Elastic phononic plates with first-order and second-order topological phases

Abstract

Topologically protected 1D edge states and the 2D surface states have been observed in variant classical wave systems. By extending the quantized polarization, Berry phase, to higher multipole moments, the higher-order topological phases, expressed as 0D corner states, have been theoretically predicted and recently experimentally observed in electric, electromagnetic and acoustic systems. In this paper, we design an elastic phononic plate consisting of a bi-layered hexagonal lattice. The valley-polarized gapless 1D edge state is observed in the elastic phononic plate, by lifting the Dirac cones at the Brillouin zone (BZ) corners. When the bi-layered phononic plates are stacked one by one, the chirality of the oblique columns along the z axis guarantees this 2D elastic phononic plate to be a 3D chiral phononic system. Weyl cones and topologically protected gapless 2D surface states are yielded in this 3D chiral phononic system. The above topological phases are first-order ones with gapless (d-1)-dimensional edge/surface states. By defining a composite cell consisting of three-unit cells and modulating the intra- and inter-coupling within/among the composite cells, the folded double Dirac cone at the BZ center will be gapped and the topological phase of the elastic phononic plate will evolve to a second-order one, expressed as the robust 0D corner state, instead of the gapless 1D edge state. The realization of the first-order edge/surface states and second-order corner states in a unified elastic phononic platform opens up a new path for the design of on-chip topological devices for advanced elastic wave manipulation among the bulk, edge/surface and corner modes.