Is the electronic structure of few layer transition metal dichalcogenides always two dimensional ?

Abstract

The transition metal dichalcogenides (MoS 2 etc.) are a new class of layered materials that can be prepared in variable layer thickness down to single molecular layer. Compared with the more well‐known graphene, the monolayer version of graphite, the transition metal dichalcogenides are semiconductors and hence can be more useful in applications such as light emission or photovoltaics where an energy gap is essential. Ultra thin transition metal dichalcogenides also show interesting layer thickness dependent physical properties. For example, the semiconductor gap was found to change from indirect to direct when the layer thickness is reduced to monolayer, making monolayer MoS 2 an efficient light emitter. Here we present investigation of the dimensionality of the joint density of states involved in the interband transition in MoS 2 using angle resolved as well as angle integrated electron energy loss spectroscopy [1]. To aid the analysis, we have extended the theory of joint density of states from three‐dimensional semiconductors to low‐dimensional semiconductors. Our result and analysis shows not only that the character of the interband transition changes from indirect to direct, as the layer thickness is reduced down to monolayer, as expected, but the indirect band gap retains a three dimensional character down to the monolayer limit. This is compared with the two dimensional character found for the direct bandgap transition in the monolayer MoSe and presumably also in MoS 2. This raised a question about the condition for observing a true two dimensional electronic structrue even when the atomic structure is reduced to single molecular thickness. We will discuss physical factors might affecting the dimensionality of the electronic density‐of‐states. Our result has practical implication. For example, it is consistent with the assumption made by Castellanos‐Gomez et al. [2] when interpreting the electrostatic screening effect observed in monolayer MoS 2 , which is very different from that of graphene. Our result also can explain the sensitivity of the indirect interband transition as a function of the layer thickness and the bandgap cross‐over of few layer MoS 2 from indirect to direct.