Polaritonic and Excitonic Bose Einstein Condensates in a Periodic Potential

We investigate two systems for Bose-Einstein condensation. The first consists of excitons in a bilayer of twisted TMDC nanoribbons In the second case, we examine exciton polaritons, formed by excitons in a nanoribbon of TMDC, embedded in an optical microcavity, and microcavity photons. In both systems, Bose-Einstein condensates (BECs) could be formed under periodic potentials. This periodic potential nay be caused either by the effective potential, acting on photons due to the special curvature of Bragg mirrors, or by the periodic potential, acting on excitons due to the Moiré sublattice in a twisted TMDC bilayer. We will calculate the limit of the pair correlation function for an infinitely long nanoribbon. We will analyze if it follows from this pair correlation function that the BEC in the nanoribbon subjected to the periodic potential exhibits features of the time crystal, caused by the behavior of the standing BEC wave, bounded in the transverse direction by the ribbon boundaries but unbounded along its length.