Particle-hole asymmetric phases in doped twisted bilayer graphene

Twisted bilayer graphene (TBG) has emerged as a paradigmatic platform for exploring the interplay between strong interactions in a multiband system with nearly flat bands, while offering unprecedented control over the filling fraction of electron and hole carriers. Despite much theoretical work, developing a comprehensive ab initio model for this system has proven challenging due to the inherent tradeoff between accurately describing the band structure and incorporating the interactions within the Hamiltonian, particularly given the topological obstruction---so-called fragile topology---to the description of the model in terms of localized symmetric Wannier functions within the flat band manifold. Here, we circumvent this obstruction by using an extended eight-orbital model, for which localized Wannier orbitals have been formulated by [Carr et al., Phys. Rev. Res. 1, 033072 (2019)]. We constructed an extended multiorbital Hubbard model, and performed Hartree-Fock (HF) calculations to explore its phase diagram across commensurate fillings from $\ensuremath{-}3$ to 3. We found several nearly degenerate insulating states at charge neutrality, all of which exhibit orbital orders. Crucially, TBG near magic angle is known to be particle-hole asymmetric, which is naturally captured by the single-particle band structure of our model and is reflected in the distinction between the symmetry broken states obtained at electron and hole dopings away from the charge neutral point. At filling $\ensuremath{-}1$ and $+2$, quantum anomalous hall state and inter-orbital inter-valley coherent states are obtained, while for the rest of the integer fillings away from charge neutrality, we found the system to realize metallic states with various orbital, valley and spin orderings. We also observed that most of the Hartree--Fock ground states exhibit a generalized valley Hund's-like rule, resulting in valley polarization. Importantly, we show that the incorporation of the intravalley and intervalley exchange interactions is crucial to properly stabilize the ordered symmetry-broken states. In agreement with experiments, we find significant particle-hole asymmetry, which underscores the importance of using particle-hole asymmetric models.