Gigahertz topological valley Hall effect in nanoelectromechanical phononic crystals

Topological phononic crystals can manipulate elastic waves that propagate in solids without being backscattered, and could be used to develop integrated acousto-electronic systems for classical and quantum information processing. However, acoustic topological metamaterials have been mainly limited to macroscale systems that operate at low (kilohertz to megahertz) frequencies. Here we report a topological valley Hall effect in nanoelectromechanical aluminium nitride membranes at gigahertz (up to 1.06 GHz) frequencies. We visualize the propagation of elastic waves through phononic crystals with high sensitivity (10–100 fm) and spatial resolution (10–100 nm) using transmission-mode microwave impedance microscopy. The valley Hall edge states, which are protected by band topology, are observed in both real and momentum space. Robust valley-polarized transport is evident from wave transmission across local disorder and around sharp corners. We also show that the system can be used to create an acoustic beamsplitter.