Band structure of ${\mathrm{MoS}}_2,$ ${\mathrm{MoSe}}_2,$ and $\alpha -{\mathrm{MoTe}}_2:$ Angle-resolved photoelectron spectroscopy and ab initio calculations

In this work the complete valence-band structure of the molybdenum dichalcogenides ${\mathrm{MoS}}_2,$ ${\mathrm{MoSe}}_2,$ and $\alpha -{\mathrm{MoTe}}_2$ is presented and discussed in comparison. The valence bands have been studied using both angle-resolved photoelectron spectroscopy (ARPES) with synchrotron radiation, as well as ab initio band-structure calculations. The ARPES measurements have been carried out in the constant-final-state (CFS) mode. The results of the calculations show in general very good agreement with the experimentally determined valence-band structures allowing for a clear identification of the observed features. The dispersion of the valence bands as a function of the perpendicular component $k_{\perp }$ of the wave vector reveals a decreasing three-dimensional character from ${\mathrm{MoS}}_2$ to $\alpha -{\mathrm{MoTe}}_2$ which is attributed to an increasing interlayer distance in the three compounds. The effect of this $k_{\perp }$ dispersion on the determination of the exact dispersion of the individual states as a function of $k_{\Vert }$ is discussed. By performing ARPES in the CFS mode the $k_{\Vert }$ component for off-normal emission spectra can be determined. The corresponding $k_{\perp }$ value is obtained from the symmetry of the spectra along the $\Gamma A,$ $KH,$ and $\mathrm{ML}$ lines, respectively.