Dual-band acoustic higher-order topological metamaterial composed of meta-atoms and meta-molecules

We present a dual-band topological transport of edge states and corner states in a composite acoustic higher-order topological metamaterial (AHOTM) composed of meta-atoms of hollow tubes (HTs) and meta-molecules of opened-hole hollow tubes (OHTs) arrayed as a regular triangle in a hexagonal lattice with C3v symmetry. The AHOTM has two degenerate Dirac points (DPs) in the high-symmetry point K that are separately tuned by the geometry sizes of HTs and OHTs because of their local resonances and weak interactions. The rotation of HTs and OHTs in a unit cell with an angle of -30 degrees [unit cell A (UCA)] or 30 degrees [unit cell B (UCB)] lifts the degeneracies of the two DPs and produces two entire opened band gaps, in which there are two pairs of topological edge bands. We numerically and experimentally demonstrate topological valley transports of edge states for the AHOTM in two bands. The AHOTM presents frequency-selective topological transport of edge states by rotating one structure and can sustain the topologically robust edge states against some defects. In the two frequency regions, higher-order corner states are also observed in the vertices of the triangular UCB array surrounded by the UCA array, which can also realize frequency-selective higher-order corner states by rotating one structure. This study may pave a feasible way to design multiband and broadband acoustic topological insulators for their flexible manipulation of sound waves.