Density wave and topological superconductivity in the magic-angle-twisted bilayer-graphene

The model dependence in the study of the magic-angle twisted bilayer-graphene is an important issue in the research area.It has been argued previously that the two-band tight-binding model (per spin and valley) cannot serve as a start point for succeeding studies as it cannot correctly describe the topological aspect of the continuum-theory model near the Dirac nodes in the mini Brillouin zone. For this purpose, we adopt the faithful TB model [Phys. Rev. B 99, 195455 (2019)] with five bands as our start point, which is further equipped with extended Hubbard interactions. Then after systematic randomphase-approximation based calculations, we study the electron instabilities of this model, including the density wave and superconductivity, near the van Hove singularity. The results are highly similar to the results of our previous study [arXiv:2003.09513] adopting the two-band TB modelmodel, with the reason lying in that both models share the same symmetry and Fermi-surface nesting character near the
VHS. Such a similarity suggests that the low-energy physics of the doped MA-TBG is mainly determined by the symmetry and the shape of the FS of the doped system, and is insensitive to other details of the band structure, including the topological aspects near the Dirac nodes in the MBZ.