Topological physics in classical systems, such as photonic and acoustic systems, is fast becoming an exciting field in fundamental and applied research. However, almost all existing topological acoustic materials are restricted to systems with conventional lattices and specific time-space symmetries. Here, we present a unique design of topological phononic crystals with moir\'e superlattice that are constructed by simply sliding a layer of moir\'e phononic crystals. Assisted by the sliding degree of freedom, sliding moir\'e phononic crystals exhibit nontrivial topology characterized by a dynamical Chern number, leading to topological pumping of special topological moir\'e edge states that are completely insensitive to the edge geometry. More interestingly, moir\'e phononic crystals possess one-dimensional moir\'e flat bulk bands, giving rise to one-dimensional localized states in the bulk that result in an array of compact and nearly independent one-dimensional signal channels. Various applications such as acoustic communications and isolations in integrated devices can be anticipated from the intriguing acoustic one-dimensional localized bulk states and topological moir\'e edge states enriched by the sliding modulation.
Fu et al. (Mon,) studied this question.