Thermodynamic evidence of fractional Chern insulator in moiré MoTe 2 .

Chern insulators, which are the lattice analogs 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 . To date, integer Chern insulators have been experimentally demonstrated in several systems at zero magnetic field 3, 4-8 , but fractional Chern insulators have been reported only in graphene-based systems under a finite magnetic field 9,10 . The emergence of semiconductor moiré materials 11 , which support tunable topological flat bands 12,13 , opens a new 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 MoTe 2 by combining the local electronic compressibility and magneto-optical measurements. At hole filling factor [Formula: see text] = 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 filling factor with applied magnetic field. We further demonstrate electric-field-tuned topological phase transitions involving the Chern insulators. Our findings pave the way for demonstration of quantized fractional Hall conductance and anyonic excitation and braiding 17 in semiconductor moiré materials.