Square lattice model with staggered magnetic fluxes: Zero Chern number topological states and topological flat bands

Staggered magnetic fluxes (SMFs) play a crucial role in achieving Chern insulators (CIs), by which a series of CI models have been established on various lattices. In addition, a SMF induced higher-order topological insulator (HOTI) in a lattice model has been reported. In this work, we propose a square lattice model with SMF. We find intracellular SMF can induce a zero-Chern-number topological insulator at quarter filling which hosts topologically protected edge states characterized by the quantized polarization, in analogy to the topological state in a two dimensional Su-Schrieffer-Heeger model. When lattice dimerization and intracellular SMF are introduced, there exists a HOTI state at half filling. Furthermore, this model hosts a topological flat band (TFB) by considering the next-nearest-neighbor hoppings. Several fractional Chern insulator states are investigated when hard-core bosons are filled into this TFB model.