First-principles calculations for the effect of energetic point defect formation on electronic properties of the Weyl MX family (M = Nb, Ta; X = P, As)

By the first-principles of the density functional theory (DFT) approach, the structural parameters, elastic, vibrational, electronic properties, and enthalpies of formation of four stoichiometric Weyl semimetal compounds were evaluated. Besides, we calculated point defect formation energies and electronic band structures of defect-containing supercells by using an unfolding technique to highlight the effects of point defects (vacancies and anti-sites) on Weyl points in the electronic structure of these compounds. The transition metal Nb and Ta vacancies are energetically nearer to stability in the cases of NbAs and TaAs, but the pnictide P vacancy is energetically favorable among four possible point defects in both NbP and TaP. The band structure results, obtained from the unfold method, agree with defect formation energies at the ground state. Moreover, a true and accurate description of defects is based on the well-ordered compounds (NbAs, TaAs, NbP, and TaP). A relationship between temperature (K based on defect formation energies) and defect concentrations for these Weyl compounds was derived. In particular, for TaAs, the Ta vacancy concentration is significantly higher than all other types of defect concentrations.