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Heterobilayer transition metal dichalcogenide (TMDC) moir\'e systems providean ideal framework to investigate strongly correlated physics. Here wetheoretically study bosonic many-body phases of excitons in moir\'e TMDCs. Byusing two moir\'e models and cluster mean-field theory, we reveal that, due tonon-local Coulomb interactions, moir\'e excitons can feature exotic supersolidphases, i.e. superfluids of broken translational invariance, and correlatedinsulating states. The correlated phases exist at experimentally accessibletemperatures and are tunable via the twist angle and exciton density.

Non-local interactions and supersolidity of moir\'e excitons