Chiral SO(4) spin-charge density wave and degenerate topological superconductivity in the MA-TBG

Starting from a realistic extended Hubbard model on the Honeycomb lattice, we perform a thorough investigation on the possible electron instabilities in the magic-angle-twisted bilayer-graphene near the van Hove (VH) dopings. Here we focus on the interplay between the approximate SU(2)×SU(2) symmetry and the D_3 symmetry of the system, which leads to intriguing quantum states relevant to recent experiments, as revealed by our systematic random-phase-approximation plus mean-field study. At the SU(2)×SU(2) symmetric point, the degenerate inter-valley SDW and CDW are mixed into a new state of matter dubbed as the chiral SO(4) spin-charge DW. This state simultaneously hosts three mutually perpendicular 4-component vectorial spin-charge DW orders, and possesses intriguing topological properties and Goldstone-mode fluctuations. Adding a weak symmetry-breaking perturbation can change this state to a nematic DW state with coexisting stripy CDW and SDW order parameters, consistent with recent STM observations. On the aspect of SC, we obtain degenerate triplet p + ip and singlet d + id topological superconductivity near the VH dopings. In addition, the two asymmetric doping-dependent behaviors of the obtained pairing phase diagram are well consistent with experiments.