Observation of Hofstadter butterfly and topological edge states in reconfigurable quasi-periodic acoustic crystals

Xiang Ni, Kai Chen, Matthew Weiner, David J. Apigo, Camelia Prodan, Andrea Alù, Emil Prodan, Alexander B. Khanikaev

Research output: Contribution to journalArticlepeer-review

22 Scopus citations

Abstract

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 quasi-crystalline systems in higher dimensions.

Original languageEnglish (US)
Article number55
JournalCommunications Physics
Volume2
Issue number1
DOIs
StatePublished - Dec 1 2019

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

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