首页|Classification of high-ordered topological nodes towards Moiré flat bands in twisted bilayers

Classification of high-ordered topological nodes towards Moiré flat bands in twisted bilayers

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At magic twisted angles,Dirac cones in twisted bilayer graphene(TBG)can evolve into flat bands,serving as a critical play-ground for the study of strongly correlated physics.When chiral symmetry is introduced,rigorous mathematical proof confirms that the flat bands are locked at zero energy in the entire Moiré Brillouin zone(BZ).Yet,TBG is not the sole platform that exhibits this absolute band flatness.Central to this flatness phenomenon are topological nodes and their specific locations in the BZ.In this study,considering twisted bilayer systems that preserve chiral symmetry,we classify various ordered topological nodes in base layers and all possible node locations across different BZs.Specifically,we constrain the node locations to rotational centers,such as Γ and M points,to ensure the interlayer coupling retains equal strength in all directions.Using this classification as a foundation,we systematically identify the conditions under which Moiré flat bands emerge.Additionally,through the extension of holomorphic functions,we provide proof that flat bands are locked at zero energy,shedding light on the origin of the band flatness.Remarkably,beyond Dirac cones,numerous twisted bilayer nodal platforms can host flat bands with a degeneracy num-ber of more than two,such as four-fold,six-fold,and eight-fold.This multiplicity of degeneracy in flat bands might unveil more complex and enriched correlation physics.

twisted bilayer systemshigh-ordered topological nodesMorié flat bandshigh degeneracy

Fan Cui、Congcong Le、Qiang Zhang、Xianxin Wu、Jiangping Hu、Ching-Kai Chiu

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Beijing National Laboratory for Condensed Matter Physics,Institute of Physics,Chinese Academy of Sciences,Beijing 100190,China

School of Physical Sciences,University of Chinese Academy of Sciences,Beijing 100190,China

RIKEN Interdisciplinary Theoretical and Mathematical Sciences(iTHEMS),Wako 351-0198,Japan

CAS Key Laboratory of Theoretical Physics,Institute of Theoretical Physics,Chinese Academy of Sciences,Beijing 100190,China

Kavli Institute of Theoretical Sciences,University of Chinese Academy of Sciences,Beijing 100190,China

New Cornerstone Science Laboratory,Beijing 100190,China

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Japan Science and Technology Agency(JST)as part of Adopting Sustainable Partnerships for Innovative Research EcosystemJST PrestoNational Key R&D Program of ChinaNational Natural Science Foundation of ChinaStrategic Priority Research Program of the Chinese Academy of SciencesStrategic Priority Research Program of the Chinese Academy of SciencesNew Cornerstone Investigator ProgramNational Key R&D Program of ChinaNational Natural Science Foundation of China

JPMJAP2318JP-MJPR23572022YFA140390111888101XDB28000000XDB330000002023YFA140730012047503

2024

10.1007/s11433-024-2410-9

中国科学:物理学 力学 天文学(英文版)
中国科学院

中国科学:物理学 力学 天文学(英文版)

CSTPCD
影响因子：0.91
ISSN：1674-7348
年,卷(期)：2024.67(9)