Dirac cones in two-dimensional acoustic metamaterials

Abstract

Dirac cones show many extraordinary properties, including Klein tunneling, pseudo-diffusive behavior, phase reconstruction, and topological edge states, and are thus attracting increasing research attention. However, no studies of Dirac cones on a subwavelength scale have been reported to date. In this paper, subwavelength-scale Dirac cones are realized using acoustic metamaterials that consist of hexagonal arrays of hexagonal columns with Helmholtz resonators. We have calculated the band structures of the three types of unit cells that are yielded by space group symmetry operations of the triangular Helmholtz resonators. The results show that these acoustic metamaterials with Helmholtz resonators can be used successfully to reduce the Dirac cone frequencies. Subwavelength Dirac cones of acoustic metamaterials with p6 mm or p6 symmetries are robust to rotation, while subwavelength Dirac cones of acoustic metamaterials with p31m symmetry are sensitive to rotation. In addition, the Dirac cone frequency decreases gradually with increasing filling ratio, which indicates a possible way to control wave propagation on the subwavelength scale. Numerical simulation results show that acoustic metamaterials can behave like zero-refractive-index media and can be applied to acoustic tunneling. The acoustic metamaterials designed in this work offer a route towards the design of functional acoustic devices operating on subwavelength scales.