
Topological insulators are materials whose band structure contains touching points that are topologically nontrivial and can host quasiparticle excitations that behave as Weyl fermions. These so-called Weyl points not only exist in electronic systems, but can also be found in artificial periodic structures with classical waves, such as electromagnetic waves in photonic crystals and acoustic waves in phononic crystals.
Here we show how Weyl physics can also inspire the design of novel elastic/sonic structures. We construct a single-phase 3D structure, an analog of the honeycomb lattice, and predict the existence of Weyl points with opposite topological charges, elastic Fermi arcs, and the associated gapless topologically protected surface states. We apply fullscale numerical simulations on the 3D structure and present a clear visualization of topological surface states that are directional and robust. Such designed lattices can pave the wat for novel vibration control and energy harvesting on structures that are ubiquitous in many engineering applications.