  Recent advances in cavity-optomechanics have now made it possible to use
light not just as a passive measuring device of mechanical motion, but also to
manipulate the motion of mechanical objects down to the level of individual
quanta of vibrations (phonons). At the same time, microfabrication techniques
have enabled small-scale optomechanical circuits capable of on-chip
manipulation of mechanical and optical signals. Building on these developments,
theoretical proposals have shown that larger scale optomechanical arrays can be
used to modify the propagation of phonons, realizing a form of topologically
protected phonon transport. Here, we report the observation of topological
phonon transport within a multiscale optomechanical crystal structure
consisting of an array of over $800$ cavity-optomechanical elements. Using
sensitive, spatially resolved optical read-out we detect thermal phonons in a
$0.325-0.34$GHz band traveling along a topological edge channel, with
substantial reduction in backscattering. This represents an important step from
the pioneering macroscopic mechanical systems work towards topological phononic
systems at the nanoscale, where hypersonic frequency ($\gtrsim$GHz) acoustic
wave circuits consisting of robust delay lines and non-reciprocal elements may
be implemented. Owing to the broadband character of the topological channels,
the control of the flow of heat-carrying phonons, albeit at cryogenic
temperatures, may also be envisioned.
