· essay
A law from 1853, broken this month
In ultraclean graphene, heat and charge have come uncoupled by more than two hundred times — and with them, one of the oldest relations in metal physics.
Take a sheet of graphene — one atom thick, carbon — and sandwich it between two flakes of hexagonal boron nitride so the sheet doesn't touch the rest of the world. Cool it down. Tune the carrier density, with a voltage on a gate beneath, to the exact point at which electrons and holes exist in equal numbers and the conductivity is as low as it will go. This is the Dirac point, named because the excitations there obey an equation Dirac wrote in 1928 for relativistic electrons. Now, at the same time, in the same device, measure how well the sheet carries electric current and how well it carries heat.
The electrical conductivity goes up; the thermal conductivity goes down. Electrical goes down; thermal goes up. They are, to a good approximation, decoupled.
This is not what was supposed to happen. For 170-odd years, one of the quieter load-bearing equations of solid-state physics has insisted that the two conductivities are proportional. Gustav Wiedemann and Rudolph Franz noticed it first in 1853, measuring a bench full of metals for the Annalen der Physik: the ratio of heat to electrical conductivity, κ/σ, came out about the same for different metals at the same temperature.[^1] In 1872 the Danish physicist Ludvig Lorenz (not the Dutch Lorentz — a different man) added that the ratio is proportional to temperature, so that κ/σT is a constant — the Lorenz number. When quantum mechanics arrived, Sommerfeld derived the value from first principles: L₀ = (π²/3)(k_B/e)² ≈ 2.44 × 10⁻⁸ V²/K². The derivation is short. You assume the same particles carry both the charge and the heat, and that they scatter elastically. You get the number.
A group at the Indian Institute of Science in Bangalore, working with the National Institute for Materials Science in Japan, reported last year — and the news cycle has picked up again this week — that in their graphene samples, near the Dirac point and at low temperatures, the Lorenz number deviates from its textbook value by a factor of more than two hundred.[^2] Not fifty percent; not a factor of five. Two hundred.
The interesting sentence is not "law broken." It is: the assumptions the law is built on don't apply here.
At the Dirac point, there is no Fermi sea to speak of. There are equal populations of electrons and holes, strongly coupled through Coulomb repulsion; the energy of an excitation is set by temperature, not by a Fermi energy. In that regime, electron-electron collisions happen faster than collisions with the lattice, and the carriers stop behaving like independent particles. They behave collectively, like a fluid. A relativistic fluid of massless fermions — a Dirac fluid. What does that do to conductivity? A charge current requires the electrons and holes to move in opposite directions, and they scatter off each other, so the charge current is strongly damped. A heat current does not require opposite motion — everyone can drift the same way — so it flows almost freely. Charge transport suffers; heat transport does not. The Lorenz number collapses.
The other place in physics where a strongly-interacting relativistic fluid of charged fermions shows up is the quark–gluon plasma, the brief soup that appears when heavy nuclei are smashed together at CERN. It has been famous since the 2000s for being a near-perfect fluid, with a shear viscosity to entropy density ratio η/s close to the lower bound ℏ/(4πk_B) proposed from string-theoretic arguments. The Dirac fluid in graphene sits near the same bound. This is not a metaphor. The equations of relativistic hydrodynamics that describe the two systems are the same equations. One of them sits on a silicon wafer in a low-temperature cryostat; the other sits, for a few yoctoseconds, in a cavern fifty-six meters under the Franco-Swiss border.
Laws in physics, except for a few stubborn ones, are not commandments — they are descriptions of regimes. The Wiedemann-Franz law still holds, beautifully, where metals behave like metals. What the graphene measurement does is draw a boundary around it: on the far side, the assumption of independent carriers with elastic scattering fails, and the number that was 2.44 × 10⁻⁸ turns into something smaller by two hundred. Finding the edge of a law is not the same as losing one. It tells us where we had been describing the world a little too coarsely, and what the finer description looks like when the first one runs out.
[^1]: Wiedemann and Franz, "Ueber die Wärme-Leitungsfähigkeit der Metalle," Annalen der Physik 165 (1853), 497–531. [^2]: Majumdar et al., "Universality in quantum critical flow of charge and heat in ultraclean graphene," Nature Physics (2025), DOI 10.1038/s41567-025-02972-z. Press re-reports here (ScienceDaily, 15 April 2026) and here (Phys.org, 1 September 2025).