Theory of multi-exciton states in semiconductor nanocrystals

In this article, the fundamental physics of multi-exciton states in semicon ductor nanocrystals is reviewed focusing on the mesoscopic enhancement of t he excitonic radiative decay rate and the excitonic optical nonlinearity an d the mechanism of their saturation with increase of the nanocrystal size. In the case of the radiative decay rate the thermal excitation of excited e xciton slates having small oscillator strength within the homogeneous linew idth of the exciton ground state is essential in determining the saturation behavior. The weakly correlated exciton pair states are found to cause a c ancellation effect in the third-order nonlinear optical susceptibility at t he exciton resonance, providing the first consistent understanding of the e xperimentally observed saturation of the mesoscopic enhancement of the exci tonic optical nonlinearity. The presence of the weakly correlated exciton p air states is confirmed convincingly from the good correspondence between t heory and experiments on the induced absorption spectra from the exciton st ate in CuCl nanocrystals. Furthermore, ultrafast relaxation processes of bi excitons are discussed in conjunction with the observed very fast rise of t he biexciton gain in nanocrystals. In prospect of future progress in resear ch, the theoretical formulation to calculate the triexciton states as one o f the multi-exciton states beyond the biexciton is presented for the first time including the electron-hole exchange interaction.