(a) The checkerboard lattice. The blue (red) dots represent lattice sites of the A ( B ) sublattice. Black solid and black dashed lines represent nearest-neighbor and diagonal links, respectively. We choose the distance between the nearest neighbors as the length unit in this article. The yellow box containing four lattice sites marks one cluster used in the CDMFT calculation. (b) The first Brillouin zone (BZ) of the checkerboard lattice. We also show the reduced first Brillouin zone for the chosen cluster in CDMFT calculations. High-symmetry points of the BZ are marked with Γ , K, and M. (c) Non-interacting band structure of a tight-binding model on a homogeneous ( t 2 = t 1 ) checkerboard lattice. (d) Non-interacting density of states when t 2 = t 1 .