Strange metals and linear-temperature resistivity

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 R2 R4

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 R4 R6

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 R3

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

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

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

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

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

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

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 R5

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 R8 R4

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 R6

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 R5 R6

Related topics

Linear-T resistivity, Planckian dissipation, and 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.