Crystal and electronic structure of GaTa4Se8 from first-principles calculations

${\text{GaTa}}₄{\text{Se}}₈$ belongs to the lacunar spinel family and there have been intensive studies on its novel properties, such as its possible Mott-insulator state and superconductivity under pressure. However, its crystal structure and phase transition are still not well known. In this work, we investigated three different crystal structures, proposed in experiments, using first-principles calculations. For the cubic phase with space group $F\overline{4}3m$, its phonon spectra have three soft modes in the whole Brillouin zone, indicating the strong dynamical instability. The second one is the trigonal phase with space group $R3m$, which has been proposed based on Raman spectra under high pressure. This phase can be deduced from the soft phonon modes at $\mathrm{\ensuremath{\Gamma}}$ of the cubic phase and it is dynamically stable according to its phonon spectra. The third one is the tetragonal phase with space group $P\overline{4}{2}₁m$, which is also stable according to its phonon spectra and may be the low-temperature phase from x-ray diffraction. Within local density approximation calculations, the cubic and trigonal phases are metals, while the tetragonal phase is a band insulator consistent with the insulating feature in experiments. Our results suggest the possibility of the non-Mott state of ${\text{GaTa}}₄{\text{Se}}₈$ at low temperature and ambient pressure as a result of lattice distortion. On the other hand, the electronic structure of the trigonal phase can be viewed as a single-band Hubbard model. The Mott-insulator state has been obtained within dynamical mean-field theory calculation when the interaction parameter $U$ is larger than 0.40 eV vs a bandwidth of 0.25 eV. We hope these findings would be helpful in solving the long-standing problem of the ambiguity in the structural phase of ${\text{GaTa}}₄{\text{Se}}₈$.