Biexciton-biexciton interaction in semiconductors

Abstract

For a semiconductor with single isotropic conduction and valence bands, the effective biexciton-biexciton interaction is derived starting from the second-quantization representation for the Hamiltonian of the system of interacting excitons and for the biexciton wave function within the framework of the adiabatic approximation. The interaction is found to be an average of the sum of effective interactions between excitons forming interacting biexcitons over the envelope functions of these biexcitons. Depending on the momentum transfer and on the difference between the momenta of interacting biexcitons, the interaction admits an analytical study when the first vanishes. In this case, the interaction has in the r space the form of a function of the interbiexciton distance consisting of a strong repulsive and a weak attractive part. At low temperatures the function describes main features in the behavior of the interaction among biexcitons, in which repulsion predominates over attraction. It is shown that while biexcitons remain stable quasiparticles they weakly attract each other for any value of the distance. A quantitative analysis of obtained results for the CuCl crystal shows that the biexciton system in this model substance is a weakly nonideal Bose gas with positive scattering length ${\mathrm{a}}_{\mathrm{s}}$\ensuremath{\simeq}${3\mathrm{a}}_{\mathrm{x}}$, which closely approaches the ideal one at excitation densities n\ensuremath{\leqslant}${10}^{18}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$.