Topological quantum phase transitions on the kagome 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 kagome lattice and the square-octagon lattice. By considering the nearest-neighbor and next-nearest-neighbor hopping parameters (t(1) and t(2)) and the staggered flux parameter phi, we obtain rich topological quantum phase transitions for both the lattices. The whole phase diagram for the kagome lattice in the t(2)-phi 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 (t(3)) is included.