Congcong Le, Qiang Zhang, Fan Cui, Xianxin Wu, Ching-Kai Chiu
{"title":"Double and Quadruple Flat Bands Tuned by Alternative Magnetic Fluxes in Twisted Bilayer Graphene","authors":"Congcong Le, Qiang Zhang, Fan Cui, Xianxin Wu, Ching-Kai Chiu","doi":"10.1103/physrevlett.132.246401","DOIUrl":null,"url":null,"abstract":"Twisted bilayer graphene (TBG) can host the moiré energy flat bands with twofold degeneracy serving as a fruitful playground for strong correlations and topological phases. However, the number of degeneracy is not limited to two. Introducing a spatially alternative magnetic field, we report that the induced magnetic phase becomes an additional controllable parameter and leads to an undiscovered generation of fourfold degenerate flat bands. This emergence stems from the band inversion at the <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi mathvariant=\"normal\">Γ</mi></math> point near the Fermi level with a variation of both twisted angle and magnetic phase. We present the conditions for the emergence of multifold degenerate flat bands, which are associated with the eigenvalue degeneracy of a Birman-Schwinger operator. Using holomorphic functions, which explain the origin of the double flat bands in the conventional TBG, we can generate analytical wave functions in the magnetic TBG to show absolute flatness with fourfold degeneracy. Moreover, we identify an orbital-related intervalley coherent state as the many-body ground state at charge neutrality. In contrast, the conventional TBG has only two moiré energy flat bands, and the highly degenerate flat bands with additional orbital channels in this magnetic platform might bring richer correlation physics.","PeriodicalId":20069,"journal":{"name":"Physical review letters","volume":null,"pages":null},"PeriodicalIF":8.1000,"publicationDate":"2024-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physical review letters","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1103/physrevlett.132.246401","RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
Twisted bilayer graphene (TBG) can host the moiré energy flat bands with twofold degeneracy serving as a fruitful playground for strong correlations and topological phases. However, the number of degeneracy is not limited to two. Introducing a spatially alternative magnetic field, we report that the induced magnetic phase becomes an additional controllable parameter and leads to an undiscovered generation of fourfold degenerate flat bands. This emergence stems from the band inversion at the point near the Fermi level with a variation of both twisted angle and magnetic phase. We present the conditions for the emergence of multifold degenerate flat bands, which are associated with the eigenvalue degeneracy of a Birman-Schwinger operator. Using holomorphic functions, which explain the origin of the double flat bands in the conventional TBG, we can generate analytical wave functions in the magnetic TBG to show absolute flatness with fourfold degeneracy. Moreover, we identify an orbital-related intervalley coherent state as the many-body ground state at charge neutrality. In contrast, the conventional TBG has only two moiré energy flat bands, and the highly degenerate flat bands with additional orbital channels in this magnetic platform might bring richer correlation physics.
期刊介绍:
Physical review letters(PRL)covers the full range of applied, fundamental, and interdisciplinary physics research topics:
General physics, including statistical and quantum mechanics and quantum information
Gravitation, astrophysics, and cosmology
Elementary particles and fields
Nuclear physics
Atomic, molecular, and optical physics
Nonlinear dynamics, fluid dynamics, and classical optics
Plasma and beam physics
Condensed matter and materials physics
Polymers, soft matter, biological, climate and interdisciplinary physics, including networks