Topological wave insulators: a review

Abstract

Originally discovered in condensed matter systems, topological insulators (TIs) have been ubiquitously extended to various fields of classical wave physics including photonics, phononics, acoustics, mechanics, and microwaves. In the bulk, like any other insulator, electronic TIs exhibit an excessively high resistance to the flow of mobile charges, prohibiting metallic conduction. On their surface, however, they support one-way conductive states with inherent protection against certain types of disorder and defects, defying the common physical wisdom of electronic transport in presence of impurities. When transposed to classical waves, TIs open a wealth of exciting engineering-oriented applications, such as robust routing, lasing, signal processing, switching, etc., with unprecedented robustness against various classes of defects. In this article, we first review the basic concept of topological order applied to classical waves, starting from the simple onedimensional example of the Su-Schrieffer-Heeger (SSH) model. We then move on to two-dimensional wave TIs, discussing classical wave analogues of Chern, quantum Hall, spin-Hall, Valley-Hall, and Floquet TIs. Finally, we review the most recent developments in the field, including Weyl and nodal semimetals, higherorder topological insulators, and self-induced non-linear topological states.

Fused‐Silica 3D Chiral Metamaterials via Helium‐Assisted Microcasting Supporting Topologically Protected Twist Edge Resonances with High Mechanical Quality Factors

“…We have encountered this limitation when working toward implementing a theoretically suggested laser-beam scanner based on a protected edge mode in a 1D topological bandgap of a diatomic chain of 3D chiral metamaterial unit cells. [25] This structure, the design of which builds on extensive previous work on topological phonons, [26][27][28][29] is illustrated in Figure 1a. Therefore, we have searched for novel means of manufacturing this particular 3D microarchitecture as well as related ones in fused-silica form.…”

Parallel wave-based analog computing using metagratings

“…For a few decades, digital processors have been widely used to execute computational tasks, as an alternative to analog mechanical and electrical computers. Despite their reliability and high-speed operation, digital processors suffer from high-power consumption, expensive analog-to-digital conversion, and sharp performance degradation at high frequencies, leading to large limitations even for performing simple computing tasks such as differentiation or integration, equation solving, matrix inversion, edge detection, and image processing [ 1 , 2 ]. With the advent of metamaterials and metasurfaces, spatial analog optical computing resurfaced, finding important applications as compact solutions for high speed, high throughput image processing and parallel computing.…”

Synthetically Non-Hermitian Nonlinear Wave-like Behavior in a Topological Mechanical Metamaterial

“…The study of topological band theory in condensed matter physics has led to novel classes of materials termed topological insulators (1,2) and topological superconductors (3), which support localized modes at the materials' edges that are highly robust to defects and perturbation (4). The stability of these modes stems from topological protection conferred by the material's bulk properties.…”

“…dimensional (2D) topological Maxwell lattices, the study of nonlinear effects have been so far limited to perturbation theories (23). This is an important gap, as nonlinear systems do not obey superposition and, as such, support an ability to control the spatiotemporal allocation of energy in materials that vastly exceeds their linear counterparts (32)(33)(34) through phenomena such as self-localization (35,36), frequency conversion and dynamic tunability (37,38), and chaos (39), as well as rich interplay with finite-frequency topological states (2,23,(40)(41)(42)(43)(44)(45). As already suggested for Maxwell lattices in the linear regime, we envision that combining nonlinear responses with the strong localization, non-reciprocity, and the robust nature of topological protection will lead to an important expansion of the ability to tailor spatiotemporal stress, deformation, and energy fields, with application areas demonstrated for nonlinear dynamical systems ranging from impact mitigation (46) to neuromorphic (47) and ultrafast mechanoacoustic computation (48,49).…”