Exciton band structure of molybdenum disulfide: from monolayer to bulk

Exciton band structures analysis provides a powerful tool to identify the exciton character of
materials, from bulk to isolated systems, and goes beyond the mere analysis of the optical spectra.
In this work, we focus on the exciton properties of molybdenum sisulfide (MoS 2 ) by solving the ab
initio many-body Bethe–Salpeter equation, as a function of momentum, to obtain the excitation
spectra of both monolayer and bulk MoS 2 . We analyse the spectrum and the exciton dispersion on
the basis of a model excitonic Hamiltonian capable of providing an efficient description of the
excitations in the bulk crystal, starting from the knowledge of the excitons of a single layer. In this
way, we obtain a general characterization of both bright and darks excitons in terms of the interplay
between the electronic band dispersion (i.e. interlayer hopping) and the electron–hole exchange
interaction. We identify for both the 2D and the 3D limiting cases the character of the
lowest-energy excitons in MoS 2 , we explain the effects and relative weights of both band dispersion
and electron–hole exchange interaction and finally we interpret the differences observed when
changing the dimensionality of the system.