Abstract

Excitons, bound electron–hole pairs, are responsible for strong optical resonances near the bandgap in low-dimensional materials and wide-bandgap insulators. Although current ab initio methods can accurately determine exciton energies and eigenstates, their symmetries have been much less explored. In this work, we employ standard group-theory methods to analyse the transformation properties of excitonic states, obtained by solving the Bethe–Salpeter equation, under crystal symmetry operations. We develop an approach to assign irreducible-representation labels to excitonic states, providing a state-of-the-art framework for analysing their symmetries and selection rules (including, for example, the case of exciton-phonon coupling). Complementary to the symmetry classification, we introduce the concept of total crystal angular momentum for excitons in the presence of rotational symmetries, allowing the derivation of conservation laws. Furthermore, we demonstrate how these symmetry properties can be exploited to greatly enhance the computational efficiency of exciton calculations with the Bethe–Salpeter equation. We apply our methodology to three prototypical systems: LiF, monolayer MoSe2, and bulk hBN.

Abstract

Excitons, bound electron–hole pairs, are responsible for strong optical resonances near the bandgap in low-dimensional materials and wide-bandgap insulators. Although current ab initio methods can accurately determine exciton energies and eigenstates, their symmetries have been much less explored. In this work, we employ standard group-theory methods to analyse the transformation properties of excitonic states, obtained by solving the Bethe–Salpeter equation, under crystal symmetry operations. We develop an approach to assign irreducible-representation labels to excitonic states, providing a state-of-the-art framework for analysing their symmetries and selection rules (including, for example, the case of exciton-phonon coupling). Complementary to the symmetry classification, we introduce the concept of total crystal angular momentum for excitons in the presence of rotational symmetries, allowing the derivation of conservation laws. Furthermore, we demonstrate how these symmetry properties can be exploited to greatly enhance the computational efficiency of exciton calculations with the Bethe–Salpeter equation. We apply our methodology to three prototypical systems: LiF, monolayer MoSe2, and bulk hBN.

Abstract

Excitons, bound electron–hole pairs, are responsible for strong optical resonances near the bandgap in low-dimensional materials and wide-bandgap insulators. Although current ab initio methods can accurately determine exciton energies and eigenstates, their symmetries have been much less explored. In this work, we employ standard group-theory methods to analyse the transformation properties of excitonic states, obtained by solving the Bethe–Salpeter equation, under crystal symmetry operations. We develop an approach to assign irreducible-representation labels to excitonic states, providing a state-of-the-art framework for analysing their symmetries and selection rules (including, for example, the case of exciton-phonon coupling). Complementary to the symmetry classification, we introduce the concept of total crystal angular momentum for excitons in the presence of rotational symmetries, allowing the derivation of conservation laws. Furthermore, we demonstrate how these symmetry properties can be exploited to greatly enhance the computational efficiency of exciton calculations with the Bethe–Salpeter equation. We apply our methodology to three prototypical systems: LiF, monolayer MoSe2, and bulk hBN.

Abstract

Excitons, bound electron–hole pairs, are responsible for strong optical resonances near the bandgap in low-dimensional materials and wide-bandgap insulators. Although current ab initio methods can accurately determine exciton energies and eigenstates, their symmetries have been much less explored. In this work, we employ standard group-theory methods to analyse the transformation properties of excitonic states, obtained by solving the Bethe–Salpeter equation, under crystal symmetry operations. We develop an approach to assign irreducible-representation labels to excitonic states, providing a state-of-the-art framework for analysing their symmetries and selection rules (including, for example, the case of exciton-phonon coupling). Complementary to the symmetry classification, we introduce the concept of total crystal angular momentum for excitons in the presence of rotational symmetries, allowing the derivation of conservation laws. Furthermore, we demonstrate how these symmetry properties can be exploited to greatly enhance the computational efficiency of exciton calculations with the Bethe–Salpeter equation. We apply our methodology to three prototypical systems: LiF, monolayer MoSe2, and bulk hBN.