Fig. 3: Topological heavy fermion (THF) picture for understanding the link between cascade phenomenon and CCIs.
a Schematic illustration of the THF model with localized f-electrons (centered at AA stacking sites) serving as local moments (black arrow) and itinerant c electrons (centered at AB/BA stacking sites) with topological bands. b Schematics of the density of state suppression at integer νf. When the f-orbitals are occupied by integer electrons/holes, the suppression of the charge fluctuation on the f-orbitals and the electronic correlation becomes strongest, leading to a minimum in the local electronic density of state (DOS) and the enhanced local moments. c Calculated occupancy of the f- and c-orbitals upon electron filling. The integer filling of the f-orbitals νf naturally occurs at non-integer ν, and the deviation Δν equals the filling of the conduction orbitals νc. d Schematics of the emergence of a correlated Chern insulators (CCI) state exemplified by the electron-doped side. Stabilizing CCI requires both a strong Hubbard interaction among the f-orbitals and the integer filling of Chern bands (schematically illustrated by the red curve). As a result, the CCIs emerge when the integer νf (blue bar) crosses the Streda line (dotted line), accounting for the observed link between cascade phenomenon and CCIs.
