Fractional Chern Insulator in Twisted Bilayer MoTe_{2}

A recent experiment has reported the first observation of a zero-field fractional Chern insulator (FCI) phase in twisted bilayer MoTe_{2} moiré superlattices [J. Cai et al., Signatures of fractional quantum anomalous Hall states in twisted MoTe_{2}, Nature (London) 622, 63 (2023).NATUAS0028-083610.1038/s41586-023-06289-w]. The experimental observation is at an unexpected large twist angle 3.7° and calls for a better understanding of the FCI in real materials. In this Letter, we perform large-scale density functional theory calculation for the twisted bilayer MoTe_{2} and find that lattice reconstruction is crucial for the appearance of an isolated flat Chern band. The existence of the FCI state at ν=-2/3 is confirmed by exact diagonalization. We establish phase diagrams with respect to the twist angle and electron interaction, which reveal an optimal twist angle of 3.5° for the observation of FCI. We further demonstrate that an external electric field can destroy the FCI state by changing band geometry and show evidence of the ν=-3/5 FCI state in this system. Our research highlights the importance of accurate single-particle band structure in the quest for strong correlated electronic states and provides insights into engineering fractional Chern insulator in moiré superlattices.