Elastic fractal higher-order topological states

In this work, elastic fractal higher-order topological states are investigated. Bott index is adopted to characterize the topological property of elastic fractal structures. The topological corner and edge states of elastic waves in fractal structures are realized theoretically and experimentally. Different from traditional two-dimension (2D) high-order topological insulators based on periodic structures, the high-order topological states based on elastic fractal structures in this work intuitively reflect the fractal dimension in physics, supporting not only abundant topological outer corner states, but also rich inner corner states. The richness of corner states is much higher than that of topological insulators based on periodic structures. The strong robustness of the topological corner states in the fractal structure are verified by introducing disorders and defects. The topological phenomenon of in elastic fractal structures revealed in this work enriches the topological physics of elastic systems and breaks the limitation of that relies on periodic elastic structures. The results have important application prospects in energy harvesting, information transmissions, elastic energy acquisitions and high-sensitivity detections