Yu Wei-Wang, Liu Ying, He Zeqing, Wang Lirong, Zhang Xiaoming, Liu Guodong
State Key Laboratory of Reliability and Intelligence of Electrical Equipment, Hebei University of Technology, Tianjin, 300130, China.
School of Materials Science and Engineering, Hebei University of Technology, Tianjin, 300130, China.
Phys Chem Chem Phys. 2023 Aug 2;25(30):20680-20685. doi: 10.1039/d3cp01621h.
The advent of topological phonons has been attracting tremendous attention. However, studies in two-dimensional (2D) systems are limited. Here, we reveal a 2D novel combination of Weyl phonons - a Weyl complex composed of two linear Weyl nodes and one quadratic Weyl node. This Weyl complex consists of crossing points of two specific branches. We show that the coexistence of threefold symmetry - rotation symmetry, inversion symmetry, and time-reversal symmetry - could lead to the presence of the Weyl complex. Based on the symmetry requirement, we further construct the tight-binding model and effective · model for characterizing the Weyl complex. Moreover, due to the presence of the spacetime inversion symmetry, the linear and quadratic Weyl nodes feature a quantized (π and 2π) Berry phase, thus defining the corresponding topological charge. Furthermore, Weyl complexes consisting of Weyl points possess an emergent chiral symmetry, an integer topological charge is thus defined. Then, distinguished phenomena for the Weyl complex are studied, in particular, the edge states with three terminals. Our work predicts the presence of this novel 2D topological phase, and provides the symmetry guidance to realize it. Based on the first-principles calculations, we identify an existing material CuSi, as a concrete example to demonstrate the presence of the Weyl complex, and also study the phase transition under symmetry breaking.
拓扑声子的出现一直备受关注。然而，二维（2D）系统中的研究却很有限。在此，我们揭示了一种二维新型的外尔声子组合——由两个线性外尔点和一个二次外尔点组成的外尔复合体。这个外尔复合体由两个特定分支的交叉点构成。我们表明，三重对称性（旋转对称性、反演对称性和时间反演对称性）的共存会导致外尔复合体的出现。基于对称性要求，我们进一步构建了用于表征外尔复合体的紧束缚模型和有效模型。此外，由于时空反演对称性的存在，线性和二次外尔点具有量子化（π和2π）的贝里相位，从而定义了相应的拓扑电荷。此外，由外尔点组成的外尔复合体具有一种涌现的手征对称性，因此定义了一个整数拓扑电荷。然后，我们研究了外尔复合体的独特现象，特别是具有三个终端的边缘态。我们的工作预测了这种新型二维拓扑相的存在，并为实现它提供了对称性指导。基于第一性原理计算，我们确定现有的材料CuSi作为一个具体例子来证明外尔复合体的存在，并研究了对称性破缺下的相变。
