Wang Jianhua, Wang Yang, Zhou Feng, Wang Wenhong, Cheng Zhenxiang, Qian Shifeng, Wang Xiaotian, Yu Zhi-Ming
Institute of Quantum Materials and Devices, Tiangong University, Tianjin, 300387, China.
Institute for Superconducting and Electronic Materials, Faculty of Engineering and Information Sciences, University of Wollongong, Wollongong, 2500, Australia.
Adv Sci (Weinh). 2025 Aug;12(32):e04812. doi: 10.1002/advs.202504812. Epub 2025 Jun 17.
A pair of Weyl points (WPs) with opposite topological charges can exhibit an additional higher-order Z topological charge, giving rise to the formation of a Z Weyl dipole (WD). Owing to the nontrivial topological charge, Z WDs should also appear in pairs, and the WPs within each Z WD can not be annihilated when meeting together. As a novel topological state, the topological Weyl dipole (TWD) phase has garnered significant attention, yet its realization in crystalline materials remains a challenge. Here, through first-principles calculations and theoretical analysis, the existence of the nontrivial unconventional WD phase is demonstrated in the phonon spectra of the P6 type Y(OH). Particularly, the nontrivial unconventional WD in this system is protected by a quantized quadrupole moment, and it is distinguished from conventional WD, as it comprises an unconventional charge-3 WP with charge of -3 and three conventional charge-1 WPs with charge of +1. Consequently, the nontrivial unconventional WD phase in Y(OH) features unique 2D sextuple-helicoid Fermi-arc states on the top and bottom surfaces, protected by the topological charges, as well as 1D hinge states that connect the two nontrivial unconventional WDs along the side hinges, guaranteed by the quantized quadrupole moment.
一对具有相反拓扑电荷的外尔点（WPs）可以展现出额外的高阶Z拓扑电荷，从而导致Z外尔偶极子（WD）的形成。由于非平凡拓扑电荷，Z WD也应该成对出现，并且每个Z WD内的WPs在相遇时不会湮灭。作为一种新颖的拓扑态，拓扑外尔偶极子（TWD）相已经引起了广泛关注，但其在晶体材料中的实现仍然是一个挑战。在此，通过第一性原理计算和理论分析，在P6型Y(OH)的声子谱中证明了非平凡非常规WD相的存在。特别地，该系统中的非平凡非常规WD由一个量子化的四极矩保护，并且它与传统WD不同，因为它包含一个电荷为 -3的非常规电荷 -3 WP和三个电荷为 +1的传统电荷 -1 WPs。因此，Y(OH)中的非平凡非常规WD相在顶面和底面上具有由拓扑电荷保护的独特二维六重螺旋面费米弧态，以及由量子化四极矩保证的沿着侧面铰链连接两个非平凡非常规WD的一维铰链态。
