Helical Higher-Order Topological States in an Acoustic Crystalline Insulator

The topological states in quantum Hall insulators and quantum spin Hall insulators that emerge helical are considered nondissipative. However, in crystalline systems without spin-orbit couplings, the existing higher-order topological states are considered not helical, and the energy suffers from dissipation during propagation. In this work, by introducing the intrinsic pseudospin degree of freedom, we theoretically and experimentally present the existence of the helical higher-order topological states in the ${C}_{6}$-symmetric topological crystalline insulators based on the acoustic samples. Crucially, rather than considering the global interaction of the large bulk, we further intuitively reveal the impacts of the geometries of the crystal on the generation mechanisms and natural behaviors of these states based on the simple equivalent models. These results provide a versatile way for guiding the design of the desired topological materials.