Pseudo-time-reversal symmetry and topological edge states in two-dimensional acoustic crystals

TL;DR

This paper introduces a two-dimensional acoustic crystal design that supports topologically protected edge states, enabling robust, unidirectional acoustic wave propagation with potential applications across a wide frequency spectrum.

Contribution

The work presents a novel acoustic crystal structure utilizing pseudo-time-reversal symmetry to realize topological edge states, with an effective Hamiltonian model and numerical validation.

Findings

Demonstrated unidirectional edge state propagation

Proved robustness against defects and sharp bends

Linked band inversion to topological phase transition

Abstract

We propose a simple two-dimensional acoustic crystal to realize topologically protected edge states for acoustic waves. The acoustic crystal is composed of a triangular array of core-shell cylinders embedded in a water host. By utilizing the point group symmetry of two doubly degenerate eigenstates at the \Gamma point, we can construct pseudo-time-reversal symmetry as well as pseudo-spin states in this classical system. We develop an effective Hamiltonian model for the associated dispersion bands around the Brillouin zone center, and find the inherent link between the band inversion and the topological phase transition. With numerical simulations, we unambiguously demonstrate the unidirectional propagation of acoustic edge states along the interface between a topologically nontrivial acoustic crystal and a trivial one, and the robustness of the edge states against defects with sharp bends. Our work provides a new design paradigm for manipulating and transporting acoustic waves in a topologically protected manner. Technological applications and devices based on our design are expected in various frequency ranges of interest, spanning from infrasound to ultrasound.