Realization of multiple topological boundary states in phononic crystals

Acoustic topological insulators that host the topological boundary states, which is insensitive to defects and disorder, have become an important research topic and provide completely new ways to manipulate acoustic waves. However, most of the acoustic topological boundary states generally appear in a single or two band gaps, hindering the applications in multiband acoustic devices. Compared to previous work, in this paper, we experimentally observe the acoustic multiple topological boundary states in four band gaps, including the end (corner) states in one-dimensional (two-dimensional) phononic crystals, based on the acoustic quartic-root topological insulators. These topological boundary states originate from two consecutive square-root procedures, which is similar to the square-root topological insulators. Our paper provides a brand-new approach to achieve the multiple boundary states by simply inserting additional cavities without elaborate designing the structure, which makes the manipulation of the acoustic more flexible.