{"schemaVersion":"1.0","revision":"fa961ab24277a91737c3","article":{"id":"scwiki-a8","topicId":"scwiki-topic-a8","code":"A8","slug":"linear-t-resistivity","title":"Linear-T resistivity: strange-metal evidence and model limits","summary":"Read linear-temperature transport with its fit window, field and carrier assumptions. Distinguish total resistivity, parallel conduction channels and inferred scattering rates.","aliases":["strange metal","linear temperature resistivity","T-linear transport","parallel conduction","Planckian coefficient"],"evidenceTypes":["experiment","theory","hypothesis"],"relatedCodes":["H2","A1","A6","A3","D3","B12"],"editorialStatus":"scoped-check","contentState":"pilot","modifiedAt":"2026-10-19","review":{"checkedAt":"2026-10-19","scope":"Pinned A8 chapter; selected published Cao passages, Legros/Romero earlier manuscripts and Martin abstract; independent fit-window, Drude-degeneracy, parallel-channel and frequency-convention checks. Follow-up explicitly separates Legros v1 p. 4 from the local degeneracy and parallel-channel examples.","limitations":["Selected checks are not full scientific acceptance, experimental replication or complete uncertainty propagation.","Legros and Romero earlier manuscript passages are version-specific; exhaustive comparison with final published articles remains open.","Cooper and Bruin are bibliographic pointers only; no cross-family numerical alpha table reproduced.","Synthetic model checks do not identify a material mechanism. No equilibrium Tc is inferred from normal-state transport."]},"provenance":{"repository":"JackZH26/jzis-superconductivity","commit":"0a7c9d6696804ec26aa12f8eed68b55c9b3c0fcf","path":"A_phenomenology/A8_strange_metal_linear_T.md","sha256":"53878789a42ed20ba0a911bbf42c65c61aa731342e681ff2a2200a02cb13e906","sourceId":"file-1200e0814ac4879e"},"sourceMap":[{"startLine":1,"endLine":6,"targetSections":["scope"],"decision":"edited-with-scoped-evidence","note":"Phenomenology versus lifetime/mechanism boundaries retained."},{"startLine":7,"endLine":20,"targetSections":["scope","mathematical-assumptions","experimental-criteria"],"decision":"edited-with-scoped-evidence","note":"Fit-window and parallel-channel limits made explicit."},{"startLine":21,"endLine":30,"targetSections":["mathematical-assumptions","limits-and-disputes"],"decision":"edited-with-scoped-evidence","note":"Drude parameters and degeneracy conventions; no universal bound inferred."},{"startLine":31,"endLine":36,"targetSections":["experimental-criteria","limits-and-disputes"],"decision":"edited-with-scoped-evidence","note":"Martin abstract retained; Cooper metadata pointer; Legros selected passages added."},{"startLine":37,"endLine":40,"targetSections":["experimental-criteria"],"decision":"edited-with-scoped-evidence","note":"Cao published passages and low-temperature parameter assumptions."},{"startLine":41,"endLine":44,"targetSections":["experimental-criteria","limits-and-disputes"],"decision":"edited-with-scoped-evidence","note":"Romero version-specific narrow-channel fit window and ordinary-frequency convention."},{"startLine":45,"endLine":54,"targetSections":["experimental-criteria","discovery-implications"],"decision":"edited-with-scoped-evidence","note":"Reporting checklist preserved and expanded."},{"startLine":55,"endLine":66,"targetSections":["limits-and-disputes","discovery-implications","related-topics"],"decision":"edited-with-scoped-evidence","note":"All six source identities retained with explicit review scope; no unsupported universal table."}],"references":[{"id":"source-a5d6480d08ee8555","doi":"10.1103/PhysRevB.41.846","title":"Normal-state transport properties of Bi2+xSr2-yCuO6+delta crystals","year":1990,"url":"https://doi.org/10.1103/PhysRevB.41.846","publicationStatus":"journal-article","verification":{"scope":"primary-abstract-scoped-check","checkedAt":"2026-10-18","evidenceUrl":"https://journals.aps.org/prb/abstract/10.1103/PhysRevB.41.846","note":"Publisher abstract only: anisotropic normal-state transport in Bi-based crystals. Full measurement protocol and numerical curves not checked."}},{"id":"source-1610fd228e679225","doi":"10.1126/science.1165015","title":"Anomalous Criticality in the Electrical Resistivity of La2-xSrxCuO4","year":2009,"url":"https://doi.org/10.1126/science.1165015","publicationStatus":"journal-article","verification":{"scope":"crossref-metadata-only","checkedAt":"2026-10-18","evidenceUrl":"https://api.crossref.org/works/10.1126/science.1165015","note":"Bibliographic identity only in A8. No numerical result or complete experimental claim extracted."}},{"id":"source-e6d342432f3409ae","doi":"10.1126/science.1227612","title":"Similarity of Scattering Rates in Metals Showing T-Linear Resistivity","year":2013,"url":"https://doi.org/10.1126/science.1227612","publicationStatus":"journal-article","verification":{"scope":"crossref-metadata-only","checkedAt":"2026-10-18","evidenceUrl":"https://api.crossref.org/works/10.1126/science.1227612","note":"Bibliographic identity only in A8. Cross-material numerical comparisons not reproduced."}},{"id":"source-c1ae7869b672a8e8","doi":"10.1038/s41567-018-0334-2","title":"Universal T-linear resistivity and Planckian dissipation in overdoped cuprates","year":2019,"url":"https://doi.org/10.1038/s41567-018-0334-2","publicationStatus":"journal-article","verification":{"scope":"earlier-author-manuscript-scoped-check","checkedAt":"2026-10-18","evidenceUrl":"https://arxiv.org/pdf/1805.02512v1","note":"Selected v1 pp. 4, 7–8 and Figs. 1–2 captions: Drude assumptions, film method and magnetoresistance correction. Published volume year 2019; final-version comparison and complete data fitting remain open."}},{"id":"source-8135909144b6b16b","doi":"10.1103/PhysRevLett.124.076801","title":"Strange Metal in Magic-Angle Graphene with near Planckian Dissipation","year":2020,"url":"https://doi.org/10.1103/PhysRevLett.124.076801","publicationStatus":"journal-article","verification":{"scope":"primary-fulltext-scoped-check","checkedAt":"2026-10-18","evidenceUrl":"https://physics.aps.org/featured-article-pdf/10.1103/PhysRevLett.124.076801","note":"Selected published pp. 1–4, Fig. 1 and Eq. (1). Four-probe device, filling dependence and low-temperature SdH parameter assumptions checked; supplementary fits not reproduced."}},{"id":"source-05b2d5ff6757b5eb","doi":"10.1038/s41567-026-03266-8","title":"Planckian scattering and parallel conduction channels in an iron chalcogenide superconductor","year":2026,"url":"https://doi.org/10.1038/s41567-026-03266-8","publicationStatus":"journal-article","verification":{"scope":"earlier-author-manuscript-scoped-check","checkedAt":"2026-10-18","evidenceUrl":"https://arxiv.org/html/2505.00623v1","note":"Selected v1 Fig. 1–3 discussion: films, spectral range, fit window and frequency convention. Publisher identity checked; complete final-version comparison and fit reproduction remain open."}}],"claims":[{"id":"scwiki-a8-claim-scope-1","sectionId":"scope","statement":"Linear-temperature resistivity describes a measured dependence over a specified range. The fit $\\rho(T)=\\rho_0+AT$ needs a sample, current direction, field, temperature interval and residuals. A straight-looking trace is not by itself evidence for a quantum critical point, a universal lifetime or a pairing interaction. This entry treats transport phenomenology; the linked Planckian entry discusses lifetime interpretations.","evidenceType":"hypothesis","sourceIds":["source-8135909144b6b16b"],"conditions":"Editorial reporting and inference criteria; no universal lifetime, pairing mechanism or transition temperature follows from a fitted slope.","verificationScope":"Pinned A8 chapter edited with explicit source/model limitations."},{"id":"scwiki-a8-claim-scope-2","sectionId":"scope","statement":"Separate a finite-field normal state, the region affected by superconducting fluctuations, and a higher-temperature regime that may have different scattering. Martin and colleagues' Bi-based crystal abstract reports strongly anisotropic transport; an in-plane trend is not an isotropic resistivity law.","evidenceType":"experiment","sourceIds":["source-a5d6480d08ee8555"],"conditions":"Sample-, probe-, field-, fit-window- and version-specific observations; no material-independent coefficient or new equilibrium Tc record.","verificationScope":"Selected primary passages as specified by the cited reference; no raw-data reproduction."},{"id":"scwiki-a8-claim-mathematical-assumptions-1","sectionId":"mathematical-assumptions","statement":"A least-squares slope depends on both the model and the sampled window. For exact synthetic data $\\rho=r_0+aT+bT^2$, equally weighted temperatures symmetric about $\\bar T$ give","evidenceType":"theory","sourceIds":["source-c1ae7869b672a8e8"],"conditions":"Conditional local models: symmetric equal-weight quadratic fit; single isotropic constant-parameter Drude channel; circular parabolic 2D band with explicit degeneracy; scalar zero-field parallel conductance; stated frequency denominator.","verificationScope":"Independent synthetic/algebra/finite-difference checks, not experimental calibration or original dataset fitting.","sourceRelationship":"context-for-local-derivation","derivationNote":"Legros v1 p. 4 supplies the isotropic Drude relation and its twofold-degenerate 2D expression. Explicit total-degeneracy counting, fitting-window examples and the parallel-channel counterexample are local conditional derivations; they are not fitted results from that paper."},{"id":"scwiki-a8-claim-mathematical-assumptions-2","sectionId":"mathematical-assumptions","statement":"$$A_{\\mathrm{fit}}=a+2b\\bar T.$$","evidenceType":"theory","sourceIds":["source-c1ae7869b672a8e8"],"conditions":"Conditional local models: symmetric equal-weight quadratic fit; single isotropic constant-parameter Drude channel; circular parabolic 2D band with explicit degeneracy; scalar zero-field parallel conductance; stated frequency denominator.","verificationScope":"Independent synthetic/algebra/finite-difference checks, not experimental calibration or original dataset fitting.","sourceRelationship":"context-for-local-derivation","derivationNote":"Legros v1 p. 4 supplies the isotropic Drude relation and its twofold-degenerate 2D expression. Explicit total-degeneracy counting, fitting-window examples and the parallel-channel counterexample are local conditional derivations; they are not fitted results from that paper."},{"id":"scwiki-a8-claim-mathematical-assumptions-3","sectionId":"mathematical-assumptions","statement":"This follows by inserting the quadratic into $\\operatorname{cov}(T,\\rho)/\\operatorname{var}(T)$. A narrower interval can hide curvature while changing the inferred slope. Independent synthetic fits confirm this counterexample; they are not fits to any material. Experimental model comparison also needs uncertainties, correlations and a justified treatment of residuals.","evidenceType":"theory","sourceIds":["source-c1ae7869b672a8e8"],"conditions":"Conditional local models: symmetric equal-weight quadratic fit; single isotropic constant-parameter Drude channel; circular parabolic 2D band with explicit degeneracy; scalar zero-field parallel conductance; stated frequency denominator.","verificationScope":"Independent synthetic/algebra/finite-difference checks, not experimental calibration or original dataset fitting.","sourceRelationship":"context-for-local-derivation","derivationNote":"Legros v1 p. 4 supplies the isotropic Drude relation and its twofold-degenerate 2D expression. Explicit total-degeneracy counting, fitting-window examples and the parallel-channel counterexample are local conditional derivations; they are not fitted results from that paper."},{"id":"scwiki-a8-claim-mathematical-assumptions-4","sectionId":"mathematical-assumptions","statement":"For a single isotropic Drude channel with temperature-independent carrier density $n$ and mass $m^*$, an inelastic pole relaxation rate $\\gamma=\\alpha k_BT/\\hbar$ gives $A=\\alpha m^*k_B/(ne^2\\hbar)$. Thus a slope fixes $\\alpha$ only after the carrier parameters and response model are specified. If those parameters change with temperature, differentiating resistivity produces additional terms. This conditional connection underlies the selected Legros analysis.","evidenceType":"theory","sourceIds":["source-c1ae7869b672a8e8"],"conditions":"Conditional local models: symmetric equal-weight quadratic fit; single isotropic constant-parameter Drude channel; circular parabolic 2D band with explicit degeneracy; scalar zero-field parallel conductance; stated frequency denominator.","verificationScope":"Independent synthetic/algebra/finite-difference checks, not experimental calibration or original dataset fitting.","sourceRelationship":"mixed-source-and-local-derivation","derivationNote":"Legros v1 p. 4 supplies the isotropic Drude relation and its twofold-degenerate 2D expression. Explicit total-degeneracy counting, fitting-window examples and the parallel-channel counterexample are local conditional derivations; they are not fitted results from that paper."},{"id":"scwiki-a8-claim-mathematical-assumptions-5","sectionId":"mathematical-assumptions","statement":"For a circular, parabolic two-dimensional band with total degeneracy $g$, use total sheet density $n_{2D}=gk_F^2/(4\\pi)$ and $k_BT_F=\\hbar^2k_F^2/(2m^*)$. The preceding Drude model then yields","evidenceType":"theory","sourceIds":["source-c1ae7869b672a8e8"],"conditions":"Conditional local models: symmetric equal-weight quadratic fit; single isotropic constant-parameter Drude channel; circular parabolic 2D band with explicit degeneracy; scalar zero-field parallel conductance; stated frequency denominator.","verificationScope":"Independent synthetic/algebra/finite-difference checks, not experimental calibration or original dataset fitting.","sourceRelationship":"mixed-source-and-local-derivation","derivationNote":"Legros v1 p. 4 supplies the isotropic Drude relation and its twofold-degenerate 2D expression. Explicit total-degeneracy counting, fitting-window examples and the parallel-channel counterexample are local conditional derivations; they are not fitted results from that paper."},{"id":"scwiki-a8-claim-mathematical-assumptions-6","sectionId":"mathematical-assumptions","statement":"$$A_{\\square}T_F=\\frac{\\alpha h}{g e^2}.$$","evidenceType":"theory","sourceIds":["source-c1ae7869b672a8e8"],"conditions":"Conditional local models: symmetric equal-weight quadratic fit; single isotropic constant-parameter Drude channel; circular parabolic 2D band with explicit degeneracy; scalar zero-field parallel conductance; stated frequency denominator.","verificationScope":"Independent synthetic/algebra/finite-difference checks, not experimental calibration or original dataset fitting.","sourceRelationship":"mixed-source-and-local-derivation","derivationNote":"Legros v1 p. 4 supplies the isotropic Drude relation and its twofold-degenerate 2D expression. Explicit total-degeneracy counting, fitting-window examples and the parallel-channel counterexample are local conditional derivations; they are not fitted results from that paper."},{"id":"scwiki-a8-claim-mathematical-assumptions-7","sectionId":"mathematical-assumptions","statement":"The familiar factor of two corresponds to $g=2$, not an arbitrary multiband system. A bulk slope converted per conducting plane uses $A_{\\square}=A/d$ with the stated effective plane spacing $d$. Independent occupied-disk and algebra checks cover $g=1,2,4$; neither degeneracy nor a mass should be transferred between materials without justification.","evidenceType":"theory","sourceIds":["source-c1ae7869b672a8e8"],"conditions":"Conditional local models: symmetric equal-weight quadratic fit; single isotropic constant-parameter Drude channel; circular parabolic 2D band with explicit degeneracy; scalar zero-field parallel conductance; stated frequency denominator.","verificationScope":"Independent synthetic/algebra/finite-difference checks, not experimental calibration or original dataset fitting.","sourceRelationship":"mixed-source-and-local-derivation","derivationNote":"Legros v1 p. 4 supplies the isotropic Drude relation and its twofold-degenerate 2D expression. Explicit total-degeneracy counting, fitting-window examples and the parallel-channel counterexample are local conditional derivations; they are not fitted results from that paper."},{"id":"scwiki-a8-claim-mathematical-assumptions-8","sectionId":"mathematical-assumptions","statement":"Parallel channels add conductivities. As an independent scalar, zero-field example, let $r(T)=r_0+aT>0$ describe one channel and let $\\sigma_b\\ge0$ be a constant background conductivity in matching units. Then","evidenceType":"theory","sourceIds":["source-c1ae7869b672a8e8"],"conditions":"Conditional local models: symmetric equal-weight quadratic fit; single isotropic constant-parameter Drude channel; circular parabolic 2D band with explicit degeneracy; scalar zero-field parallel conductance; stated frequency denominator.","verificationScope":"Independent synthetic/algebra/finite-difference checks, not experimental calibration or original dataset fitting.","sourceRelationship":"context-for-local-derivation","derivationNote":"Legros v1 p. 4 supplies the isotropic Drude relation and its twofold-degenerate 2D expression. Explicit total-degeneracy counting, fitting-window examples and the parallel-channel counterexample are local conditional derivations; they are not fitted results from that paper."},{"id":"scwiki-a8-claim-mathematical-assumptions-9","sectionId":"mathematical-assumptions","statement":"$$\\rho_{\\mathrm{tot}}=\\frac{r(T)}{1+\\sigma_b r(T)},\\qquad\\frac{d\\rho_{\\mathrm{tot}}}{dT}=\\frac{a}{[1+\\sigma_b r(T)]^2}.$$","evidenceType":"theory","sourceIds":["source-c1ae7869b672a8e8"],"conditions":"Conditional local models: symmetric equal-weight quadratic fit; single isotropic constant-parameter Drude channel; circular parabolic 2D band with explicit degeneracy; scalar zero-field parallel conductance; stated frequency denominator.","verificationScope":"Independent synthetic/algebra/finite-difference checks, not experimental calibration or original dataset fitting.","sourceRelationship":"context-for-local-derivation","derivationNote":"Legros v1 p. 4 supplies the isotropic Drude relation and its twofold-degenerate 2D expression. Explicit total-degeneracy counting, fitting-window examples and the parallel-channel counterexample are local conditional derivations; they are not fitted results from that paper."},{"id":"scwiki-a8-claim-mathematical-assumptions-10","sectionId":"mathematical-assumptions","statement":"The total slope is generally temperature dependent even though the first channel's resistance is exactly linear. Nine numerical derivative checks verify this model. It is not a multiband fit; in magnetic field, conductivity tensors must be added before inversion. Adding scattering mechanisms within one channel is a different assumption from adding parallel conductivities.","evidenceType":"theory","sourceIds":["source-c1ae7869b672a8e8"],"conditions":"Conditional local models: symmetric equal-weight quadratic fit; single isotropic constant-parameter Drude channel; circular parabolic 2D band with explicit degeneracy; scalar zero-field parallel conductance; stated frequency denominator.","verificationScope":"Independent synthetic/algebra/finite-difference checks, not experimental calibration or original dataset fitting.","sourceRelationship":"context-for-local-derivation","derivationNote":"Legros v1 p. 4 supplies the isotropic Drude relation and its twofold-degenerate 2D expression. Explicit total-degeneracy counting, fitting-window examples and the parallel-channel counterexample are local conditional derivations; they are not fitted results from that paper."},{"id":"scwiki-a8-claim-experimental-criteria-1","sectionId":"experimental-criteria","statement":"Legros and colleagues' earlier manuscript measures a Bi2212 film with nominal hole doping 0.23 in pulsed fields. Its 55 T trace and magnetoresistance-corrected, extrapolated zero-field curve are distinct datasets. The analysis estimates carrier parameters and geometric uncertainty; the checked passages do not turn its interpretation into a model-independent universal bound.","evidenceType":"experiment","sourceIds":["source-c1ae7869b672a8e8"],"conditions":"Sample-, probe-, field-, fit-window- and version-specific observations; no material-independent coefficient or new equilibrium Tc record.","verificationScope":"Selected primary passages as specified by the cited reference; no raw-data reproduction."},{"id":"scwiki-a8-claim-experimental-criteria-2","sectionId":"experimental-criteria","statement":"Cao and colleagues measure four-probe transport in gated twisted bilayer graphene. Their linear regime depends on filling and a crossover temperature. The operational scattering coefficient uses density and mass from low-temperature quantum oscillations; those assumptions matter when interpreting higher-temperature transport. The selected passages do not establish one shared microscopic mechanism across material families.","evidenceType":"experiment","sourceIds":["source-8135909144b6b16b"],"conditions":"Sample-, probe-, field-, fit-window- and version-specific observations; no material-independent coefficient or new equilibrium Tc record.","verificationScope":"Selected primary passages as specified by the cited reference; no raw-data reproduction."},{"id":"scwiki-a8-claim-experimental-criteria-3","sectionId":"experimental-criteria","statement":"Romero and colleagues' earlier manuscript studies two 100 nm FeTe1-xSex films, x = 0.45 and 0.35, over 0.2–3 THz. Its narrow-channel fits use 20–40 K and report coefficients 3.02 and 2.42 in $\\Gamma=\\Gamma_0+\\alpha k_BT/h$. These are channel-specific fit results, not coefficients of the total DC resistivity.","evidenceType":"experiment","sourceIds":["source-05b2d5ff6757b5eb"],"conditions":"Sample-, probe-, field-, fit-window- and version-specific observations; no material-independent coefficient or new equilibrium Tc record.","verificationScope":"Selected primary passages as specified by the cited reference; no raw-data reproduction."},{"id":"scwiki-a8-claim-experimental-criteria-4","sectionId":"experimental-criteria","statement":"Record the raw voltage/current or conductivity data, geometry, composition, field direction, fit interval and uncertainty model. Identify excluded transition regions and test alternative fit windows and curvature. A successful fit does not establish that its parameters are uniquely identifiable. Normal-state measurement temperatures remain separate from superconducting transition temperatures in the records below.","evidenceType":"hypothesis","sourceIds":["source-8135909144b6b16b"],"conditions":"Editorial reporting and inference criteria; no universal lifetime, pairing mechanism or transition temperature follows from a fitted slope.","verificationScope":"Pinned A8 chapter edited with explicit source/model limitations."},{"id":"scwiki-a8-claim-limits-and-disputes-1","sectionId":"limits-and-disputes","statement":"Frequency conventions can create a factor-of-$2\\pi$ error. For a Drude denominator $\\Gamma-i\\nu$ with ordinary frequency $\\nu$, the corresponding pole rate is $\\gamma=1/\\tau=2\\pi\\Gamma$ in a denominator $\\gamma-i\\omega$, where $\\omega=2\\pi\\nu$. Consequently $\\Gamma=\\alpha k_BT/h$ converts to $\\gamma=\\alpha k_BT/\\hbar$. State the denominator and linewidth convention before comparing coefficients. This is a convention check, not a new measurement of a lifetime.","evidenceType":"theory","sourceIds":["source-8135909144b6b16b"],"conditions":"Conditional local models: symmetric equal-weight quadratic fit; single isotropic constant-parameter Drude channel; circular parabolic 2D band with explicit degeneracy; scalar zero-field parallel conductance; stated frequency denominator.","verificationScope":"Independent synthetic/algebra/finite-difference checks, not experimental calibration or original dataset fitting."},{"id":"scwiki-a8-claim-limits-and-disputes-2","sectionId":"limits-and-disputes","statement":"A shared temperature exponent does not identify a unique microscopic interaction. Drude transport, optical fits and single-particle lifetimes measure or infer different quantities. Extrapolating carrier parameters, suppressing superconductivity by field, or neglecting a parallel channel can affect an inferred coefficient. Report these choices alongside any claimed universality rather than treating the fit exponent as a proof.","evidenceType":"hypothesis","sourceIds":["source-8135909144b6b16b"],"conditions":"Editorial reporting and inference criteria; no universal lifetime, pairing mechanism or transition temperature follows from a fitted slope.","verificationScope":"Pinned A8 chapter edited with explicit source/model limitations."},{"id":"scwiki-a8-claim-limits-and-disputes-3","sectionId":"limits-and-disputes","statement":"Cooper's LSCO study and Bruin's cross-metal comparison remain bibliographic starting points here. Their complete datasets and numerical conclusions have not been reanalyzed in this entry. Selected manuscript checks above also leave final-version comparison and full uncertainty reproduction open.","evidenceType":"hypothesis","sourceIds":["source-1610fd228e679225","source-e6d342432f3409ae"],"conditions":"Editorial reporting and inference criteria; no universal lifetime, pairing mechanism or transition temperature follows from a fitted slope.","verificationScope":"Pinned A8 chapter edited with explicit source/model limitations."},{"id":"scwiki-a8-claim-discovery-implications-1","sectionId":"discovery-implications","statement":"Use linear-T transport to organize experiments, not to rank superconductors or predict a transition temperature by itself. A stronger comparison holds sample state, probe definition and fitting procedure fixed, then asks whether independent optical, thermodynamic or quantum-oscillation information supports the same parameter interpretation. Retain counterexamples and failed fits; correlation with superconductivity does not identify its cause.","evidenceType":"hypothesis","sourceIds":["source-8135909144b6b16b"],"conditions":"Editorial reporting and inference criteria; no universal lifetime, pairing mechanism or transition temperature follows from a fitted slope.","verificationScope":"Pinned A8 chapter edited with explicit source/model limitations."}],"corrections":[{"id":"scwiki-a8-correction-1","description":"Made ordinary-frequency versus angular-frequency rate convention explicit before comparing Planckian coefficients.","sourceId":"source-05b2d5ff6757b5eb","scope":"Model units and channel distinction; not a correction to the reported experiment."}],"equationChecks":[{"targetSectionId":"mathematical-assumptions","tex":"A_{fit}=a+2b\\bar T","check":"Three exact synthetic quadratic windows; residual and slope changes computed."},{"targetSectionId":"mathematical-assumptions","tex":"A_\\square T_F=\\alpha h/(g e^2)","check":"Occupied-disk carrier counting with degeneracies 1, 2, 4."},{"targetSectionId":"mathematical-assumptions","tex":"d\\rho/dT=a/[1+\\sigma_b r(T)]^2","check":"Nine independent centered finite-difference comparisons."},{"targetSectionId":"limits-and-disputes","tex":"\\gamma=2\\pi\\Gamma","check":"Three coefficients converted consistently with h=2 pi hbar."}],"materialCases":[{"id":"scwiki-a8-material-1","formula":"Bi2Sr2CaCu2O8+delta","sample":"Legros v1 Bi2212 film; nominal p = 0.23","recordType":"experiment","tcK":null,"reportedTemperatureK":null,"temperatureKind":"normal-state","temperatureNote":"Normal-state transport or fit interval; no equilibrium Tc assigned here","criterion":"normal-state-transport","pressureRegime":"unknown","pressureGPa":null,"equilibrium":"unknown","probe":"Six-point transport in pulsed fields; 55 T trace and magnetoresistance-corrected extrapolation distinguished","sourceId":"source-c1ae7869b672a8e8","aliases":["cuprate","cuprates"]},{"id":"scwiki-a8-material-2","formula":"C","sample":"Cao gated twisted bilayer graphene; device and filling dependent","recordType":"experiment","tcK":null,"reportedTemperatureK":null,"temperatureKind":"normal-state","temperatureNote":"Normal-state transport or fit interval; no equilibrium Tc assigned here","criterion":"normal-state-transport","pressureRegime":"unknown","pressureGPa":null,"equilibrium":"unknown","probe":"Four-probe longitudinal transport; low-temperature SdH carrier parameters used in operational rate estimate","sourceId":"source-8135909144b6b16b"},{"id":"scwiki-a8-material-3","formula":"FeTe1-xSex","sample":"Romero v1 films: x = 0.45 and 0.35; thickness 100 nm","recordType":"experiment","tcK":null,"reportedTemperatureK":null,"temperatureKind":"normal-state","temperatureNote":"Normal-state transport or fit interval; no equilibrium Tc assigned here","criterion":"normal-state-transport","pressureRegime":"unknown","pressureGPa":null,"equilibrium":"unknown","probe":"0.2–3 THz spectroscopy with DC constraint; narrow-channel 20–40 K fit; ordinary-frequency rate","sourceId":"source-05b2d5ff6757b5eb","aliases":["iron-based","iron based superconductors"]}],"body":"## Scope\n\nLinear-temperature resistivity describes a measured dependence over a specified range. The fit $\\rho(T)=\\rho_0+AT$ needs a sample, current direction, field, temperature interval and residuals. A straight-looking trace is not by itself evidence for a quantum critical point, a universal lifetime or a pairing interaction. This entry treats transport phenomenology; the linked Planckian entry discusses lifetime interpretations.\n\nSeparate a finite-field normal state, the region affected by superconducting fluctuations, and a higher-temperature regime that may have different scattering. Martin and colleagues' Bi-based crystal abstract reports strongly anisotropic transport; an in-plane trend is not an isotropic resistivity law. [R1](#ref-source-a5d6480d08ee8555)\n\n## Mathematical assumptions\n\nA least-squares slope depends on both the model and the sampled window. For exact synthetic data $\\rho=r_0+aT+bT^2$, equally weighted temperatures symmetric about $\\bar T$ give\n\n$$A_{\\mathrm{fit}}=a+2b\\bar T.$$\n\nThis follows by inserting the quadratic into $\\operatorname{cov}(T,\\rho)/\\operatorname{var}(T)$. A narrower interval can hide curvature while changing the inferred slope. Independent synthetic fits confirm this counterexample; they are not fits to any material. Experimental model comparison also needs uncertainties, correlations and a justified treatment of residuals.\n\nFor a single isotropic Drude channel with temperature-independent carrier density $n$ and mass $m^*$, an inelastic pole relaxation rate $\\gamma=\\alpha k_BT/\\hbar$ gives $A=\\alpha m^*k_B/(ne^2\\hbar)$. Thus a slope fixes $\\alpha$ only after the carrier parameters and response model are specified. If those parameters change with temperature, differentiating resistivity produces additional terms. This conditional connection underlies the selected Legros analysis. [R4](#ref-source-c1ae7869b672a8e8)\n\nFor a circular, parabolic two-dimensional band with total degeneracy $g$, use total sheet density $n_{2D}=gk_F^2/(4\\pi)$ and $k_BT_F=\\hbar^2k_F^2/(2m^*)$. The preceding Drude model then yields\n\n$$A_{\\square}T_F=\\frac{\\alpha h}{g e^2}.$$\n\nThe familiar factor of two corresponds to $g=2$, not an arbitrary multiband system. A bulk slope converted per conducting plane uses $A_{\\square}=A/d$ with the stated effective plane spacing $d$. Independent occupied-disk and algebra checks cover $g=1,2,4$; neither degeneracy nor a mass should be transferred between materials without justification.\n\nParallel channels add conductivities. As an independent scalar, zero-field example, let $r(T)=r_0+aT>0$ describe one channel and let $\\sigma_b\\ge0$ be a constant background conductivity in matching units. Then\n\n$$\\rho_{\\mathrm{tot}}=\\frac{r(T)}{1+\\sigma_b r(T)},\\qquad\\frac{d\\rho_{\\mathrm{tot}}}{dT}=\\frac{a}{[1+\\sigma_b r(T)]^2}.$$\n\nThe total slope is generally temperature dependent even though the first channel's resistance is exactly linear. Nine numerical derivative checks verify this model. It is not a multiband fit; in magnetic field, conductivity tensors must be added before inversion. Adding scattering mechanisms within one channel is a different assumption from adding parallel conductivities.\n\n## Experimental criteria\n\nLegros and colleagues' earlier manuscript measures a Bi2212 film with nominal hole doping 0.23 in pulsed fields. Its 55 T trace and magnetoresistance-corrected, extrapolated zero-field curve are distinct datasets. The analysis estimates carrier parameters and geometric uncertainty; the checked passages do not turn its interpretation into a model-independent universal bound. [R4](#ref-source-c1ae7869b672a8e8)\n\nCao and colleagues measure four-probe transport in gated twisted bilayer graphene. Their linear regime depends on filling and a crossover temperature. The operational scattering coefficient uses density and mass from low-temperature quantum oscillations; those assumptions matter when interpreting higher-temperature transport. The selected passages do not establish one shared microscopic mechanism across material families. [R5](#ref-source-8135909144b6b16b)\n\nRomero and colleagues' earlier manuscript studies two 100 nm FeTe1-xSex films, x = 0.45 and 0.35, over 0.2–3 THz. Its narrow-channel fits use 20–40 K and report coefficients 3.02 and 2.42 in $\\Gamma=\\Gamma_0+\\alpha k_BT/h$. These are channel-specific fit results, not coefficients of the total DC resistivity. [R6](#ref-source-05b2d5ff6757b5eb)\n\nRecord the raw voltage/current or conductivity data, geometry, composition, field direction, fit interval and uncertainty model. Identify excluded transition regions and test alternative fit windows and curvature. A successful fit does not establish that its parameters are uniquely identifiable. Normal-state measurement temperatures remain separate from superconducting transition temperatures in the records below.\n\n## Limits and disputes\n\nFrequency conventions can create a factor-of-$2\\pi$ error. For a Drude denominator $\\Gamma-i\\nu$ with ordinary frequency $\\nu$, the corresponding pole rate is $\\gamma=1/\\tau=2\\pi\\Gamma$ in a denominator $\\gamma-i\\omega$, where $\\omega=2\\pi\\nu$. Consequently $\\Gamma=\\alpha k_BT/h$ converts to $\\gamma=\\alpha k_BT/\\hbar$. State the denominator and linewidth convention before comparing coefficients. This is a convention check, not a new measurement of a lifetime.\n\nA shared temperature exponent does not identify a unique microscopic interaction. Drude transport, optical fits and single-particle lifetimes measure or infer different quantities. Extrapolating carrier parameters, suppressing superconductivity by field, or neglecting a parallel channel can affect an inferred coefficient. Report these choices alongside any claimed universality rather than treating the fit exponent as a proof.\n\nCooper's LSCO study and Bruin's cross-metal comparison remain bibliographic starting points here. Their complete datasets and numerical conclusions have not been reanalyzed in this entry. Selected manuscript checks above also leave final-version comparison and full uncertainty reproduction open. [R2](#ref-source-1610fd228e679225) [R3](#ref-source-e6d342432f3409ae)\n\n## Discovery implications\n\nUse linear-T transport to organize experiments, not to rank superconductors or predict a transition temperature by itself. A stronger comparison holds sample state, probe definition and fitting procedure fixed, then asks whether independent optical, thermodynamic or quantum-oscillation information supports the same parameter interpretation. Retain counterexamples and failed fits; correlation with superconductivity does not identify its cause.\n\n## Related topics\n\nContinue with [Planckian dissipation](/scwiki/planckian-dissipation), [zero resistance](/scwiki/zero-resistance), [critical fields](/scwiki/critical-fields), [specific heat](/scwiki/specific-heat-jump), [cuprates](/scwiki/cuprates), and [multiband pairing](/scwiki/multiband-pairing).","revision":"5e7255f1fca8b8c1a2e3","sections":[{"id":"scope","title":"Scope","markdown":"## Scope\n\nLinear-temperature resistivity describes a measured dependence over a specified range. The fit $\\rho(T)=\\rho_0+AT$ needs a sample, current direction, field, temperature interval and residuals. A straight-looking trace is not by itself evidence for a quantum critical point, a universal lifetime or a pairing interaction. This entry treats transport phenomenology; the linked Planckian entry discusses lifetime interpretations.\n\nSeparate a finite-field normal state, the region affected by superconducting fluctuations, and a higher-temperature regime that may have different scattering. Martin and colleagues' Bi-based crystal abstract reports strongly anisotropic transport; an in-plane trend is not an isotropic resistivity law. [R1](#ref-source-a5d6480d08ee8555)"},{"id":"mathematical-assumptions","title":"Mathematical assumptions","markdown":"## Mathematical assumptions\n\nA least-squares slope depends on both the model and the sampled window. For exact synthetic data $\\rho=r_0+aT+bT^2$, equally weighted temperatures symmetric about $\\bar T$ give\n\n$$A_{\\mathrm{fit}}=a+2b\\bar T.$$\n\nThis follows by inserting the quadratic into $\\operatorname{cov}(T,\\rho)/\\operatorname{var}(T)$. A narrower interval can hide curvature while changing the inferred slope. Independent synthetic fits confirm this counterexample; they are not fits to any material. Experimental model comparison also needs uncertainties, correlations and a justified treatment of residuals.\n\nFor a single isotropic Drude channel with temperature-independent carrier density $n$ and mass $m^*$, an inelastic pole relaxation rate $\\gamma=\\alpha k_BT/\\hbar$ gives $A=\\alpha m^*k_B/(ne^2\\hbar)$. Thus a slope fixes $\\alpha$ only after the carrier parameters and response model are specified. If those parameters change with temperature, differentiating resistivity produces additional terms. This conditional connection underlies the selected Legros analysis. [R4](#ref-source-c1ae7869b672a8e8)\n\nFor a circular, parabolic two-dimensional band with total degeneracy $g$, use total sheet density $n_{2D}=gk_F^2/(4\\pi)$ and $k_BT_F=\\hbar^2k_F^2/(2m^*)$. The preceding Drude model then yields\n\n$$A_{\\square}T_F=\\frac{\\alpha h}{g e^2}.$$\n\nThe familiar factor of two corresponds to $g=2$, not an arbitrary multiband system. A bulk slope converted per conducting plane uses $A_{\\square}=A/d$ with the stated effective plane spacing $d$. Independent occupied-disk and algebra checks cover $g=1,2,4$; neither degeneracy nor a mass should be transferred between materials without justification.\n\nParallel channels add conductivities. As an independent scalar, zero-field example, let $r(T)=r_0+aT>0$ describe one channel and let $\\sigma_b\\ge0$ be a constant background conductivity in matching units. Then\n\n$$\\rho_{\\mathrm{tot}}=\\frac{r(T)}{1+\\sigma_b r(T)},\\qquad\\frac{d\\rho_{\\mathrm{tot}}}{dT}=\\frac{a}{[1+\\sigma_b r(T)]^2}.$$\n\nThe total slope is generally temperature dependent even though the first channel's resistance is exactly linear. Nine numerical derivative checks verify this model. It is not a multiband fit; in magnetic field, conductivity tensors must be added before inversion. Adding scattering mechanisms within one channel is a different assumption from adding parallel conductivities."},{"id":"experimental-criteria","title":"Experimental criteria","markdown":"## Experimental criteria\n\nLegros and colleagues' earlier manuscript measures a Bi2212 film with nominal hole doping 0.23 in pulsed fields. Its 55 T trace and magnetoresistance-corrected, extrapolated zero-field curve are distinct datasets. The analysis estimates carrier parameters and geometric uncertainty; the checked passages do not turn its interpretation into a model-independent universal bound. [R4](#ref-source-c1ae7869b672a8e8)\n\nCao and colleagues measure four-probe transport in gated twisted bilayer graphene. Their linear regime depends on filling and a crossover temperature. The operational scattering coefficient uses density and mass from low-temperature quantum oscillations; those assumptions matter when interpreting higher-temperature transport. The selected passages do not establish one shared microscopic mechanism across material families. [R5](#ref-source-8135909144b6b16b)\n\nRomero and colleagues' earlier manuscript studies two 100 nm FeTe1-xSex films, x = 0.45 and 0.35, over 0.2–3 THz. Its narrow-channel fits use 20–40 K and report coefficients 3.02 and 2.42 in $\\Gamma=\\Gamma_0+\\alpha k_BT/h$. These are channel-specific fit results, not coefficients of the total DC resistivity. [R6](#ref-source-05b2d5ff6757b5eb)\n\nRecord the raw voltage/current or conductivity data, geometry, composition, field direction, fit interval and uncertainty model. Identify excluded transition regions and test alternative fit windows and curvature. A successful fit does not establish that its parameters are uniquely identifiable. Normal-state measurement temperatures remain separate from superconducting transition temperatures in the records below."},{"id":"limits-and-disputes","title":"Limits and disputes","markdown":"## Limits and disputes\n\nFrequency conventions can create a factor-of-$2\\pi$ error. For a Drude denominator $\\Gamma-i\\nu$ with ordinary frequency $\\nu$, the corresponding pole rate is $\\gamma=1/\\tau=2\\pi\\Gamma$ in a denominator $\\gamma-i\\omega$, where $\\omega=2\\pi\\nu$. Consequently $\\Gamma=\\alpha k_BT/h$ converts to $\\gamma=\\alpha k_BT/\\hbar$. State the denominator and linewidth convention before comparing coefficients. This is a convention check, not a new measurement of a lifetime.\n\nA shared temperature exponent does not identify a unique microscopic interaction. Drude transport, optical fits and single-particle lifetimes measure or infer different quantities. Extrapolating carrier parameters, suppressing superconductivity by field, or neglecting a parallel channel can affect an inferred coefficient. Report these choices alongside any claimed universality rather than treating the fit exponent as a proof.\n\nCooper's LSCO study and Bruin's cross-metal comparison remain bibliographic starting points here. Their complete datasets and numerical conclusions have not been reanalyzed in this entry. Selected manuscript checks above also leave final-version comparison and full uncertainty reproduction open. [R2](#ref-source-1610fd228e679225) [R3](#ref-source-e6d342432f3409ae)"},{"id":"discovery-implications","title":"Discovery implications","markdown":"## Discovery implications\n\nUse linear-T transport to organize experiments, not to rank superconductors or predict a transition temperature by itself. A stronger comparison holds sample state, probe definition and fitting procedure fixed, then asks whether independent optical, thermodynamic or quantum-oscillation information supports the same parameter interpretation. Retain counterexamples and failed fits; correlation with superconductivity does not identify its cause."},{"id":"related-topics","title":"Related topics","markdown":"## Related topics\n\nContinue with [Planckian dissipation](/scwiki/planckian-dissipation), [zero resistance](/scwiki/zero-resistance), [critical fields](/scwiki/critical-fields), [specific heat](/scwiki/specific-heat-jump), [cuprates](/scwiki/cuprates), and [multiband pairing](/scwiki/multiband-pairing)."},{"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); Legros v1 Bi2212 film; nominal p = 0.23 | Normal-state transport or fit interval; no equilibrium Tc assigned here | normal-state; normal-state-transport | Six-point transport in pulsed fields; 55 T trace and magnetoresistance-corrected extrapolation distinguished | unknown; unknown GPa | unknown | experiment; [source](#ref-source-c1ae7869b672a8e8) |\n| C; Cao gated twisted bilayer graphene; device and filling dependent | Normal-state transport or fit interval; no equilibrium Tc assigned here | normal-state; normal-state-transport | Four-probe longitudinal transport; low-temperature SdH carrier parameters used in operational rate estimate | unknown; unknown GPa | unknown | experiment; [source](#ref-source-8135909144b6b16b) |\n| FeTe1-xSex (aliases: iron-based, iron based superconductors); Romero v1 films: x = 0.45 and 0.35; thickness 100 nm | Normal-state transport or fit interval; no equilibrium Tc assigned here | normal-state; normal-state-transport | 0.2–3 THz spectroscopy with DC constraint; narrow-channel 20–40 K fit; ordinary-frequency rate | unknown; unknown GPa | unknown | experiment; [source](#ref-source-05b2d5ff6757b5eb) |"}],"markdown":"# Linear-T resistivity: strange-metal evidence and model limits\n\nRead linear-temperature transport with its fit window, field and carrier assumptions. Distinguish total resistivity, parallel conduction channels and inferred scattering rates.\n\n## Scope\n\nLinear-temperature resistivity describes a measured dependence over a specified range. The fit $\\rho(T)=\\rho_0+AT$ needs a sample, current direction, field, temperature interval and residuals. A straight-looking trace is not by itself evidence for a quantum critical point, a universal lifetime or a pairing interaction. This entry treats transport phenomenology; the linked Planckian entry discusses lifetime interpretations.\n\nSeparate a finite-field normal state, the region affected by superconducting fluctuations, and a higher-temperature regime that may have different scattering. Martin and colleagues' Bi-based crystal abstract reports strongly anisotropic transport; an in-plane trend is not an isotropic resistivity law. [R1](#ref-source-a5d6480d08ee8555)\n\n## Mathematical assumptions\n\nA least-squares slope depends on both the model and the sampled window. For exact synthetic data $\\rho=r_0+aT+bT^2$, equally weighted temperatures symmetric about $\\bar T$ give\n\n$$A_{\\mathrm{fit}}=a+2b\\bar T.$$\n\nThis follows by inserting the quadratic into $\\operatorname{cov}(T,\\rho)/\\operatorname{var}(T)$. A narrower interval can hide curvature while changing the inferred slope. Independent synthetic fits confirm this counterexample; they are not fits to any material. Experimental model comparison also needs uncertainties, correlations and a justified treatment of residuals.\n\nFor a single isotropic Drude channel with temperature-independent carrier density $n$ and mass $m^*$, an inelastic pole relaxation rate $\\gamma=\\alpha k_BT/\\hbar$ gives $A=\\alpha m^*k_B/(ne^2\\hbar)$. Thus a slope fixes $\\alpha$ only after the carrier parameters and response model are specified. If those parameters change with temperature, differentiating resistivity produces additional terms. This conditional connection underlies the selected Legros analysis. [R4](#ref-source-c1ae7869b672a8e8)\n\nFor a circular, parabolic two-dimensional band with total degeneracy $g$, use total sheet density $n_{2D}=gk_F^2/(4\\pi)$ and $k_BT_F=\\hbar^2k_F^2/(2m^*)$. The preceding Drude model then yields\n\n$$A_{\\square}T_F=\\frac{\\alpha h}{g e^2}.$$\n\nThe familiar factor of two corresponds to $g=2$, not an arbitrary multiband system. A bulk slope converted per conducting plane uses $A_{\\square}=A/d$ with the stated effective plane spacing $d$. Independent occupied-disk and algebra checks cover $g=1,2,4$; neither degeneracy nor a mass should be transferred between materials without justification.\n\nParallel channels add conductivities. As an independent scalar, zero-field example, let $r(T)=r_0+aT>0$ describe one channel and let $\\sigma_b\\ge0$ be a constant background conductivity in matching units. Then\n\n$$\\rho_{\\mathrm{tot}}=\\frac{r(T)}{1+\\sigma_b r(T)},\\qquad\\frac{d\\rho_{\\mathrm{tot}}}{dT}=\\frac{a}{[1+\\sigma_b r(T)]^2}.$$\n\nThe total slope is generally temperature dependent even though the first channel's resistance is exactly linear. Nine numerical derivative checks verify this model. It is not a multiband fit; in magnetic field, conductivity tensors must be added before inversion. Adding scattering mechanisms within one channel is a different assumption from adding parallel conductivities.\n\n## Experimental criteria\n\nLegros and colleagues' earlier manuscript measures a Bi2212 film with nominal hole doping 0.23 in pulsed fields. Its 55 T trace and magnetoresistance-corrected, extrapolated zero-field curve are distinct datasets. The analysis estimates carrier parameters and geometric uncertainty; the checked passages do not turn its interpretation into a model-independent universal bound. [R4](#ref-source-c1ae7869b672a8e8)\n\nCao and colleagues measure four-probe transport in gated twisted bilayer graphene. Their linear regime depends on filling and a crossover temperature. The operational scattering coefficient uses density and mass from low-temperature quantum oscillations; those assumptions matter when interpreting higher-temperature transport. The selected passages do not establish one shared microscopic mechanism across material families. [R5](#ref-source-8135909144b6b16b)\n\nRomero and colleagues' earlier manuscript studies two 100 nm FeTe1-xSex films, x = 0.45 and 0.35, over 0.2–3 THz. Its narrow-channel fits use 20–40 K and report coefficients 3.02 and 2.42 in $\\Gamma=\\Gamma_0+\\alpha k_BT/h$. These are channel-specific fit results, not coefficients of the total DC resistivity. [R6](#ref-source-05b2d5ff6757b5eb)\n\nRecord the raw voltage/current or conductivity data, geometry, composition, field direction, fit interval and uncertainty model. Identify excluded transition regions and test alternative fit windows and curvature. A successful fit does not establish that its parameters are uniquely identifiable. Normal-state measurement temperatures remain separate from superconducting transition temperatures in the records below.\n\n## Limits and disputes\n\nFrequency conventions can create a factor-of-$2\\pi$ error. For a Drude denominator $\\Gamma-i\\nu$ with ordinary frequency $\\nu$, the corresponding pole rate is $\\gamma=1/\\tau=2\\pi\\Gamma$ in a denominator $\\gamma-i\\omega$, where $\\omega=2\\pi\\nu$. Consequently $\\Gamma=\\alpha k_BT/h$ converts to $\\gamma=\\alpha k_BT/\\hbar$. State the denominator and linewidth convention before comparing coefficients. This is a convention check, not a new measurement of a lifetime.\n\nA shared temperature exponent does not identify a unique microscopic interaction. Drude transport, optical fits and single-particle lifetimes measure or infer different quantities. Extrapolating carrier parameters, suppressing superconductivity by field, or neglecting a parallel channel can affect an inferred coefficient. Report these choices alongside any claimed universality rather than treating the fit exponent as a proof.\n\nCooper's LSCO study and Bruin's cross-metal comparison remain bibliographic starting points here. Their complete datasets and numerical conclusions have not been reanalyzed in this entry. Selected manuscript checks above also leave final-version comparison and full uncertainty reproduction open. [R2](#ref-source-1610fd228e679225) [R3](#ref-source-e6d342432f3409ae)\n\n## Discovery implications\n\nUse linear-T transport to organize experiments, not to rank superconductors or predict a transition temperature by itself. A stronger comparison holds sample state, probe definition and fitting procedure fixed, then asks whether independent optical, thermodynamic or quantum-oscillation information supports the same parameter interpretation. Retain counterexamples and failed fits; correlation with superconductivity does not identify its cause.\n\n## Related topics\n\nContinue with [Planckian dissipation](/scwiki/planckian-dissipation), [zero resistance](/scwiki/zero-resistance), [critical fields](/scwiki/critical-fields), [specific heat](/scwiki/specific-heat-jump), [cuprates](/scwiki/cuprates), and [multiband pairing](/scwiki/multiband-pairing).\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); Legros v1 Bi2212 film; nominal p = 0.23 | Normal-state transport or fit interval; no equilibrium Tc assigned here | normal-state; normal-state-transport | Six-point transport in pulsed fields; 55 T trace and magnetoresistance-corrected extrapolation distinguished | unknown; unknown GPa | unknown | experiment; [source](#ref-source-c1ae7869b672a8e8) |\n| C; Cao gated twisted bilayer graphene; device and filling dependent | Normal-state transport or fit interval; no equilibrium Tc assigned here | normal-state; normal-state-transport | Four-probe longitudinal transport; low-temperature SdH carrier parameters used in operational rate estimate | unknown; unknown GPa | unknown | experiment; [source](#ref-source-8135909144b6b16b) |\n| FeTe1-xSex (aliases: iron-based, iron based superconductors); Romero v1 films: x = 0.45 and 0.35; thickness 100 nm | Normal-state transport or fit interval; no equilibrium Tc assigned here | normal-state; normal-state-transport | 0.2–3 THz spectroscopy with DC constraint; narrow-channel 20–40 K fit; ordinary-frequency rate | unknown; unknown GPa | unknown | experiment; [source](#ref-source-05b2d5ff6757b5eb) |\n\n## Sources\n\n### Ref source-a5d6480d08ee8555\n\n[R1] Normal-state transport properties of Bi2+xSr2-yCuO6+delta crystals (1990). [DOI 10.1103/PhysRevB.41.846](https://doi.org/10.1103/PhysRevB.41.846). Publication: journal-article. Check: primary-abstract-scoped-check. Checked: 2026-10-18. Publisher abstract only: anisotropic normal-state transport in Bi-based crystals. Full measurement protocol and numerical curves not checked.\n### Ref source-1610fd228e679225\n\n[R2] Anomalous Criticality in the Electrical Resistivity of La2-xSrxCuO4 (2009). [DOI 10.1126/science.1165015](https://doi.org/10.1126/science.1165015). Publication: journal-article. Check: crossref-metadata-only. Checked: 2026-10-18. Bibliographic identity only in A8. No numerical result or complete experimental claim extracted.\n### Ref source-e6d342432f3409ae\n\n[R3] Similarity of Scattering Rates in Metals Showing T-Linear Resistivity (2013). [DOI 10.1126/science.1227612](https://doi.org/10.1126/science.1227612). Publication: journal-article. Check: crossref-metadata-only. Checked: 2026-10-18. Bibliographic identity only in A8. Cross-material numerical comparisons not reproduced.\n### Ref source-c1ae7869b672a8e8\n\n[R4] Universal T-linear resistivity and Planckian dissipation in overdoped cuprates (2019). [DOI 10.1038/s41567-018-0334-2](https://doi.org/10.1038/s41567-018-0334-2). Publication: journal-article. Check: earlier-author-manuscript-scoped-check. Checked: 2026-10-18. Selected v1 pp. 4, 7–8 and Figs. 1–2 captions: Drude assumptions, film method and magnetoresistance correction. Published volume year 2019; final-version comparison and complete data fitting remain open.\n### Ref source-8135909144b6b16b\n\n[R5] Strange Metal in Magic-Angle Graphene with near Planckian Dissipation (2020). [DOI 10.1103/PhysRevLett.124.076801](https://doi.org/10.1103/PhysRevLett.124.076801). Publication: journal-article. Check: primary-fulltext-scoped-check. Checked: 2026-10-18. Selected published pp. 1–4, Fig. 1 and Eq. (1). Four-probe device, filling dependence and low-temperature SdH parameter assumptions checked; supplementary fits not reproduced.\n### Ref source-05b2d5ff6757b5eb\n\n[R6] Planckian scattering and parallel conduction channels in an iron chalcogenide superconductor (2026). [DOI 10.1038/s41567-026-03266-8](https://doi.org/10.1038/s41567-026-03266-8). Publication: journal-article. Check: earlier-author-manuscript-scoped-check. Checked: 2026-10-18. Selected v1 Fig. 1–3 discussion: films, spectral range, fit window and frequency convention. Publisher identity checked; complete final-version comparison and fit reproduction remain open.\n\n## Claim evidence and conditions\n\n### scwiki-a8-claim-scope-1\n\nLinear-temperature resistivity describes a measured dependence over a specified range. The fit $\\rho(T)=\\rho_0+AT$ needs a sample, current direction, field, temperature interval and residuals. A straight-looking trace is not by itself evidence for a quantum critical point, a universal lifetime or a pairing interaction. This entry treats transport phenomenology; the linked Planckian entry discusses lifetime interpretations.\n\nEvidence: hypothesis. Sources: source-8135909144b6b16b.\n\nConditions: Editorial reporting and inference criteria; no universal lifetime, pairing mechanism or transition temperature follows from a fitted slope.\n\nVerification scope: Pinned A8 chapter edited with explicit source/model limitations.\n\n### scwiki-a8-claim-scope-2\n\nSeparate a finite-field normal state, the region affected by superconducting fluctuations, and a higher-temperature regime that may have different scattering. Martin and colleagues' Bi-based crystal abstract reports strongly anisotropic transport; an in-plane trend is not an isotropic resistivity law.\n\nEvidence: experiment. Sources: source-a5d6480d08ee8555.\n\nConditions: Sample-, probe-, field-, fit-window- and version-specific observations; no material-independent coefficient or new equilibrium Tc record.\n\nVerification scope: Selected primary passages as specified by the cited reference; no raw-data reproduction.\n\n### scwiki-a8-claim-mathematical-assumptions-1\n\nA least-squares slope depends on both the model and the sampled window. For exact synthetic data $\\rho=r_0+aT+bT^2$, equally weighted temperatures symmetric about $\\bar T$ give\n\nEvidence: theory. Sources: source-c1ae7869b672a8e8.\n\nSource relationship: context-for-local-derivation. Legros v1 p. 4 supplies the isotropic Drude relation and its twofold-degenerate 2D expression. Explicit total-degeneracy counting, fitting-window examples and the parallel-channel counterexample are local conditional derivations; they are not fitted results from that paper.\n\nConditions: Conditional local models: symmetric equal-weight quadratic fit; single isotropic constant-parameter Drude channel; circular parabolic 2D band with explicit degeneracy; scalar zero-field parallel conductance; stated frequency denominator.\n\nVerification scope: Independent synthetic/algebra/finite-difference checks, not experimental calibration or original dataset fitting.\n\n### scwiki-a8-claim-mathematical-assumptions-2\n\n$$A_{\\mathrm{fit}}=a+2b\\bar T.$$\n\nEvidence: theory. Sources: source-c1ae7869b672a8e8.\n\nSource relationship: context-for-local-derivation. Legros v1 p. 4 supplies the isotropic Drude relation and its twofold-degenerate 2D expression. Explicit total-degeneracy counting, fitting-window examples and the parallel-channel counterexample are local conditional derivations; they are not fitted results from that paper.\n\nConditions: Conditional local models: symmetric equal-weight quadratic fit; single isotropic constant-parameter Drude channel; circular parabolic 2D band with explicit degeneracy; scalar zero-field parallel conductance; stated frequency denominator.\n\nVerification scope: Independent synthetic/algebra/finite-difference checks, not experimental calibration or original dataset fitting.\n\n### scwiki-a8-claim-mathematical-assumptions-3\n\nThis follows by inserting the quadratic into $\\operatorname{cov}(T,\\rho)/\\operatorname{var}(T)$. A narrower interval can hide curvature while changing the inferred slope. Independent synthetic fits confirm this counterexample; they are not fits to any material. Experimental model comparison also needs uncertainties, correlations and a justified treatment of residuals.\n\nEvidence: theory. Sources: source-c1ae7869b672a8e8.\n\nSource relationship: context-for-local-derivation. Legros v1 p. 4 supplies the isotropic Drude relation and its twofold-degenerate 2D expression. Explicit total-degeneracy counting, fitting-window examples and the parallel-channel counterexample are local conditional derivations; they are not fitted results from that paper.\n\nConditions: Conditional local models: symmetric equal-weight quadratic fit; single isotropic constant-parameter Drude channel; circular parabolic 2D band with explicit degeneracy; scalar zero-field parallel conductance; stated frequency denominator.\n\nVerification scope: Independent synthetic/algebra/finite-difference checks, not experimental calibration or original dataset fitting.\n\n### scwiki-a8-claim-mathematical-assumptions-4\n\nFor a single isotropic Drude channel with temperature-independent carrier density $n$ and mass $m^*$, an inelastic pole relaxation rate $\\gamma=\\alpha k_BT/\\hbar$ gives $A=\\alpha m^*k_B/(ne^2\\hbar)$. Thus a slope fixes $\\alpha$ only after the carrier parameters and response model are specified. If those parameters change with temperature, differentiating resistivity produces additional terms. This conditional connection underlies the selected Legros analysis.\n\nEvidence: theory. Sources: source-c1ae7869b672a8e8.\n\nSource relationship: mixed-source-and-local-derivation. Legros v1 p. 4 supplies the isotropic Drude relation and its twofold-degenerate 2D expression. Explicit total-degeneracy counting, fitting-window examples and the parallel-channel counterexample are local conditional derivations; they are not fitted results from that paper.\n\nConditions: Conditional local models: symmetric equal-weight quadratic fit; single isotropic constant-parameter Drude channel; circular parabolic 2D band with explicit degeneracy; scalar zero-field parallel conductance; stated frequency denominator.\n\nVerification scope: Independent synthetic/algebra/finite-difference checks, not experimental calibration or original dataset fitting.\n\n### scwiki-a8-claim-mathematical-assumptions-5\n\nFor a circular, parabolic two-dimensional band with total degeneracy $g$, use total sheet density $n_{2D}=gk_F^2/(4\\pi)$ and $k_BT_F=\\hbar^2k_F^2/(2m^*)$. The preceding Drude model then yields\n\nEvidence: theory. Sources: source-c1ae7869b672a8e8.\n\nSource relationship: mixed-source-and-local-derivation. Legros v1 p. 4 supplies the isotropic Drude relation and its twofold-degenerate 2D expression. Explicit total-degeneracy counting, fitting-window examples and the parallel-channel counterexample are local conditional derivations; they are not fitted results from that paper.\n\nConditions: Conditional local models: symmetric equal-weight quadratic fit; single isotropic constant-parameter Drude channel; circular parabolic 2D band with explicit degeneracy; scalar zero-field parallel conductance; stated frequency denominator.\n\nVerification scope: Independent synthetic/algebra/finite-difference checks, not experimental calibration or original dataset fitting.\n\n### scwiki-a8-claim-mathematical-assumptions-6\n\n$$A_{\\square}T_F=\\frac{\\alpha h}{g e^2}.$$\n\nEvidence: theory. Sources: source-c1ae7869b672a8e8.\n\nSource relationship: mixed-source-and-local-derivation. Legros v1 p. 4 supplies the isotropic Drude relation and its twofold-degenerate 2D expression. Explicit total-degeneracy counting, fitting-window examples and the parallel-channel counterexample are local conditional derivations; they are not fitted results from that paper.\n\nConditions: Conditional local models: symmetric equal-weight quadratic fit; single isotropic constant-parameter Drude channel; circular parabolic 2D band with explicit degeneracy; scalar zero-field parallel conductance; stated frequency denominator.\n\nVerification scope: Independent synthetic/algebra/finite-difference checks, not experimental calibration or original dataset fitting.\n\n### scwiki-a8-claim-mathematical-assumptions-7\n\nThe familiar factor of two corresponds to $g=2$, not an arbitrary multiband system. A bulk slope converted per conducting plane uses $A_{\\square}=A/d$ with the stated effective plane spacing $d$. Independent occupied-disk and algebra checks cover $g=1,2,4$; neither degeneracy nor a mass should be transferred between materials without justification.\n\nEvidence: theory. Sources: source-c1ae7869b672a8e8.\n\nSource relationship: mixed-source-and-local-derivation. Legros v1 p. 4 supplies the isotropic Drude relation and its twofold-degenerate 2D expression. Explicit total-degeneracy counting, fitting-window examples and the parallel-channel counterexample are local conditional derivations; they are not fitted results from that paper.\n\nConditions: Conditional local models: symmetric equal-weight quadratic fit; single isotropic constant-parameter Drude channel; circular parabolic 2D band with explicit degeneracy; scalar zero-field parallel conductance; stated frequency denominator.\n\nVerification scope: Independent synthetic/algebra/finite-difference checks, not experimental calibration or original dataset fitting.\n\n### scwiki-a8-claim-mathematical-assumptions-8\n\nParallel channels add conductivities. As an independent scalar, zero-field example, let $r(T)=r_0+aT>0$ describe one channel and let $\\sigma_b\\ge0$ be a constant background conductivity in matching units. Then\n\nEvidence: theory. Sources: source-c1ae7869b672a8e8.\n\nSource relationship: context-for-local-derivation. Legros v1 p. 4 supplies the isotropic Drude relation and its twofold-degenerate 2D expression. Explicit total-degeneracy counting, fitting-window examples and the parallel-channel counterexample are local conditional derivations; they are not fitted results from that paper.\n\nConditions: Conditional local models: symmetric equal-weight quadratic fit; single isotropic constant-parameter Drude channel; circular parabolic 2D band with explicit degeneracy; scalar zero-field parallel conductance; stated frequency denominator.\n\nVerification scope: Independent synthetic/algebra/finite-difference checks, not experimental calibration or original dataset fitting.\n\n### scwiki-a8-claim-mathematical-assumptions-9\n\n$$\\rho_{\\mathrm{tot}}=\\frac{r(T)}{1+\\sigma_b r(T)},\\qquad\\frac{d\\rho_{\\mathrm{tot}}}{dT}=\\frac{a}{[1+\\sigma_b r(T)]^2}.$$\n\nEvidence: theory. Sources: source-c1ae7869b672a8e8.\n\nSource relationship: context-for-local-derivation. Legros v1 p. 4 supplies the isotropic Drude relation and its twofold-degenerate 2D expression. Explicit total-degeneracy counting, fitting-window examples and the parallel-channel counterexample are local conditional derivations; they are not fitted results from that paper.\n\nConditions: Conditional local models: symmetric equal-weight quadratic fit; single isotropic constant-parameter Drude channel; circular parabolic 2D band with explicit degeneracy; scalar zero-field parallel conductance; stated frequency denominator.\n\nVerification scope: Independent synthetic/algebra/finite-difference checks, not experimental calibration or original dataset fitting.\n\n### scwiki-a8-claim-mathematical-assumptions-10\n\nThe total slope is generally temperature dependent even though the first channel's resistance is exactly linear. Nine numerical derivative checks verify this model. It is not a multiband fit; in magnetic field, conductivity tensors must be added before inversion. Adding scattering mechanisms within one channel is a different assumption from adding parallel conductivities.\n\nEvidence: theory. Sources: source-c1ae7869b672a8e8.\n\nSource relationship: context-for-local-derivation. Legros v1 p. 4 supplies the isotropic Drude relation and its twofold-degenerate 2D expression. Explicit total-degeneracy counting, fitting-window examples and the parallel-channel counterexample are local conditional derivations; they are not fitted results from that paper.\n\nConditions: Conditional local models: symmetric equal-weight quadratic fit; single isotropic constant-parameter Drude channel; circular parabolic 2D band with explicit degeneracy; scalar zero-field parallel conductance; stated frequency denominator.\n\nVerification scope: Independent synthetic/algebra/finite-difference checks, not experimental calibration or original dataset fitting.\n\n### scwiki-a8-claim-experimental-criteria-1\n\nLegros and colleagues' earlier manuscript measures a Bi2212 film with nominal hole doping 0.23 in pulsed fields. Its 55 T trace and magnetoresistance-corrected, extrapolated zero-field curve are distinct datasets. The analysis estimates carrier parameters and geometric uncertainty; the checked passages do not turn its interpretation into a model-independent universal bound.\n\nEvidence: experiment. Sources: source-c1ae7869b672a8e8.\n\nConditions: Sample-, probe-, field-, fit-window- and version-specific observations; no material-independent coefficient or new equilibrium Tc record.\n\nVerification scope: Selected primary passages as specified by the cited reference; no raw-data reproduction.\n\n### scwiki-a8-claim-experimental-criteria-2\n\nCao and colleagues measure four-probe transport in gated twisted bilayer graphene. Their linear regime depends on filling and a crossover temperature. The operational scattering coefficient uses density and mass from low-temperature quantum oscillations; those assumptions matter when interpreting higher-temperature transport. The selected passages do not establish one shared microscopic mechanism across material families.\n\nEvidence: experiment. Sources: source-8135909144b6b16b.\n\nConditions: Sample-, probe-, field-, fit-window- and version-specific observations; no material-independent coefficient or new equilibrium Tc record.\n\nVerification scope: Selected primary passages as specified by the cited reference; no raw-data reproduction.\n\n### scwiki-a8-claim-experimental-criteria-3\n\nRomero and colleagues' earlier manuscript studies two 100 nm FeTe1-xSex films, x = 0.45 and 0.35, over 0.2–3 THz. Its narrow-channel fits use 20–40 K and report coefficients 3.02 and 2.42 in $\\Gamma=\\Gamma_0+\\alpha k_BT/h$. These are channel-specific fit results, not coefficients of the total DC resistivity.\n\nEvidence: experiment. Sources: source-05b2d5ff6757b5eb.\n\nConditions: Sample-, probe-, field-, fit-window- and version-specific observations; no material-independent coefficient or new equilibrium Tc record.\n\nVerification scope: Selected primary passages as specified by the cited reference; no raw-data reproduction.\n\n### scwiki-a8-claim-experimental-criteria-4\n\nRecord the raw voltage/current or conductivity data, geometry, composition, field direction, fit interval and uncertainty model. Identify excluded transition regions and test alternative fit windows and curvature. A successful fit does not establish that its parameters are uniquely identifiable. Normal-state measurement temperatures remain separate from superconducting transition temperatures in the records below.\n\nEvidence: hypothesis. Sources: source-8135909144b6b16b.\n\nConditions: Editorial reporting and inference criteria; no universal lifetime, pairing mechanism or transition temperature follows from a fitted slope.\n\nVerification scope: Pinned A8 chapter edited with explicit source/model limitations.\n\n### scwiki-a8-claim-limits-and-disputes-1\n\nFrequency conventions can create a factor-of-$2\\pi$ error. For a Drude denominator $\\Gamma-i\\nu$ with ordinary frequency $\\nu$, the corresponding pole rate is $\\gamma=1/\\tau=2\\pi\\Gamma$ in a denominator $\\gamma-i\\omega$, where $\\omega=2\\pi\\nu$. Consequently $\\Gamma=\\alpha k_BT/h$ converts to $\\gamma=\\alpha k_BT/\\hbar$. State the denominator and linewidth convention before comparing coefficients. This is a convention check, not a new measurement of a lifetime.\n\nEvidence: theory. Sources: source-8135909144b6b16b.\n\nConditions: Conditional local models: symmetric equal-weight quadratic fit; single isotropic constant-parameter Drude channel; circular parabolic 2D band with explicit degeneracy; scalar zero-field parallel conductance; stated frequency denominator.\n\nVerification scope: Independent synthetic/algebra/finite-difference checks, not experimental calibration or original dataset fitting.\n\n### scwiki-a8-claim-limits-and-disputes-2\n\nA shared temperature exponent does not identify a unique microscopic interaction. Drude transport, optical fits and single-particle lifetimes measure or infer different quantities. Extrapolating carrier parameters, suppressing superconductivity by field, or neglecting a parallel channel can affect an inferred coefficient. Report these choices alongside any claimed universality rather than treating the fit exponent as a proof.\n\nEvidence: hypothesis. Sources: source-8135909144b6b16b.\n\nConditions: Editorial reporting and inference criteria; no universal lifetime, pairing mechanism or transition temperature follows from a fitted slope.\n\nVerification scope: Pinned A8 chapter edited with explicit source/model limitations.\n\n### scwiki-a8-claim-limits-and-disputes-3\n\nCooper's LSCO study and Bruin's cross-metal comparison remain bibliographic starting points here. Their complete datasets and numerical conclusions have not been reanalyzed in this entry. Selected manuscript checks above also leave final-version comparison and full uncertainty reproduction open.\n\nEvidence: hypothesis. Sources: source-1610fd228e679225, source-e6d342432f3409ae.\n\nConditions: Editorial reporting and inference criteria; no universal lifetime, pairing mechanism or transition temperature follows from a fitted slope.\n\nVerification scope: Pinned A8 chapter edited with explicit source/model limitations.\n\n### scwiki-a8-claim-discovery-implications-1\n\nUse linear-T transport to organize experiments, not to rank superconductors or predict a transition temperature by itself. A stronger comparison holds sample state, probe definition and fitting procedure fixed, then asks whether independent optical, thermodynamic or quantum-oscillation information supports the same parameter interpretation. Retain counterexamples and failed fits; correlation with superconductivity does not identify its cause.\n\nEvidence: hypothesis. Sources: source-8135909144b6b16b.\n\nConditions: Editorial reporting and inference criteria; no universal lifetime, pairing mechanism or transition temperature follows from a fitted slope.\n\nVerification scope: Pinned A8 chapter edited with explicit source/model limitations.\n\n## Revision and review\n\nArticle ID: scwiki-a8. Revision: 5e7255f1fca8b8c1a2e3. Updated: 2026-10-19.\n\nReview scope: Pinned A8 chapter; selected published Cao passages, Legros/Romero earlier manuscripts and Martin abstract; independent fit-window, Drude-degeneracy, parallel-channel and frequency-convention checks. Follow-up explicitly separates Legros v1 p. 4 from the local degeneracy and parallel-channel examples.\n\n- Selected checks are not full scientific acceptance, experimental replication or complete uncertainty propagation.\n- Legros and Romero earlier manuscript passages are version-specific; exhaustive comparison with final published articles remains open.\n- Cooper and Bruin are bibliographic pointers only; no cross-family numerical alpha table reproduced.\n- Synthetic model checks do not identify a material mechanism. No equilibrium Tc is inferred from normal-state transport.\n\nSource: [A_phenomenology/A8_strange_metal_linear_T.md](https://github.com/JackZH26/jzis-superconductivity/blob/0a7c9d6696804ec26aa12f8eed68b55c9b3c0fcf/A_phenomenology/A8_strange_metal_linear_T.md), commit 0a7c9d6696804ec26aa12f8eed68b55c9b3c0fcf, SHA-256 53878789a42ed20ba0a911bbf42c65c61aa731342e681ff2a2200a02cb13e906.\n","wordCount":827}}