Dirac points and the transition towards Weyl points in three-dimensional sonic crystals

Boyang Xie,Zhengyou Liu,Shuqi Chen,Hua Cheng,Jianguo Tian,Hui Liu

doi:10.1038/s41377-020-00416-2

Boyang Xie, Zhengyou Liu + Show 4 more

Open Access

https://doi.org/10.1038/s41377-020-00416-2

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Abstract

A four-fold-degenerate three-dimensional (3D) Dirac point, represents a degenerate pair of Weyl points carrying opposite chiralities. Moreover, 3D Dirac crystals have shown many exotic features different from those of Weyl crystals. How these features evolve from 3D Dirac to Weyl crystals is important in research on 3D topological matter. Here, we realized a pair of 3D acoustic Dirac points from band inversion in a hexagonal sonic crystal and observed the surface states and helical interface states connecting the Dirac points. Furthermore, each Dirac point can transition into a pair of Weyl points with the introduction of chiral hopping. The exotic features of the surface states and interface states are inherited by the resulting Weyl crystal. Our work may serve as an ideal platform for exploring exotic physical phenomena in 3D topological semimetals.

Highlights

A three-dimensional (3D) Dirac point is a four-fold band crossing in 3D momentum space, away from which the energy band exhibits linear dispersion in all directions[1]
A 3D Dirac point can be treated as a degenerate pair of two Weyl points with opposite chiralities that can be separated in momentum space when their time-reversal symmetry or inversion symmetry is broken[1,9]
We report the theoretical and experimental realization of a pair of class I acoustic 3D Dirac points in a hexagonal sonic crystal and demonstrate how the exotic features of the surface states and interface states evolve in the transition towards Weyl points

Summary

Introduction

A three-dimensional (3D) Dirac point is a four-fold band crossing in 3D momentum space, away from which the energy band exhibits linear dispersion in all directions[1]. As a fundamental topological band structure, a 3D Dirac point can transit into topological band gaps[6,7], line nodes[8] or Weyl points[9,10]. A 3D Dirac point can be treated as a degenerate pair of two Weyl points with opposite chiralities that can be separated in momentum space when their time-reversal symmetry or inversion symmetry is broken[1,9]. 3D Dirac points can exhibit exotic anomalous effects compared with Weyl points, such as

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