Topological materials for elastic wave in continuum

Elastic wave has wide applications, such as signal processing, sensor, and communication. It is highly desired to control the propagation of elastic wave efficiently. Inspired by various topological phenomena in electronic systems, robust transports of elastic wave have attracted much attention. In this paper, we review the recent progress on elastic wave topologies, including elastic quantum spin Hall effect, valley Hall effect, Weyl semimetal, higher-order topology, and other topological effects. Finally, we give some brief outlooks on elastic wave topologies. Three-dimensional topological materials and non-Hermitian physics for elastic waves are yet to be explored. Due to the strong intrinsic nonlinearity, it is an ideal platform to investigate nonlinear properties in nanomechanical structures. In addition to passive materials, active materials may be introduced to realize tunable multifunctionalities. Topological elastic materials have promising prospects in device applications.