Moir\'e-mediated phases in synthetic Kondo superlattices

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.