Exciton dispersion from first principles

We present a scheme to calculate exciton dispersions in real materials that is based on the first-principles many-body Bethe-Salpeter equation. We assess its high level of accuracy by comparing our results for LiF with recent inelastic x-ray scattering experimental data on a wide range of energy and momentum transfer. We show its great analysis power by investigating the role of the different electron-hole interactions that determine the exciton band structure and the peculiar “exciton revival” at large momentum transfer. Our calculations for solid argon are a prediction and a suggestion for future experiments. These results demonstrate that the first-principles Bethe-Salpeter equation is able to describe the dispersion of localized and delocalized excitons on equal footing and represent a key step for the ab initio study of the exciton mobility.

Figure 1

Dynamic structure factor of LiF as a function of energy (vertical axis) and momentum transfer $\mathbf{q}$ (horizontal axis) along $\Gamma X$ in units of $\Gamma X$. Left panel: Experimental data from Ref. 32. Right panel: Bethe-Salpeter calculations. The absolute scale for theoretical data is reported, but none is available for experimental data.

Figure 2

Exciton band structure of LiF. Three directions are investigated: $\Gamma X$, $\Gamma K$, and $\Gamma W$.

Figure 3

(a) Exciton wave function of LiF, when the hole is on top of the fluorine atom (violet in the center of the cell). (b) Cut along the [111] direction of the exciton wave function. (c) Same as (b), but for the triplet excitation. The physical picture is unchanged.

Figure 4

(a) Exciton dispersion in LiF in a minimal F $2p$ and Li $2s$ model with “flat bands” or with the full band dispersion for the singlet and the triplet. (b) Cumulative function $C_{\lambda }^{\mathbf{q}}\left(E\right)$ for the bound exciton in LiF as a function of the e-h transition energy $E$ (see text) for the intensity maxima at $\mathbf{q}=\Gamma X$ and $3\Gamma X$, and for the minimum at $\mathbf{q}=1.5\Gamma X$ (see Fig. 1).

Figure 5

Dynamic structure factor of solid argon as a function of energy (vertical axis) and momentum transfer $\mathbf{q}$ (horizontal axis) along $\Gamma X$ in units of $\Gamma X$: predictions from the Bethe-Salpeter equation. The white line is the quasiparticle direct band gap as a function of $\mathbf{q}$. The dots mark the dispersion of two excitons located between the two most prominent peaks.