Electronic structure and energetics of the tetragonal distortion for TiH2 , ZrH2 , and HfH2 : A first-principles study

The electronic structure and energetics of the tetragonal distortion for the fluorite-type dihydrides TiH₂ , ZrH₂ , and HfH₂ are studied by means of highly accurate first-principles total-energy calculations. For HfH₂ , in addition to the calculations using the scalar relativistic (SR) approximation, calculations including the spin-orbit coupling have also been performed. The results show that TiH₂ , ZrH₂ , and HfH₂ in the cubic phase are unstable against tetragonal strain. For the three systems, the total energy shows two minima as a function of the c/a ratio with the lowest-energy minimum at c/a<1 in agreement with the experimental observations. The band structure of TiH₂ , ZrH₂ , and HfH₂ (SR) around the Fermi level shows two common features along the two major symmetry directions of the Brillouin zone, Γ-L and Γ-K , a nearly flat doubly degenerate band, and a van Hove singularity, respectively. In cubic HfH₂ the spin-orbit coupling lifts the degeneracy of the partially filled bands in the Γ-L path, while the van Hove singularity in the Γ-K path remains unchanged. The density of states of the three systems in the cubic phase shows a sharp peak at the Fermi level. We found that the tetragonal distortion produces a strong reduction in the density of states at the Fermi level resulting mainly from the splitting of the doubly-degenerate bands in the Γ-L direction and the shift of the van Hove singularity to above the Fermi level. The validity of the Jahn-Teller model in explaining the tetragonal distortion in this group of dihydrides is discussed.