Twisted Bilayer Graphene IV. Exact Insulator Ground States and Phase Diagram

Understand

We derive the exact insulator ground states of the projected Hamiltonian of magic-angle twisted bilayer graphene (TBG) flat bands with Coulomb interactions in various limits, and study the perturbations away from these limits.

• We define the (first) chiral limit where the AA stacking hopping is zero, and a flat limit with exactly flat bands.
• In the chiral-flat limit, the TBG Hamiltonian has a U(4)$\times$U(4) symmetry, and we find that the exact ground states at integer filling $-4\le \nu\le 4$ relative to charge neutrality are Chern insulators of Chern numbers $\nu_C=4-|\nu|,2-|\nu|,\cdots,|\nu|-4$, all of which are degenerate.
• This confirms recent experiments where Chern insulators are found to be competitive low-energy states of TBG.