positive by construction and expressed per Fe. It discards the Hall sign and is not a direct count of all mobile carriers in a multiband metal. The reported phase-diagram alignment concerns the studied strained films and selected bulk comparisons. The superconducting temperature uses a resistive onset criterion, rather than silently substituting zero resistance or magnetic shielding. [R4](#ref-source-362cf0fd861683c3)\n\nBadoux's YBa2Cu3Oy experiment distinguishes a charge-order reconstruction endpoint near p=0.16 from a pseudogap endpoint near p=0.19. The Hall-number interpretation changes from approximately 1+p toward p; this is not evidence for a mandatory Hall-sign reversal at the latter point. Pulsed fields reached 88 T, with a 50 K, 80 T cross-sample comparison. The author manuscript establishes normal-state access down to at least 40 K and explicitly leaves the lower-temperature p=0.16 behavior unresolved. Its vortex-melting field is not automatically the upper critical field. [R5](#ref-source-fae77f2c38d4cf72)"},{"id":"limits-and-disputes","title":"Limits and disputes","markdown":"## Limits and disputes\n\nNormal-state extraction needs more than a high-field label. Retain temperature, current, field direction, hysteresis branch and the independently justified superconducting boundary; vortex motion and magnetic contributions can contaminate a transverse signal. Yang's field-induced superconductivity study is a boundary example, not a source of an ordinary-Hall reversal field. Its superconducting phase-diagram scales must not be relabeled as Hall or anomalous-Hall thresholds. [R5](#ref-source-fae77f2c38d4cf72) [R6](#ref-source-7faba5d556864a32) [R8](#ref-source-3504ee9027165d0a)\n\nComplete scientific acceptance remains open. Most experimental checks here cover selected author-manuscript methods, results and figures, not complete final articles or raw-data reproduction. Brouet remains abstract-scoped; Ong's full geometric derivation and the anomalous-Hall review remain incompletely read. Apparent numeric typographical inconsistencies in the Mun and Iida author versions require final-version comparison; those uncertain composition values are not adopted. The independent Drude checks establish model algebra, not a unique interpretation of any experimental Hall curve. [R1](#ref-source-7acbaed4e62141d9) [R2](#ref-source-8c3b378d8802f683) [R3](#ref-source-e24f6678715b4917) [R4](#ref-source-362cf0fd861683c3) [R5](#ref-source-fae77f2c38d4cf72) [R6](#ref-source-7faba5d556864a32) [R7](#ref-source-fd33407c49db2caf)"},{"id":"discovery-implications","title":"Discovery implications","markdown":"## Discovery implications\n\nTreat a sign change as a prompt to test competing transport explanations. Combine field-dependent longitudinal and transverse resistivity, magnetoresistance, magnetic characterization and independent Fermi-surface information. Compare constrained models and retain geometry, strain, oxygen content and uncertainty. A mobility crossover, reconstructed Fermi surface and anomalous contribution can produce different predictions beyond a single Hall slope; a defensible conclusion specifies which alternatives the measurements actually exclude. [R1](#ref-source-7acbaed4e62141d9) [R2](#ref-source-8c3b378d8802f683) [R4](#ref-source-362cf0fd861683c3) [R5](#ref-source-fae77f2c38d4cf72) [R7](#ref-source-fd33407c49db2caf)"},{"id":"related-topics","title":"Related topics","markdown":"## Related topics\n\n[Parallel conduction channels](/scwiki/parallel-conduction-channels), [Nonlinear Hall effect](/scwiki/nonlinear-hall-effect), and [Field-induced superconductivity](/scwiki/field-induced-superconductivity)."},{"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| La2-xSrxCuO4 (aliases: LSCO, La2-xSrxCuO4); Tsukada epitaxial LSCO films on SrTiO3; room-temperature doping series | 300 K; Hall measurement temperature, not a superconducting transition temperature. | measurement; normal-state-hall-measurement | Transverse transport with applied field | ambient; unknown GPa | unknown | experiment; [source](#ref-source-7acbaed4e62141d9) |\n| Ba(Fe1-xCox)2As2 (aliases: Co-doped Ba122, Ba(Fe1-xCox)2As2); Mun WDS-characterized Co-substituted crystals; Figure5 | 25 K; Hall measurement temperature, not a superconducting transition temperature. | measurement; normal-state-hall-measurement | Transverse transport with applied field | ambient; unknown GPa | unknown | experiment; [source](#ref-source-e24f6678715b4917) |"}],"markdown":"# Hall-coefficient sign reversal: carriers, mobility and evidence\n\nSeparate a Hall sign change from a Hall-number inference, account for multiband mobility and anomalous terms, and retain each experiment's normal-state boundary.\n\n## Scope\n\nA Hall-coefficient sign reversal is a change in the sign of the transverse response under a declared wiring and field convention. It is distinct from a change in Hall magnitude, a peak, or an inferred Hall number. Electron and hole contributions can exchange transport weight without either Fermi-surface pocket disappearing. Neither a sign change nor a Hall anomaly by itself proves superconductivity, a Lifshitz transition or a particular pairing mechanism. [R1](#ref-source-7acbaed4e62141d9) [R2](#ref-source-8c3b378d8802f683) [R3](#ref-source-e24f6678715b4917) [R5](#ref-source-fae77f2c38d4cf72)\n\nHere $E_y=R_HJ_xB_z$ defines the sign. The elementary single-band Drude values are $R_H=-1/(n_e e)$ for electrons and $R_H=1/(n_h e)$ for holes, with $e>0$. These density interpretations require restrictive assumptions. Even a single crystalline band can have a complicated Hall response because Fermi-surface curvature and a momentum-dependent mean free path affect the weak-field conductivity. A temperature-dependent Hall coefficient is therefore not sufficient evidence for multiple bands. [R7](#ref-source-fd33407c49db2caf)\n\n## Mathematical assumptions\n\nFor independent isotropic electron and hole Drude channels with positive mobilities and $\\mu_i B\\ll1$, $R_H=(n_h\\mu_h^2-n_e\\mu_e^2)/[e(n_h\\mu_h+n_e\\mu_e)^2]$. The sign changes when the mobility-squared weights cross. Fixed carrier densities can therefore produce a reversal as the mobility ratio varies. At zero field $\\sigma_0=e(n_h\\mu_h+n_e\\mu_e)$; even simultaneous values of $\\sigma_0$ and weak-field $R_H$ do not uniquely determine four density/mobility parameters. Independent tensor-inversion checks illustrate this degeneracy without fitting a material. [R4](#ref-source-362cf0fd861683c3) [R7](#ref-source-fd33407c49db2caf)\n\nBeyond weak field, add conductivity tensors and invert the sum. In the same classical model, when both $\\mu_iB\\gg1$ and $n_h\\ne n_e$, the asymptotic slope is $\\rho_{yx}/B\\to1/[e(n_h-n_e)]$. Exact compensation is a different limit: for $n_h=n_e=n$, $\\rho_{yx}/B=(\\mu_h-\\mu_e)/[en(\\mu_h+\\mu_e)]$ at all fields in this model. A large laboratory field alone establishes neither of these asymptotic conditions. Quantum effects, coupled scattering and reconstructed bands may require a different model. [R4](#ref-source-362cf0fd861683c3) [R7](#ref-source-fd33407c49db2caf)\n\nOrdinary and anomalous contributions must also be distinguished. A schematic $\\rho_{yx}=R_0B+\\rho_{yx}^{A}$ is not a universal fit, and an anomalous term need not be proportional to magnetization with a constant coefficient. Intrinsic Berry curvature, skew scattering and side jump are distinct mechanisms. Field antisymmetrization, $[\\rho_{yx}(B)-\\rho_{yx}(-B)]/2$, removes even longitudinal contact leakage but retains an odd anomalous Hall contribution. It does not isolate ordinary Hall transport by itself. [R6](#ref-source-7faba5d556864a32)\n\n## Experimental criteria\n\nTsukada and Ono studied epitaxial La2−xSrxCuO4 films on SrTiO3 with residual tensile strain. Their room-temperature Hall coefficient changes from positive to negative between x=0.28 and x=0.32. The heavily overdoped samples used field sweeps to ±6 T. This is a sample-series result at 300 K, not a universal cuprate doping boundary. The x=0.32 film lacks zero resistance but has a reported resistive onset, which the authors discuss in relation to possible oxygen inhomogeneity. Describing it simply as having no superconducting evidence would erase that distinction. [R1](#ref-source-7acbaed4e62141d9)\n\nBrouet's Ba(Fe0.65Ru0.35)2As2 study reports a temperature-dependent Hall sign together with electron and hole pockets. The checked primary abstract supports that limited statement; complete transport methods and a precise reversal temperature remain unreviewed here. Mun's Co- and Cu-substituted BaFe2As2 crystals provide a separate comparison: thermopower and Hall changes occur at comparable added-electron counts, but the Cu comparison does not show the corresponding resistive superconductivity. These Hall anomalies are not a superconductivity criterion or a universal sign-change threshold. [R2](#ref-source-8c3b378d8802f683) [R3](#ref-source-e24f6678715b4917)\n\nMun's experiment measured composition by wavelength-dispersive spectroscopy and applied the Hall field along the crystal c axis, reversing field polarity to reduce contact offsets. Its 25 K comparison is a measurement temperature, not a transition temperature. Sample exfoliation can alter geometric factors, so normalized trends and absolute Hall magnitudes carry different uncertainties. Co/Cu substitution fraction and inferred added-electron count are also different horizontal axes. [R3](#ref-source-e24f6678715b4917)\n\nIida's strained Ba(Fe1−xCox)2As2 films used MgO and CaF2 substrates and Hall measurements at 9 T. Their effective Hall number $n_H=V/(4e|R_H|)$, with unit-cell volume $V$, is positive by construction and expressed per Fe. It discards the Hall sign and is not a direct count of all mobile carriers in a multiband metal. The reported phase-diagram alignment concerns the studied strained films and selected bulk comparisons. The superconducting temperature uses a resistive onset criterion, rather than silently substituting zero resistance or magnetic shielding. [R4](#ref-source-362cf0fd861683c3)\n\nBadoux's YBa2Cu3Oy experiment distinguishes a charge-order reconstruction endpoint near p=0.16 from a pseudogap endpoint near p=0.19. The Hall-number interpretation changes from approximately 1+p toward p; this is not evidence for a mandatory Hall-sign reversal at the latter point. Pulsed fields reached 88 T, with a 50 K, 80 T cross-sample comparison. The author manuscript establishes normal-state access down to at least 40 K and explicitly leaves the lower-temperature p=0.16 behavior unresolved. Its vortex-melting field is not automatically the upper critical field. [R5](#ref-source-fae77f2c38d4cf72)\n\n## Limits and disputes\n\nNormal-state extraction needs more than a high-field label. Retain temperature, current, field direction, hysteresis branch and the independently justified superconducting boundary; vortex motion and magnetic contributions can contaminate a transverse signal. Yang's field-induced superconductivity study is a boundary example, not a source of an ordinary-Hall reversal field. Its superconducting phase-diagram scales must not be relabeled as Hall or anomalous-Hall thresholds. [R5](#ref-source-fae77f2c38d4cf72) [R6](#ref-source-7faba5d556864a32) [R8](#ref-source-3504ee9027165d0a)\n\nComplete scientific acceptance remains open. Most experimental checks here cover selected author-manuscript methods, results and figures, not complete final articles or raw-data reproduction. Brouet remains abstract-scoped; Ong's full geometric derivation and the anomalous-Hall review remain incompletely read. Apparent numeric typographical inconsistencies in the Mun and Iida author versions require final-version comparison; those uncertain composition values are not adopted. The independent Drude checks establish model algebra, not a unique interpretation of any experimental Hall curve. [R1](#ref-source-7acbaed4e62141d9) [R2](#ref-source-8c3b378d8802f683) [R3](#ref-source-e24f6678715b4917) [R4](#ref-source-362cf0fd861683c3) [R5](#ref-source-fae77f2c38d4cf72) [R6](#ref-source-7faba5d556864a32) [R7](#ref-source-fd33407c49db2caf)\n\n## Discovery implications\n\nTreat a sign change as a prompt to test competing transport explanations. Combine field-dependent longitudinal and transverse resistivity, magnetoresistance, magnetic characterization and independent Fermi-surface information. Compare constrained models and retain geometry, strain, oxygen content and uncertainty. A mobility crossover, reconstructed Fermi surface and anomalous contribution can produce different predictions beyond a single Hall slope; a defensible conclusion specifies which alternatives the measurements actually exclude. [R1](#ref-source-7acbaed4e62141d9) [R2](#ref-source-8c3b378d8802f683) [R4](#ref-source-362cf0fd861683c3) [R5](#ref-source-fae77f2c38d4cf72) [R7](#ref-source-fd33407c49db2caf)\n\n## Related topics\n\n[Parallel conduction channels](/scwiki/parallel-conduction-channels), [Nonlinear Hall effect](/scwiki/nonlinear-hall-effect), and [Field-induced superconductivity](/scwiki/field-induced-superconductivity).\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| La2-xSrxCuO4 (aliases: LSCO, La2-xSrxCuO4); Tsukada epitaxial LSCO films on SrTiO3; room-temperature doping series | 300 K; Hall measurement temperature, not a superconducting transition temperature. | measurement; normal-state-hall-measurement | Transverse transport with applied field | ambient; unknown GPa | unknown | experiment; [source](#ref-source-7acbaed4e62141d9) |\n| Ba(Fe1-xCox)2As2 (aliases: Co-doped Ba122, Ba(Fe1-xCox)2As2); Mun WDS-characterized Co-substituted crystals; Figure5 | 25 K; Hall measurement temperature, not a superconducting transition temperature. | measurement; normal-state-hall-measurement | Transverse transport with applied field | ambient; unknown GPa | unknown | experiment; [source](#ref-source-e24f6678715b4917) |\n\n## Sources\n\n### Ref source-7acbaed4e62141d9\n\n[R1] Negative Hall coefficients of heavily overdoped La2-xSrxCuO4 (2006). [DOI 10.1103/PhysRevB.74.134508](https://doi.org/10.1103/PhysRevB.74.134508). Publication: journal-article. Check: selected-author-methods-and-figure-check. Checked: 2026-10-19. Author v2,25August2006: selected pp1–6 andp10caption read;p11Figure2 visually checked. Tensile-strained epitaxial films on SrTiO3(100); Hall sweeps ±1T forx.08–.22 and ±6T forx.24–.40. Atx.32 no zero resistance but onset is reported, possibly from oxygen inhomogeneity. Final comparison/raw data remain open.\n### Ref source-8c3b378d8802f683\n\n[R2] Significant reduction of electronic correlations upon isovalent Ru substitution of BaFe2As2 (2010). [DOI 10.1103/PhysRevLett.105.087001](https://doi.org/10.1103/PhysRevLett.105.087001). Publication: journal-article. Check: publisher-abstract-check. Checked: 2026-10-19. Publisher abstract checked: Ba(Fe0.65Ru0.35)2As2 electron/hole pockets and temperature-dependent Hall sign. Full sample/transport methods not read; no precise sign-change temperature extracted.\n### Ref source-e24f6678715b4917\n\n[R3] Thermoelectric power and Hall coefficient measurements on Ba(Fe1-xTMx)2As2 (TM=Co and Cu) (2009). [DOI 10.1103/PhysRevB.80.054517](https://doi.org/10.1103/PhysRevB.80.054517). Publication: journal-article. Check: selected-author-methods-and-figure-check. Checked: 2026-10-19. Author v2,7August2009: selected pp1–6 read;p15Figure5 visually checked. WDS compositions, FeAs-flux crystals; AC four-wire Hall, field alongc, polarity reversed;25KFigure5 and90kOe temperature series. Exfoliation geometry uncertainty noted. p4 printed x>=0.38 conflicts with nearby0.038 scale: final-version comparison pending, numeric threshold not adopted.\n### Ref source-362cf0fd861683c3\n\n[R4] Hall-plot of the phase diagram for Ba(Fe1-xCox)2As2 (2016). [DOI 10.1038/srep28390](https://doi.org/10.1038/srep28390). Publication: journal-article. Check: selected-author-methods-and-figure-check. Checked: 2026-10-19. Author v2,10June2016; published22June2016. Selected p7Hall analysis, pp9–10methods,p18supplement Tc definition read; pp4Figure2 and9methods visually checked. Hall measured9T;14T belongs to separate MR/available field range. nH=V/(4e|RH|) perFe is positive by definition. p9prints0.74±0.017 for nominal0.08, an unresolved apparent typo; no measured concentration imported.\n### Ref source-fae77f2c38d4cf72\n\n[R5] Change of carrier density at the pseudogap critical point of a cuprate superconductor (2016). [DOI 10.1038/nature16983](https://doi.org/10.1038/nature16983). Publication: journal-article. Check: selected-author-methods-and-figure-check. Checked: 2026-10-19. Author v1,25November2015: selected pp1–5,pp28–29methods/errors read;p11Figure2 visually checked. Pulses to88T; normal-state coverage at least40K, lower-temperature p=.16 limit explicit. Figure2 uses vortex melting Hvs, not Hc2. Absolute geometry error up to15percent distinct from relative temperature uncertainty. Published online22February2016. Final/supplement/raw analysis incomplete.\n### Ref source-7faba5d556864a32\n\n[R6] Anomalous Hall effect (2010). [DOI 10.1103/RevModPhys.82.1539](https://doi.org/10.1103/RevModPhys.82.1539). Publication: journal-article. Check: review-abstract-background-check. Checked: 2026-10-19. Author review abstract checked; intrinsic Berry curvature and extrinsic scattering mechanisms. Background only, not a complete primary experimental audit.\n### Ref source-fd33407c49db2caf\n\n[R7] Geometric interpretation of the weak-field Hall conductivity in two-dimensional metals with arbitrary Fermi surface (1991). [DOI 10.1103/PhysRevB.43.193](https://doi.org/10.1103/PhysRevB.43.193). Publication: journal-article. Check: selected-final-first-page-check. Checked: 2026-10-19. Printedp193 scanned final page visually checked: abstract,introduction and startSectionII. Weak-field Boltzmann regime, mean-free-path curve l=v tau and Fermi-surface curvature; magnetic skew scattering and magnetic breakdown excluded. Complete geometric derivation not read.\n### Ref source-3504ee9027165d0a\n\n[R8] Field re-entrant superconductivity in Eu-doped infinite-layer nickelates (2026). [DOI 10.1038/s41586-026-10547-y](https://doi.org/10.1038/s41586-026-10547-y). Publication: journal-article. Check: selected-author-text-and-figures. Checked: 2026-10-18. Published23April2026; read authorv3 dated25April2026, selectedpp2–8, captionsp12, methodsp13–14; Fig2p19/Fig3p20 visually checked. Full final equivalence, calibration and all raw data remain open.\n\n## Claim evidence and conditions\n\n### scwiki-h9-claim-scope-1\n\nA Hall-coefficient sign reversal is a change in the sign of the transverse response under a declared wiring and field convention. It is distinct from a change in Hall magnitude, a peak, or an inferred Hall number. Electron and hole contributions can exchange transport weight without either Fermi-surface pocket disappearing. Neither a sign change nor a Hall anomaly by itself proves superconductivity, a Lifshitz transition or a particular pairing mechanism.\n\nEvidence: hypothesis. Sources: source-7acbaed4e62141d9, source-8c3b378d8802f683, source-e24f6678715b4917, source-fae77f2c38d4cf72.\n\nConditions: Retain sign convention, field and temperature, normal-state criterion, composition/strain, tensor model, geometry and source version. Hall number and sign are distinct.\n\nVerification scope: Selected primary text/figures and independent Drude tensor checks; full scientific acceptance remains open.\n\n### scwiki-h9-claim-scope-2\n\nHere $E_y=R_HJ_xB_z$ defines the sign. The elementary single-band Drude values are $R_H=-1/(n_e e)$ for electrons and $R_H=1/(n_h e)$ for holes, with $e>0$. These density interpretations require restrictive assumptions. Even a single crystalline band can have a complicated Hall response because Fermi-surface curvature and a momentum-dependent mean free path affect the weak-field conductivity. A temperature-dependent Hall coefficient is therefore not sufficient evidence for multiple bands.\n\nEvidence: hypothesis. Sources: source-fd33407c49db2caf.\n\nConditions: Retain sign convention, field and temperature, normal-state criterion, composition/strain, tensor model, geometry and source version. Hall number and sign are distinct.\n\nVerification scope: Selected primary text/figures and independent Drude tensor checks; full scientific acceptance remains open.\n\n### scwiki-h9-claim-mathematical-assumptions-1\n\nFor independent isotropic electron and hole Drude channels with positive mobilities and $\\mu_i B\\ll1$, $R_H=(n_h\\mu_h^2-n_e\\mu_e^2)/[e(n_h\\mu_h+n_e\\mu_e)^2]$. The sign changes when the mobility-squared weights cross. Fixed carrier densities can therefore produce a reversal as the mobility ratio varies. At zero field $\\sigma_0=e(n_h\\mu_h+n_e\\mu_e)$; even simultaneous values of $\\sigma_0$ and weak-field $R_H$ do not uniquely determine four density/mobility parameters. Independent tensor-inversion checks illustrate this degeneracy without fitting a material.\n\nEvidence: theory. Sources: source-362cf0fd861683c3, source-fd33407c49db2caf.\n\nConditions: Retain sign convention, field and temperature, normal-state criterion, composition/strain, tensor model, geometry and source version. Hall number and sign are distinct.\n\nVerification scope: Selected primary text/figures and independent Drude tensor checks; full scientific acceptance remains open.\n\n### scwiki-h9-claim-mathematical-assumptions-2\n\nBeyond weak field, add conductivity tensors and invert the sum. In the same classical model, when both $\\mu_iB\\gg1$ and $n_h\\ne n_e$, the asymptotic slope is $\\rho_{yx}/B\\to1/[e(n_h-n_e)]$. Exact compensation is a different limit: for $n_h=n_e=n$, $\\rho_{yx}/B=(\\mu_h-\\mu_e)/[en(\\mu_h+\\mu_e)]$ at all fields in this model. A large laboratory field alone establishes neither of these asymptotic conditions. Quantum effects, coupled scattering and reconstructed bands may require a different model.\n\nEvidence: theory. Sources: source-362cf0fd861683c3, source-fd33407c49db2caf.\n\nConditions: Retain sign convention, field and temperature, normal-state criterion, composition/strain, tensor model, geometry and source version. Hall number and sign are distinct.\n\nVerification scope: Selected primary text/figures and independent Drude tensor checks; full scientific acceptance remains open.\n\n### scwiki-h9-claim-mathematical-assumptions-3\n\nOrdinary and anomalous contributions must also be distinguished. A schematic $\\rho_{yx}=R_0B+\\rho_{yx}^{A}$ is not a universal fit, and an anomalous term need not be proportional to magnetization with a constant coefficient. Intrinsic Berry curvature, skew scattering and side jump are distinct mechanisms. Field antisymmetrization, $[\\rho_{yx}(B)-\\rho_{yx}(-B)]/2$, removes even longitudinal contact leakage but retains an odd anomalous Hall contribution. It does not isolate ordinary Hall transport by itself.\n\nEvidence: theory. Sources: source-7faba5d556864a32.\n\nConditions: Retain sign convention, field and temperature, normal-state criterion, composition/strain, tensor model, geometry and source version. Hall number and sign are distinct.\n\nVerification scope: Selected primary text/figures and independent Drude tensor checks; full scientific acceptance remains open.\n\n### scwiki-h9-claim-experimental-criteria-1\n\nTsukada and Ono studied epitaxial La2−xSrxCuO4 films on SrTiO3 with residual tensile strain. Their room-temperature Hall coefficient changes from positive to negative between x=0.28 and x=0.32. The heavily overdoped samples used field sweeps to ±6 T. This is a sample-series result at 300 K, not a universal cuprate doping boundary. The x=0.32 film lacks zero resistance but has a reported resistive onset, which the authors discuss in relation to possible oxygen inhomogeneity. Describing it simply as having no superconducting evidence would erase that distinction.\n\nEvidence: experiment. Sources: source-7acbaed4e62141d9.\n\nConditions: Retain sign convention, field and temperature, normal-state criterion, composition/strain, tensor model, geometry and source version. Hall number and sign are distinct.\n\nVerification scope: Selected primary text/figures and independent Drude tensor checks; full scientific acceptance remains open.\n\n### scwiki-h9-claim-experimental-criteria-2\n\nBrouet's Ba(Fe0.65Ru0.35)2As2 study reports a temperature-dependent Hall sign together with electron and hole pockets. The checked primary abstract supports that limited statement; complete transport methods and a precise reversal temperature remain unreviewed here. Mun's Co- and Cu-substituted BaFe2As2 crystals provide a separate comparison: thermopower and Hall changes occur at comparable added-electron counts, but the Cu comparison does not show the corresponding resistive superconductivity. These Hall anomalies are not a superconductivity criterion or a universal sign-change threshold.\n\nEvidence: experiment. Sources: source-8c3b378d8802f683, source-e24f6678715b4917.\n\nConditions: Retain sign convention, field and temperature, normal-state criterion, composition/strain, tensor model, geometry and source version. Hall number and sign are distinct.\n\nVerification scope: Selected primary text/figures and independent Drude tensor checks; full scientific acceptance remains open.\n\n### scwiki-h9-claim-experimental-criteria-3\n\nMun's experiment measured composition by wavelength-dispersive spectroscopy and applied the Hall field along the crystal c axis, reversing field polarity to reduce contact offsets. Its 25 K comparison is a measurement temperature, not a transition temperature. Sample exfoliation can alter geometric factors, so normalized trends and absolute Hall magnitudes carry different uncertainties. Co/Cu substitution fraction and inferred added-electron count are also different horizontal axes.\n\nEvidence: experiment. Sources: source-e24f6678715b4917.\n\nConditions: Retain sign convention, field and temperature, normal-state criterion, composition/strain, tensor model, geometry and source version. Hall number and sign are distinct.\n\nVerification scope: Selected primary text/figures and independent Drude tensor checks; full scientific acceptance remains open.\n\n### scwiki-h9-claim-experimental-criteria-4\n\nIida's strained Ba(Fe1−xCox)2As2 films used MgO and CaF2 substrates and Hall measurements at 9 T. Their effective Hall number $n_H=V/(4e|R_H|)$, with unit-cell volume $V$, is positive by construction and expressed per Fe. It discards the Hall sign and is not a direct count of all mobile carriers in a multiband metal. The reported phase-diagram alignment concerns the studied strained films and selected bulk comparisons. The superconducting temperature uses a resistive onset criterion, rather than silently substituting zero resistance or magnetic shielding.\n\nEvidence: experiment. Sources: source-362cf0fd861683c3.\n\nConditions: Retain sign convention, field and temperature, normal-state criterion, composition/strain, tensor model, geometry and source version. Hall number and sign are distinct.\n\nVerification scope: Selected primary text/figures and independent Drude tensor checks; full scientific acceptance remains open.\n\n### scwiki-h9-claim-experimental-criteria-5\n\nBadoux's YBa2Cu3Oy experiment distinguishes a charge-order reconstruction endpoint near p=0.16 from a pseudogap endpoint near p=0.19. The Hall-number interpretation changes from approximately 1+p toward p; this is not evidence for a mandatory Hall-sign reversal at the latter point. Pulsed fields reached 88 T, with a 50 K, 80 T cross-sample comparison. The author manuscript establishes normal-state access down to at least 40 K and explicitly leaves the lower-temperature p=0.16 behavior unresolved. Its vortex-melting field is not automatically the upper critical field.\n\nEvidence: experiment. Sources: source-fae77f2c38d4cf72.\n\nConditions: Retain sign convention, field and temperature, normal-state criterion, composition/strain, tensor model, geometry and source version. Hall number and sign are distinct.\n\nVerification scope: Selected primary text/figures and independent Drude tensor checks; full scientific acceptance remains open.\n\n### scwiki-h9-claim-limits-and-disputes-1\n\nNormal-state extraction needs more than a high-field label. Retain temperature, current, field direction, hysteresis branch and the independently justified superconducting boundary; vortex motion and magnetic contributions can contaminate a transverse signal. Yang's field-induced superconductivity study is a boundary example, not a source of an ordinary-Hall reversal field. Its superconducting phase-diagram scales must not be relabeled as Hall or anomalous-Hall thresholds.\n\nEvidence: hypothesis. Sources: source-fae77f2c38d4cf72, source-7faba5d556864a32, source-3504ee9027165d0a.\n\nConditions: Retain sign convention, field and temperature, normal-state criterion, composition/strain, tensor model, geometry and source version. Hall number and sign are distinct.\n\nVerification scope: Selected primary text/figures and independent Drude tensor checks; full scientific acceptance remains open.\n\n### scwiki-h9-claim-limits-and-disputes-2\n\nComplete scientific acceptance remains open. Most experimental checks here cover selected author-manuscript methods, results and figures, not complete final articles or raw-data reproduction. Brouet remains abstract-scoped; Ong's full geometric derivation and the anomalous-Hall review remain incompletely read. Apparent numeric typographical inconsistencies in the Mun and Iida author versions require final-version comparison; those uncertain composition values are not adopted. The independent Drude checks establish model algebra, not a unique interpretation of any experimental Hall curve.\n\nEvidence: hypothesis. Sources: source-7acbaed4e62141d9, source-8c3b378d8802f683, source-e24f6678715b4917, source-362cf0fd861683c3, source-fae77f2c38d4cf72, source-7faba5d556864a32, source-fd33407c49db2caf.\n\nConditions: Retain sign convention, field and temperature, normal-state criterion, composition/strain, tensor model, geometry and source version. Hall number and sign are distinct.\n\nVerification scope: Selected primary text/figures and independent Drude tensor checks; full scientific acceptance remains open.\n\n### scwiki-h9-claim-discovery-implications-1\n\nTreat a sign change as a prompt to test competing transport explanations. Combine field-dependent longitudinal and transverse resistivity, magnetoresistance, magnetic characterization and independent Fermi-surface information. Compare constrained models and retain geometry, strain, oxygen content and uncertainty. A mobility crossover, reconstructed Fermi surface and anomalous contribution can produce different predictions beyond a single Hall slope; a defensible conclusion specifies which alternatives the measurements actually exclude.\n\nEvidence: hypothesis. Sources: source-7acbaed4e62141d9, source-8c3b378d8802f683, source-362cf0fd861683c3, source-fae77f2c38d4cf72, source-fd33407c49db2caf.\n\nConditions: Retain sign convention, field and temperature, normal-state criterion, composition/strain, tensor model, geometry and source version. Hall number and sign are distinct.\n\nVerification scope: Selected primary text/figures and independent Drude tensor checks; full scientific acceptance remains open.\n\n## Revision and review\n\nArticle ID: scwiki-h9. Revision: 85ed19f928fa45dc6c34. Updated: 2026-10-18T17:26:39.189322+00:00.\n\nReview scope: Selected Tsukada,Mun,Iida,Badoux author methods/results and figures; Ong final first page; Brouet primary abstract; inherited anomalous-Hall and Yang scopes; independent two-band tensor checks.\n\n- Complete scientific acceptance remains open.\n- Complete final-version comparison, supplementary controls, calibration and raw-data reproduction remain open.\n- Brouet is abstract-scoped; Ong complete derivation and anomalous-Hall review not fully checked.\n- Mun/Iida apparent author-version composition typos are recorded but not silently repaired or used.\n\nSource: [H_anomalous_normal_state/H9_Hall_sign_reversal.md](https://github.com/JackZH26/jzis-superconductivity/blob/0a7c9d6696804ec26aa12f8eed68b55c9b3c0fcf/H_anomalous_normal_state/H9_Hall_sign_reversal.md), commit 0a7c9d6696804ec26aa12f8eed68b55c9b3c0fcf, SHA-256 34e045c73f1a28ec7177001c5fcf0edbced1a63d2ce2f2c8c5e6722f4ed19613.\n","wordCount":970}}