Observation of Gigahertz Topological Valley Hall Effect in Nanoelectromechanical Phononic Crystals*

Topological phononics offers numerous opportunities in manipulating elastic waves that can propagate in solids without being backscattered. Due to the lack of nanoscale imaging tools that aid the system design, however, acoustic topological metamaterials have been mostly demonstrated in macroscale systems operating at low (kilohertz to megahertz) frequencies. Here, we report the realization of gigahertz topological valley Hall effect in nanoelectromechanical AlN membranes. Propagation of elastic wave through phononic crystals is directly visualized by microwave microscopy with unprecedented sensitivity and spatial resolution. The valley Hall edge states, protected by band topology, are vividly seen in both real- and momentum-space. The robust valley-polarized transport is evident from the wave transmission across local disorder and around sharp corners, as well as the power distribution into multiple edge channels. Our work paves the way to exploit topological physics in integrated acousto-electronic systems for classical and quantum information processing in the microwave regime.