Non-Fermi Liquids: Evidence and Discriminating Tests

Non-Fermi-liquid research studies metallic states for which the quasiparticle description fails or gives an incomplete low-energy account. The practical question is which observation diagnoses that failure and which microscopic mechanism explains it. Linear resistivity alone does not uniquely identify either a non-Fermi liquid or a universal dissipation bound.

Helpful background. Non-Fermi liquids supplies the conceptual distinctions; quantum criticality explains one route to anomalous metallic behavior.

A transport time is not every relaxation time

A simple Drude interpretation writes

$$\rho=\frac{m^\ast}{ne^2\tau_{\rm tr}}, \qquad \tau_{\rm Pl}=\frac{\hbar}{k_BT}.$$

Inferring $\tau_{\rm tr}$ from resistivity requires assumptions about carrier density, effective mass, and transport channels. A single-particle spectral lifetime, a momentum-relaxation time, and a many-body equilibration time need not agree.

Established: many metals exhibit temperature dependences and spectral responses that challenge simple quasiparticle descriptions. Active: explain common transport patterns and their relation to quantum criticality, disorder, and interactions. Conjectural: a universal Planckian bound applying to every time inferred from every transport fit. Hartnoll and Mackenzie explicitly distinguish the relevant time scales.

Conventional phonon scattering can also produce nearly linear resistivity in appropriate regimes. A scaling form should therefore be tested against a physical alternative, not only against a polynomial.

Competing theoretical routes

Quantum-critical metals couple fermions to collective fluctuations. Solvable large-parameter models expose mechanisms of incoherence but require a careful connection to finite-parameter materials. Hydrodynamic or memory-based approaches emphasize slow conserved quantities and momentum relaxation. Disorder and spatial inhomogeneity can alter transport without the same microscopic quasiparticle physics.

The meaningful comparison is between multiple observables predicted with one parameter set: dc and optical conductivity, thermodynamics, Hall response, or spectroscopy. A model flexible enough to fit each separately has weaker explanatory power.

Starter project: audit a Planckian inference

Generate or use a documented transport dataset with independent estimates of density and mass. Propagate their uncertainty into the inferred dimensionless rate $\hbar/(k_BT\tau_{\rm tr})$. Compare a constant-density Drude extraction with a model allowing a temperature-dependent carrier contribution.

Deliver uncertainty bands, sensitivity to residual-resistivity subtraction, and a comparison with an explicit phonon or multiband baseline. A laptop suffices for the inference study. The failure test is a claimed universal coefficient that changes substantially under independently plausible mass, density, or background assumptions.

Extend to research by combining optical spectral weight with dc transport to reduce the degeneracy, or by designing a joint fit whose parameters predict an unused observable. Report when data cannot distinguish microscopic mechanisms.

Open questions and scope

Which response functions reveal the disappearance of quasiparticles most directly? When do apparently similar transport laws arise from different slow modes? How does superconductivity mask the normal state’s lowest-temperature regime?

A first project should avoid promising a theory of all strange metals. Choose a material family or controlled model and one falsifiable relation. Unconventional superconductivity addresses the adjoining pairing problem.

Entry points and evidence horizon

Hartnoll and Mackenzie is the entry review for terminology and time-scale distinctions. Its evidence horizon is 2022; links were checked on 2026-10-11. New material-specific claims require additional primary sources.

References

• Hartnoll, S. A., and Mackenzie, A. P., “Colloquium: Planckian dissipation in metals,” Reviews of Modern Physics 94, 041002 (2022), arXiv:2107.07802.