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. 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 to a Chern insulator existing in subdimensions. With the synthetic coordinates fixed, the THMs and TSMs, respectively, manifest as topological edge modes 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 number of TCMs, which is highly desirable for applications.
- Received 16 January 2020
- Revised 10 June 2020
- Accepted 15 December 2020
DOI:https://doi.org/10.1103/PhysRevX.11.011016
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
In most cases, waves spread out in space, making them suitable as a carrier of energy and information. However, a certain degree of wave confinement is often necessary to better manipulate them for many applications. Here, we draw on powerful notions from topology—used by physicists to describe invariant properties such as a wave function’s symmetry—to demonstrate a novel approach to wave engineering that goes beyond our familiar three spatial dimensions.
By using an acoustic crystal with two spatial dimensions and two “synthetic dimensions”—artificial degrees of freedom in the parameter space—we report the realization of a 4D topological system that can simultaneously sustain both 3D and 2D topological boundary modes, which are not possible for any system dwelling only in 3D real space. Importantly, the 4D topological origin leads to a versatile recipe for designing and tuning said topological modes manifesting in real space.
Our work not only offers a deeper understanding of the 4D topology and the topological boundary modes in lower dimensions but also paves a new route for topological wave engineering.
