Polaritonic and excitonic semiclassical time crystals based on TMDC strips in an external periodic potential

We investigated the dynamics of Bose–Einstein condensates (BECs) under an external periodic potential. We consider two such systems, the first being made of exciton–polaritons in a nanoribbon of transition metal dichalcogenides (TMDCs), such as MoSe[Formula: see text] , embedded in a microcavity with a spatial curvature, which serves as the source of the external periodic potential. The second, made of bare excitons in a nanoribbon of twisted TMDC bilayer, which naturally creates a periodic Moiré potential that can be controlled by the twist angle. We proved that such systems behave as semiclassical time crystals (TCs). This was demonstrated by the fact that the calculated BEC spatial density profile shows a non-trivial long-range two-point correlator that oscillates in time. These BECs density profiles were calculated by solving the quantum Lindblad master equations for the density matrix within the mean-field approximation. We then go beyond the usual mean-field approach by adding a stochastic term to the master equation which corresponds to quantum corrections. We show that the TC phase is still present.