Exciton dispersion in molecular solids

The investigation of the exciton dispersion (i.e. the exciton energy dependence as a function of the momentum carried by the electron\textendashhole pair) is a powerful approach to identify the exciton character, ranging from the strongly localised Frenkel to the delocalised Wannier\textendashMott limiting cases. We illustrate this possibility at the example of four prototypical molecular solids (picene, pentacene, tetracene and coronene) on the basis of the parameter-free solution of the many-body Bethe\textendashSalpeter equation. We discuss the mixing between Frenkel and charge-transfer excitons and the origin of their Davydov splitting in the framework of many-body perturbation theory and establish a link with model approaches based on molecular states. Finally, we show how the interplay between the electronic band dispersion and the exchange electron\textendashhole interaction plays a fundamental role in setting the nature of the exciton. This analysis has a general validity holding also for other systems in which the electron wavefunctions are strongly localized, as in strongly correlated insulators.