By means of first-principles density-functional theory calculations, we investigate the role of hydrostatic pressure in the electronic structure of the $T_d$ ($Pmn{2}_1$) and $1T^{″}$ ($Pm$) phases of the Weyl semimetal ${\mathrm{Mo}}_{0.5}{\mathrm{W}}_{0.5}{\mathrm{Te}}_2$, which is a promising material for phase-change memory technology and superconductivity. We particularly focus on changes occurring in the distribution of the gapless Weyl points (WPs) within the 0 to 45 GPa pressure range. We further investigate the structural phase transition and lattice dynamics of the $T_d$ and $1T^{″}$ phases within the aforementioned pressure range. Our calculations suggest that both the $T_d$ and $1T^{″}$ phases of ${\mathrm{Mo}}_{0.5}{\mathrm{W}}_{0.5}{\mathrm{Te}}_2$ host four WPs in their full Brillouin zone at zero pressure. The total number of WPs increases to 44 (36) with increasing pressure via pair creation up to 20 (15) GPa for the $T_d$ ($1T^{″}$) phase, and beyond this pressure pair annihilation of WPs starts occurring, leaving only 16 WPs at 45 GPa in both phases. The enthalpy versus pressure data reveal that the $1T^{″}$ phase is more favorable below the critical pressure of 7.5 GPa; however, beyond this critical pressure the $T_d$ phase becomes enthalpically favorable. We also provide the calculated x-ray diffraction spectra along with the calculated Raman- and infrared-active phonon frequencies to facilitate the experimental identification of the studied phases.

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• Electronic structure of atoms & molecules
• First-principles calculations
• Pressure effects
• Structural phase transition
• Topological materials
• Weyl semimetal
• Density functional calculations