Mechanical Quantum Hall Effect in Time-Modulated Elastic Materials

Floquet topological insulators have inspired analogs in photonics, optics, and acoustics, in which nonreciprocal wave propagation in time-modulated materials is achieved by breaking time-reversal symmetry. This paper investigates a mechanical-wave analog of Thouless pumping and the quantum Hall effect respectively in one- and two-dimensional periodically time-modulated materials. These systems feature robust edge states that are immune to back-scattering by sharp corners, defects, and nonuniform phases. The work sheds light on the design and fabrication of quantum-Hall-type elastic topological insulators, to control elastic waves for broadband one-way transport in practical applications.