Unconventional superconductivity and density waves in twisted bilayer graphene

We study electronic ordering instabilities of twisted bilayer graphene with n=2 electrons per supercell, where correlated insulator state and superconductivity are recently observed. Motivated by the Fermi surface nesting and the proximity to Van Hove singularity, we introduce a hot-spot model to study the effect of various electron interactions systematically. Using the renormalization group method, we find d/p-wave superconductivity and charge/spin density wave emerge as the two types of leading instabilities driven by Coulomb repulsion. The density wave state has a gapped energy spectrum at n=2 and yields a single doubly-degenerate pocket upon doping to n>2. The intertwinement of density wave and superconductivity and the quasiparticle spectrum in the density wave state are consistent with experimental observations.