Dimensional cross-over of the bandgap transition in quasi-two-dimensional MoS2

The anisotropy of the electronic transition is an important physical property not only determining the materials' optical property, but also revealing the underlying character of the electronic states involved. Here we used momentum-resolved electron energy-loss spectroscopy to study the evolution of the anisotropy of the electronic transition involving the low energy valence electrons in the free-standing MoS2 systems as the layer thickness was reduced to monolayer. We used the orientation and the spectral-density analysis to show that indirect to direct band-gap transition is accompanied by a three- to two-dimensional anisotropy cross-over. The result provides a logical explanation for the large sensitivity of indirect transition to the change of thickness compared with that for direct transition. By tracking the energy of indirect transition, we also revealed the asymmetric response of the valence band and conduction band to the quantum confinement effect. Our results have implication for future optoelectronic applications of atomic thin MoS2.