In the first part of the talk I will discuss the topology of the narrow bands and its effect on the electron-electron Coulomb interactions in the magic angle twisted bilayer graphene. In the strong coupling limit, when the projected Coulomb interactions dominate the narrow band kinetic energy, the ground states at even integer fillings can be determined exactly. They correspond to generalized spin-valley ferromagnets, a manifold of states which includes Chern insulators. The excitations of these strong coupling ground states will be shown to disperse, with a bandwidth set by the Coulomb interaction. I will also discuss the effect of the external out-of-plane magnetic field on these excitations and compare the ensuing Landau level degeneracies with the experimental observations.
In the second part of the talk, I will discuss the effects of perturbations which take the realistic system away from the strong coupling limit and present experimental consequences of these perturbations in view of existing data.
[1] J.Kang and O. Vafek PRL 122, 246401 (2019); PRB 102, 035161 (2020); PRL 125, 257602 (2020)
[2] J.Kang, B.A.Bernevig and O. Vafek PRL 127, 266402 (2021); D Călugăru et. al PRL 129, 117602 (2022)
[3] X.Wang et. al PNAS 120, e2307151120 (2023)
[4] X.Wang and O.Vafek PRX 14, 021042 (2024); K.Singh et. al Nature Comm. 15, 5257 (2024)
