Square-root-like higher-order topological states in three-dimensional sonic crystals.

Area of Science:

• Condensed Matter Physics
• Acoustics
• Materials Science

Background:

• Higher-order topological insulators possess unique topological properties derived from their Hamiltonians.
• Recent theoretical work introduced square-root descendants of topological insulators.

Purpose of the Study:

• To experimentally realize a three-dimensional (3D) square-root-like sonic crystal.
• To investigate the emergence of acoustic localized modes in this system.
• To explore the potential for designing advanced functional acoustic devices.

Main Methods:

• Constructing a 3D sonic crystal by stacking 2D square-root lattices.
• Analyzing intralayer couplings and their effect on energy degeneracies.
• Introducing staggered interlayer couplings to induce higher-order topological phenomena.

Main Results:

• Observed emergence of 2D surface states and 1D hinge states due to the square-root topology.
• Demonstrated tunability of topological states by modifying boundary cavities.
• Proposed and characterized a third-order topological corner state with nontrivial bulk polarization.

Conclusions:

• The 3D square-root sonic crystal successfully hosts multiple acoustic localized modes.
• This system offers a platform for high-dimensional square-root topological materials.
• Potential applications include advanced sound trapping and acoustic sensing devices.