The study of the exciton dispersion (as a function of momentum transfer) is of
paramount importance for all applications involving light harvesting, beside provideing
fundamental knowledge about exciton mobility and migration.
Using state-of-the-art ab initio many-body approach, like the Bethe-Salpeter equation [1], we present
a first principle study of exciton dispersions in layered materials and 2D systems.
Results for the former systems (on the prototypical hBN and MoS2) have been recently confirmed
by experiments carried out at the Synchrotron ESRF [2]. For the latter (2D) systems we investigate
exciton dispersion in graphane and hBN. From our results we provide a general picture of the
mechanisms governing the
dispersion of neutral excitations in 2D systems, and of the role played by the confinement of the
electronic charge in setting the exciton binding energy.
In particular we found that due to the strongly reduced screening of the Coulomb interaction in low-
dimensional materials, the binding energy of both Wannier and Frenkel excitons in the optical
spectra is large and comparable in size. Therefore, contrarily to bulk materials, it cannot serve as a
criterion to distinguish different kinds of excitons. Here we demonstrate that the exciton band
structure, which can be accessed experimentally, instead provides a powerful way to identify the
exciton character[3].

[1] M. Gatti and F. Sottile, Phys. Rev. B 88, 155113 (2013)
[2] G. Fugallo et al. Phys. Rev. B 92, 165122 (2015)
[3] P. Cudazzo et al. Phys. Rev. Lett. 116, 066803 (2016)