Tunable Nonlinear Topological Insulator for Acoustic Waves

Inspired by the quantum spin Hall effect, we propose the first two-dimensional tunable nonlinear topological insulator for acoustic waves that activates simply by inputting energy. Tunability is derived from an energy-dependent topological band structure, where the topological band gap opens intrinsically using nonlinear elements. A discrete hexagonal unit cell (composed of six masses, 12 linear, and three nonlinear springs) is repeated to construct a phononic system exhibiting topological character. The corresponding band structure of the proposed hexagonal unit cell is obtained analytically using Bloch's theorem and zone-folding techniques, which documents double degenerate Dirac cones. Breaking of inversion symmetry creates energy-dependent topologically protected band gaps, with topologically protected edge states robust against backscattering at arbitrary interfaces of two structures with opposite Chern numbers. The proposed topological insulator can be a stepping-stone platform towards building tunable acoustic devices, interconnects, and electroacoustic integrated circuits.