Efficient numerical method for calculating Coulomb coupling elements and its application to two-dimensional spectroscopy

Abstract

Typically, to calculate the two-particle Coulomb interaction between nanostructures, a six dimensional spatial integral need to be evaluated. For increasing size or complexity of the system, the calculation of the Coulomb coupling elements presents a significant limiting factor for simulations. The number of integrals in real space can be reduced by using a Green's function representation of the solution of a generalized Poisson equation. Without the restriction to specific symmetries, this efficient numerical method allows the inclusion of an arbitrary dielectric function.The Coulomb interaction between two colloidal quantum dots (QDs) is calculated without specifying the Green's function to an explicit analytic form. Nevertheless, the monopole-monopole interaction and the Förster induced excitation transfer are calculated separately. The Coulomb coupling between semiconductor QDs depends on the center-to-center distance between the nanostructures as well as on their relative dipole orientation to each other. To identify the effects of the spatially dependent Coulomb coupling on single excitons and biexcitons, a multidimensional coherent spectroscopy is used. The characteristic two dimensional optical signatures of different spatial arranged colloidal QDs are calculated with respect to the arrangement dependent Coulomb coupling between the nanostructures.