Twisted bilayer graphene near the magic angle is known to have a cascade of insulating phases at integer filling factors of the low-energy bands. Through a self-consistent Hartree-Fock calculation on the lattice that accounts for all electronic bands, in combination with numerically unbiased methods, we address the nature of those insulating states.  We show that Coulomb interactions screened only by metallic gates produce ferromagnetic insulating states at integer fillings ν ∈ [−4, 4] with maximal spin polarization MFM = 4 − |ν|. With the exception of the ν = 0, −2 states, all other integer fillings have insulating phases with additional sublattice symmetry breaking and antiferromagnetism in the remote bands. Valley polarization is found away from half filling. Odd filling factors |ν| = 1,3 have anomalous quantum Hall states with Chern number |C| = 1, whereas the |ν| = 3 states show strong particle-hole asymmetry in the small-gap regime. We map the metal-insulator transitions of these phases as a function of the background dielectric constant. Read more: arXiv:2308.03843 (2023).

Mott Insulators are systems that would naively be expected to behave as metals, but instead show insulating behavior as a result of strong correlations. All known examples exhibit antiferromagnetism due to a strong degree of electronic localization at the lattice sites, which favors superexchange. Recent experiments have found indication of Mott physics in twisted graphene bilayers at the magic angle, where interference effects reconstruct the low energy spectrum into flat bands. In the letter Physical Review Letters 122, 246402 (2019), we showed that the unusual nature of the Wannier orbitals in this system favors instead the exchange interaction, which leads to an exotic ferromagnetic Mott phase at quarter filling.