Time-dependent density-functional approach for exciton binding energies

Optical processes in insulators and semiconductors, including excitonic effects, can be described in principle exactly using time-dependent density-functional theory (TDDFT). Starting from a linearization of the TDDFT semiconductor Bloch equations in a two-band model, we derive a simple formalism for calculating exciton binding energies. This formalism leads to a generalization of the standard Wannier equation for excitons, featuring a nonlocal effective electron-hole interaction determined by long-range and dynamical exchange-correlation (XC) effects. We calculate exciton binding energies in several direct-gap semiconductors using exchange-only and model XC kernels.

Figure 1

Effective electron-hole interaction $V_{eh}\left(\mathbf{r},0\right)$ for GaAs and different XC kernels plotted along the $x$ direction, where $a$ is the lattice constant. The parameters $A$ and $\alpha$ for the contact and the LRC XC kernels are given in Table .