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

Jun Mei,Ying Wu,Zeguo Chen

doi:10.1038/srep32752

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 Γ point, we can construct pseudo-time-reversal symmetry as well as pseudo-spin states in this classical system. We develop an effective Hamiltonian 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.

Highlights

Band inversion and the topological phase transition
In the Method section, we demonstrate that the spatial symmetry of the E1 and E2 representations can be utilized to construct pseudo-time-reversal symmetry
We consider a flat edge between a topologically nontrivial phase and a trivial phase, as shown in Fig. 4, where the whole structure is surrounded by perfectly matched layers (PMLs) to absorb outgoing waves

Summary

Introduction

Band inversion and the topological phase transition. We unambiguously demonstrate topologically protected acoustic one-way edge states with robust propagation against scattering from defects. In the Method section, we demonstrate that the spatial symmetry of the E1 and E2 representations can be utilized to construct pseudo-time-reversal symmetry.

Results

Conclusion