Observation of an acoustic octupole topological insulator

Abstract

Berry phase associated with energy bands in crystals can lead to quantised observables like quantised dipole polarizations in one-dimensional topological insulators. Recent theories have generalised the concept of quantised dipoles to multipoles, resulting in the discovery of multipole topological insulators which exhibit a hierarchy of multipole topology: a quantised octupole moment in a three-dimensional bulk induces quantised quadrupole moments on its two-dimensional surfaces, which in turn induce quantised dipole moments on onedimensional hinges. Here, we report on the realisation of an octupole topological insulator in a three-dimensional acoustic metamaterial. We observe zero-dimensional topological corner states, one-dimensional gapped hinge states, two-dimensional gapped surface states, and three-dimensional gapped bulk states, representing the hierarchy of octupole, quadrupole and dipole moments. Conditions for forming a nontrivial octupole moment are demonstrated by comparisons with two different lattice configurations having trivial octupole moments. Our work establishes the multipole topology and its full hierarchy in three-dimensional geometries.

Non-Hermitian route to higher-order topology in an acoustic crystal

“…The wall thickness of each resonator is 6 mm. The sign of a coupling can be chosen by the location of the thin waveguide 41 , 42 , 56 , 57 (see more details in Supplementary Note 3 ). Waveguides exhibiting positive and negative couplings are colored in yellow and gray in Fig.…”

Simulating Floquet topological phases in static systems

“…Systems with gapless corner modes have successfully been realized in many different platforms [35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50], most of them being the classical analogs of condensed matter systems. Even though such realizations offer a better control over disorder, its complete elimination remains a challenging task.…”

“…The method relies on two parts: (1) constructing a HOTI and (2) measuring the eigenphases of its reflection matrix. The first part has already been achieved in photonic [35][36][37], phononic [38], microwave [39], acoustic [41][42][43][44][45][46][47]50], topoelectric [40], and condensed-matter [49] metamaterials, producing HOTI Hamiltonians similar to Eq. (1).…”

“…The required ingredients, a HOTI probed by means of a scattering measurement, are presently available in the lab. HOTIs have been achieved in a variety of metamaterials [35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50]. The reflection matrix can be determined by standard interferometric techniques [51,52], or by simply visualizing the standing wave pattern formed between incoming and outgoing modes [49,53].…”

Study on several novel topological phases in classical wave systems

“…This work thus establishes the multipole topology and its full hierarchy in 3D geometries. The findings presented in this section are published in Ref [116].…”