Replica higher-order topology of Hofstadter butterflies in twisted bilayer graphene  

作　　者：Sun-Woo Kim Sunam Jeon Moon Jip Park Youngkuk Kim 

机构地区：[1]Department of Physics,KAIST,Daejeon,Republic of Korea [2]Department of Materials Science and Metallurgy,University of Cambridge,Cambridge,UK [3]Department of Energy Science,Sungkyunkwan University,Suwon,Republic of Korea [4]Center for Theoretical Physics of Complex Systems,Institute for Basic Science(IBS),Daejeon,Republic of Korea [5]Department of Physics,Hanyang University,Seoul,Republic of Korea [6]Department of Physics,Sungkyunkwan University,Suwon,Republic of Korea

出　　处：《npj Computational Materials》2023年第1期783-791,共9页计算材料学（英文）

基　　金：This work was supported by the Korean National Research Foundation(NRF)Basic Research Laboratory(NRF-2020R1A4A307970713);the NRF Grant numbers(NRF-2021R1A2C101387112 and NRF-2021M3H3A1038085);This work was also supported by the National Research Foundation of Korea(NRF)grant funded by the Korea government(MSIT)(RS-2023-00252085,RS-2023-00218998);The computational resource was provided by the Korea Institute of Science and Technology Information(KISTI)(KSC-2020-CRE-0108).

摘　　要：The Hofstadter energy spectrum of twisted bilayer graphene(TBG)is found to have recursive higher-order topological properties.We demonstrate that higher-order topological insulator(HOTI)phases,characterized by localized corner states,occur as replicas of the original HOTIs to fulfill the self-similarity of the Hofstadter spectrum.We show the existence of exact flux translational symmetry in TBG at all commensurate angles.Based on this result,we identify that the original HOTI phase at zero flux is re-entrant at a half-flux periodicity,where the effective twofold rotation is preserved.In addition,numerous replicas of the original HOTIs are found for fluxes without protecting symmetries.Like the original HOTIs,replica HOTIs feature both localized corner states and edge-localized real-space topological markers.The replica HOTIs originate from the different interaction scales,namely,intralayer and interlayer couplings,in TBG.The topological aspect of Hofstadter butterflies revealed in our results highlights symmetry-protected topology in quantum fractals.

关 键 词：properties SPECTRUM TOPOLOGICAL 

分 类 号：O61[理学—无机化学]