Role of interactions on topological flat bands in twisted bilayer graphene at high magnetic field

We study the role of interactions in small angle twisted bilayer graphene in the presence of high
magnetic fields. The physics of small angle twisted bilayer graphene depends of two parameters
wAA and wAB, that denote the inter-layer tunneling between local AA and AB stacking regions.
At high magnetic fields and rational flux per Morie unit cell, when the energy associated with
the Landau levels dominates the interlayer hopping (i.e wAA;wAB << ~v=lB), we find a collection
of degenerate weakly dispersing or flat bands at zero energy. We study the effect of Coulomb
interactions which are expected to lift this degeneracy resulting in interaction induced quantum
Hall ferromagnetic states. We determine the phase diagram and stability of the quantum Hall
ferromagnetic states with respect to the inter-layer tunneling parameters (wAA;wAB). We also
show that the topological and neutral excitations are determined by the quantum metric of the
weakly dispersing and flat bands.