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Motivated by the recent experiments on van der Waals heterostructures involving metallic and Mott insulating layers, we construct a moir\'e extension of the Kondo-Heisenberg model and study its phase diagram via Abrikosov fermion mean field theory in one and two dimensions. Our analysis indicates that the stacking dependent Kondo interaction can lead to a variety of new phases. In particular, we show that magnetic order and heavy quasiparticles can nucleate at different regions in the moir\'e unit cell leading to a macroscopic real space phase separation. We observe that these factors can lead to a metal to Kondo insulator percolation transition in two dimensions. Our results highlight the rich physics that can arise in moir\'e superlattices that are composed of inherently strongly correlated layers.
Das et al. (Fri,) studied this question.