Enginering flat band describled by topological heavy Fermion with Moiré potential

The topological heavy Fermion model has been instrumental in understanding topological flat bands in moiré systems, such as twisted bilayer graphene and twisted checkerboards. In this work we propose a general mechansim to enginer topological flat band with concentrated Berry curvature in narrow gap system, which can be mapped to topological heavy Fermion model. The core of the mechanism is to create band inversion between a flat valance band and a dispersive conduction band with Moiré potential. We illustrate this mechanism via Bernevig-Hughes-Zhang (BHZ) model, under two types of moiré superlattice potentials: a hexagonal superlattice potential and a delta superlattice potential. In the hexagonal superlattice case, we show that there are parameter regions in which the topological flat band can be mapped to topological heavy Fermion model. Furthermore, we show that this mechanism is not limited to the hexagonal potential—similar results are obtained in the delta superlattice potential.