Dirac surface states, multiorbital dimerization, and superconductivity in Nb- and Ta-based A15 compounds

Using first-principle calculations, we investigate the electronic, topological, and superconducting properties of Nb₃X (X=Ge, Sn, Sb) and Ta₃Y (Y=As, Sb, Bi) A15 compounds. We demonstrate that these compounds host Dirac surface states, which are related to a nontrivial Z₂ topological value. The spin-orbit coupling (SOC) splits the highly degenerate R point close to the Fermi level enhancing the amplitude of the spin Hall conductance. Indeed, despite the moderate spin orbit of the Nb-compounds, a large spin Hall effect is also obtained in Nb₃Ge and Nb₃Sn compounds. We show that the Coulomb interaction opens the gap at the R point thus making the occurrence of Dirac surface states more obvious. We then investigate the superconducting properties by determining the strength of the electron-phonon BCS coupling. The evolution of the critical temperature is tracked down to the 2D limit indicating a reduction of the transition temperature, which mainly arises from the suppression of the density of states at the Fermi level. Finally, we propose a minimal tight-binding model based on three coupled Su-Schrieffer-Heeger chains with t₂₆ Ta and Nb orbitals reproducing the spin-orbit splittings at the R point among the -bond bands in this class of compounds. We separate the kinetic parameters in and bonds, in intradimer and interdimer hoppings, and discuss their relevance for the topological electronic structure. We point out that Nb₃Ge might represent a Z₂ topological metal with the highest superconducting temperature ever recorded.