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The interplay between strong correlations and topology can lead to theemergence of intriguing quantum states of matter. One well-known example is thefractional quantum Hall effect, where exotic electron fluids with fractionallycharged excitations form in partially filled Landau levels. The emergence oftopological moir\'e flat bands provides exciting opportunities to realize thelattice analogs of both the integer and fractional quantum Hall states withoutthe need for an external magnetic field. These states are known as the integerand fractional quantum anomalous Hall (IQAH and FQAH) states. Here, we presentdirect transport evidence of the existence of both IQAH and FQAH states intwisted bilayer MoTe2 (AA stacked). At zero magnetic field, we observewell-quantized Hall resistance of h/e2 around moir\'e filling factor {\nu} = -1(corresponding to one hole per moir\'e unit cell), and nearly-quantized Hallresistance of 3h/2e2 around {\nu} = -2/3, respectively. Concomitantly, thelongitudinal resistance exhibits distinct minima around {\nu} = -1 and -2/3.The application of an electric field induces topological quantum phasetransition from the IQAH state to a charge transfer insulator at {\nu} = -1,and from the FQAH state to a generalized Wigner crystal state, furthertransitioning to a metallic state at {\nu} = -2/3. Our study paves the way forthe investigation of fractionally charged excitations and anyonic statistics atzero magnetic field based on semiconductor moir\'e materials.

Observation of integer and fractional quantum anomalous Hall effects in twisted bilayer MoTe2