Coexistence of nematic superconductivity and spin density wave in magic-angle twisted bilayer graphene

We argue that doped twisted bilayer graphene with magical twist angle can become superconducting. In our theoretical scenario, the superconductivity coexists with the spin-density-wave--like ordering. Numerical mean-field analysis demonstrates that the spin-density-wave order, which is much stronger than the superconductivity, leaves parts of the Fermi surface ungapped. This Fermi surface serves as a host for the superconductivity. Since the magnetic texture at finite doping breaks the point group of the twisted bilayer graphene, the stabilized superconducting order parameter is nematic. We also explore the possibility of a purely Coulomb-based mechanism of superconductivity in the studied system. The screened Coulomb interaction is calculated within the random phase approximation. It is shown that near the half-filling the renormalized Coulomb repulsion indeed induces the superconducting state, with the order parameter possessing two nodes on the Fermi surface. We estimate the superconducting transition temperature, which turns out to be very low. The implications of our proposal are discussed.