Fractional Chern insulator candidate on a twisted bilayer checkerboard 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 checkerboard lattice (MATBCB). There are two nearly flat low lying bands in the single-particle energy spectrum under the first magic angle $\ensuremath{\phi}\ensuremath{\approx}1.{608}^{\ensuremath{\circ}}$ and chiral limit. We find that MATBCB hosts a nearly uniform Berry curvature distribution and exhibits tiny violation of quantum geometric trace condition in the first moir\'e Brillouin 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 10-fold ground-state quasidegeneracy in many-body energy spectrum with filling fraction $\ensuremath{\nu}=1/5$. The 10-fold quasidegenerate 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 quasihole state counting consistent with Halperin spin singlet generalized Pauli principle, suggesting that a $C=2$ Abelian fractional Chern insulator is realized in this system.