Elastic Higher-Order Topological Insulator with Topologically Protected Corner States

Abstract

Topologically gapless edge states, characterized by topological invariants and Berry's phases of bulk energy bands, provide amazing techniques to robustly control the reflectionless propagation of electrons, photons and phonons. Recently, a new family of topological phases, dictated by the bulk polarization, has been observed, leading to the discovery of the higher-order topological insulators (HOTIs). So far, the HOTIs are only demonstrated in discrete mechanical and electromagnetic systems and electrical circuits with the quantized quadrupole polarization.Here, we realize the higher-order topological states in a two-dimensional (2D) continuous elastic system whose energy bands can be well described. We experimentally observe the gapped onedimensional (1D) edge states, the trivially gapped zero-dimensional (0D) corner states and the topologically protected 0D corner states. Compared with the trivial corner modes, the topological ones, immunizing against defects, are robustly localized at the obtuse-angled but not the acuteangled corners. The topological shape-dependent corner states open a new route for the design of the topologically-protected but reconfigurable 0D local eigenmodes and provide an excellent platform for the topological transformation of elastic energy among 2D bulk, 1D edge and 0D corner modes.

Second-order topological phases protected by chiral symmetry

“…Higher-order topological insulators have recently drawn research interest as new topological crystalline phases 1- 30 . Unlike conventional first-order topological insulators, two-dimensional (2D) second-order topological insulators (SOTIs) have topologically protected corner states, and three-dimensional (3D) SOTIs have topological gapless modes on the hinges.…”

Higher-order Floquet topological phases with corner and bulk bound states

“…Moreover, the connection between corner and hinge states and bulk defects can also be generalized to any model with a vectorial mass generating the bulk gap. This covers, for example, systems with reflection and/or discrete rotational symmetries [33,44]. As the frequency is lowered in these protocols, we would expect a series of transitions with multiple bulk Floquet bound states appearing at the Floquet zone edge and center.…”

“…For example, a two-dimensional electric quadrupole topological insulator binds corner states with fractional charge e/2. Such higher-order topological phases have been predicted to exist in engineered lattices of cold atoms [23] and in natural elemental bismuth [27], and have been observed in a mechanical system of coupled microwave resonators [28,29], optical waveguides [30], topolectrical circuits [31], mechanical metamaterials [32], and elastic acoustic structures [33]. In this work, we show that higher-order Floquet topological phases can be realized and controlled in a periodically driven system, supporting lower-dimensional Floquet bound states at the Floquet zone center and/or edge.…”

Deep‐Subwavelength Holey Acoustic Second‐Order Topological Insulators

“…To date, HOTIs have been theoretically predicted and experimentally realized in elastics, [34,35] microwaves, [36] electric circuits, [37] photonics, [38][39][40] and acoustic systems. To date, HOTIs have been theoretically predicted and experimentally realized in elastics, [34,35] microwaves, [36] electric circuits, [37] photonics, [38][39][40] and acoustic systems.…”