Valley Topological Phases in Bilayer Sonic Crystals

Abstract: Recently, the topological physics in artificial crystals for classical waves has become an emerging research area. In this Letter, we propose a unique bilayer design of sonic crystals that are constructed by two layers of coupled hexagonal array of triangular scatterers. Assisted by the additional layer degree of freedom, a rich topological phase diagram is achieved by simply rotating scatterers in both layers. Under a unified theoretical framework, two kinds of valley-projected topological acoustic insulators are distinguished analytically, i.e., the layer-mixed and layer-polarized topological valley Hall phases, respectively. The theory is evidently confirmed by our numerical and experimental observations of the nontrivial edge states that propagate along the interfaces separating different topological phases. Various applications such as sound communications in integrated devices, can be anticipated by the intriguing acoustic edge states enriched by the layer information.

Valley Topological Phases in Bilayer Sonic Crystals

This paper presents an innovative bilayer design of sonic crystals (SCs) and explores topological physics in classical wave systems, focusing on valley-projected topological phases. The researchers propose a bilayer sonic crystal (BSC) system that leverages an additional layer degree of freedom to achieve a complex topological phase diagram by simply rotating scatterers in each layer. This effectively distinguishes two types of valley-projected topological acoustic insulators: layer-mixed and layer-polarized valley Hall phases.

The study builds upon previous work that demonstrates monolayer SCs can exhibit valley-projected topological sound transport. This bilayer approach enriches the complexity of the topological phase diagram accessible, offering enhanced control and tunability over acoustic edge states through layer manipulation. The findings are supported by analytical models and confirmed through numerical simulation and experimental observation, showcasing nontrivial edge states propagating along interfaces separating distinct topological phases.

The authors detail the BSC design encompassing hexagonal lattices formed by triangular scatterers whose orientation varies. The study finds that by manipulating the relative angles ( (\alpha, \beta) ) of these scatterers, different band structures emerge, providing crucial control over band degeneracies and omnidirectional gap formation necessary for topological phase transitions.

Key numerical results reveal the existence and manipulation of omnidirectional band gaps using controlled rotation of scatterers. By assessing edge frequencies along varied angular paths, the authors identify phase boundaries characterized by quantized topological invariants ( C_V ) and ( C_L ). The phase diagram illustrates regions where topological transitions occur, distinguishing valley Hall phases from layer-valley Hall phases based on these invariants.

Experimental validation supports theoretical predictions, employing sound propagation along interfaces of distinct BSC configurations. The observed acoustic valley Hall phases exhibit layer-mixed edge modes, while acoustic layer-valley Hall phases present layer-polarized modes. These experiments confirm layer-selective excitation potential, enhancing application prospects in sound communications within integrated devices.

Several implications arise from this research, notably the potential for novel sound manipulation and intra/inter-layer communications in practical applications. The authors propose a sound inter-layer converter, utilizing distinct edge modes to achieve sound concentration shifts between layers, demonstrating functional integration of the topological phenomena in devices.

In terms of future developments, the research opens avenues for exploring such bilayer designs in other classical wave platforms, such as electromagnetic or elastic waves. The dual-index scheme (layer and valley) provides versatile controllability that may inspire fundamental and applied physics advancements, including coupling with intrinsic polarizations.

Overall, this paper contributes notable insights into topological acoustic insulators by introducing a bilayer SC paradigm, further refining control mechanisms for valley-projected edge modes and paving the way for advanced applications in topological physics of classical wave systems.