Efficient ab initio calculations of bound and continuum excitons

TL;DR

This paper compares various computational methods for calculating the absorption spectra of semiconductors and insulators, demonstrating that even simplified approaches can accurately reproduce excitonic features.

Contribution

It introduces a new parameter-free scheme for deriving approximations to the Bethe-Salpeter equation within time-dependent density-functional theory.

Findings

All methods accurately reproduce bound and continuum excitons.

Simplest static approximation is computationally efficient, scaling similarly to RPA.

Proposed scheme offers a versatile, parameter-free approach.

Abstract

We present calculations of the absorption spectrum of semiconductors and insulators comparing various approaches: (i) the two-particle Bethe-Salpeter equation of Many-Body Perturbation Theory; (ii) time-dependent density-functional theory using a recently developed kernel that was derived from the Bethe-Salpeter equation; (iii) a scheme that we propose in the present work and that allows one to derive different parameter-free approximations to (ii). We show that all methods reproduce the series of bound excitons in the gap of solid argon, as well as continuum excitons in semiconductors. This is even true for the simplest static approximation, which allows us to reformulate the equations in a way such that the scaling of the calculations with number of atoms equals the one of the Random Phase Approximation.