Flat topological bands in twisted van der Waals homobilayers*

We construct a continuum model Hamiltonian to describe electronic structures of Moiré superlattices made by twisted van der Waals homobilayers. The calculated band structures exhibit isolated flat bands at a small twist angle. We further find that the different interlayer couplings from different stacking regions facilitate the emergence of topological phases. Finally, we obtain the phase diagram of these isolated bands by tuning the twist angle, staggered layer potential, and magnetic field, which make the twisted homobilayers a promising platform for realizing rich topological phases.