Vibrational and optical properties of MoS2: From monolayer to bulk

Molybdenum disulfide, MoS2, has recently gained considerable attention as a layered material where neighboring layers are only weakly interacting and can easily slide against each other. Therefore, mechanical exfoliation allows the fabrication of single and multi-layers and opens the possibility to generate atomically thin crystals with outstanding properties. In contrast to graphene, it has an optical gap of ~1.9 eV. This makes it a prominent candidate for transistor and opto-electronic applications. Single-layer MoS2 exhibits remarkably different physical properties compared to bulk MoS2 due to the absence of interlayer hybridization. For instance, while the band gap of bulk and multi-layer MoS2 is indirect, it becomes direct with decreasing number of layers. In this review, we analyze from a theoretical point of view the electronic, optical, and vibrational properties of single-layer, few-layer and bulk MoS2. In particular, we focus on the effects of spin–orbit interaction, number of layers, and applied tensile strain on the vibrational and optical properties. We examine the results obtained by different methodologies, mainly ab initio approaches. We also discuss which approximations are suitable for MoS2 and layered materials. The effect of external strain on the band gap of single-layer MoS2 and the crossover from indirect to direct band gap is investigated. We analyze the excitonic effects on the absorption spectra. The main features, such as the double peak at the absorption threshold and the high-energy exciton are presented. Furthermore, we report on the the phonon dispersion relations of single-layer, few-layer and bulk MoS2. Based on the latter, we explain the behavior of the Raman-active A1g and E2g1 modes as a function of the number of layers. Finally, we compare theoretical and experimental results of Raman, photoluminescence, and optical-absorption spectroscopy.