Valley edge states as bound states in the continuum.

Bound states in the continuum (BICs) are spatially localized states with energy embedded in the continuum spectrum of extended states. The combination of BICs physics and nontrivial band topology theory givs rise to topological BICs, which are robust against disorders and meanwhile, the merit of conventional BICs is attracting wide attention recently. Here, we report valley edge states as topological BICs, which appear at the domain wall between two distinct valley topological phases. The robustness of such BICs is demonstrated. The simulations and experiments show great agreement. Our findings of valley related topological BICs shed light on both BICs and valley physics, and may foster innovative applications of topological acoustic devices.