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Recent experiments observed fractional Chern insulators (FCI) in twistedbilayer MoTe$_2$ at zero magnetic field, yet even the single-particle model ofthis material is controversial, leading to unreliable predictions of theexperimental phase diagram as discussed in [Yu et al., 2023]. In this light, werevisit the single-particle model of twisted bilayer MoTe$_2$. Utilizinglarge-scale density functional theory, we calculate the band structure oftwisted AA-stacked bilayer MoTe$_2$ at various twist angles relevant toexperiment. We find that a band inversion occurs near $4.41^\circ$ between thesecond and third bands. Our ab initio band structure is in qualitativeagreement with [Wang et al., 2023], but shows important differences in theremote bands and in the $\Gamma$ valley. We incorporate two higher harmonicterms into the continuum model to capture the highest 3 valence bands pervalley. We confirm that the two highest valence bands per valley have oppositeChern numbers with $|C|=1$ for small angles, and also use our model to predicta variety of Chern states in the remote bands accessible by displacement field.Finally, we perform DFT calculations and build models for the AB stackingconfiguration. Our work serves as a foundation for accurate determination ofthe correlated phases in twisted bilayer MoTe$_2$.

Moir\'e Fractional Chern Insulators I: First-principles calculations and Continuum Models of Twisted Bilayer MoTe$_2$