Moiré semiconductors on the twisted bilayer dice lattice

We propose an effective lattice model for the moir\'e structure of the twisted bilayer dice lattice. In the chiral limit, we find that there are flat bands at the zero-energy level at any twist angle besides the magic ones and these flat bands are broadened by small perturbation away from the chiral limit. The flat bands contain both bands with zero Chern number which originate from the destructive interference of the states on the dice lattice and the topological nontrivial bands at the magic angle. The existence of the flat bands can be detected from the peak-splitting structure of the optical conductance at all angles, while the transition peaks do not split and only occur at magic angles in twisted bilayer graphene.