Ferromagnetism and heavy Fermi liquid in MoTe$_2$/WSe$_2$ bilayer: the Kondo lattice model and beyond

The moir'e superlattice formed by AB-stacked MoTe$_2$/WSe$_2$ is a versatile and highly tunable platform for strong correlation phenomena. At total hole filling $ u=1+x$, it has been argued to provide a realization of a Kondo lattice. Recent experiments find a heavy Fermi liquid with high Kondo temperature and a ferromagnetic Kondo breakdown transition. In this talk, I will discuss the crucial role of spin-polaron physics, which leads to ferromagnetism and enhances the Kondo temperature scale. We propose a phase diagram for the Kondo model, which is supported by an infinite density matrix renormalization group (iDMRG) simulation of the appropriate Kondo lattice model. In addition, to fully address the puzzle of high Kondo temperature, we demonstrate the importance of charge fluctuations by a slave rotor theory study of the full Hubbard model. With an intermediate Hubbard $U$ for the MoTe$_2$ layer, we find a reasonable Kondo temperature scale and qualitative agreement with experiments on displacement field dependence. In this regime, the density in the MoTe$_2$ layer is not pinned to be one per site. Instead, orbital selective Mott localization arises only under a small but finite Zeeman field.