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  All Magic Angles in Twisted Bilayer Graphene are Topological

Song, Z., Wang, Z., Shi, W., Li, G., Fang, C., & Bernevig, B. A. (2019). All Magic Angles in Twisted Bilayer Graphene are Topological. Physical Review Letters, 123(3): 036401, pp. 1-6. doi:10.1103/PhysRevLett.123.036401.

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 Creators:
Song, Zhida1, Author
Wang, Zhijun1, Author
Shi, Wujun2, Author              
Li, Gang1, Author
Fang, Chen1, Author
Bernevig, B. Andrei1, Author
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1External Organizations, ou_persistent22              
2Inorganic Chemistry, Max Planck Institute for Chemical Physics of Solids, Max Planck Society, ou_1863425              

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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.

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Language(s): eng - English
 Dates: 2019-07-162019-07-16
 Publication Status: Published in print
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Title: Physical Review Letters
  Abbreviation : Phys. Rev. Lett.
Source Genre: Journal
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Publ. Info: Woodbury, N.Y. : American Physical Society
Pages: - Volume / Issue: 123 (3) Sequence Number: 036401 Start / End Page: 1 - 6 Identifier: ISSN: 0031-9007
CoNE: https://pure.mpg.de/cone/journals/resource/954925433406_1