Topological quantum phase transitions and topological flat bands on the star lattice

We study a tight-binding model on the two-dimensional star lattice (also called the decorated honeycomb lattice) with short-range hoppings modulated by staggered fluxes. We observe a series of topological quantum phase transitions when tuning the hopping parameters, and find nontrivial topological bands with high Chern numbers. We also find in some parameter regions, the system exhibits the interesting topological flat bands with large flatness ratios of the band gaps over the bandwidths. We further illustrate the 1/2 fractional quantum Hall effect of interacting hard-core bosons filled in a lowest topological flat band of the star lattice.