Ideal topological flat bands in two-dimensional moiré heterostructures with type-II band alignment

Topological flat bands play an essential role in inducing exotic interacting physics, ranging from fractional Chern insulators to superconductivity, in moiré materials. In this work, we propose a design principle for realizing topological flat bands with "ideal quantum geometry", namely the trace of Fubini-Study metric equals to the Berry curvature, in a class of two-dimensional moiré heterostructures with type-II band alignment. We first introduce a moiré Chern-band model to describe this system and show that topological flat bands can be realized in this model when the moiré superlattice potential is stronger than the type-II atomic band gap of the heterostructure. Next, we map this model into a topological heavy fermion model that consists of a localized orbital for "f-electron" and a conducting band for "c-electron". We find that both the flatness and quantum geometry of the flat band in the topological heavy fermion model depend on the energy gap between c-electron and f-electron bands at $Γ$ which is experimentally controllable via external gate voltages. This tunability will allow us to realize an ideal topological flat band with zero band-width and ideal quantum geometry. Our design strategy of topological flat bands is insensitive of twist angle. We also discuss possible material candidates for moiré heterostructures with type-II band alignment.