Probing the local temperature of a two-dimensional electron gas microdomain with a quantum dot: Measurement of electron-phonon interaction

The analysis of the performance and the very understanding of the physical mechanisms governing the behavior of nanostructured devices requires the detailed knowledge of all parameters of electronic systems confined in ever shrinking microdomains. The role of temperature and the investigation of heat transport in solidstate nanoscale systems are currently under the spotlight [1]. Electronic thermometers [2‐4], refrigerators [5‐8] and heat transistors [9] based on metallic and superconductor nanostructures were already demonstrated. Such devices are typically operated at subkelvin temperatures, where electron-phonon interaction is weak and, as a result, the relevant electronic temperature may significantly dier from that of the lattice (if at all defined). In this context, the ability to perform local measurements of the electronic temperature becomes highly desirable. While in metallic systems superconducting tunnel junctions are routinely employed for this purpose, for the case of two-dimensional electron gases (2DEGs) or semiconductor nanowires at thermal equilibrium, quantum dots (QDs) were shown to be suitable for absolute thermometry [10, 11], due to the fact that in these conditions the linewidth of zero-bias Coulomb blockade (CB) peaks in the weak-coupling regime is directly related to the electronic temperature of the leads. Here, we propose a method for the detection of the local electronic temperature in a 2DEG, based on the analysis of the CB-peak lineshape. We shall first discuss zero-bias transport through a weakly-coupled QD in the presence of a temperature bias and show that zerobias conductance measurements can be used to experimentally determine both temperature values. We shall then employ this technique to investigate energy relaxation mechanisms in an electronic microdomain defined electrostatically in a GaAs/AlGaAs heterostructure and heated by an externally-driven current. The domain is connected to the surrounding 2DEG regions through the QD and three quantum point contacts (QPCs). As a known heating power is delivered to the domain, conductance across the QD is probed and the steady-state temperature detected. The dependence of the measured electron temperature on heating power will also be studied for dierent values of the QPC resistances: as the coupling to the surrounding 2DEG regions is reduced, we observe the crossover from a regime where excess heat is carried away by hot quasiparticles tunneling through the QPCs to one where power exchange with lattice phonons dominates. We shall show that the latter mechanism follows the T 5 power law expected [12] for the screened electron-acoustic phonon piezoelectric interaction, and obtain a measurement of the relative coupling constant consistent with theoretical estimates [1, 13].

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