Acoustic phonon confinement by band inversion

We study the formation of a topological interface mode between two nanometric acoustic superlattices presenting inverted band structures. That is, the two lattices share a common band gap but present opposite spatial mode symmetries of the two Bloch modes bounding the gap from below and above. We first show that by tuning the acoustic-thickness ratio between the two materials in a unit cell of a GaAs/AlAs superlattice a band structure inversion can be induced at the Brillouin zone center. Secondly, we show that two concatenated superlattices with inverted band structures form a topological interface mode with its strain spatially confined.