Did you know that ultraclean graphene is not the only material (or the first) to deviate from the Wiedemann–Franz (WF) law? Deviations have been observed in many other materials and systems for over a decade.
Here are some earlier examples (many predating 2025):
- Graphene itself (2016 Science paper, Crossno et al.): Breakdown of WF law in doped graphene due to hydrodynamic electron flow, with deviations by factors of ~10–20 in some regimes.
- Vanadium dioxide (VO₂) nanobeams (2016–2017): Electronic thermal conductivity ~10× smaller than WF prediction near the insulator-metal transition; electrons carry charge but not heat effectively. Often called a “first” at the time, but other violations were already known.
- Quasi-1D Luttinger liquid (lithium molybdenum purple bronze, Li₀.₉Mo₆O₁₇, 2011): Hall thermal/electrical conductivity ratio diverges by up to five orders of magnitude due to spin-charge separation.
- Weyl semimetals (e.g., WP₂ in 2018; topological compensated semimetals like TaAs₂ or similar, 2025): Large downward deviations and T⁴ thermal conductivity behavior at ultralow temperatures.
- MXenes (Ti₃C₂Tₓ flakes, 2024): Effective Lorenz number only ~0.25× the classical value, with ultralow anisotropic thermal conductivity.
- Heavy-fermion compounds (e.g., CeCoIn₅, UPt₃), cuprates, Heusler alloys, and thin gold films: Violations driven by electron-electron scattering, quantum criticality, or reduced dimensionality—sometimes drastic and temperature-dependent.
Deviations can be upward (L ≫ L₀, as in the new graphene) or downward (L ≪ L₀) and are now a diagnostic tool for non-Fermi-liquid behavior rather than a shocking anomaly.