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

TL;DR

This paper introduces a 4D topological insulator system that combines higher-order and hypersurface modes, experimentally realized in an acoustic lattice, revealing new protected topological states with potential for tunable applications.

Contribution

It presents the first experimental realization of a 4D higher-order Chern insulator with coexistence of hypersurface and higher-order topological modes, protected by complex topological invariants.

Findings

Observation of 4D hypersurface and higher-order topological modes in a 2D acoustic lattice

Protection of modes by second and first Chern numbers

Tunability of topological corner modes for potential applications

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.