Time-dependent density-functional approach for exciton binding energies

TL;DR

This paper develops a simplified TDDFT-based formalism to calculate exciton binding energies, generalizing the Wannier equation by incorporating nonlocal, dynamical exchange-correlation effects, and applies it to various semiconductors.

Contribution

It introduces a new formalism derived from TDDFT that extends the Wannier equation to include long-range and dynamical XC effects for excitons.

Findings

Calculated excitonic binding energies for several semiconductors.

Demonstrated the importance of nonlocal and dynamical XC effects.

Validated the formalism with exchange-only and model XC kernels.

Abstract

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 excitonic 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 excitonic binding energies in several direct-gap semiconductors, using exchange-only and model XC kernels.