articlePhysical Review LettersJul 16, 2019GREEN OA

All Magic Angles in Twisted Bilayer Graphene are Topological

ZSZhida SongZWZhijun WangWSWujun ShiGLGang LiCFChen Fang

Princeton University · Chinese Academy of Sciences · +7 more institutions

PubMed
Indexed inarxivcrossrefpubmed

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 moiré unit cell. The topological index is given as the winding number (a Z number) of the Wilson loop in the moiré 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}…

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505
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25.33
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100%
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62
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Authors

6

Topics & keywords

Topics
Keywords
  • Bilayer graphene
  • Topology (electrical circuits)
  • Brillouin zone
  • Physics
  • Graphene
  • Condensed matter physics
  • Electronic band structure
  • Symmetry (geometry)
UN Sustainable Development Goals
  • Affordable and clean energy
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