Colloquium: Topologically protected transport in engineered mechanical systems

Mechanical vibrations are being harnessed for a variety of purposes and at many length scales, from the macroscopic world down to the nanoscale. The considerable design freedom in mechanical structures allows one to engineer new functionalities. In recent years, this has been exploited to generate setups that offer topologically protected transport of vibrational waves (topological phonon transport), both in the solid state and in fluids. Borrowing concepts from electronic physics and being cross fertilized by concurrent studies for cold atoms and electromagnetic waves, this field of topological transport in engineered mechanical systems offers a rich variety of phenomena and platforms. In this Colloquium, a unifying overview of the various ideas employed in this area is provided, different approaches and experimental implementations are summarized, and the challenges as well as the prospects are commented upon.