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.

拓扑声子晶体可以操纵在固体中传播而不被反向散射的弹性波，并可用于开发用于经典和量子信息处理的集成声电子系统。然而，声学拓扑超材料主要限于在低（千赫到兆赫）频率下运行的宏观系统。在这里，我们报告了千兆赫兹（高达 1.06 GHz）频率下纳米机电氮化铝膜中的拓扑谷霍尔效应。我们使用透射模式微波阻抗显微镜以高灵敏度（10-100 fm）和空间分辨率（10-100 nm）可视化弹性波通过声子晶体的传播。在真实空间和动量空间中都观察到了受能带拓扑保护的谷霍尔边缘状态。从波在局部无序和尖角周围的传输中可以明显看出强大的谷极化传输。我们还展示了该系统可用于创建声学分束器。