Proximity effects and nonequilibrium superconductivity in transition-edge sensors

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Abstract
We have recently shown that normal-metal/superconductor (N/S) bilayer superconducting transition-edge sensors (TESs) exhibit weak-link behavior.[1] Here, we extend our understanding to include TESs with added noise-mitigating normal-metal structures (N structures). We find that TESs with added Au structures also exhibit weak-link behavior as evidenced by the exponential temperature dependence of the critical current and Josephson-like oscillations of the critical current with applied magnetic field. We explain our results in terms of an effect converse to the longitudinal proximity effect (LoPE),[1] the lateral inverse proximity effect (LaiPE), for which the order parameter in the N/S bilayer is reduced due to the neighboring N structures. Resistance and critical current measurements are presented as a function of temperature and magnetic field taken on square Mo/Au bilayer TESs with lengths ranging from 8 to 130 $\mu${}m with and without added N structures. We observe the inverse proximity effect on the bilayer over in-plane distances many tens of microns and find the transition shifts to lower temperatures scale approximately as the inverse square of the in-plane N-structure separation distance, without appreciable broadening of the transition width. We also present evidence for nonequilbrium superconductivity and estimate a quasiparticle lifetime of 1.8\ifmmode\times\else\texttimes\fi{}10$-${}10 s for the bilayer. The LoPE model is also used to explain the increased conductivity at temperatures above the bilayer's steep resistive transition.
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