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Moiré superlattice in a MoSe$_2$/hBN/MoSe$_2$ heterostructure: from coherent coupling of inter- and intra-layer excitons to correlated Mott-like states of electrons

Two dimensional materials and their heterostructures constitute a promising platform to study correlated electronic states as well as many body physics of excitons. Here, we present experiments that unite these hitherto separate efforts and show how excitons that are dynamically screened by itinerant electrons to form exciton-polarons, can be used as a spectroscopic tool to study interaction-induced incompressible states of electrons. The MoSe$_2$/hBN/MoSe$_2$ heterostructure that we study exhibits a long-period Moiré superlattice as evidenced by coherent-hole tunneling mediated avoided crossings between the intra-layer exciton with three inter-layer exciton resonances separated by $\sim$ 3meV. For electron densities corresponding to half-filling of the lowest Moiré subband, we observe strong layer-paramagnetism demonstrated by an abrupt transfer of all $\sim$ 1500 electrons from one MoSe$_2$ layer to the other upon application of a small perpendicular electric field. Remarkably, the electronic state at half-filling of each MoSe$_2$ layer is resilient towards charge redistribution by the applied electric field, demonstrating an incompressible Mott-like state of electrons. Our experiments demonstrate that optical spectroscopy provides a powerful tool for investigating strongly correlated electron physics in the bulk and pave the way for investigating Bose-Fermi mixtures of degenerate electrons and dipolar excitons.