Elastic fractal higher-order topological states

TL;DR

This paper explores elastic-wave higher-order topological states in fractal structures, revealing unique topological phenomena, robust corner states, and a significant increase in topological states compared to periodic structures, with promising applications.

Contribution

It introduces the first investigation of elastic-wave topological states in fractal structures, characterizes their topology with real-space quadrupole moments, and demonstrates their unique properties experimentally.

Findings

Topological edge and corner states are realized in elastic fractal systems.

Robustness of corner states varies between rhombus and Sierpinski fractals.

Number of topological states in fractals exceeds that in periodic structures.

Abstract

Fractal is an intriguing geometry with self-similarity and non-integer dimensions, the elastic-wave topological phase based on fractal structures has not been revealed up to now. In this work, elastic-wave higher-order topological states in fractal structures are investigated. Elastic real-space quantized quadrupole moment is calculated and used to characterize the topology of elastic fractal metamaterials, and formation conditions of topological phase transitions in elastic fractal systems are revealed. The topological edge and corner states of elastic waves in fractal structures are realized theoretically and experimentally. It is found that different from the acoustic fractal system, the topological outer and inner edge states can emerge separately in elastic fractal systems, which is important for the integrated sensing and particle manipulation in microfluidics. Besides, the results show that the robustness of the topological corner states in rhombus fractal structures is obviously stronger than that in Sierpinski fractal structures, and the physical mechanism is clarified. Compared with traditional elastic-wave topological insulators based on periodic structures, the richness of topological states in elastic fractal structures is much higher (for the Sierpinski fractal structure, the number of topological states is 156, much greater than that of the periodic structure (only 28)), which is vital in integrated sensing and energy-location applications. The topological phenomena of elastic fractal systems revealed in this work, provides an unprecedented way of controlling elastic waves, enriches the topological physics of elastic systems and breaks the limitation of that relying on periodic elastic structures. The results have great application prospects in high-Q resonators, high-resolution elastic-wave energy locations, energy harvester, and high-sensitivity sensors.