Dirac Hierarchy in Acoustic Topological Insulators

Area of Science:

• Acoustics
• Condensed Matter Physics
• Materials Science

Background:

• Dirac cones are fundamental to electronic band structures in materials like graphene and topological insulators (TIs).
• Recent research explores Dirac cones in classical wave physics using engineered artificial lattices.

Purpose of the Study:

• To demonstrate an acoustic 3D honeycomb lattice featuring a hierarchy of Dirac cones.
• To explore the topological properties and potential applications of this engineered acoustic system.

Main Methods:

• Fabrication of a 3D acoustic honeycomb lattice.
• Analytical investigation of the topological origin of bulk, surface, hinge, and corner states.
• Characterization of topological states using winding numbers.

Main Results:

• Observation of an eightfold bulk Dirac cone, a 2D fourfold surface state Dirac cone, and a 1D twofold hinge state Dirac cone.
• Demonstration of first-order, second-order, and third-order topological insulator properties in the acoustic lattice.
• Identification of topological surface, hinge, and corner states characterized by winding numbers.

Conclusions:

• The engineered acoustic lattice exhibits a rich hierarchy of Dirac cones and topological states.
• This system offers new possibilities for controlling sound and vibration.
• Potential applications include acoustic steering, ultrasonic energy concentration, and filtering.