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All Magic Angles in Twisted Bilayer Graphene are Topological

Author(s): Song, Zhida; Wang, Zhijun; Shi, Wujun; Li, Gang; Fang, Chen; et al

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Abstract: 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.
Publication Date: 19-Jul-2019
Electronic Publication Date: 16-Jul-2019
Citation: 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, doi:10.1103/PhysRevLett.123.036401
DOI: doi:10.1103/PhysRevLett.123.036401
ISSN: 0031-9007
EISSN: 1079-7114
Pages: 036401-1 - 036401-6
Type of Material: Journal Article
Journal/Proceeding Title: PHYSICAL REVIEW LETTERS
Version: Final published version. Article is made available in OAR by the publisher's permission or policy.

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