Simple screened exact-exchange approach for excitonic properties in solids

We present a screened exact-exchange (SXX) method for the efficient and accurate calculation of the optical properties of solids, where the screening is achieved through the zero-wave-vector limit of the inverse dielectric function. The SXX approach can be viewed as a simplification of the Bethe-Salpeter equation (BSE) or, in the context of time-dependent density-functional theory, as a first step towards a new class of hybrid functionals for the optical properties of solids. SXX performs well for bound excitons and continuum spectra in both small-gap semiconductors and large-gap insulators, with a computational cost much lower than that of the BSE.

Figure 1

Comparison of calculated and experimental exciton binding energies $E_b$ (see Table 1 for details) in various semiconductors (GaAs, $\alpha$-GaN, $\beta$-GaN, CdS, CdSe, AlN, ZnO, MgO) and insulators (LiF, Ar, Ne). “Boot” and JGM represent bootstrap kernel [10] and jellium-with-gap models [11]. The solid line indicates where the calculated and experimental values of $E_b$ coincide.

Figure 2

SXX screening parameter $\gamma$ [Eq. (12)] and experimental value of ${\epsilon }_{\infty }^{-1}$ versus the fitted $\gamma$ reproducing the first exciton, for various materials. B3LYP corresponds to a constant value of $\gamma =0.2$.

Figure 3

Absorption spectrum of LiF calculated with SXX and RPA, compared with experiment [44].

Figure 4

Absorption spectrum of AlN calculated with SXX, RPA, and BSE, compared with experiment [45]. The BSE spectrum of Benedict et al. [46] is also shown.

Figure 5

Absorption spectrum of Si calculated with SXX, RPA, and BSE, compared with experiment [47].