Valley-based splitting of topologically protected helical waves in elastic plates

Topological protection offers unprecedented opportunities for wave manipulation and energy transport in various fields of physics, including elasticity, acoustics, quantum mechanics, and electromagnetism. Distinct classes of topological waves have been investigated by establishing analogs with the quantum, spin, and valley Hall effects. We here propose and experimentally demonstrate the possibility of supporting multiple classes of topological modes within a single platform. Starting from a patterned elastic plate featuring a double Dirac cone, we create distinct topological interfaces by lifting such degeneracy through selective breaking of symmetries across the thickness and in the plane of the plate. We observe the propagation of a new class of heterogeneous helical-valley edge waves capable of isolating modes on the basis of their distinct polarization, i.e., the specific mode wave field distribution within the unit cell. Our results show the onset of wave splitting resulting from the interaction of multiple topological equal-frequency wave modes, which may have significance in applications involving elastic beam splitters, switches, and filters.