All Magic Angles in Twisted Bilayer Graphene are Topological

doi:10.1103/PhysRevLett.123.036401

	All Magic Angles in Twisted Bilayer Graphene are Topological
	Song, Zhida 1; Wang, Zhijun 2,3,4; Shi, Wujun5,6 ; Li, Gang5 ; Fang, Chen 2,3,7; Bernevig, B. Andrei 1,8,9
	2019-07-16
发表期刊	PHYSICAL REVIEW LETTERS
ISSN	0031-9007
卷号	123 期号:3
发表状态	已发表
DOI	10.1103/PhysRevLett.123.036401
摘要	We show that the electronic structure of the low-energy bands in the small angle-twisted bilayer graphene consists of a series of semimetallic and topological phases. In particular, we are able to prove, using an approximate low-energy particle-hole symmetry, that the gapped set of bands that exist around all magic angles have a nontrivial topology stabilized by a magnetic symmetry, provided band gaps appear at fillings of +/- 4 electrons per moire unit cell. The topological index is given as the winding number (a Z number) of the Wilson loop in the moire Brillouin zone. Furthermore, we also claim that, when the gapped bands are allowed to couple with higher-energy bands, the Z index collapses to a stable Z(2) index. The approximate, emergent particle-hole symmetry is essential to the topology of graphene: When strongly broken, nontopological phases can appear. Our Letter underpins topology as the crucial ingredient to the description of low-energy graphene. We provide a four-band short-range tight-binding model whose two lower bands have the same topology, symmetry, and flatness as those of the twisted bilayer graphene and which can be used as an effective low-energy model. We then perform large-scale (11000 atoms per unit cell, 40 days per k-point computing time) ab initio calculations of a series of small angles, from 3 degrees to 1 degrees, which show a more complex and somewhat different evolution of the symmetry of the low-energy bands than that of the theoretical moire model but which confirm the topological nature of the system.
收录类别	SCI ; SCIE ; EI
语种	英语
资助项目	NSF-MRSEC[DMR-142051]
WOS研究方向	Physics
WOS类目	Physics, Multidisciplinary
WOS记录号	WOS:000476695900007
出版者	AMER PHYSICAL SOC
EI入藏号	20193107261706
EI主题词	Calculations ; Electronic structure ; Energy gap ; Graphene
EI分类号	Nanotechnology:761 ; Chemical Products Generally:804 ; Mathematics:921 ; Combinatorial Mathematics, Includes Graph Theory, Set Theory:921.4
WOS关键词	INSULATOR
原始文献类型	Article
引用统计
文献类型	期刊论文
条目标识符	https://kms.shanghaitech.edu.cn/handle/2MSLDSTB/61077
专题	硬x射线自由电子激光装置项目物质科学与技术学院_PI研究组_李刚组
通讯作者	Fang, Chen; Bernevig, B. Andrei
作者单位	1.Princeton Univ, Dept Phys, Princeton, NJ 08544 USA 2.Chinese Acad Sci, Beijing Natl Res Ctr Condensed Matter Phys, Beijing 100190, Peoples R China 3.Chinese Acad Sci, Inst Phys, Beijing 100190, Peoples R China 4.Univ Chinese Acad Sci, Beijing 100049, Peoples R China 5.ShanghaiTech Univ, Sch Phys Sci & Technol, Shanghai 200031, Peoples R China 6.Max Planck Inst Chem Phys Solids, D-01187 Dresden, Germany 7.Chinese Acad Sci, Ctr Excellence Topol Quantum Computat, Beijing 100190, Peoples R China 8.Free Univ Berlin, Phys Dept, Arnimallee 14, D-14195 Berlin, Germany 9.Max Planck Inst Microstruct Phys, D-06120 Halle, Germany
推荐引用方式 GB/T 7714	Song, Zhida,Wang, Zhijun,Shi, Wujun,et al. All Magic Angles in Twisted Bilayer Graphene are Topological[J]. PHYSICAL REVIEW LETTERS,2019,123(3).
APA	Song, Zhida,Wang, Zhijun,Shi, Wujun,Li, Gang,Fang, Chen,&Bernevig, B. Andrei.(2019).All Magic Angles in Twisted Bilayer Graphene are Topological.PHYSICAL REVIEW LETTERS,123(3).
MLA	Song, Zhida,et al."All Magic Angles in Twisted Bilayer Graphene are Topological".PHYSICAL REVIEW LETTERS 123.3(2019).