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Understanding heating and cooling mechanisms in mesoscopicsuperconductor-semiconductor hybrid devices is crucial for their application inquantum technologies. Owing to the poor thermal conductivity of typicaldevices, heating effects can drive superconducting-to-normal phase transitionseven at low applied bias, observed as sharp conductance dips through the lossof Andreev excess currents. Tracking such dips across magnetic field, cryostattemperature, and applied microwave power, which constitutes Joule spectroscopy,allows to uncover the underlying cooling bottlenecks in different parts of adevice. By applying this technique, we analyze heat dissipation in devicesbased on full-shell InAs-Al nanowires and reveal that superconducting islandsare strongly susceptible to heating as their cooling is limited by the ratherinefficient electron-phonon coupling, as opposed to grounded superconductorsthat primarily cool by quasiparticle diffusion. Our measurements indicate thatpowers as low as 50-150 pW are able to fully suprpress the superconductivity ofan island. Finally, we show that applied microwaves lead to similar heatingeffects as DC signals, and explore the interplay of the microwave frequency andthe effective electron-phonon relaxation time.

Heat dissipation mechanisms in hybrid superconductor-semiconductor devices revealed by Joule spectroscopy