Theory of third-order polarizability of interlayer excitons due to intra-excitonic energy level transitions

n this paper, we employ a fully microscopic approach to the study of interlayer excitons in layered materials. We discuss the utilization of Fowlers and Karplus method to access the dynamical polarizability of non--interacting interlayer excitons in a $mathrm{WSe}_{2}/mathrm{WS}_{2}$--based van der Waals heterostructure. Following from the calculation of the linear polarizability, we consider Svendsens variational method to the dynamic third--order polarizability. With this variational method, we study both two--photon absorption and third--harmonic generation processes for interlayer excitons in a $mathrm{WSe}_{2}/mathrm{WS}_{2}$ hetero--bilayer, discussing the various intra--excitonic energy level transitions observed.