Band structure of twisted bilayer graphene: Emergent symmetries, commensurate approximants, and Wannier obstructions

Abstract

Motivated by the exciting discovery of correlated insulating behavior and superconductivity in magic-angle bilayer graphene, the authors discuss here the salient features of the band structure of this system. A remarkable feature is the appearance of isolated, nearly flat bands around the magic angles. The authors discuss the importance of emergent symmetries of this system and clarify some potential confusion regarding commensurate structures of twisted bilayer graphene. Furthermore, they discuss the band topology, which leads to obstructions to constructing well-localized Wannier functions of the nearly flat bands, and give directions towards overcoming the difficulties.