  Nanophononics is essential for the engineering of thermal transport in
nanostructured electronic devices, it greatly facilitates the manipulation of
mechanical resonators in the quantum regime, and could unveil a new route in
quantum communications using phonons as carriers of information. Acoustic
phonons also constitute a versatile platform for the study of fundamental wave
dynamics, including Bloch oscillations, Wannier Stark ladders and other
localization phenomena. Many of the phenomena studied in nanophononics were
indeed inspired by their counterparts in optics and electronics. In these
fields, the consideration of topological invariants to control wave dynamics
has already had a great impact for the generation of robust confined states.
Interestingly, the use of topological phases to engineer nanophononic devices
remains an unexplored and promising field. Conversely, the use of acoustic
phonons could constitute a rich platform to study topological states. Here, we
introduce the concept of topological invariants to nanophononics and
experimentally implement a nanophononic system supporting a robust topological
interface state at 350 GHz. The state is constructed through band inversion,
i.e. by concatenating two semiconductor superlattices with inverted spatial
mode symmetries. The existence of this state is purely determined by the Zak
phases of the constituent superlattices, i.e. that one-dimensional Berry phase.
We experimentally evidenced the mode through Raman spectroscopy. The reported
robust topological interface states could become part of nanophononic devices
requiring resonant structures such as sensors or phonon lasers.
