Observation of Hofstadter butterfly and topological edge states in reconfigurable quasi-periodic acoustic crystals
Observation of Hofstadter butterfly and topological edge states in reconfigurable quasi-periodic acoustic crystals
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DOI：
10.1038/s42005-019-0151-7
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发表时间：
2019-06-06
影响因子：
5.5
通讯作者：
Khanikaev, Alexander B.
中科院分区：
文献类型：
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作者：
Ni, Xiang;Chen, Kai;Khanikaev, Alexander B.
分形能谱的出现是两个长度尺度不相称的周期参数相互作用的结果。晶体可以模拟这种相互作用，并且还表现出拓扑体边界对应，这是由它们在虚拟维度中的非平凡拓扑所实现的。在这里，我们提出，制造和实验测试了一个可重构的一维（1D）声学阵列，其中每个元件的谐振频率可以通过活塞独立微调。我们通过测量分布在频率上的状态的声密度，同时改变阵列的远程顺序，实验地绘制了完整的霍夫施塔特蝴蝶光谱。此外，通过绝热改变阵列的相位，我们映射了拓扑保护的分形边界态，这些分形边界态显示为从一个边缘泵送到另一个边缘。这种可重构晶体可以作为未来扩展到电子学、光子学和力学以及高维准晶体系统的模型。
The emergence of a fractal energy spectrum is the quintessence of the interplay between two periodic parameters with incommensurate length scales. crystals can emulate such interplay and also exhibit a topological bulk-boundary correspondence, enabled by their nontrivial topology in virtual dimensions. Here we propose, fabricate and experimentally test a reconfigurable one-dimensional (1D) acoustic array, in which the resonant frequencies of each element can be independently fine-tuned by a piston. We map experimentally the full Hofstadter butterfly spectrum by measuring the acoustic density of states distributed over frequency while varying the long-range order of the array. Furthermore, by adiabatically changing the phason of the array, we map topologically protected fractal boundary states, which are shown to be pumped from one edge to the other. This reconfigurable crystal serves as a model for future extensions to electronics, photonics and mechanics, as well as to quasicrystalline systems in higher dimensions.