We study electronic ordering instabilities of twisted bilayer graphene around the filling of n = 2 electrons per supercell, where correlated insulator state and superconductivity have been 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 that d or p -wave superconductivity and charge or spin density wave emerge as the two types of leading instabilities driven by Coulomb repulsion. The density-wave state has a gapped energy spectrum around 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.
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