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

TL;DR

This paper develops a time-dependent density-functional theory framework to analyze nonlinear exciton-exciton correlations in semiconductors, emphasizing the importance of non-adiabatic exchange-correlation kernels for accurately describing biexcitons.

Contribution

It introduces a nonlinear TDDFT equation for excitonic polarization that incorporates non-adiabatic effects, advancing the theoretical modeling of exciton interactions in optical responses.

Findings

Non-adiabatic XC kernel is essential for modeling biexcitons.

The approach successfully reproduces experimental 2D Fourier spectra.

Nonlinear exciton-exciton interactions are captured by the derived TDDFT framework.

Abstract

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 (non-adiabatic) 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 2D Fourier spectra of the system and compare it with experimental data. We find that it is necessary to use a non-adiabatic XC kernel to describe excitonic bound states - biexcitons, which are formed due to the retarded TDDFT exciton-exciton interaction.