Topological interface states in deep-subwavelength phononic beams

Abstract

We propose deep-subwavelength phononic beams capable of supporting topological interface states (TISs) at ultra-low frequencies. The topological phononic beams are designed using unit cells with acoustic black hole (ABH) configurations to obtain the first band gap in a low-frequency range, for which the unit cell size is much smaller than the wavelength of the wave to be controlled. We control the topological phases of the phononic beams by modifying the ABH configuration and breaking the inversion symmetry of unit-cell. Two topologically distinct beams are then connected to produce the TIS in their low band gaps. Numerical and experimental results show that TISs are achieved at low frequencies of 4.3-8.5 Hz using the designed phononic beams whose lattice constants (a) are less than A/20. The value of a/A is reduced further by adjusting unit-cell arrays of the phononic beams. Given that topological phononic crystals reported in previous studies usually had lattice constants comparable to or several times smaller than wavelengths, the present work offers the possibility of designing a more compact system for to-pological states at low frequencies.