Electrically tunable and enhanced nonlinearity of moir\'e exciton-polaritons in transition metal dichalcogenide bilayers

We develop a microscopic theory for nonlinear optical response of moir\'e exciton-polaritons in bilayers of transition metal dichalcogenides (TMDs). Our theory allows to study the tunnel-coupled intralayer and interlayer excitonic modes for a wide range of twist angles ($\theta$), external electric field, and light-matter coupling, providing insights into the hybridization regime inaccessible before. Specifically, we account for the Umklapp scattering processes of two exciton-polaritons responsible for enhanced nonlinearity, and show that it is crucial for describing interactions at strong hybridization. We reveal a regime of attractive nonlinearity for moir\'e polaritons, stemming from the anisotropic Coulomb interactions, which can explain some of experimental features of optical response in TMD bilayers. Furthermore, within our theory we demonstrate that the attractive nonlinearity can be tuned into repulsive by applying an external electric field. Our findings show that nonlinear moir\'e polaritons offer a controllable platform nonlinear polaritonic devices.