  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.

Materials Science