Fig. 2: Correlated Chern insulators (CCIs) emerging at finite magnetic fields.

a The spectral evolution of the sample under a perpendicular magnetic field. With increasing field strength, more peaks become identifiable and gradually shift in doping densities. Fan diagram constructed with the extracted energy ΔE (b) and intensity (c) of the 2 s state. Features with large ΔE and small intensity are associated with discernible states. d Schematics of the fan diagram (upper) and the spectrum in Fig. 1c for reference (lower). The integer quantum Hall (IQH) sequences originate from ν = 0 and ν = ±4, while the correlated Chern insulators (CCIs) emanate from ν = ±1, ±2, ±3 (guided by the dashed lines) with their corresponding Chern numbers marked in red. As indicated by the blue bars, the onsets of the CCIs consistently occur at the doping density where the electronic compressibility is minimized at zero magnetic fields (marked by the vertical dashed lines).