Twisted bilayer graphene: effective model, topological states and relevant symmetries

Correlated Mott-insulating states alternated with unconventional superconductivity have been lately observed in magic-angle graphene superlattices. For small angles of rotation the band structure of twisted bilayer graphene (TBG) exhibits isolated nearly flat bands, which are responsible for such correlated behaviour. At first, we describe TBG effective model in order to construct a topological phase diagram for the mini-bands near charge neutrality. Then, through symmetry analysis, we try to unravel and understand the limit of such model, when one tries to revert back to localised low-energy orbitals in real space (Wannier functions) for Hubbard-like descriptions.