Multiple Open and Closed Nodal‐Line Phonons in Solids with a P3¯m$P\overline{3}m$1 Space Group

• Published in: Advanced Physics Research Vol. 4; no. 3
• Main Authors: Wang, Xiaotian, Sun, Tingting, Xie, Chengwu, Yuan, Hongkuan, Tie, Yang, Zhang, Zeying, Zhang, Gang
• Format: Journal Article
• Language: English
• Published: Edinburgh John Wiley & Sons, Inc 01.03.2025
• Subjects: Barium; Euclidean space; Lattice theory; nodal line; Phonons; Symmetry; topological phonon; topological states
• ISSN: 2751-1200; 2751-1200
• DOI: 10.1002/apxr.202200085

Unlike electron systems, the phonon system has its own advantages (such as no limitations regarding Fermi energy and the effect of spin‐orbit coupling) and, therefore, can be viewed as a unique platform to predict spinless nodal‐line states. Nodal‐line phonons can be divided into open and closed nodal‐line phonons from a mathematical point of view. In this work, using first‐principle calculations, we select Ba(AgS)2 and Ca(ZnP)2, with the space group P3¯m$P\overline{3}m$1, as examples of realistic materials to investigate the difference between the open and closed nodal‐line phonons. Two phonon band‐crossing points (PBCPs) along the K–Γ and H–A paths are present in their phonon spectra, and they correspond to closed nodal lines in Ba(AgS)2 and open nodal lines in Ca(ZnP)2, respectively. The difference between these two types nodal‐line phonons is explained through symmetry analysis. All the nodal‐line phonons are topologically nontrivial, with the prominent phonon surface states well separated from the bulk states, favorable for experimental detection. This work offers a deep understanding of the open and closed nodal‐line phonons. It also proposes ideal candidates with multiple open and closed nodal‐line phonons for follow‐up experimental confirmation. Nodal‐line phonons can be divided into open and closed nodal‐line states according to their spatial configurations. Based on the theoretical calculations, the open and closed nodal‐line phonons are examined in the realistic materials Ba(AgS)2 and Ca(ZnP) 2 with the space group P3¯m$P\overline{3}m$1, and also detailed explanations of their difference through topological symmetry arguments and effective model analysis are provided.