Electronic structure of cubicV3Si andNb3Sn

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 62×62 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 $N\left(E\right)\mathrm{}$, including a decomposition into angular momentum and orbital components $N_{\alpha }\mathrm{}\left(E\right)\mathrm{}$. The results of these studies provide new and important insight regarding the orbital character of the extremely flat ${\Gamma }_{12}$ 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) $d\left(\sigma \right)$ orbitals with (3$z^2-r^2$) symmetry along the TM-atom chains parallel to the $z$ axis. It is also shown that the small dispersion of the ${\Gamma }_{12}$ subbands (∼2 mRy) over a large fraction of the Brillouin zone is due primarily to strong interchain hybridization with TM $d\left(\pi \right)$- and $p\left(\pi \right)$-type orbitals. We believe that this novel combination of strong but compensating $d-d$ and $p-d$ interactions within the ${\Gamma }_{12}$ 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.