Fractional Chern Insulators in Twisted BilayerMoTe2: A Composite Fermion Perspective

The discovery of fractional Chern insulators (FCIs) in twisted bilayer MoTe2 has sparked significant interest in fractional topological matter without external magnetic fields. Unlike the flat dispersion of Landau levels, moiré electronic states are influenced by lattice effects within a nanometer-scale superlattice. This Letter examines the impact of these lattice effects on the topological phases in twisted bilayer MoTe2, uncovering a family of FCIs with Abelian anyonic quasiparticles. Using a composite fermion approach, we identify a sequence of FCIs with fractional Hall conductivities 𝜎𝑥⁢𝑦=[𝐶/(2⁢𝐶+1)]⁢(𝑒2/ℎ) linked to partial filling 𝜈h of holes of the topmost moiré valence band. These states emerge from incompressible composite fermion bands of Chern number 𝐶 within a complex Hofstadter spectrum. This approach explains FCIs with Hall conductivities 𝜎𝑥⁢𝑦=(2/3)⁢𝑒2/ℎ and 𝜎𝑥⁢𝑦=(3/5)⁢𝑒2/ℎ at fractional fillings 𝜈h=2/3 and 𝜈h=3/5 observed in experiments, and uncovers other fractal FCI states. The Hofstadter spectrum reveals new phenomena, distinct from Landau levels, including a higher-order Van Hove singularity (HOVHS) at half-filling, leading to novel quantum phase transitions. This Letter offers a comprehensive framework for understanding FCIs in transition metal dichalcogenide moiré systems and highlights mechanisms for topological quantum criticality.