Correlated fermionic-bosonic insulating states in twisted hetero-trilayer semiconductors

Correlated insulating states such as fermionic and bosonic insulators have been observed individually in transition metal dichalcogenide heterostructures. However, the interplay between fermionic and bosonic correlated states and their dynamical evolution on a single system, remain largely unexplored. Here, we demonstrate that the twisted trilayer heterostructures host an unconventional fermionic complex, namely the charge-layer-locked trion with a symmetric charge configuration. Owing to its spatially-indirect charge distribution, this fermionic trion can dynamically evolve into a bosonic inter-layer exciton plus an extra charge under an external optical or electric field, making the trilayer system a flexible platform to generate fermionic and bosonic quasiparticles as well as their mixtures. Notably, this charge-layer-locked trion can serve as a reservoir for both charge and exciton fillings of the lattice, where the resulting correlated insulating state can evolve from fermionic, fermionic-bosonic, to bosonic nature as controllably tuning of the external optical and electric fields. These results highlight that the hetero-trilayer semiconductors are an informative toy-model system to simulate the many-body correlations ranging from Fermi-, Fermi-Bose-, to Bose-Hubbard Hamiltonians.