Valence and conduction band states of ${\mathrm{HfS}}_2:$ From bulk to a single layer

Electronic states of a material are intimately related to the dimension of the system. Epitaxial layers of transition metal dichalcogenides provide model systems in which the dimension can gradually be reduced by varying the film thickness. Applying combined angle-resolved photoemission and inverse photoemission on bulk ${\mathrm{HfS}}_2$ and epitaxial layers of ${\mathrm{HfS}}_2$ on ${\mathrm{WSe}}_2,$ we investigate the influence of the film thickness on two- and three-dimensional valence and conduction band states. While the direct band gap is observed to be independent of the thickness, the dispersion of states interacting perpendicularly to the layers is strongly affected as found from normal emission spectra with varying photon energy. The latter, a decreasing band width with decreasing number of layers, may be expected from general physical arguments, whereas the former appears to be rather surprising. However, both is confirmed by ab initio extended linear augmented plane wave $\mathbf{k}\cdot \mathbf{p}$ band structure calculations.