声子晶体中的Weyl点及相关效应研究

Weyl semi-metal, because of the existence of the Weyl points in the band structure of the material, arouses increasing interest in recent years and becomes the hot field in condensed matter physics. More recently, Weyl points have also been observed for classical waves in artificial periodic structures, for example, for electromagnetic waves in photonic crystals and for acoustic in phononic crystals, and for now it is the time to begin a systematic research on this topic. In this project, we will carry out extensive studies on the Weyl points of acoustic waves in phononic crystals, including the dependence of the type and the existence of the Weyl points of the symmetry, the inter-change of the Dirac points and the Weyl points due to the variation of the symmetries, the effect of the Weyl points on the propagation of the bulk waves, and the Fermi arc and the one-way propagation of the topologically protected surface states. The novel properties of both the bulk and the surface waves in Weyl phononic crystals, may bring about innovative acoustic devices in applications. Therefore, the research in the project is of important scientific significance as well as potential practical value.

近几年来，Weyl半金属由于其能带结构中受拓扑保护的Weyl点的存在引起强烈研究兴趣，成为凝聚态物理的研究热点。最近，研究者在光子晶体和声子晶体等人工周期结构的能带结构中，也观察到光波（或电磁波）和声波等经典波的Weyl点，但仅有零散几个工作，缺乏系统深入的研究。本项目拟对声子晶体中声波的Weyl点进行全方位的研究，包括Weyl点的类型及存在性与对称性的关系，Weyl点与Dirac点在对称性改变时的相互转化，Weyl点对体态传播性质的影响及效应，受拓扑保护的界面态的费米弧及单向性等等。Weyl声子晶体中体态和界面态展现出新颖传播特性，可望带来全新声功能器件，因而本项目的研究不仅具有科学意义，同时也具有潜在应用价值。

近年来，人们对具有非平庸能带交叉特征的拓扑半金属进行了大量的研究。主要包括Dirac和Weyl半金属，在它们的三维布里流区具有孤立的四重和双重线性简并费米点，称为Dirac和Weyl点。在该项目的资助下，我们主要研究了：声子晶体中不同类型Weyl点诱导的边缘态实现拓扑折射现象；（b）Weyl点与Dirac点/节线/节面在对称性改变时的相互转化及其拓扑输运性质；（c）声学高阶拓扑Weyl半金属相及其特征性的铰链态；（d）其他类型的二维拓扑声子晶体中声拓扑输运特性。总体而言，我们出色的完成了项目的既定目标，基本弄清了声子晶体中Weyl点的类型及存在性与对称性的关系，利用不同类型Weyl点诱导的边缘态实现了新颖声输运；此外，还研究了Weyl点与Dirac点/节线/节面在对称性改变时的相互转化；额外地，我们也研究了一些二维拓扑声子晶体中的其他效应，如声自旋陈绝缘体、高阶拓扑绝缘相、声谷态的拓扑输运等。在该面上基金的资助下，项目研究进展顺利，总共发表学术论文32篇，其中包括在顶级期刊上发表Nature 1篇，Nature Materials 2篇，Nature Communications 4篇，Physical Review Letters 6篇（均为通讯作者）。

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