Fig. 3: Acoustic helical edge states in the spin-Chern insulator phase.

Schematic and photo of (a and b), the top boundary and (c and d), the bottom boundary for a phononic crystal (PC) ribbon. Green (pink) arrows represent a pair of edge states counterpropagating along the top (bottom) boundary. e and f Projected dispersions of the PC ribbon for the top and bottom boundaries, respectively. Gray dots show the simulated bulk modes, while the green and pink dots represent the simulated edge modes. Color maps denote the experimental data. g Measured sound field distributions excited at top and bottom boundaries, respectively. Color map denotes the intensity of measured sound fields.