Topological network and valley beam splitter in acoustic biaxially strained moiré superlattices

Moir\'e superlattices consist of parallel but staggered periodic lattices and have been extensively explored due to their salient physical properties. However, there are limited demonstrations of such concepts for classical wave systems. Here, we construct an acoustic biaxially strained moir\'e superlattice by mismatching lattice constants in both $x$ and $y$ directions. The interface between two different topological regions with opposite valley Chern numbers forms a valley-induced network along which acoustic waves can travel efficiently. Taking a unit cell from the superlattice as a six-terminal device, the incoming acoustic waves can be partitioned into the left-adjacent, the right-adjacent, and the forward-facing channels. The acoustic beam splitting is protected by the valley polarization. Our results provide a comprehensive analysis of the transport properties of acoustic waves in the moir\'e superlattice and can provide useful insights for designing topological acoustic devices ranging from topological networks, valley filters, to energy splitters.