Four-Dimensional Higher-Order Chern Insulator and Its Acoustic Realization

Abstract

We present a theoretical study and experimental realization of a system that is simultaneously a four-dimensional (4D) Chern insulator and a higher-order topological insulator (HOTI). The system sustains the coexistence of (4-1)-dimensional chiral topological hypersurface modes (THMs) and (4-2)-dimensional chiral topological surface modes (TSMs). Our study reveals that the THMs are protected by second Chern numbers, and the TSMs are protected by a topological invariant composed of two first Chern numbers, each belonging a Chern insulator existing in sub-dimensions. With the synthetic coordinates fixed, the THMs and TSMs respectively manifest as topological edge modes (TEMs) and topological corner modes (TCMs) in the real space, which are experimentally observed in a 2D acoustic lattice. These TCMs are not related to quantized polarizations, making them fundamentally distinctive from existing examples. We further show that our 4D topological system offers an effective way for the manipulation of the frequency, location, and the number of the TCMs, which is highly desirable for applications.

arXiv commentMain text 19 pages, 6 figures. Supplemental materials 18 pages, 12 figures

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• Realization of a Z classified chiral-symmetric higher-order topological insulator in a coupling-inversion acoustic crystal
• Demonstration of acoustic high-order Stiefel-Whitney semimetal in bilayer graphene sonic crystals
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• Numerical calculation of the $k$-space second Chern number in four dimensions