Electronic structure and scanning-tunneling-microscopy image of molybdenum dichalcogenide surfaces.

Electronic structures of ${\mathrm{MoS}}_{2}$ and ${\mathrm{MoSe}}_{2}$ surfaces are investigated by first-principles electronic-structure calculations. The ultrasoft pseudopotential by Vanderbilt is used to perform band calculations with a plane-wave basis. Calculated band structures are consistent with recent calculations using other methods. Scanning-tunneling-microscopy (STM) images are calculated from the results of the band calculations, and it is found that bright spots in experimental STM images correspond to chalcogen atoms of the outermost layer. First-principles band calculations by linear combination of atomic orbitals (LCAO) are also performed. It is found that the LCAO method is not so accurate in expressing the electronic properties of conduction bands of molybdenum dichalcogenides. The calculated band structures near the Fermi level show large dispersions along the direction perpendicular to the surface, which explains indirectly the fact that, in spite of the weak van der Waals interlayer interaction, moir\'e patterns are observed in the STM images of a ${\mathrm{MoSe}}_{2}$ surface grown on a ${\mathrm{MoS}}_{2}$ substrate. The appearance of the moir\'e patterns is more directly demonstrated by performing a band calculation of a ${\mathrm{MoSe}}_{2}$ surface with an irregular structure modeling the ${\mathrm{MoSe}}_{2}$/${\mathrm{MoS}}_{2}$ surface. It is found that the influence of the substrate on the outermost layer propagating through several Se-Mo-Se sandwiches is sufficiently large to reproduce the moir\'e patterns. However, the simulated image cannot explain some features of the experimental moir\'e patterns, which suggests that relaxation of atomic structures is also necessary to explain the moir\'e patterns.