Third-order polarizability of interlayer excitons in hetero-bilayers

In this paper, we employ a fully microscopic approach to the study of interlayer excitons in hetero-bilayers. We use Fowler’s and Karplus’ method to access the dynamical polarizability of non–interacting interlayer excitons in a ${\mathrm{W}\mathrm{S}\mathrm{e}}_2\mathrm{/}{\mathrm{W}\mathrm{S}}_2$–based van der Waals heterostructure. Following from the calculation of the linear polarizability, we consider Svendsen’s variational method to the calculation of 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 ${\mathrm{W}\mathrm{S}\mathrm{e}}_2\mathrm{/}{\mathrm{W}\mathrm{S}}_2$ hetero–bilayer, discussing the various selection rules of intra–excitonic energy level transitions.