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Photoluminescence spectroscopy maps electron temperature in GaAs channels, revealing deviations from classical heat transport. The study confirms Wiedemann–Franz law violation, advancing understanding of nanoscale thermal transport mechanisms.
Study: Spectroscopy of heat transport and violation of the Wiedemann-Franz law in GaAs hydrodynamic mesoscopic channel. Image Credit: H_Ko/Shutterstock
In a recent article published in the journal Scientific Reports, researchers investigated heat transport in a narrow GaAs mesoscopic channel with high-mobility two-dimensional (2D) electrons, emphasizing the breakdown of the Wiedemann-Franz (WF) law in the hydrodynamic transport regime.
Wiedemann–Franz Law
In metals and degenerate semiconductors at low temperature, electrons govern both electrical and thermal transport, usually following the WF law. This is based on the assumption that both heat and charge are carried by the same quasiparticles with equivalent scattering mechanisms. In the hydrodynamic regime, where momentum-conserving electron-electron (e-e) collisions prevail, thermal and electrical currents relax differently.
To date, GaAs quantum wells are promising platforms for studying hydrodynamics and WF violation because of their ultra-high mobility and well-understood semiconductor properties. Despite numerous successes in demonstrating hydrodynamic charge flow in GaAs, optical methods to spatially resolve electron temperature and directly probe heat transport in GaAs mesoscopic channels remain underexplored. Addressing this gap, the study applies photoluminescence (PL) spectroscopy as a non-invasive, high-resolution thermometer for the electron system.
Using Light to Measure Electron Temperature: Experimental Approach
The authors fabricated a mesoscopic Hall bar device from a single 14 nm thick GaAs quantum well grown by molecular beam epitaxy. The 2D electron gas had a density of approximately 9.1 × 1011 cm-2 and an ultra-high mobility of 2.0 × 106 cm2/Vs at 1.4 K. The channel width was 5 μm, and the length was 100 μm. Electron heating was introduced by applying an electric current perpendicular to the channel through potentiometric contacts, generating localized hot-electron regions.
Electron temperature profiles were measured using spatially resolved PL spectroscopy with micrometer precision. A 730 nm (1.7 eV) laser was tightly focused to a ~1 μm spot and scanned along the channel at temperatures ranging from 4 to 50 K. The underlying principle is that the high-energy tail of the optical emission from the GaAs quantum well depends sensitively on the electron and hole distributions, which thermalize to a common temperature. By fitting the spectral shape of the PL high-energy edge, the electron temperature could be extracted with high spatial resolution.
This approach provides a direct optical thermometer for hot electrons without the complications of electrical noise or contact effects. The PL spectra exhibit a narrow exciton-bound donor peak near 1.515 eV, with a broader high-energy tail whose form depends on electron temperature. By carefully modeling recombination and carrier distributions based on a degenerate semiconductor model, the authors extract local electron temperatures from these spectral shapes.
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Electron Behavior Revealed by Temperature Profiles
The PL thermometry measurements revealed distinct spatial profiles of electron temperature along the hydrodynamic GaAs channel. Hot electrons generated near the current-injection contacts exhibited temperature gradients with relaxation lengths on the order of tens of micrometers. These profiles showed deviations from simple diffusive heat transport, consistent with theoretical expectations for hydrodynamic heat flow where e-e collisions are frequent.
Fitting the measured electron temperature profiles using the heat transfer equation allowed determination of an effective Lorenz number that characterizes the ratio of thermal to electrical conductivity. The extracted Lorenz numbers showed a strong temperature dependence and were significantly lower than the standard Sommerfeld value predicted by the WF law. This suppression confirms the anticipated violation of the WF law in this hydrodynamic regime.
The experimental optical measurements demonstrated that thermal currents relax more effectively than charge currents due to e-e scattering in the mesoscopic channel. Moreover, the role of boundaries became evident: while boundary scattering enhances electrical conductivity via electron viscosity effects (the Gurzhi effect), it does not similarly affect thermal conductivity, accentuating the violation. A simple theoretical model incorporating momentum relaxation, e-e scattering, and diffusive boundary scattering reproduced the main features of the Lorenz ratio data.
Comparing the Lorenz ratios extracted from PL thermometry with those derived from magnetotransport measurements revealed some discrepancies. These were attributed to differences between conditions during electron heating and equilibrium temperature measurements. The PL spectroscopy technique effectively averages over a hot electron ensemble, while magnetotransport probes electrons equilibrated with the lattice. Adjusting temperature scales to account for this led to good agreement between the optical and electrical data.
Implications for Future Nanoscale Heat Transport Studies
This study successfully demonstrated the application of photoluminescence spectroscopy as a precise and spatially resolved optical thermometer for hot electrons in a GaAs mesoscopic channel. The combination of optical temperature profiling and transport measurements, supported by a theoretical model including boundary scattering and hydrodynamic viscosity, provided a consistent framework to understand heat transport beyond classical diffusive regimes.
Beyond fundamental insights, the optical technique offers advantages over traditional electrical or noise-based thermometry, including minimal disturbance to the system and the ability to spatially map temperature distributions. This work thus paves the way for future studies using optical methods to probe mesoscopic and nanoscale energy transport in low-dimensional electronic materials.
Journal Reference
Pusep Y.A., Patricio M.A.T., et al. (2026). Spectroscopy of heat transport and violation of the Wiedemann-Franz law in GaAs hydrodynamic mesoscopic channel. Scientific Reports. DOI: 10.1038/s41598-026-45858-7, https://www.nature.com/articles/s41598-026-45858-7