Time-dependent density-functional theory of exciton-exciton correlations in the nonlinear optical response

摘要

We analyze possible nonlinear exciton-exciton correlation effects in the optical response of semiconductors by using a time-dependent density-functional theory (TDDFT) approach. For this purpose we derive the nonlinear (third-order) TDDFT equation for the excitonic polarization. In this equation the nonlinear time-dependent effects are described by the time-dependent (nonadiabatic) part of the effective exciton-exciton interaction, which depends on the exchange-correlation (XC) kernel. We apply the approach to study the nonlinear optical response of a GaAs quantum well. In particular, we calculate the two-dimensional Fourier spectrum (2DFS) of the system and compare it with experimental data. We find that the memory effects play a crucial role in this response, and in particular that it is necessary to use a nonadiabatic XC kernel to describe excitonic bound states, biexcitons, which are formed due to the retarded TDDFT exciton-exciton interaction.