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Low-dimensional transport in semiconductor meso- and nanostructures is a topical field of fundamental research with potential applications in future quantum devices. However, thermal non-equilibrium may destroy phase-coherence and remains to be explored experimentally. Here, we present effects of thermal non-equilibrium in various implementations of low-dimensional (non-interacting) electron systems, fabricated by etching AlGaAs/GaAs heterostructures. These include narrow quasi-two-dimensional (2D) channels, quasi-one-dimensional (1D) waveguide networks, quantum rings (QRs), and single 1D constrictions, such as quantum point contacts (QPCs). Thermal non-equilibrium is realized by current heating. The charge carrier temperature is determined by noise thermometry. The electrical conductance and the voltage–noise are measured with respect to bath temperatures, heating currents, thermal gradients, and electric fields. We determine and discuss heat transport processes, electron-energy loss rates, and electron–phonon interaction, and our results are consistent with the Wiedemann–Franz relation. Additionally, we show how non-thermal current fluctuations can be used to identify electric conductance anomalies due to charge states.

Cross-correlated noise measurements are performed in etched Al x Ga 1 − xAs/GaAs based quantum rings in equilibrium at a bath temperature of T bath = 4.2 K. The measured white noise exceeds the thermal (Johnson–Nyquist) noise expected from the measured electron temperature T e and the electrical resistance R. This excess part of the white noise decreases as T bath increases and vanishes for T bath ≥ 12 K. Excess noise is neither observed if one arm of a quantum ring is depleted of electrons nor in one-dimensional-constrictions that have a length and width comparable to the quantum rings. A model is presented that suggests that the excess noise originates from the correlation of noise sources, mediated by phase-coherent propagation of electrons.

Cross-correlated measurements of thermal noise are performed to determine the electron temperature in nanopatterned channels of a GaAs/AlGaAs heterostructure at 4.2 K. Two-dimensional (2D) electron reservoirs are connected via an extended one-dimensional (1D) electron waveguide network. Hot electrons are produced using a current $I_{\text{h}}$ in a source 2D reservoir, are transmitted through the ballistic 1D waveguide and relax in a drain 2D reservoir. We find that the electron temperature increase ${\Delta}T_{\text{e}}$ in the drain is proportional to the square of the heating current $I_{\text{h}}$, as expected from Joule's law. No temperature increase is observed in the drain when the 1D waveguide does not transmit electrons. Therefore, we conclude that electron-phonon interaction is negligible for heat transport between 2D reservoirs at temperatures below 4.2 K. Furthermore, mode control of the 1D electron waveguide by application of a top-gate voltage reveals that ${\Delta}T_{\text{e}}$ is not proportional to the number of populated subbands $N$, as previously observed in single 1D conductors. This can be explained with the splitting of the heat flow in the 1D waveguide network., Comment: 4 pages, 4 figures

We study in experiment and theory thermal energy and charge transfer close to the quantum limit in a ballistic nanodevice, consisting of multiply connected one-dimensional electron waveguides. The fabricated device is based on an AlGaAs/GaAs heterostructure and is covered by a global top-gate to steer the thermal energy and charge transfer in the presence of a temperature gradient, which is established by a heating current. The estimate of the heat transfer by means of thermal noise measurements shows the device acting as a switch for charge and thermal energy transfer. The wave-packet simulations are based on the multi-terminal Landauer-Büttiker approach and confirm the experimental finding of a mode-dependent redistribution of the thermal energy current, if a scatterer breaks the device symmetry.