Parity-Frequency-Space Elastic Spin Control of Wave Routing in Topological Phononic Circuits

Topological phononic cavities, such as ring resonators with topological whispering gallery modes (TWGMs), offer a flexible platform for the realization of robust phononic circuits. However, the chiral mechanism governing TWGMs and their selective routing in integrated phononic circuits remain unclear. This work reveals, both experimentally and theoretically, that at a phononic topological interface, the elastic spin texture is intricately linked to, and can be explained through a knowledge of, the phonon eigenmodes inside each unit cell. Furthermore, for paired, counterpropagating TWGMs based on such interfaces in a waveguide resonator, this study demonstrates that the elastic spin exhibits locking at discrete frequencies. Backed up by theory, experiments on kHz TWGMs in thin honeycomb-lattice aluminum plates bored with clover-leaf shaped holes show that together with this spin-texture related angular-momentum locking mechanism at a single topological interface, there are triplicate parity-frequency-space selective wave routing mechanisms. In the future, these mechanisms can be harnessed for the versatile manipulation of elastic-spin based routing in phononic topological insulators.