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

作　　者：Fan Cui Congcong Le Qiang Zhang Xianxin Wu Jiangping Hu Ching-Kai Chiu 

机构地区：[1]Beijing National Laboratory for Condensed Matter Physics,Institute of Physics,Chinese Academy of Sciences,Beijing 100190,China [2]School of Physical Sciences,University of Chinese Academy of Sciences,Beijing 100190,China [3]RIKEN Interdisciplinary Theoretical and Mathematical Sciences(iTHEMS),Wako 351-0198,Japan [4]CAS Key Laboratory of Theoretical Physics,Institute of Theoretical Physics,Chinese Academy of Sciences,Beijing 100190,China [5]Kavli Institute of Theoretical Sciences,University of Chinese Academy of Sciences,Beijing 100190,China [6]New Cornerstone Science Laboratory,Beijing 100190,China

出　　处：《Science China(Physics,Mechanics & Astronomy)》2024年第9期133-147,共15页中国科学：物理学、力学、天文学（英文版）

基　　金：supported by Japan Science and Technology Agency(JST)as part of Adopting Sustainable Partnerships for Innovative Research Ecosystem(Grant No.JPMJAP2318);the JST Presto(Grant No.JPMJPR2357);supported by the National Key R&D Program of China(Grant No.2022YFA1403901);the National Natural Science Foundation of China(Grant No.11888101);the National Natural Science Foundation of China(Grant No.12047503);the Strategic Priority Research Program of the Chinese Academy of Sciences(Grant Nos.XDB28000000 and XDB33000000);the New Cornerstone Investigator Program;supported by the National Key R&D Program of China(Grant No.2023YFA1407300)。

摘　　要：At magic twisted angles,Dirac cones in twisted bilayer graphene(TBG)can evolve into flat bands,serving as a critical playground 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 number 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.

关 键 词：twisted bilayer systems high-ordered topological nodes Moriéflat bands high degeneracy 

分 类 号：O469[理学—凝聚态物理]