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This article puts forward theory and design approaches for three thermally controlled subwavelength acoustic topological insulators. They are presented by immersing arrays of split hollow spheres (SHSs) or cubes in an air background and performing a study on the band structures and topological interface states. The periodically immersed rhombic shape unit cell comprising of two SHSs is analyzed firstly. A subwavelength local resonance bandgap and a Dirac point at the corner of the irreducible Brillouin zone are observed. After inducing a gap for the Dirac cone with unequal inner radius of spheres, we observe topological phase transition by mode shape and valley Chern-number analysis. Generally, local resonance systems are always limited to narrow and fixed bandgaps, therefore active and passive control of the structure are demonstrated. A strip supercell is constructed to induce topologically protected interface mode and to capture highly localized acoustic energies at the interface. Similar analyses are performed on the enlarged hexagonal model with six SHSs and the rhombic model with two split hollow cubes. This study provides a new degree of freedom for active control of acoustic topological modes and sound wave propagation.

Subwavelength thermally controlled acoustic topological interface states in split hollow spheres