  Topological phononics enabling backscattering-immune transport is expected to
improve the performance of electromechanical systems for classical and quantum
information technologies. Nonetheless, most of the previous demonstrations
utilized macroscale and low-frequency structures and thus offered little
experimental insight into ultrahigh frequency phonon transport, especially in
chip-scale circuits. Here, we report microwave phonon transmissions in a
microscopic topological ring-waveguide coupled system, which is an important
building block for wave-based signal processing. The elastic waves in the
topological waveguide evanescently couple to the ring resonator, while
maintaining the valley pseudospin polarization. The resultant waves are robust
to backscattering even in the tiny hexagonal ring, generating a resonant phonon
circulation. Furthermore, the evanescently coupled structure allows for a
critical coupling, where valley-dependent ring-waveguide interference enables
blocking of the topological edge transmission. Our demonstrations reveal the
capability of using topological phenomena to manipulate ultrahigh frequency
elastic waves in intricate phononic circuits for classical and quantum
signal-processing applications.

Mesoscale and Nanoscale Physics