Fig. 4. Experimental demonstration of satellite-valley interface states.

a Photograph of the sample, consisting of two phases with different on-site biases $\delta$. The red dashed line denotes the interface. b Simulated Berry curvature distribution around $K$ for the two phases. c Measured (colormaps) and simulated (dots) dispersions of guiding modes along the interface shown in (a). d, e Simulated and experimentally measured acoustic pressure field splitting. The red dashed lines denote the interfaces, and the numbers indicate the three output channels. The green dotted lines in (e) outline the region of the interface states, and the red and blue points further highlight the cavities with different $\delta$. f–i Measured Fourier spectra of the acoustic field for the four channels, with the red dots indicating the positions of valleys.