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 (MoS2) 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 MoS2. 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 MoS2, 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.