Observation of squeezed Chern insulator in an acoustic fractal lattice

Topological insulators are a new phase of matter with the distinctive characteristics of an insulating bulk and conducting edge states. Recent theories indicate there even exist topological edge states in the fractal-dimensional lattices, which are fundamentally different from the current studies that rely on the integer dimensions. Here, we propose and experimentally demonstrate the squeezed Chern insulator in a fractal-dimensional acoustic lattice. First, through calculating the topological invariant of our topological fractal system, we find the topological phase diagram is squeezed by about 0.54 times, compared with that of the original Haldane model. Then by introducing synthetic gauge flux into an acoustic fractal lattice, we experimentally observe the one-way edge states that are protected by a robust mobility gap within the squeezed topological regimes. Our work demonstrates the first example of acoustic topological fractal insulators and provides new directions for the advanced control of sound waves.