Diffusion of fast and slow excitons with an exchange in quasi-two-dimensional systems

By means of analytical calculations and numerical simulations, we study the diffusion properties in quasi-two-dimensional structures with two exciton subsystems with an exchange between them. The experimental realization is possible in systems where fast and slow exciton subsystems appear. For substantially different diffusion coefficients of the species, the negative diffusion can be observed if one measures the transport properties of only a single subsystem, just as was obtained in experimental studies for quasi-two-dimensional semiconductor systems. The initial transition from a fast subsystem to a slow one results in a delayed release of fast excitons in the area close to the original excitation spot. Hence, the signal from the fast excitons alone includes the delayed replenishment from the transition of slow quasiparticles. This is seen as the narrowing of the exciton density profile or decrease of mean-squared displacement which is then interpreted as a negative diffusion. We show that the analytical theory matches the available experimental data for negative diffusion quite well. The average diffusion coefficients for the combined population are analytically expressed through the diffusion coefficients of fast and slow excitons. Simple analytical expressions for effective diffusion coefficients obtained in limiting cases are of interest both for theoretical and experimental analysis of not only the exciton transport, but also for a variety of systems, where fast and slow moving subsystems are present.