We find that the motion of the valley electrons—electronic states close to the $K$ and $K^{\prime }$ points of the Brillouin zone—is confined into two dimensions when the layers of ${\mathrm{MoS}}_2$ form the $3R$ stacking, while in the $2H$ polytype, the bands have dispersion in all three dimensions. According to our first-principles band-structure calculations, the valley states have no interlayer hopping in $3R\text{−}{\mathrm{MoS}}_2$, which is proven to be the consequence of the rotational symmetry of the Bloch functions. By measuring the reflectivity spectra and analyzing an anisotropic hydrogen-atom model, we confirm that the valley excitons in $3R\text{−}{\mathrm{MoS}}_2$ have two-dimensional hydrogenlike spectral series, and the spreads of the wave function are smaller than the interlayer distance. In contrast, the valley excitons in $2H\text{−}{\mathrm{MoS}}_2$ are well described by the three-dimensional model and, thus, not confined in a single layer. Our results indicate that the dimensionality of the valley degree of freedom can be controlled simply by the stacking geometry, which can be utilized in future valleytronics.

• Received 13 November 2014

DOI:https://doi.org/10.1103/PhysRevApplied.4.014002