Fractional Chern Insulating States in flat bands derived from systems with quadratic band crossing points*

Topological flat bands in two-dimensional lattice systems are known for their potential to host strongly correlated electronic quantum states and fractional Chern insulators. We focus on flat bands induced by periodic strain potentials over systems with quadratic band crossing points (QBCP). In such systems, there are exactly flat bands at different strain potential strengths, each having very different Berry curvature distributions [Wan et al. Phys. Rev. Lett. 130, 216401 (2023)]. Utilizing exact diagonalization, we investigate the many body instabilities in the systems with Coulomb repulsion projected into the flat bands. We identify the fractional Chern insulating ground states at various fractional electron fillings. Moreover, at half-filling, the composite Fermi liquid (CFL) is stabilized.  We will discuss the role of the quantum geometry and particle-hole symmetry on the fractional Chern insulating state and composite Fermi liquid.