Correlated Topological Mixed-Valence Insulators in Moir\'e Hetero-Bilayers

Moir\'e transition metal dichalcogenide (TMD) materials provide an ideal playground for studying the combined interplay of strong interactions and band-topology over a range of electronic fillings. Here we investigate the panoply of interaction-induced electronic phases that arise at a total commensurate filling of $\nu_T=2$ in moir\'e TMD heterobilayers, focusing specifically on their renormalized band-topology. We carry out a comprehensive self-consistent parton mean-field analysis on an interacting mixed-valence Hamiltonian describing AB-stacked MoTe$_2$/WSe$_2$ to highlight different ingredients that arise due to "Mottness", band-flattening, an enhanced excitonic tendency, and band-inversion, leading to correlated topological semi-metals and insulators. We also propose a possible route towards realizing fractionalized insulators with emergent neutral fermionic excitations in this and other closely related platforms.