Frenkel versus charge-transfer exciton dispersion in molecular crystals

By solving the many-body Bethe-Salpeter equation at finite momentum transfer, we characterize the exciton dispersion in two prototypical molecular crystals, picene and pentacene, in which localized Frenkel excitons compete with delocalized charge-transfer excitons. We explain the exciton dispersion on the basis of the interplay between electron and hole hopping and electron-hole exchange interaction, unraveling a simple microscopic description to distinguish Frenkel and charge-transfer excitons. This analysis is general and can be applied to other systems in which the electron wave functions are strongly localized, as in strongly correlated insulators.

Figure 1

Molecular units of picene and pentacene.

Figure 2

Absorption spectrum of pentacene (along $a^{*}$) where only transitions between HOMO-LUMO bands with zero dispersion are considered. The BSE is solved by (a) neglecting both the direct and the exchange e-h interactions ($\overline{v}=W=0$); (b) including only the exchange e-h interaction ($W=0$); (c) including only the direct e-h interaction ($\overline{v}=0$); (d) and including both the direct and the exchange e-h interactions $W$ and $\overline{v}$.

Figure 3

Exciton dispersion in pentacene: (a, b) without hopping and (c, d) including the full band dispersion. Solid and dashed black lines in (c) and (d) refer to excitons related to the coupling between the FR and the lowest CT states. Red, green, and blue lines are other excitons related to the coupling between the FR and the higher-energy CT states.

Figure 4

Map of the imaginary part of the macroscopic dielectric function ${\epsilon }_2$ evaluated as a function of the energy (vertical axis) and momentum transfer (horizontal axis) along (a) the $a^{*}$ axis and (b) the $b^{*}$ axis of pentacene and along (c) the $a^{*}$ axis and (d) the $b^{*}$ axis of picene. Black circles are guides for the eye for the lowest-energy excitons.