Due to the forming of low-energy flat bands, the moiré superlattices of the transition metal dichalcogenides are fascinating platforms for studying novel correlated states when such flat bands are fractionally filled, with the Coulomb interaction dominating. Here, we demonstrate that pressure can efficiently tune the flatness and quantum geometry of the single-particle bands in twisted bilayer ${\mathrm{MoTe}}_2$ ($t{\mathrm{MoTe}}_2$). By fractionally filling the topmost valence band, we find that pressure can act as a flexible means to modulate the fractional Chern insulator (FCI) and the generalized Wigner crystal (GWC) and control their many-body topological phase transitions. Moreover, our results indicate a remarkable correspondence between the single-particle band geometry and the formation of FCI and GWC. As the recent experiments report the presence of FCI phases in $t{\mathrm{MoTe}}_2$, our predictions could be readily implemented experimentally.

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• Fractional quantum Hall effect
• Topological phases of matter
• Superlattices
• Twisted heterostructures
• Wigner crystal
• Exact diagonalization
• k dot p method