| CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES |
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Constructing Hopf Insulator from Geometric Perspective of Hopf Invariant |
| Zhi-Wen Chang1, Wei-Chang Hao2, Miguel Bustamante3, and Xin Liu1* |
1Institute of Theoretical Physics, School of Physics and Optoelectronic Engineering, Beijing University of Technology, Beijing 100124, China
2School of Physics, Beihang University, Beijing 100191, China
3Complex and Adaptive Systems Laboratory, School of Mathematics and Statistics, University College Dublin, Belfield, 4, Dublin, Ireland
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| Cite this article: |
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Zhi-Wen Chang, Wei-Chang Hao, Miguel Bustamante et al 2024 Chin. Phys. Lett. 41 037302 |
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Abstract 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.
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Received: 17 November 2023
Editors' Suggestion
Published: 05 March 2024
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| PACS: |
73.43.-f
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(Quantum Hall effects)
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03.65.Vf
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(Phases: geometric; dynamic or topological)
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73.20.At
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(Surface states, band structure, electron density of states)
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05.30.Rt
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(Quantum phase transitions)
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