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The sensitivity of a low-noise superconducting transition edge sensor (TES)is determined by the thermal conductance of the support structure that connectsthe active elements of the device to the heat bath. Low-noise devices requireconductances in the range 0.1 to 10 pWK$^{-1}$, and so have to rely ondiffusive phonon scattering in long, narrow, amorphous SiN$_\text{x}$ legs. Weshow that it is possible to manufacture and operate TESs having short,ballistic low-dimensional legs (cross section 500$\times$200 nm) that containmulti-element phononic interferometers and ring resonators. These legstransport heat in effectively just 5 elastic modes at the TES's operatingtemperature (< 150 mK), which is close to the quantised limit of 4. Thephononic filters then reduce the thermal flux further by frequency-domainfiltering. For example, a micromachined 3-element ring resonator reduced theflux to 19 % of a straight-legged ballistic device operating at the quantisedlimit, and 38 % of a straight-legged diffusive reference device. This workopens the way to manufacturing TESs where performance is determined entirely byfiltered, few-mode, ballistic thermal transport in short, low-heat capacitylegs, free from the artifacts of two level systems.

Superconducting transition edge sensors with phononic thermal isolation