K. Norowski, M. Foltyn, A. Savin, M. Zgirski, arXiv:2411.16614 (2024)
Abstract: We use time-resolved thermometry to monitor the decay of nonequilibrium quasiparticles (QPs) in superconducting aluminum in the temperature range from 0.3 K to 1.2 K. The quasiparticle lifetime at higher temperatures (T > 0.7 K) agrees well with the calculated energy flow from electrons to phonons, but at lower temperatures it is significantly shorter than the theory predicts. We show well-defined internal equilibrium of quasiparticle system in the studied thermal transients, which implicates that quasiparticle-quasiparticle relaxation is much faster than electron-phonon interaction.
Our presentation is the most comprehensive treatment of QP relaxation in a superconducting aluminum available in the literature. It combines state-of-the-art experimental measurements of dynamical thermal transients in a broad temperature range with a thorough comparison of the obtained results against the existing theoretical predictions. The knowledge of QPs dynamics is critical for proper understanding of almost any kind of superconducting devices, involving qubits, SQUIDs, single electron boxes, single photon detectors and NIS microcoolers. Our work is the first to adapt fully thermodynamical approach in the relaxation of QPs in a superconductor.
We address the dynamics of electron-electron interaction in the superconducting state, which has not been studied experimentally so far for lack of sufficiently fast nanothermometers. The measurements point to the existence of quasi-equilibrium within an energy-relaxing QP system in a superconducting state, allowing to assign to the QPs a well-defined temperature during relaxation process. Our experiment is the first to touch this issue and as such opens a new field of investigations of electron-electron interaction and associated non-equilibrium states in superconducting nanostructures.
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Fig. 1. Quasiparticle relaxation time τqp versus bath temperature T0. Measurements (filled dots), literature data (open dots) and theoretical prediction resulting exclusively from electron-phonon coupling in the linear regime (solid orange line). Curves displaying relaxation time below 10 µs for T0 > 0.3 K are results measured by us for nanowires of various lengths L. The data presenting τqp larger than 10 µs for T0 < 0.32 K are extracted from literature. Adapted from arXiv:2411.16614 (2024). |
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Fig. 2. The comparison of the switching probability dependencies (so called S curves) collected in the static and dynamic measurements. The main panel shows the temporal trace of the switching probability after exciting electrons with a short heating pulse at delay = 0. The inset shows the dynamic S curves (open squares), collected for various delays corresponding to points A, B, C and D of the main trace, as assigned to the static S curves (filled circles) measured at the fixed bath temperatures displayed on the labels. If to assume that S curve is a unique fingerprint of quasiparticle occupation, the remarkable coincidence of the dynamic and static S curves implicates well-defined thermodynamic temperature of the electron gas overheated with respect to the lattice during thermal transient. The inset shows pulse sequence used to perform relaxation experiment: the pulse testing a nanobridge (blue) is delayed with respect to the heating pulse (red). |