Broadband Coupled Valley Transmission and Rainbow Trapping in Topological Phononic Crystals with Dendritic Fractal Structure

Topological phononic crystals (PnCs) have revolutionized the manipulation of acoustic and elastic waves by leveraging various topological phases proposed originally in condensed matter, leading to robust and backscattering‐immune transport of signals. However, designing broadband topological PnCs is still a challenge. Herein, by employing the dendritic fractal structures, the broadband coupled valley transport and rainbow trapping are invented for elastic waves in the 2D topological phononic heterostructure. First, the gradually fractal PnCs structures are constructed, and the corresponding band structures are calculated to obtain the broadband topological bandgap. By constructing the sandwiched heterostructures with two different valley topological phases of PnCs, the topologically protected edge states of elastic wave are achieved. Further controlling the layer numbers of the middle region in sandwiched heterostructures, the coupled property of the valley edge states is revealed. Then, the robust transport and frequency‐selective multi‐channel routing for the coupled valley edge states are demonstrated. Finally, by gradually disposing the vein‐width of the dendritic fractal structure, the rainbow trapping of elastic waves is achieved in dual‐band gaps. The results may facilitate practical applications in broadband and multichannel acoustic signal sensing devices.