Space-time phononic crystals with anomalous topological edge states

We introduce a one-dimensional topological phononic phase system with a dynamic modulation of its intrinsic properties that keep the topological feature of the system unchanged, while it leads to a multiplication of the edges-state into the continuum at the subwavelength regime. We use this feature to access the functionality of exciting the edge-state in the Bragg regime using harmonic deep subwavelength acoustic wave where the wavelength is about 55 times the whole topological system's length. This remarkable property introduces a promising alternative to achieve wave manipulation at the deep-subwavelength scale.