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Pressure-induced gap closing and metallization of MoSe$_{2}$ and MoTe$_{2}$

Layered molybdenum dichalchogenides are semiconductors whose gap is controlled by delicate interlayer interactions. The gap tends to drop together with the interlayer distance, suggesting collapse and metallization under pressure. We predict, based on first principles calculations, that layered semiconductors 2H$_c$-MoSe$_2$ and 2H$_c$-MoTe$_2$ should undergo metallization at pressures between 28 and 40 GPa (MoSe$_2$) and 13 and 19 GPa (MoTe$_2$). Unlike MoS$_2$ where a 2H$_c$ $\to$ 2H$_a$ layer sliding transition is known to take place, these two materials appear to preserve the original 2H$_c$ layered structure at least up to 100 GPa and to increasingly resist lubric layer sliding under pressure. Similar to metallized MoS$_2$ they are predicted to exhibit a low density of states at the Fermi level, and presumably very modest superconducting temperatures if any. We also study the $β$-MoTe$_2$ structure, metastable with a higher enthalpy than 2H$_c$-MoTe$_2$. Despite its ready semimetallic and (weakly) superconducting character already at zero pressure, metallicity is not expected to increase dramatically with pressure.