Synthesizing spin–orbit couplings and symmetry-protected topological phase in acoustic metamaterials

Spin–orbit couplings (SOCs) underlie several key concepts of topological matter. However, acoustic waves lack intrinsic spin and SOCs, which makes some topological phases impossible. We develop in the present work a realistic scheme to synthesize simultaneously the intrinsic and Rashba–Dresselhaus SOCs in acoustic systems and explore the symmetry-protected topological phase induced by the SOCs. To be precise, we construct a two-leg ladder composed of acoustic resonators and linking tubes. Utilizing the concept of pseudospin, the spin-1/2 is encoded by the leg degree of freedom of the ladder, and meanwhile, the SOCs are achieved by engineering the couplings between resonators. We further highlight the emergence of the symmetry-protected topological phase respecting the chiral unitary (AIII) symmetry in such acoustic SOC lattices. This scheme is confirmed by the full-wave simulations. Our acoustic structure is within immediate experimental reach and enables the direct visualization of symmetry-protected topological boundary states, not yet been observed experimentally. Our results represent a route to synthesize the SOCs and will benefit an in-depth study of the spin–orbit physics in acoustics.