High-pressure phases, vibrational properties, and electronic structure of $\text{Ne}{\left(\text{He}\right)}_2$ and $\text{Ar}{\left(\text{He}\right)}_2$: A first-principles study

We have carried out a comprehensive first-principles study of the energetic, structural, and electronic properties of solid rare-gas (RG)-helium binary compounds, in particular, $\text{Ne}{\left(\text{He}\right)}_2$ and $\text{Ar}{\left(\text{He}\right)}_2$, under pressure and at temperatures within the range of $0\le T\le 2000\text{K}$. Our approach is based on density-functional theory and the generalized gradient approximation for the exchange-correlation energy; we rely on total Helmholtz free-energy calculations performed within the quasiharmonic approximation for most of our analysis. In $\text{Ne}{\left(\text{He}\right)}_2$, we find that at pressures of around 20 GPa the system stabilizes in the ${\text{MgZn}}_2$ Laves structure, in accordance to what was suggested in previous experimental investigations. In the same compound, we predict a solid-solid phase transition among structures of the Laves family of the type ${\text{MgZn}}_2\to {\text{MgCu}}_2$, at a pressure of $P_t=120\left(1\right)\text{GPa}$. In $\text{Ar}{\left(\text{He}\right)}_2$, we find that the system stabilizes in the ${\text{MgCu}}_2$ Laves phase at low pressures but it transitates toward the ${\text{AlB}}_2$-type structure by effect of compression at $P_t=13.8\left(4\right)\text{GPa}$. The phonon spectra of the $\text{Ne}{\left(\text{He}\right)}_2$ crystal in the ${\text{MgZn}}_2$ and ${\text{MgCu}}_2$ Laves structures, and that of $\text{Ar}{\left(\text{He}\right)}_2$ in the ${\text{AlB}}_2$-type phase, are reported. We observe that the compressibility of RG-RG and He-He bond distances in $\text{RG}{\left(\text{He}\right)}_2$ crystals is practically identical to that found in respective RG and He pure solids. This behavior emulates that of a system of noninteracting hard spheres in closed-packed configuration and comes to show the relevance of short-range interactions on this type of mixtures. Based on size-ratio arguments and empirical observations, we construct a generalized phase diagram for all $\text{RG}{\left(\text{He}\right)}_2$ crystals up to a pressure of 200 GPa where we map out systematic structural trends. Excellent qualitative agreement between such generalized phase diagram and accurate ab initio calculations is proved. A similar construction is done for $\text{RG}{\left({\text{H}}_2\right)}_2$ crystals; we find that the ${\text{MgCu}}_2$ Laves structure, which has been ignored in all ${\text{RG-H}}_2$ works so far, might turn out to be competitive with respect to the ${\text{MgZn}}_2$ and ${\text{AlB}}_2$-type structures. Furthermore, we explore the pressure evolution of the energy-band gap in $\text{RG}{\left(\text{He}\right)}_2$ solids and elaborate an argument based on electronic-band theory which explains the observed trends.