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Researchers measured how heat and charge move in a narrow gallium arsenide (GaAs) device and found that the usual link between thermal and electrical conductivity breaks down. Using micrometer-resolution photoluminescence (PL) thermometry, they tracked the temperature of “hot” electrons along a mesoscopic two-dimensional channel and extracted a temperature-dependent Lorenz number. A Lorenz number that departs from the standard Sommerfeld value is a direct sign that the Wiedemann–Franz (WF) law does not hold in this device.
The WF law says that, at low temperatures, the ratio of electronic thermal conductivity to electrical conductivity is universal. That ratio is expressed by the Lorenz number. The experiments target a hydrodynamic regime of electron transport. In that regime electron–electron (e–e) collisions happen much more often than collisions that relax momentum (for example with impurities). E–e collisions conserve total momentum but redistribute energy between electrons. As a result, heat flow can be relaxed while charge flow is not, and the WF law can fail.
The device was a high-mobility GaAs quantum well that hosts a two-dimensional electron gas. The authors created hot electrons by sending a transverse current through potentiometric contacts so that heating occurs in a narrow region. They measured the local electron temperature by fitting the high-energy tail of the photoluminescence spectrum. Because the optical probe maps temperature with micrometer resolution and heating is local, the team could build temperature profiles along the channel and use a one-dimensional heat-balance equation to extract the Lorenz number without driving charge and heat in parallel.
The measurements show clear, temperature-dependent deviations of the Lorenz number from the standard WF value. The experiments also highlight the strong role of narrow constrictions in enhancing the violation. The authors present a simple theoretical model that combines e–e scattering and boundary effects in a mesoscopic geometry. In the studied temperature range Poiseuille-like flow is not fully developed, and a “bulk” form of the Lorenz ratio (which accounts for the separate relaxation times of charge and heat) gives better agreement with the data. The paper also notes that Lorenz numbers extracted from hot-electron, nonequilibrium temperature profiles can differ from those inferred using relaxation times measured in thermal equilibrium.
The work has important caveats. The analysis assumes weak heating so that temperature dependence of conductivity and the Lorenz number can be neglected in the fitting. The extraction of the Lorenz number depends on assumptions about electron–phonon cooling and on relaxation times that can differ between nonequilibrium and equilibrium conditions. The authors also stress that their results apply in a mesoscopic regime where the device width sits between the electron–electron interaction length and the mean free path, and that Poiseuille flow is not fully developed in their samples. Despite these limitations, the study provides direct optical evidence that hydrodynamic electron behavior in a conventional semiconductor (GaAs) can lead to violations of the Wiedemann–Franz law, a result previously explored mostly in graphene.