Fractional Chern insulator candidate in twisted bilayer checkboard lattice

We investigate a fractional Chern insulator (FCI) candidate arising from Moir\'e bands with higher Chern number C=2 on a magic angle twisted bilayer checkboard lattice (MATBCB). There are two nearly flat low lying bands in the single particle energy spectrum under the first magic angle 1. 608^ and chiral limit. We find MATBCB hosts a nearly uniform Berry curvature distribution and exhibits tiny violation of quantum geometric trace condition in the first moir\'e Brillourin Zone (mBZ), indicating that there is a nearly ideal quantum geometry in MATBCB in single particle level. Turning on projected Coulomb interactions, we perform exact diagonalization and find a ten-fold ground state quasi-degeneracy in many body energy spectrum with filling fraction =1/5. The ten-fold quasi-degenrate ground states further show spectra flow under flux pumping. By diagnosing the particle entanglement spectrum (PES) of the ground states, we obtain a clear PES gap and quasi-hole state counting consistent with Halperin spin singlet generalized Pauli principle, suggesting that a fractional Chern insulator is realized in this system.