Theory of highly excited semiconductor nanostructures including Auger coupling: exciton-bi-exciton mixing in CdSe nanocrystals

摘要

We present a theory of highly excited interacting carriers confined in asemiconductor nanostructure, incorporating Auger coupling between excitedstates with different number of excitations. The Coulomb matrix elementsconnecting exciton, bi-exciton and tri-exciton complexes are derived and anintuitive picture of breaking neutral multi-exction complexes into positivelyand negatively charged multi-exciton complexes is given. The general approachis illustrated by analyzing the coupling of biexciton and exciton in CdSespherical nanocrystals. The electron and hole states are computed usingatomistic $sp^3d^5s^*$ tight binding Hamiltonian including an effective crystalfield splitting and surface passivation. For each number of electron-hole pairsthe many-body spectrum is computed in the configuration-interaction approach.The low-energy correlated biexciton levels are broken into charged complexes: ahole and a negatively charged trion and an electron and a positively chargedtrion. Out of a highly excited exciton spectrum a subspace coupled tobi-exciton levels via Auger processes is identified. The interaction betweencorrelated bi-exciton and exciton states is treated using exact diagonalizationtechniques. This allows to extract the spectral function of the biexciton andrelate its characteristic width and amplitude to the characteristic amplitudeand timescale of the coherent time evolution of the coupled system. It is shownthat this process can be described by the Fermi's Golden Rule only if a fastrelaxation of the excitonic subsystem is accounted for.