Link between cascade transitions and correlated Chern insulators in magic-angle twisted bilayer graphene

Chern insulators are topologically non-trivial states of matter characterized by incompressible bulk and chiral edge states. Incorporating topological Chern bands with strong electronic correlations provides a versatile playground for studying emergent quantum phenomena. In this study, we resolve the correlated Chern insulators (CCIs) in magic-angle twisted bilayer graphene (MATBG) through Rydberg exciton sensing spectroscopy, and unveil their direct link with the zero-field cascade features in the electronic compressibility. The compressibility minima in the cascade are found to deviate substantially from nearby integer fillings (by Δν) and coincide with the onsets of CCIs in doping densities, yielding a quasi-universal relation B_c=Φ_0Δν/C (onset magnetic field B_c, magnetic flux quantum Φ_0 and Chern number C). We suggest these onsets lie on the intersection where the integer filling of localized "f-orbitals" and Chern bands are simultaneously reached. Our findings update the field-dependent phase diagram of MATBG and directly support the topological heavy fermion model.