Ab initio four-band Wannier tight-binding model for generic twisted graphene systems

The newly realized twisted graphene systems such as twisted bilayer graphene (TBG), twisted double bilayer graphene (TDBG), and twisted trilayer graphene (TTG) have attracted widespread attention. Therefore, a simple and exact model of the systems is urgent and vital for further study. Here, we construct the symmetry-adapted localized Wannier functions and the corresponding ab initio minimal two-valley four-band effective tight-binding models for generic twisted graphene systems with small twist angle. Such a two-valley model circumvents the Wannier obstruction caused by the fragile topology in the one-valley model. The real-space valley operator is introduced to explicitly describe the valley Uv(1) symmetry. Each symmetry-adapted Wannier orbital shows a peculiar three-peak form with its maximum at AA spots and its center at AB or BA spots. An extended Hubbard model is also given and the related interaction parameters are presented explicitly. We provide an approach to systematically build the Wannier tight-binding model for generic twisted graphene systems. Our model provides a firm basis for further study of the many-body effects in these systems.