High-order topological states using alignment of different bandgaps in 1D superlattices

Acoustic interface states have been evidenced in superlattices with frequencies at tens to hundreds of GHz. A recently demonstrated scheme to generate interface states in one-dimensional superlattices is based on the principle of band inversion, obtained by concatenating two periodic lattices with inverted spatial mode symmetries around the bandgap. Most of the realizations exploit a given bandgap for which there is one symmetry inversion. In this work, we present high-order topological nanophononic interface states in multilayered structures, achieved by concatenating two superlattices with different bandgap orders centered around the same frequency. In this case, inverted mode symmetries are not required to achieve the interface state, which is enabled by modifying the unit cells of the two superlattices. We showcase designs for versatile topological devices where interface states can be simultaneously created across a wide frequency range. The topological modes can be experimentally accessed in Brillouin or pump-probe experiments. The ability to explore higher bandgap order acoustic interface states in the GHz range is unique in nanophononic superlattices due to the linear dispersion relation of acoustic phonons. The demonstrated systems can thus be exploited to investigate schemes that are difficult or impossible to study in electronics or optics, due to their non-linear dispersion relations.