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

Abstract

Using first-principle calculations, we investigate the electronic, topological, and superconducting properties of ${\mathrm{Nb}}_{3}X$ $(X=\mathrm{Ge}, \mathrm{Sn}, \mathrm{Sb})$ and ${\mathrm{Ta}}_{3}Y$ $(Y=\mathrm{As}, \mathrm{Sb}, \mathrm{Bi})$ A15 compounds. We demonstrate that these compounds host Dirac surface states, which are related to a nontrivial ${\mathbb{Z}}_{2}$ 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 ${\mathrm{Nb}}_{3}\mathrm{Ge}$ and ${\mathrm{Nb}}_{3}\mathrm{Sn}$ 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 ${\mathrm{t}}_{2g}$ Ta and Nb orbitals reproducing the spin-orbit splittings at the R point among the $\ensuremath{\pi}$-bond bands in this class of compounds. We separate the kinetic parameters in $\ensuremath{\pi}$ and $\ensuremath{\delta}$ bonds, in intradimer and interdimer hoppings, and discuss their relevance for the topological electronic structure. We point out that ${\mathrm{Nb}}_{3}\mathrm{Ge}$ might represent a ${\mathbb{Z}}_{2}$ topological metal with the highest superconducting temperature ever recorded.

Topics & Concepts