Stark effect and orbitals hybridization of moir\'e interlayer exciton in $ MoSe{2}/ WSe{2} $ heterobilayer.

Abstract We theoretically investigate the interlayer excitons response in the $WSe_{2}/MoSe_{2}$ heterobilayer under the effects of in-plane and out-of-plane static electric fields. We thoroughly analyze a wide range of properties pertaining to the interlayer exciton, including the binding energy, Stark shift, orbital hybridization, photoluminescence (PL) spectrum, and radiative lifetime. We examine various factors influencing interlayer exciton behavior, including the dielectric environment and the moir\'e traps effects. Our results demonstrate that the in-plane electric field significantly affects the binding energies of the interlayer exciton, leading to energy splitting between states with non-zero angular momentum, such as the $2p_{\pm}$ dark states. Furthermore, we show that the applied in-plane electric field results in orbitals hybridization of the interlayer exciton, including hybrid states such as $1s$, $2p_{\pm}$, and $2s$. In counterpart, we demonstrate that an out-of-plane electric field induced by a double-gate setup causes a quadratic Stark effect on the center of mass eigenenergies of the interlayer exciton and leads to energy splitting of degenerate states, result in an orbitals hybridization of center of mass eigenvectors. Finally, we determine the PL spectra and radiative lifetime of the moiré interlayer exciton as a function of electric field strength. Our results reveal that the $2p_{\pm}$ dark state becomes brighter through a one-photon PL process as the in-plane electric field strength increases. This phenomenon is directly attributed to the coupling between the $ns$ and $ np_{\pm} $ states generated by the in-plane electric field. In short, our investigation can help experimenters to designing novel optoelectronic applications, such as on-chip electro-optic modulators and TeraHertz devices.