Twisted bilayer graphene has emerged as a paradigmatic platform for exploring the interplay between strong interactions and topological obstructions. While the majority of previous studies had used the effective (k.p) model of Bistritzer and MacDonald, the present work [2] aims at a more precise microscopic understanding using faithful tight-binding modeling of the twisted bilayer graphene. Here, based on the Wannier orbitals obtained by Carr et al. [1], we construct an extended Hubbard model with 8 orbitals, and perform a Hartree-Fock (HF) analysis to explore its phase diagram across  commensurate fillings from -3 to 3. In addition to the previously recognized role of the valley degree of freedom, we find that the orbitals also play a central role in determining the ground state at all fillings. In particular, a nearly-degenerate pair of insulating states are obtained at charge neutrality, both exhibiting orbital polarization. Doping the system away from the neutrality point result in insulating quantum anomalous hall states at fillings -1 and +2, while symmetry-broken metallic states are obtained at all other charged fillings. A universal feature away from charge-neutrality is the distinction between correlated states obtained at fillings , which results from the particle-hole asymmetry in the single-particle band structure. Thus, our extended Hubbard model provides a suitable microscopic starting point for examining the strongly correlated phenomena in twisted bilayer graphene.

[1] S. Carr, S. Fang, H. C. Po, A. Vishwanath, and E. Kaxiras, Phys. Rev. Res.1, 033072 (2019).

[2] R. Hou, S. Sur, L. K. Wagner and A. H. Nevidomskyy, to appear (2023)