"The Moving Road"

The Wiedemann-Franz law says the ratio of thermal to electrical conductivity is proportional to temperature, with a universal constant — the Lorenz number. It works because the same electrons carry both charge and heat. Same carriers, same scattering, proportional transport.

This paper identifies a clean mechanism for its violation: the electronic band structure shifts with temperature.

In interacting electron systems, the quasiparticle energy depends on temperature. The derivative of this energy with respect to temperature is nonzero — meaning the band structure itself drifts as the system heats or cools. This energy drift acts as an effective driving force on heat transport that has no counterpart in charge transport.

Charge responds to electric fields. Heat responds to temperature gradients. But when the bands move with temperature, heat transport acquires an extra push — the carriers are driven not just by the gradient but by the changing landscape through which they move. Charge carriers feel no such push, because electric fields don’t shift the bands.

The result: heat and charge decouple. The Lorenz ratio deviates from its universal value by an amount directly connected to the system’s thermoelectric response.

The authors propose using the Lorenz ratio as a diagnostic — its deviation fingerprints the nature of electron interactions and can distinguish topological robustness from Fermi liquid instabilities.

The structural insight: when the road itself moves, travelers with different sensitivities to the road are affected differently. Heat feels the shifting bands. Charge doesn’t. The universality of the Wiedemann-Franz law rests on the assumption that the landscape is static. Interactions make it dynamic.