Temperature Dependence of the Indirect Gap and the Direct Optical Transitions at the High-Symmetry Point of the Brillouin Zone and Band Nesting in MoS₂, MoSe₂, MoTe₂, WS₂, and WSe₂Crystals

Following the rise of interest in the properties of transition metal dichalcogenides, many experimental techniques were employed to research them. However, the temperature dependencies of optical transitions, especially those related to band nesting, were not analyzed in detail for many of them. Here, we present successful studies utilizing the photoreflectance method, which, due to its derivative and absorption-like character, allows investigating direct optical transitions at the high-symmetry point of the Brillouin zone and band nesting. By studying the mentioned optical transitions with temperature from 20 to 300 K, we tracked changes in the electronic band structure for the common transition metal dichalcogenides (TMDs), namely, MoS₂, MoSe₂, MoTe₂, WS₂, and WSe₂. Moreover, transmission and photoacoustic spectroscopies were also employed to investigate the indirect gap in these crystals. For all observed optical transitions assigned to specific k-points of the Brillouin zone, their temperature dependencies were analyzed using the Varshni relation and Bose-Einstein expression. It was shown that the temperature energy shift for the transition associated with band nesting is smaller when compared with the one at high-symmetry point, revealing reduced average electron-phonon interaction strength.