Realization of Spin-locked Acoustic Helical Landau Levels in both Hexagonal and Square Lattices.

Topological zeroth-order Landau levels offer a promising avenue for steering acoustic and electromagnetic waves. However, the helical Landau levels in 2D acoustic systems remain an unresolved challenge. Moreover, previous studies on zeroth-order Landau levels have primarily focused on hexagonal lattices, leaving their counterparts in square lattices largely unexplored. In this study, the helical Landau levels rooted in acoustic quantum spin Hall systems are theoretically proposed and experimentally validated. By linearly increasing the local bandgap through the lifting of the double Dirac cone in acoustic crystals with both square and hexagonal lattices-achieved via topology optimization method-a position-dependent effective mass is introduced in the Dirac Hamiltonian, thereby synthesizing in-plane pseudomagnetic fields. This results in the emergence of spin-locked helical Landau levels, which has been experimentally validated. The large-area conveyance of acoustic energy facilitated by these helical Landau levels is demonstrated and the robustness of Landau-level-mediated propagation against defects is confirmed. A new pathway for exploring acoustic helical Landau levels based on spin Hall physics is opened.