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We investigate the impact of transport current on the superconducting orderparameter in superconducting islands in full-shell epitaxial Al-InAs nanowires.Depending on a device layout, the suppression of superconductivity occurs inthree fundamentally different ways -- by a critical current in the case ofsuperconducting reservoirs and by a critical voltage or by a critical Joulepower in the case of normal reservoirs. In the latter case, the collapse of thesuperconducting state depends on the ratio of the dwell time and theelectron-phonon relaxation time of quasiparticles in the island. For lowresistive and high resistive coupling to the reservoirs, respectively, therelaxation-free regime and the strong electron-phonon relaxation regime arerealized. Our results shed light on potential shortcomings of finite-biastransport spectroscopy in floating islands.

Fate of the superconducting state in floating islands of hybrid nanowire devices