A panoply of unconventional electronic states has been observed in moiré superlattices. Engineering similar bosonic phases remains, however, largely unexplored. We report the observation of a bosonic correlated insulator in tungsten diselenide/tungsten disulfide (WSe₂/WS₂) moiré superlattices composed of excitons, that is, tightly bound electron-hole pairs. We develop a pump probe spectroscopy method that we use to observe an exciton incompressible state at exciton filling ν_ex = 1 and charge neutrality, indicating a correlated insulator of excitons. With varying charge density, the bosonic correlated insulator continuously transitions into an electron correlated insulator at charge filling ν_e = 1, suggesting a mixed correlated insulating state between the two limits. Our studies establish semiconducting moiré superlattices as an intriguing platform for engineering bosonic phases.

Stacking van der Waals crystals allows for the on-demand creation of a periodic potential landscape to tailor the transport of quasiparticle excitations. We investigate the diffusion of photoexcited electron-hole pairs, or excitons, at the interface of WS₂/WSe₂ van der Waals heterostructure over a wide range of temperatures. We observe the appearance of distinct interlayer excitons for parallel and antiparallel stacking and track their diffusion through spatially and temporally resolved photoluminescence spectroscopy from 30 to 250 K. While the measured exciton diffusivity decreases with temperature, it surprisingly plateaus below 90 K. Our observations cannot be explained by classical models like hopping in the moiré potential. A combination of ab initio theory and molecular dynamics simulations suggests that low-energy phonons arising from the mismatched lattices of moiré heterostructures, also known as phasons, play a key role in describing and understanding this anomalous behavior of exciton diffusion. Our observations indicate that the moiré potential landscape is dynamic down to very low temperatures and that the phason modes can enable efficient transport of energy in the form of excitons.