Antiferromagnetism and chiral d-wave superconductivity from an effective $t-J-D$ model for twisted bilayer graphene

We derive an effective tight-binding model that captures, in real space and with only two parameters, the dominant Coulomb interactions and superconducting pairing near half-filling of magic-angle twisted bilayer graphene. We show that, in an antiferromagnetic Mott insulating ground state with intervalley coherence, magnetic fluctuations and doping mediate superconducting pairing. We find the pairing wave function to have chiral $d$-wave symmetry and obtain a self-consistent mean-field phase diagram in line with experiments on the doping-induced insulator-to-superconductor transition. We further reveal the existence of chiral Majorana edge modes implied by the nontrivial pairing symmetry, which establishes twisted bilayer graphene as a potential platform for topological superconductivity. This effective model opens the door to systematic scrutiny of the competition between correlated states in this system.