Electromagnetic field assisted exciton diffusion in moir\'e superlattices

We study exciton energy spectrum and their propagation in moir\'e superlattices formed in transition metal dichalcogenide heterobilayers. In such structures, as a result of weak interlayer interaction, an effective, moir\'e, potential acting on excitons arises. Usually, excitons are considered to be localized in such potential. Here we demonstrate that the coupling of optically active excitons with induced electromagnetic field produces linear in the wavevector energy dispersion even if the quantum mechanical tunneling between the localization sites is suppressed. The effect can be described as a result of the processes of virtual generation-recombination of excitons at the localization sites that results in the $r^{-3}$ dependence of the transfer matrix element on the intersite distance $r$. Based on the calculated energy spectrum we study exciton propagation in moir\'e superlattices with allowance for the light-exciton interaction. We consider semiclassical diffusion of excitons and take into account exciton-phonon and exciton-static defect scattering. For these mechanisms the diffusion coefficient decreases with increase of the temperature. We also analyze the hopping propagation regime and demonstrate that the temperature dependence of the exciton diffusion coefficient is described by the power-law rather than by an exponential function of the temperature.