{"title":"四维拓扑绝缘体中的拓扑缺陷和边界态","authors":"Zhi-Wen Chang, Wei-Chang Hao and Xin Liu","doi":"10.1209/0295-5075/ad397c","DOIUrl":null,"url":null,"abstract":"We show the connection between the second Chern number and topological defects, in a (4+1)-dimensional time-reversal invariant Dirac lattice model. It is discovered that two types of topological defects, the five-dimensional (5D) and four-dimensional (4D) point defects arise from the singular points of wave functions together with the geometric meaning of the second Chern number. We demonstrated that the 5D point defects appear at the band crossing positions with a topological transition, leading to a jump of the second Chern number. The 4D point defects exist in an insulating bulk, whose topological charges can give the evaluations of the second Chern number of energy bands. Finally, we discussed the possible structures of the boundary states in the light of the realization way of the 4D model. Our theory provides not only a new perspective to grasp the second Chern number, but also a simple approach to derive its values without calculating any integrals.","PeriodicalId":11738,"journal":{"name":"EPL","volume":"20 1","pages":""},"PeriodicalIF":1.8000,"publicationDate":"2024-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Topological defects and boundary states in four-dimensional topological insulator\",\"authors\":\"Zhi-Wen Chang, Wei-Chang Hao and Xin Liu\",\"doi\":\"10.1209/0295-5075/ad397c\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We show the connection between the second Chern number and topological defects, in a (4+1)-dimensional time-reversal invariant Dirac lattice model. It is discovered that two types of topological defects, the five-dimensional (5D) and four-dimensional (4D) point defects arise from the singular points of wave functions together with the geometric meaning of the second Chern number. We demonstrated that the 5D point defects appear at the band crossing positions with a topological transition, leading to a jump of the second Chern number. The 4D point defects exist in an insulating bulk, whose topological charges can give the evaluations of the second Chern number of energy bands. Finally, we discussed the possible structures of the boundary states in the light of the realization way of the 4D model. Our theory provides not only a new perspective to grasp the second Chern number, but also a simple approach to derive its values without calculating any integrals.\",\"PeriodicalId\":11738,\"journal\":{\"name\":\"EPL\",\"volume\":\"20 1\",\"pages\":\"\"},\"PeriodicalIF\":1.8000,\"publicationDate\":\"2024-04-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"EPL\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1209/0295-5075/ad397c\",\"RegionNum\":4,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"PHYSICS, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"EPL","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1209/0295-5075/ad397c","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
Topological defects and boundary states in four-dimensional topological insulator
We show the connection between the second Chern number and topological defects, in a (4+1)-dimensional time-reversal invariant Dirac lattice model. It is discovered that two types of topological defects, the five-dimensional (5D) and four-dimensional (4D) point defects arise from the singular points of wave functions together with the geometric meaning of the second Chern number. We demonstrated that the 5D point defects appear at the band crossing positions with a topological transition, leading to a jump of the second Chern number. The 4D point defects exist in an insulating bulk, whose topological charges can give the evaluations of the second Chern number of energy bands. Finally, we discussed the possible structures of the boundary states in the light of the realization way of the 4D model. Our theory provides not only a new perspective to grasp the second Chern number, but also a simple approach to derive its values without calculating any integrals.
期刊介绍:
General physics – physics of elementary particles and fields – nuclear physics – atomic, molecular and optical physics – classical areas of phenomenology – physics of gases, plasmas and electrical discharges – condensed matter – cross-disciplinary physics and related areas of science and technology.
Letters submitted to EPL should contain new results, ideas, concepts, experimental methods, theoretical treatments, including those with application potential and be of broad interest and importance to one or several sections of the physics community. The presentation should satisfy the specialist, yet remain understandable to the researchers in other fields through a suitable, clearly written introduction and conclusion (if appropriate).
EPL also publishes Comments on Letters previously published in the Journal.