Pressure coefficients for direct optical transitions in MoS₂, MoSe₂, WS₂, and WSe₂ crystals and semiconductor to metal transitions

The electronic band structure of MoS₂, MoSe₂, WS₂, and WSe₂, crystals has been studied at various hydrostatic pressures experimentally by photoreflectance (PR) spectroscopy and theoretically within the density functional theory (DFT). In the PR spectra direct optical transitions (A and B) have been clearly observed and pressure coefficients have been determined for these transitions to be: α A = 2.0 ± 0.1 and α B = 3.6 ± 0.1 meV/kbar for MoS₂, α A = 2.3 ± 0.1 and α B = 4.0 ± 0.1 meV/kbar for MoSe₂, α A = 2.6 ± 0.1 and α B = 4.1 ± 0.1 meV/kbar for WS₂, α A = 3.4 ± 0.1 and α B = 5.0 ± 0.5 meV/kbar for WSe₂. It has been found that these coefficients are in an excellent agreement with theoretical predictions. In addition, a comparative study of different computational DFT approaches has been performed and analyzed. For indirect gap the pressure coefficient have been determined theoretically to be -7.9, -5.51, -6.11, and -3.79, meV/kbar for MoS₂, MoSe₂, WS₂, and WSe₂, respectively. The negative values of this coefficients imply a narrowing of the fundamental band gap with the increase in hydrostatic pressure and a semiconductor to metal transition for MoS₂, MoSe₂, WS₂, and WSe₂, crystals at around 140, 180, 190, and 240 kbar, respectively.