Direct calculation of exciton binding energies with time-dependent density-functional theory

TL;DR

This paper introduces a method to directly calculate exciton binding energies in solids using time-dependent density-functional theory, addressing previous limitations in spectral resolution and long-range behavior of exchange-correlation functionals.

Contribution

The authors adapt the Casida equation formalism for periodic solids, enabling direct calculation of exciton binding energies and extending the approach to triplet excitons.

Findings

Successfully calculated exciton binding energies for various semiconductors and insulators.

Demonstrated the effectiveness of the bootstrap exchange-correlation kernel.

Extended the formalism to include triplet excitons.

Abstract

Excitons are electron-hole pairs appearing below the band gap in insulators and semiconductors. They are vital to photovoltaics, but are hard to obtain with time-dependent density-functional theory (TDDFT), since most standard exchange-correlation (xc) functionals lack the proper long-range behavior. Furthermore, optical spectra of bulk solids calculated with TDDFT often lack the required resolution to distinguish discrete, weakly bound excitons from the continuum. We adapt the Casida equation formalism for molecular excitations to periodic solids, which allows us to obtain exciton binding energies directly. We calculate exciton binding energies for both small- and large-gap semiconductors and insulators, study the recently proposed bootstrap xc kernel [S. Sharma et al., Phys. Rev. Lett. 107, 186401 (2011)], and extend the formalism to triplet excitons.