  We achieve high detectivity terahertz sensing using a silicon nitride
nanomechanical resonator functionalized with a metasurface absorber. High
performances are achieved by striking a fine balance between the frequency
stability of the resonator, and its responsivity to absorbed radiation. Using
this approach, we demonstrate a detectivity
$D^*=3.4\times10^9~\mathrm{cm\cdot\sqrt{Hz}/W}$ and a noise equivalent power
$\mathrm{NEP}=36~\mathrm{pW/\sqrt{Hz}}$ that outperform the best
room-temperature on-chip THz detectors (i.e., pyroelectrics). Our optical
absorber consists of a 1-mm diameter metasurface, which currently enables a
0.5-3 THz detection range but can easily be scaled to other frequencies in the
THz and infrared ranges. In addition to demonstrating high-performance
terahertz sensing, our work unveils an important fundamental trade-off between
high frequency stability and high responsivity in thermal-based nanomechanical
radiation sensors.
