Stability of the Mott phase in excitonic double layers

We study the stability of excitonic Mott phases in the presence of a periodic potential and a non-local exciton-exciton interaction. The non-local interaction is treated in a mean-field approximation, while the local repulsion of the excitons is treated in a hopping expansion. The convergence of the latter is the criterion for the stability of the Mott phase with respect to quantum and thermal fluctuations. This hybrid approach enables us to establish a phase diagram for a bosonic Mott to superfluid transition. Our results could be useful to interpret recent experiments on electron-hole crystals in van der Waals heterostructures.