Constructing Hopf Insulator from Geometric Perspective of Hopf Invariant

• Published in: Chinese physics letters Vol. 41; no. 3; pp. 37302 - 126
• Main Authors: Chang, Zhi-Wen, Hao, Wei-Chang, Bustamante, Miguel, Liu, Xin
• Format: Journal Article
• Language: English
• Published: Chinese Physical Society and IOP Publishing Ltd 01.03.2024
• ISSN: 0256-307X; 1741-3540
• DOI: 10.1088/0256-307X/41/3/037302

We propose a method to construct Hopf insulators based on the study of topological defects from the geometric perspective of Hopf invariant I . Firstly, we prove two types of topological defects naturally inhering in the inner differential structure of the Hopf mapping. One type is the four-dimensional point defects, which lead to a topological phase transition occurring at the Dirac points. The other type is the three-dimensional merons, whose topological charges give the evaluations of I . Then, we show two ways to establish the Hopf insulator models. One approach is to modify the locations of merons, thereby the contributions of charges to I will change. The other is related to the number of defects. It is found that I will decrease if the number reduces, while increase if additional defects are added. The method developed in this study is expected to provide a new perspective for understanding the topological invariants, which opens a new door in exploring and designing novel topological materials in three dimensions.