Third-order square-root topological insulators on decorated diamond sonic crystals.

Area of Science:

• Acoustics
• Condensed Matter Physics
• Topological Materials

Background:

• Topological phases can be generated using the square-root operation, inheriting properties from the parent Hamiltonian.
• Higher-order topological insulators exhibit unique boundary states.

Purpose of the Study:

• To experimentally realize third-order square-root topological insulators in an acoustic system.
• To investigate the properties and potential applications of acoustic localized modes in these novel topological phases.

Main Methods:

• Modification of a diamond lattice by adding resonators to create square-root topological phases.
• Utilizing bulk polarizations of tight-binding models to analyze topological features.
• Fabricating tetrahedron-like and rhombohedron-like sonic crystals to observe corner states.
• Introducing random disorders to test the robustness of topological states.

Main Results:

• Acoustic localized modes were observed in doubled bulk gaps due to the square-root operation.
• Third-order topological corner states emerged in specific sonic crystal geometries (tetrahedron-like and rhombohedron-like).
• The shape of the sonic crystals influenced the square-root corner states, allowing for flexible sound localization.
• Corner states demonstrated robustness against disorders in the bulk region of 3D lattices.

Conclusions:

• The study successfully extended square-root higher-order topological states into three-dimensional acoustic systems.
• The findings suggest potential applications in selective acoustic sensing and advanced sound manipulation.