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