Electronic structure of cubicV3Si andNb3Sn

Abstract

The results of self-consistent augmented-plane-wave energy-band calculations by Klein et al. for ${\mathrm{V}}_{3}$Si and ${\mathrm{Nb}}_{3}$Sn have been fitted using a nonorthogonal-tight-binding (NTB) scheme. The NTB basis includes Bloch sums formed from $s$,$p$,$d$ orbitals at the V(Nb) sites and $s$,$p$ orbitals at the Si(Sn) sites, respectively. The resulting 62\ifmmode\times\else\texttimes\fi{}62 secular equation contains approximately 80-100 independent two-center energy and overlap parameters which have been determined by means of a nonlinear-least-squares fitting procedure. Highly accurate fits have been obtained for the lowest 40 bands at 35 $k$ points in the Brillouin zone; the corresponding rms errors are about 3 and 2 mRy for ${\mathrm{V}}_{3}$Si and ${\mathrm{Nb}}_{3}$Sn, respectively. This accuracy has allowed the calculation of high-resolution density-of-states curves $N(E)$, including a decomposition into angular momentum and orbital components ${N}_{\ensuremath{\alpha}}(E)$. The results of these studies provide new and important insight regarding the orbital character of the extremely flat ${\ensuremath{\Gamma}}_{12}$ bands which lie near ${E}_{F}$ in both ${\mathrm{V}}_{3}$Si and ${\mathrm{Nb}}_{3}$Sn. They show that the principal orbital component of these subbands consists of transition-metal (TM) $d(\ensuremath{\sigma})$ orbitals with (3${z}^{2}\ensuremath{-}{r}^{2}$) symmetry along the TM-atom chains parallel to the $z$ axis. It is also shown that the small dispersion of the ${\ensuremath{\Gamma}}_{12}$ subbands (\ensuremath{\sim}2 mRy) over a large fraction of the Brillouin zone is due primarily to strong interchain hybridization with TM $d(\ensuremath{\pi})$- and $p(\ensuremath{\pi})$-type orbitals. We believe that this novel combination of strong but compensating $d\ensuremath{-}d$ and $p\ensuremath{-}d$ interactions within the ${\ensuremath{\Gamma}}_{12}$ subbands near ${E}_{F}$ is the principal source of the anomalous electronic properties which have long been associated with both ${\mathrm{V}}_{3}$Si and ${\mathrm{Nb}}_{3}$Sn.