Band topology in twisted bilayer graphene

Superconductivity and correlated insulators have been observed in “magic-angle” twisted bilayer graphene when the nearly flat bands close to charge neutrality are partially filled. The observed phenomenology resembles that of high-temperature superconductors like cuprates. Yet, the building blocks of the two systems are vastly different, since the states in TBG descend from graphene’s Dirac dispersion. We argue that the Dirac character of the relevant states endows the nearly flat bands with a nontrivial band topology, which forbids any fully symmetric tight-binding description for the nearly flat bands alone. Extended models incorporating the higher energy bands, however, are possible. We constructing a family of such tight-binding models, and from them establish that the band topology is “fragile” in nature, in that it can be dissolved simply by adding additional atomic bands. Our models pave the way to developing a theoretical understanding of twisted bilayer graphene from a strong-coupling perspective.