Superconducting transition edge sensors with phononic thermal isolation

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