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In bilayers of semiconducting transition metal dichalcogenides, the twistangle between layers can be used to introduce a highly regular periodicpotential modulation on a length scale that is large compared to the unit cell.In such structures, correlated states can emerge, in which excitons in theheterostructure are strongly localized to the potential minima due toexciton-exciton interactions. We explore the transition between Mott andextended exciton phases in terms of a moir\'e-Bose-Hubbard Hamiltonian. Hoppingand on-site interaction parameters are obtained from a Wannier representationof the interlayer-exciton wave functions, and a non-local Rytova-Keldysh modelis used to attribute for the dielectric screening of excitons in thetwo-dimensional material. For sufficiently small exciton concentrations andsubstrate screening our model predicts the emergence of Mott-insulating states,establishing twisted TMD heterostructures as possible quantum simulators forbosonic many-body systems.

Moir\'e-Bose-Hubbard model for interlayer excitons in twisted transition metal dichalcogenide heterostructures