Direct optical transitions at K- and H-point of Brillouin zone in bulk MoS_2, MoSe_2, WS_2, and WSe_2

摘要

Modulated reflectance (contactless electroreflectance (CER), photoreflectance (PR), and piezoreflectance (PzR)) has been applied to study direct optical transitions in bulk MoS_2, MoSe_2, WS_2, and WSe_2. In order to interpret optical transitions observed in CER, PR, and PzR spectra, the electronic band structure for the four crystals has been calculated from the first principles within the density functional theory for various points of Brillouin zone including K and H points. It is clearly shown that the electronic band structure at H point of Brillouin zone is very symmetric and similar to the electronic band structure at K point, and therefore, direct optical transitions at H point should be expected in modulated reflectance spectra besides the direct optical transitions at the K point of Brillouin zone. This prediction is confirmed by experimental studies of the electronic band structure of MoS_2, MoSe_2, WS_2, and WSe_2 crystals by CER, PR, and PzR spectroscopy, i.e., techniques which are very sensitive to critical points of Brillouin zone. For the four crystals besides the A transition at K point, an A_H transition at H point has been observed in CER, PR, and PzR spectra a few tens of meV above the A transition. The spectral difference between A and A_H transition has been found to be in a very good agreement with theoretical predictions. The second transition at the H point of Brillouin zone (B_H transition) overlaps spectrally with the B transition at K point because of small energy differences in the valence (conduction) band positions at H and K points. Therefore, an extra resonance which could be related to the B_H transition is not resolved in modulated reflectance spectra at room temperature for the four crystals.