Researchers measured how hot electrons carry heat inside a narrow, high-quality gallium arsenide (GaAs) channel and found that the usual rule linking heat and electrical conductance does not hold. That rule, the Wiedemann–Franz law, says the ratio of thermal conductivity to electrical conductivity should be a fixed number (the Lorenz number) at low temperatures. In this experiment the Lorenz number changed with temperature, signaling a violation of that law in the hydrodynamic, mesoscopic regime of electron flow.

The team made a mesoscopic channel in a GaAs quantum well and heated the electrons locally by running a transverse current (local Joule heating). They measured the local electron temperature with micrometer-resolution photoluminescence (PL) thermometry. In PL thermometry the high-energy tail of light emitted when electrons and holes recombine is fitted to infer the electron temperature. By scanning along the channel they obtained temperature profiles for different heating currents and sample temperatures (data shown for temperatures down to 4 K).

The key physics is that in the hydrodynamic regime electron–electron (e–e) collisions happen much more often than collisions that relax momentum, such as impurity or phonon scattering. Electron–electron collisions conserve the total momentum of the electron system, so they do not relax the electrical current. However, they do redistribute energy among electrons and thus relax directed heat flow. That difference means heat and charge can behave very differently, producing a reduced Lorenz number. In a narrow, mesoscopic channel the device boundaries also matter: viscous effects introduce another time scale (related to the channel width) that affects charge and heat in different ways.

Quantitatively, the experiments show a temperature-dependent Lorenz number and stronger deviations in the presence of narrow constrictions. The authors compare these measurements to a theoretical model that includes both electron–electron scattering and boundary-induced viscous effects. Their analysis indicates that, in the temperature range studied, the channel is not yet in the full Poiseuille (viscous) flow limit, but the two distinct relaxation times for momentum and heat are enough to produce clear departures from the Wiedemann–Franz expectation.