# Strange metals and linear-temperature resistivity

Evaluate normal-state transport without conflating a fitted exponent, a relaxation time, quantum criticality and the superconducting mechanism.

## Scope

A strange metal is identified through unusual normal-state behavior, often including resistivity approximately proportional to temperature after superconductivity is suppressed. It is an observational category, not a uniquely established microscopic phase or order parameter. The early Bi-based transport work and later overdoped-cuprate experiments concern particular specimens and temperature ranges. Their results do not provide a universal slope for all superconductors. Ordinary high-temperature electron–phonon transport can also be linear, so a room-temperature straight line alone is insufficient. [R1](#ref-source-a5d6480d08ee8555) [R2](#ref-source-1610fd228e679225) [R4](#ref-source-374c8bc13ced83e8)

This article focuses on how observations constrain explanations. Linear resistivity, a transport relaxation rate near a thermal quantum scale, proximity to a quantum critical point and a high superconducting transition temperature are separate propositions. Each requires additional evidence. Even the identity of a relevant lifetime matters: a single-particle linewidth and a current-relaxation rate need not weight scattering processes in the same way. [R3](#ref-source-c1ae7869b672a8e8) [R4](#ref-source-374c8bc13ced83e8) [R6](#ref-source-05b2d5ff6757b5eb)

## Mathematical assumptions

For a fitted normal-state curve, write $\rho(T)=\rho_0+AT+BT^2$. This is an empirical decomposition over a stated interval; its terms do not automatically identify independent microscopic mechanisms. Define a local exponent relative to a trial residual $\rho_r$ by $n_{\mathrm{eff}}=d\ln(\rho-\rho_r)/d\ln T$, wherever the logarithm is defined. Derivatives amplify noise and depend on the residual subtraction. An exponent should therefore accompany its temperature window, uncertainty and treatment of the superconducting region. [R2](#ref-source-1610fd228e679225) [R3](#ref-source-c1ae7869b672a8e8)

An independent illustration uses exactly quadratic data, $\rho=\rho_0+BT^2$. If the trial residual differs by $\epsilon=\rho_r-\rho_0$, then $n_{\mathrm{eff}}=2BT^2/(BT^2-\epsilon)$. One hundred and eight finite-difference checks verify this relation. With the correct residual, a positive mixture of linear and quadratic terms gives $n_{\mathrm{eff}}=(A+2BT)/(A+BT)$, continuously between one and two; nine parameter cases confirm that limit. No abrupt phase boundary is required by this smooth crossover. These are synthetic checks, not fits to a paper's measurements. [R2](#ref-source-1610fd228e679225)

Two additional synthetic fits use $\rho=10+0.1T^2$ in arbitrary consistent units. A best straight line over $9\leq T\leq11$ has maximum deviation below 0.4% of the mean resistivity; extending the interval to $1\leq T\leq20$ raises it above 20%. Thus apparent linearity over a narrow interval can hide curvature. These percentages depend on the chosen example and are not universal acceptance thresholds. Real analysis needs residual plots, independent temperature calibration and a measurement-specific noise model. [R2](#ref-source-1610fd228e679225)

For parallel conducting channels, conductivities add: $\sigma_{\mathrm{dc}}=\sigma_0+S/\Gamma$ in a specified Drude convention. If $S$ and $\sigma_0$ are constant and $\Gamma\propto T$, the resulting resistivity is $\rho=1/(a+b/T)$, which is generally nonlinear. Adding channel resistivities would describe a different circuit. Temperature-dependent spectral weight and finite frequency coverage must also be tested before assigning a lifetime from the total d.c. curve. [R6](#ref-source-05b2d5ff6757b5eb)

## Experimental criteria

Grissonnanche and colleagues measured angle-dependent magnetoresistance in Nd-LSCO at hole concentration $p=0.24\pm0.005$. The sample's zero-resistance transition is 11 K; the transport measurements use 45 T at 6, 12, 20 and 25 K. At the two lower temperatures, some field orientations still enter a superconducting region. A high field alone therefore does not certify that every angular data point is normal-state transport. [R4](#ref-source-374c8bc13ced83e8)

Their fit separates a temperature-independent anisotropic contribution from an isotropic temperature-dependent rate, giving $\alpha=1.2\pm0.4$ in $\hbar/\tau_{\mathrm{inel}}=\alpha k_BT$. Total scattering is not isotropic. The analysis uses a bandwidth scale $160\pm30$ meV constrained by specific heat and omits a low-temperature correction that could change it by about 20% at 6 K. Temperature stability of ±1 mK differs from absolute uncertainty of approximately ±1 K at 6 and 12 K. These qualifications belong with the extracted coefficient. [R4](#ref-source-374c8bc13ced83e8)

Romero and colleagues resolve a narrower Drude channel and a broad background in two FeTe1−xSex films. The final abstract associates most condensate spectral weight with the narrower channel. In the checked author version, the scattering-rate fits use 20–40 K, and linewidths below the approximately 0.2 THz measurement limit cannot be resolved directly. Its frequency variable uses cycles per second, so $h$ appears in $\Gamma=\Gamma_0+\alpha k_BT/h$; an angular-frequency rate instead uses $\hbar$. A fitted spectral decomposition is stronger evidence than assigning a lifetime from total resistance alone, but it does not uniquely determine the pairing interaction. [R6](#ref-source-05b2d5ff6757b5eb)

Cooper and colleagues report that a low-temperature linear contribution extends over a range of LSCO dopings and tracks superconductivity. The checked abstract supports that association, not a reanalysis of its numerical curves. Magic-angle graphene measurements provide another material setting with nearly linear transport; a similar temperature exponent across systems does not prove identical scattering or pairing mechanisms. Material geometry, filling and fit assumptions must accompany cross-system comparisons. [R2](#ref-source-1610fd228e679225) [R5](#ref-source-8135909144b6b16b)

## Limits and disputes

The marginal-Fermi-liquid proposal organizes anomalies using an assumed charge- and spin-response spectrum. Its phenomenological success would not identify a unique microscopic origin. The original article has an erratum; this review records the correction's identity but has not independently read its contents, and therefore does not reproduce a supposedly corrected derivation. Quantum critical, incoherent-metal and phonon-based explanations require separate discriminating evidence rather than a choice made from one resistivity exponent. [R7](#ref-source-5880a61b06ec84e6) [R8](#ref-source-2cdc898b9c5e504c) [R4](#ref-source-374c8bc13ced83e8)

Complete scientific acceptance remains open. Selected final passages and figures have been checked, but full version comparisons and raw-data fits remain incomplete. A slope correlation with superconductivity does not establish causation, and a channel contributing to the condensate does not identify the interaction binding its electrons. Retain alternative explanations and distinguish an experimental observable from quantities inferred through a model. [R2](#ref-source-1610fd228e679225) [R6](#ref-source-05b2d5ff6757b5eb)

## Discovery implications

Compare transport, spectroscopy and superconducting response on well-characterized samples, with field, geometry and temperature windows recorded. Use independent changes in disorder, pressure or filling to test whether a proposed scattering process also controls pairing. A useful discovery claim predicts an observable change and survives alternative fits; simply finding another straight resistivity curve adds a candidate observation, not a complete microscopic explanation. [R3](#ref-source-c1ae7869b672a8e8) [R5](#ref-source-8135909144b6b16b) [R6](#ref-source-05b2d5ff6757b5eb)

## Related topics

[Linear-T resistivity](/scwiki/linear-t-resistivity), [Planckian dissipation](/scwiki/planckian-dissipation), and [Spin-fluctuation pairing](/scwiki/spin-fluctuation-pairing).

## Material cases

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

| Material and sample | Reported temperature | Criterion | Probe | Pressure | State | Evidence |
|---|---|---|---|---|---|---|
| La1.35Nd0.4Sr0.25CuO4 (aliases: Nd-LSCO); Grissonnanche Nd-LSCO, hole concentration p=0.24 ± 0.005; nominal Sr x=0.25 | 11 K; Zero-resistance transition reported in methods; not the 6 K high-field measurement temperature. Formula follows nominal Sr x=0.25; measured hole concentration p=0.24 ± 0.005 is distinct. | transition; zero-resistance | Electrical resistivity | ambient; unknown GPa | unknown | experiment; [source](#ref-source-374c8bc13ced83e8) |
| La1.35Nd0.4Sr0.25CuO4 (aliases: Nd-LSCO); Grissonnanche Nd-LSCO, 45 T angular magnetoresistance at p=0.24 | 6 K; 6 K measurement; superconducting angular sectors excluded. Absolute temperature uncertainty about ±1 K, distinct from ±1 mK stability. | measurement; ADMR-measurement | Angle-dependent c-axis magnetoresistance | ambient; unknown GPa | unknown | experiment; [source](#ref-source-374c8bc13ced83e8) |

## Sources

### Ref source-a5d6480d08ee8555

[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.
### Ref source-1610fd228e679225

[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: primary-abstract-and-publication-check. Checked: 2026-10-19. Primary abstract reproduced by PubMed checked. Online 11 December 2008; issue 30 January 2009. Publisher full text was unavailable; numerical curves and measurement protocols remain unaudited here.
### Ref source-c1ae7869b672a8e8

[R3] 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.
### Ref source-374c8bc13ced83e8

[R4] Linear-in temperature resistivity from an isotropic Planckian scattering rate (2021). [DOI 10.1038/s41586-021-03697-8](https://doi.org/10.1038/s41586-021-03697-8). Publication: journal-article. Check: selected-final-methods-results-and-figure-check. Checked: 2026-10-19. Final results and selected methods read; printed page 669, Figure 2 visually checked. Compared selected author v2 passages. Temperature stability, absolute error, angular superconducting regions and fitted bandwidth distinguished. Complete fitting and raw-data reproduction remain open.
### Ref source-8135909144b6b16b

[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.
### Ref source-05b2d5ff6757b5eb

[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: selected-author-figure-and-final-abstract-check. Checked: 2026-10-19. Author v1, 1 May 2025: selected methods and results, pages 1–4, read; page 4 Figure 3 visually checked. Final publisher abstract and publication date, 23 April 2026, checked. Final full text requires access; the attempted PDF returned HTML. Complete version comparison and spectral-weight calibration remain open.
### Ref source-5880a61b06ec84e6

[R7] Phenomenology of the normal state of Cu-O high-temperature superconductors (1989). [DOI 10.1103/PhysRevLett.63.1996](https://doi.org/10.1103/PhysRevLett.63.1996). Publication: journal-article. Check: publisher-abstract-check. Checked: 2026-10-19. Published 30 October 1989. Marginal-Fermi-liquid hypothesis checked at abstract level. The linked 1990 erratum is recorded separately; complete corrected derivation remains open.
### Ref source-2cdc898b9c5e504c

[R8] Erratum: Phenomenology of the normal state of Cu-O high-temperature superconductors (1990). [DOI 10.1103/PhysRevLett.64.497](https://doi.org/10.1103/PhysRevLett.64.497). Publication: journal-article. Check: publisher-erratum-identity-check. Checked: 2026-10-19. Published 22 January 1990. Publisher linkage and identity verified. PDF endpoint returned 403; correction contents have not been independently read, so no corrected formula is attributed to it.

## Claim evidence and conditions

### scwiki-h1-claim-scope-1

A strange metal is identified through unusual normal-state behavior, often including resistivity approximately proportional to temperature after superconductivity is suppressed. It is an observational category, not a uniquely established microscopic phase or order parameter. The early Bi-based transport work and later overdoped-cuprate experiments concern particular specimens and temperature ranges. Their results do not provide a universal slope for all superconductors. Ordinary high-temperature electron–phonon transport can also be linear, so a room-temperature straight line alone is insufficient.

Evidence: hypothesis. Sources: source-a5d6480d08ee8555, source-1610fd228e679225, source-374c8bc13ced83e8.

Conditions: Fit window, residual subtraction, lifetime convention, angular superconducting exclusions and source version remain explicit.

Verification scope: Selected primary texts and figures plus independent synthetic identifiability checks; full scientific acceptance remains open.

### scwiki-h1-claim-scope-2

This article focuses on how observations constrain explanations. Linear resistivity, a transport relaxation rate near a thermal quantum scale, proximity to a quantum critical point and a high superconducting transition temperature are separate propositions. Each requires additional evidence. Even the identity of a relevant lifetime matters: a single-particle linewidth and a current-relaxation rate need not weight scattering processes in the same way.

Evidence: hypothesis. Sources: source-c1ae7869b672a8e8, source-374c8bc13ced83e8, source-05b2d5ff6757b5eb.

Conditions: Fit window, residual subtraction, lifetime convention, angular superconducting exclusions and source version remain explicit.

Verification scope: Selected primary texts and figures plus independent synthetic identifiability checks; full scientific acceptance remains open.

### scwiki-h1-claim-mathematical-assumptions-1

For a fitted normal-state curve, write $\rho(T)=\rho_0+AT+BT^2$. This is an empirical decomposition over a stated interval; its terms do not automatically identify independent microscopic mechanisms. Define a local exponent relative to a trial residual $\rho_r$ by $n_{\mathrm{eff}}=d\ln(\rho-\rho_r)/d\ln T$, wherever the logarithm is defined. Derivatives amplify noise and depend on the residual subtraction. An exponent should therefore accompany its temperature window, uncertainty and treatment of the superconducting region.

Evidence: theory. Sources: source-1610fd228e679225, source-c1ae7869b672a8e8.

Conditions: Fit window, residual subtraction, lifetime convention, angular superconducting exclusions and source version remain explicit.

Verification scope: Selected primary texts and figures plus independent synthetic identifiability checks; full scientific acceptance remains open.

### scwiki-h1-claim-mathematical-assumptions-2

An independent illustration uses exactly quadratic data, $\rho=\rho_0+BT^2$. If the trial residual differs by $\epsilon=\rho_r-\rho_0$, then $n_{\mathrm{eff}}=2BT^2/(BT^2-\epsilon)$. One hundred and eight finite-difference checks verify this relation. With the correct residual, a positive mixture of linear and quadratic terms gives $n_{\mathrm{eff}}=(A+2BT)/(A+BT)$, continuously between one and two; nine parameter cases confirm that limit. No abrupt phase boundary is required by this smooth crossover. These are synthetic checks, not fits to a paper's measurements.

Evidence: theory. Sources: source-1610fd228e679225.

Conditions: Fit window, residual subtraction, lifetime convention, angular superconducting exclusions and source version remain explicit.

Verification scope: Selected primary texts and figures plus independent synthetic identifiability checks; full scientific acceptance remains open.

### scwiki-h1-claim-mathematical-assumptions-3

Two additional synthetic fits use $\rho=10+0.1T^2$ in arbitrary consistent units. A best straight line over $9\leq T\leq11$ has maximum deviation below 0.4% of the mean resistivity; extending the interval to $1\leq T\leq20$ raises it above 20%. Thus apparent linearity over a narrow interval can hide curvature. These percentages depend on the chosen example and are not universal acceptance thresholds. Real analysis needs residual plots, independent temperature calibration and a measurement-specific noise model.

Evidence: theory. Sources: source-1610fd228e679225.

Conditions: Fit window, residual subtraction, lifetime convention, angular superconducting exclusions and source version remain explicit.

Verification scope: Selected primary texts and figures plus independent synthetic identifiability checks; full scientific acceptance remains open.

### scwiki-h1-claim-mathematical-assumptions-4

For parallel conducting channels, conductivities add: $\sigma_{\mathrm{dc}}=\sigma_0+S/\Gamma$ in a specified Drude convention. If $S$ and $\sigma_0$ are constant and $\Gamma\propto T$, the resulting resistivity is $\rho=1/(a+b/T)$, which is generally nonlinear. Adding channel resistivities would describe a different circuit. Temperature-dependent spectral weight and finite frequency coverage must also be tested before assigning a lifetime from the total d.c. curve.

Evidence: theory. Sources: source-05b2d5ff6757b5eb.

Conditions: Fit window, residual subtraction, lifetime convention, angular superconducting exclusions and source version remain explicit.

Verification scope: Selected primary texts and figures plus independent synthetic identifiability checks; full scientific acceptance remains open.

### scwiki-h1-claim-experimental-criteria-1

Grissonnanche and colleagues measured angle-dependent magnetoresistance in Nd-LSCO at hole concentration $p=0.24\pm0.005$. The sample's zero-resistance transition is 11 K; the transport measurements use 45 T at 6, 12, 20 and 25 K. At the two lower temperatures, some field orientations still enter a superconducting region. A high field alone therefore does not certify that every angular data point is normal-state transport.

Evidence: experiment. Sources: source-374c8bc13ced83e8.

Conditions: Fit window, residual subtraction, lifetime convention, angular superconducting exclusions and source version remain explicit.

Verification scope: Selected primary texts and figures plus independent synthetic identifiability checks; full scientific acceptance remains open.

### scwiki-h1-claim-experimental-criteria-2

Their fit separates a temperature-independent anisotropic contribution from an isotropic temperature-dependent rate, giving $\alpha=1.2\pm0.4$ in $\hbar/\tau_{\mathrm{inel}}=\alpha k_BT$. Total scattering is not isotropic. The analysis uses a bandwidth scale $160\pm30$ meV constrained by specific heat and omits a low-temperature correction that could change it by about 20% at 6 K. Temperature stability of ±1 mK differs from absolute uncertainty of approximately ±1 K at 6 and 12 K. These qualifications belong with the extracted coefficient.

Evidence: experiment. Sources: source-374c8bc13ced83e8.

Conditions: Fit window, residual subtraction, lifetime convention, angular superconducting exclusions and source version remain explicit.

Verification scope: Selected primary texts and figures plus independent synthetic identifiability checks; full scientific acceptance remains open.

### scwiki-h1-claim-experimental-criteria-3

Romero and colleagues resolve a narrower Drude channel and a broad background in two FeTe1−xSex films. The final abstract associates most condensate spectral weight with the narrower channel. In the checked author version, the scattering-rate fits use 20–40 K, and linewidths below the approximately 0.2 THz measurement limit cannot be resolved directly. Its frequency variable uses cycles per second, so $h$ appears in $\Gamma=\Gamma_0+\alpha k_BT/h$; an angular-frequency rate instead uses $\hbar$. A fitted spectral decomposition is stronger evidence than assigning a lifetime from total resistance alone, but it does not uniquely determine the pairing interaction.

Evidence: experiment. Sources: source-05b2d5ff6757b5eb.

Conditions: Fit window, residual subtraction, lifetime convention, angular superconducting exclusions and source version remain explicit.

Verification scope: Selected primary texts and figures plus independent synthetic identifiability checks; full scientific acceptance remains open.

### scwiki-h1-claim-experimental-criteria-4

Cooper and colleagues report that a low-temperature linear contribution extends over a range of LSCO dopings and tracks superconductivity. The checked abstract supports that association, not a reanalysis of its numerical curves. Magic-angle graphene measurements provide another material setting with nearly linear transport; a similar temperature exponent across systems does not prove identical scattering or pairing mechanisms. Material geometry, filling and fit assumptions must accompany cross-system comparisons.

Evidence: experiment. Sources: source-1610fd228e679225, source-8135909144b6b16b.

Conditions: Fit window, residual subtraction, lifetime convention, angular superconducting exclusions and source version remain explicit.

Verification scope: Selected primary texts and figures plus independent synthetic identifiability checks; full scientific acceptance remains open.

### scwiki-h1-claim-limits-and-disputes-1

The marginal-Fermi-liquid proposal organizes anomalies using an assumed charge- and spin-response spectrum. Its phenomenological success would not identify a unique microscopic origin. The original article has an erratum; this review records the correction's identity but has not independently read its contents, and therefore does not reproduce a supposedly corrected derivation. Quantum critical, incoherent-metal and phonon-based explanations require separate discriminating evidence rather than a choice made from one resistivity exponent.

Evidence: hypothesis. Sources: source-5880a61b06ec84e6, source-2cdc898b9c5e504c, source-374c8bc13ced83e8.

Conditions: Fit window, residual subtraction, lifetime convention, angular superconducting exclusions and source version remain explicit.

Verification scope: Selected primary texts and figures plus independent synthetic identifiability checks; full scientific acceptance remains open.

### scwiki-h1-claim-limits-and-disputes-2

Complete scientific acceptance remains open. Selected final passages and figures have been checked, but full version comparisons and raw-data fits remain incomplete. A slope correlation with superconductivity does not establish causation, and a channel contributing to the condensate does not identify the interaction binding its electrons. Retain alternative explanations and distinguish an experimental observable from quantities inferred through a model.

Evidence: hypothesis. Sources: source-1610fd228e679225, source-05b2d5ff6757b5eb.

Conditions: Fit window, residual subtraction, lifetime convention, angular superconducting exclusions and source version remain explicit.

Verification scope: Selected primary texts and figures plus independent synthetic identifiability checks; full scientific acceptance remains open.

### scwiki-h1-claim-discovery-implications-1

Compare transport, spectroscopy and superconducting response on well-characterized samples, with field, geometry and temperature windows recorded. Use independent changes in disorder, pressure or filling to test whether a proposed scattering process also controls pairing. A useful discovery claim predicts an observable change and survives alternative fits; simply finding another straight resistivity curve adds a candidate observation, not a complete microscopic explanation.

Evidence: hypothesis. Sources: source-c1ae7869b672a8e8, source-8135909144b6b16b, source-05b2d5ff6757b5eb.

Conditions: Fit window, residual subtraction, lifetime convention, angular superconducting exclusions and source version remain explicit.

Verification scope: Selected primary texts and figures plus independent synthetic identifiability checks; full scientific acceptance remains open.

## Revision and review

Article ID: scwiki-h1. Revision: fdf02bc0add09640378c. Updated: 2026-10-18T16:26:45.370525+00:00.

Review scope: Selected final Nd-LSCO methods and Figure 2, Romero author methods and Figure 3 with final abstract, inherited graphene evidence, primary abstracts and independent synthetic fit checks.

- Complete scientific acceptance remains open.
- Full raw-data fits, wider competing literature and final-version comparisons remain incomplete.
- Cooper evidence is abstract-level here; Varma erratum identity is recorded without claiming its contents were checked.
- Synthetic exponents and fitting windows do not establish a microscopic mechanism or quantum critical point.

Source: [H_anomalous_normal_state/H1_strange_metal_linear_T.md](https://github.com/JackZH26/jzis-superconductivity/blob/0a7c9d6696804ec26aa12f8eed68b55c9b3c0fcf/H_anomalous_normal_state/H1_strange_metal_linear_T.md), commit 0a7c9d6696804ec26aa12f8eed68b55c9b3c0fcf, SHA-256 d5c5f605dcb2d5fe7ea2eb72ba5530c10f3938d54760cba6d33d9656651bfc39.