Layer-dependent anisotropic electronic structure of freestanding   quasi-two-dimensional MoS$_2$
  The anisotropy of the electronic transition is a well-known characteristic of low-dimensional transition-metal dichalcogenides, but their layer-thickness dependence has not been properly in- vestigated experimentally until now. Yet, it not only determines the optical properties of these low-dimensional materials, but also holds the key in revealing the underlying character of the elec- tronic states involved. Here we used both angle-resolved electron energy-loss spectroscopy and spectral analysis of angle-integrated spectra to study the evolution of the anisotropic electronic transition involving the low energy valence electrons in the freestanding MoS$_2$ layers with different thicknesses. We are able to demonstrate that the well-known direct gap at 1.8 eV is only excited by the in-plane polarized field while the out-of-plane polarized optical gap is 2.4$\pm$0.2 eV in monolayer MoS$_2$. This contrasts with the much smaller anisotropic response found for the indirect gap in the few-layer MoS$_2$ systems. In addition, we determined that the joint density of states associated with the indirect gap transition in the multilayer systems and the corresponding indirect transition in the monolayer case has a characteristic three-dimensional-like character. We attribute this to the soft-edge behavior of the confining potential and it is an important factor when considering the dynamical screening of the electric field at the relevant excitation energies. Our result provides a logical explanation, for the large sensitivity of the indirect transition to thickness variation compared with that for the direct transition, in terms of quantum confinement. 
Jinhua Hong, Kun Li, Chuanhong Jin, Xixiang Zhang, Ze Zhang and Jun   Yuan
cond-mat.mes-hall