Efforts to engineer nearly topological flat bands (TFBs) have opened a promising avenue for realizing the lattice version of fractional quantum Hall states without an external magnetic field. Most of the TFB models are proposed based on Chern insulator (CI) models with isotropic hopping parameters. To our knowledge, rare TFBs are found in the CI models with anisotropy. In this work, we explore the TFBs in the biphenylene network by adding the hopping terms up to the next-nearest neighbor. This model hosts anisotropy which comes from the lattice structure itself and the various nearest-neighbor hoppings. By tuning the hopping parameters, the best TFB with a flatness ratio 21 appears. According to the large flatness ratio, the flat distribution of Berry curvature and band geometry, fractional Chern insulator (FCI) states possibly emerge. Very convincingly, numerical evidence suggests the existence of a $\nu =1/2$ FCI state when hard-core bosons are loaded into this anisotropic TFB model. Our findings not only demonstrate that the TFBs can be proposed in the anisotropic lattices, but also provide a promising platform to explore the geometrical description of FCIs.

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• Flat bands
• Fractional quantum Hall effect
• 2-dimensional systems
• Topological materials
• Exact diagonalization
• Tight-binding model