Second order topological hinge modes in a 3-dimensional phononic crystal

Vertical interconnection between planar layers is a common building block in 3-dimensional integrated circuits. In the circuits containing surface acoustic wave (SAW) devices, such interconnections have been only realized through electrical junctions, resulting in transmission loss at the junctions. If elastic wave devices are interconnected via a topological elastic hinge mode, one can integrate these devices without electrical junctions. Applying a theory of second order topological insulator, we design a topological waveguide based on a hinge mode in a 3-dimensional phononic crystal with stacked Kagome lattices. Topological corner modes are shown to be elaborated at a frequency around 17kHz by changing the intracell- and intercell-bonds. We further demonstrate numerically and experimentally that such topological corner modes can be extended to one-dimensional hinge mode, paving the way to robust elastic-wave interconnections.We pave the way to control elastic wave propagation in 3-dimensional integrated system.