We consider dressing of excitonic properties by strongly correlated electrons in gate-controlled twisted homobilayer heterostructures. The combined effect of the moiré potential and the Coulomb interaction supports the formation of different strongly correlated phases depending on the filling, including charge-ordered metals or incompressible insulators at integer occupation. The coupling between excitons and electrons results in a splitting of the excitonic resonance into an attractive and a repulsive polaron peak. Analyzing the properties of the exciton-polarons across the different phases of the system, we reveal a discontinuous evolution of the spectrum with the formation of a double-peak structure in the repulsive polaron branch. The double-peak structure emerges for noninteger fillings and it is controlled by the energy separation between the quasiparticle states close to the Fermi level and the high-energy doublons excitations. Our results demonstrate that exciton-polarons carry a clear hallmark of the electronic correlations and, thus, provide a direct signature of the formation of correlation-driven insulators in gate-controlled heterostructures.

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• Electronic structure
• Phase transitions
• Strongly correlated systems
• Transition metal dichalcogenides
• Dynamical mean field theory
• Electron-correlation calculations
• Green's function methods
• Lattice models in condensed matter