Charge and spin correlations in insulating and incoherent metal states of twisted bilayer graphene

We study electronic, charge, and magnetic properties of twisted bilayer graphene with fillings 2 n 6 per moire unit cell within the recently introduced formulation of extended dynamical mean-field theory for two-sublattice systems. We use previously obtained hopping parameters between the states, described by Wannier functions, centered at the lattice spots of AB and BA stacking, and the long-range Coulomb interaction, obtained within cRPA analysis. We show that account of spin exchange between AB and BA nearest-neighbor spots is crucial to introduce charge and spin correlations between these spots. The account of this exchange yields preferable concentration of electrons in the same valley, with the tendency of parallel spin alignment of electrons in AB and BA spots, in agreement with earlier results of the strong-coupling analysis, suggesting SU(2)xSU(2) emergent spin-valley symmetry. The local spectral functions show an almost gapped state at fillings n = 2, 4, 6, and incoherent metal state for the other fillings. We find that in both cases the local states of electrons have rather long lifetimes. At the same time, the nonlocal charge and spin susceptibilities, obtained within the ladder approximation, are peaked at incommensurate wave vectors, which implies that the above-discussed ordering tendencies are characterized by an incommensurate pattern.