A minimal model for excitons within time-dependent density-functional theory

TL;DR

This paper introduces a minimal one-dimensional model within TDDFT to explore how the exchange-correlation kernel influences exciton formation, revealing that adiabatic kernels can produce bound excitons without long-range interactions.

Contribution

It provides a transparent minimal model to study the role of dynamical exchange-correlation effects in exciton binding within TDDFT.

Findings

Adiabatic xc kernels can produce bound excitons.

Long spatial range of $f_{xc}$ is not always necessary.

Emergence of Wannier model from TDDFT.

Abstract

The accurate description of the optical spectra of insulators and semiconductors remains an important challenge for time-dependent density-functional theory (TDDFT). Evidence has been given in the literature that TDDFT can produce bound as well as continuum excitons for specific systems, but there are still many unresolved basic questions concerning the role of dynamical exchange and correlation (xc). In particular, the role of the long spatial range and the frequency dependence of the xc kernel $f_{\rm xc}$ for excitonic binding are still not very well explored. We present a minimal model for excitons in TDDFT, consisting of two bands from a one-dimensional Kronig-Penney model and simple approximate xc kernels, which allows us to address these questions in a transparent manner. Depending on the system, it is found that adiabatic xc kernels can produce a single bound exciton, and sometimes two bound excitons, where the long spatial range of $f_{\rm xc}$ is not a necessary condition. It is shown how the Wannier model, featuring an effective electron-hole interaction, emerges from TDDFT. The collective, many-body nature of excitons is explicitly demonstrated.