  The small mass and high coherence of nanomechanical resonators render them
the ultimate force probe, with applications ranging from biosensing and
magnetic resonance force microscopy, to quantum optomechanics. A notorious
challenge in these experiments is thermomechanical noise related to dissipation
through internal or external loss channels. Here, we introduce a novel approach
to defining nanomechanical modes, which simultaneously provides strong spatial
confinement, full isolation from the substrate, and dilution of the resonator
material's intrinsic dissipation by five orders of magnitude. It is based on a
phononic bandgap structure that localises the mode, without imposing the
boundary conditions of a rigid clamp. The reduced curvature in the highly
tensioned silicon nitride resonator enables mechanical $Q>10^{8}$ at $ 1
\,\mathrm{MHz}$, yielding the highest mechanical $Qf$-products
($>10^{14}\,\mathrm{Hz}$) yet reported at room temperature. The corresponding
coherence times approach those of optically trapped dielectric particles.
Extrapolation to $4{.}2$ Kelvin predicts $\sim$quanta/ms heating rates, similar
to trapped ions.
