Fractional Chern Insulators in Twisted Bilayer MoTe₂: A Composite Fermion Perspective

The discovery of Fractional Chern Insulators (FCIs) in twisted bilayer MoTe₂ has sparked significant interest in studying fractional topological phases without external magnetic fields. Unlike Landau levels, moiré states in such system are shaped by lattice effects within a nanometer-scale superlattice. Using a composite fermion framework, we examine these effects and identify a sequence of FCIs with fractional Hall conductivities σ_xy = [C/(2C+1)](e²/h) linked to hole fillings ν_h in the moiré valence band, emerging within a complex Hofstadter spectrum. This approach explains experimentally observed FCIs with conductivities σ_xy = 2/3(e²/h) and σ_xy = 3/5(e²/h) at fractional fillings ν_h = 2/3 and ν_h = 3/5, while also predicting other fractal FCI states. Notably, we identify a higher-order Van Hove singularity at half-filling, leading to novel quantum phase transitions distinct from traditional Landau-levels. This work provides a comprehensive framework for understanding FCIs in moiré superlattices of transition metal dichalcogenides and highlights mechanisms for topological quantum criticality.