Thermodynamic evidence of fractional Chern insulator in moiré MoTe₂

Chern insulators, which are the lattice analogues of the quantum Hall states, can potentially manifest high-temperature topological orders at zero magnetic field to enable next-generation topological quantum devices^1-3. Until now, integer Chern insulators have been experimentally demonstrated in several systems at zero magnetic field^3-8, whereas fractional Chern insulators have been reported in only graphene-based systems under a finite magnetic field^9,10. The emergence of semiconductor moiré materials¹¹, which support tunable topological flat bands^12,13, provides an opportunity to realize fractional Chern insulators^13-16. Here we report thermodynamic evidence of both integer and fractional Chern insulators at zero magnetic field in small-angle twisted bilayer MoTe₂ by combining the local electronic compressibility and magneto-optical measurements. At hole filling factor ν = 1 and 2/3, the system is incompressible and spontaneously breaks time-reversal symmetry. We show that they are integer and fractional Chern insulators, respectively, from the dispersion of the state in the filling factor with an applied magnetic field. We further demonstrate electric-field-tuned topological phase transitions involving the Chern insulators. Our findings pave the way for the demonstration of quantized fractional Hall conductance and anyonic excitation and braiding¹⁷ in semiconductor moiré materials.