Fig. 4

Exotic properties for the topological nontrivial drumhead surface states. a Acoustic pressure distributions in the depth direction experimentally scanned in a cross-sectional plane (denoted by the blue region in the inset). The red star marks the excitation point source. The fields at frequencies of 10.4 and 13.4 kHz exhibit distinctly different patterns for the drumhead surface state and the high-frequency surface state. b Left panels: the layer-average pressure fields for the surface states simulated in a square supercell. The drumhead surface state shows oscillated decay in contrast to the high-frequency state. Right panel: the frequency response in the presence of disorder for the supercell at (k_x,k_y) = (π/a,0). The drumhead surface state is more stable than the high-frequency state due to the topological protection