Phonon Dispersion in Molybdenum Chalcogenides Explained

Molybdenum chalcogenides are one of the most studied layered materials. They have hexagonal symmetry in the single layer case as many other van der Waals materials. Thus, they can serve as a model for the analysis of many physical properties, in particular the phonon modes, the appearance of new low wave number modes when going from the single layer to the bulk, the existence of a flexural acoustic mode and the grouping of the optical modes into pairs whose difference comes from the interlayer coupling. In this work, to address some of these points, we have calculated the phonon dispersion of MoS, MoSe, and MoTe in bulk and in a single layer using Density Functional Perturbation Theory and discuss the evolution of the energy branches along the different directions of the Brillouin zone. The calculated values are in very good agreement with Raman data reported in the literature. We have also calculated the static and optical dielectric constants, as well as the reflectance, which has been compared with available infrared reflectance data available in the literature. Finally, we discuss the activity of the optical modes in the bulk and single layer case.