Topological quantum phase transitions on the kagomé and square-octagon lattices

We study the topological quantum phase transitions of tight-binding electrons on two representative multi-band lattice models with superimposed staggered fluxes: the kagomé lattice and the square-octagon lattice. By considering the nearest-neighbor and next-nearest-neighbor hopping parameters (t₁ and t₂) and the staggered flux parameter ϕ, we obtain rich topological quantum phase transitions for both the lattices. The whole phase diagram for the kagomé lattice in the t₂-ϕ parameter space is obtained. We also illustrate a series of topological quantum phase transitions as well as topological bands of high Chern numbers for the square-octagon lattice. Furthermore, interesting topological flat bands with high flatness ratios (e.g. of about 43) are found in the square-octagon lattice, especially when the next-next-nearest-neighbor hopping (t₃) is included.